wind tunnel modelling of thermal effects due to ...

Proceedings of PHYSMOD2003: International Workshop on Physical Modelling of Flow and Dispersion Phenomena 3-5 September 2003, Prato, Italy

WIND TUNNEL MODELLING OF THERMAL EFFECTS DUE TO SURFACE HEATING AT MODEL SCALE

K. Richards University of Hamburg, Germany

B. Leitl University of Hamburg, Germany

ABSTRACT Established within the framework of the European Commission Training and Mobility of Researchers Programme (TMR) the primary objective of the ATREUS project (Advanced Tools for Rational Energy Use towards Sustainability with emphasis on microclimatic issues in urban applications) is to bring together current knowledge on parameters determining the microclimatic environment of urban areas and to further expand and use this knowledge in the optimization of heating and ventilation of buildings.

M. Schatzmann University of Hamburg, Germany

NOMENCLATURE A/C Fr H ∆T U W

The paper reviews literature concerning wall heating due to direct incident solar radiation, the resulting thermal effects and their influence on the flow field within the vicinity of a building or buildings. The limited number of numerical and experimental studies and inconsistencies in their findings means specific influences from thermal effects remain unclear. It is shown that numerical models over predict thermal effects due to wall heating demonstrating quite significant changes in flow regime not mirrored in experimental studies. This over prediction is believed due to inaccurate representation of near wall thermal conditions in numerical models. Within the scope of ATREUS similar numerical models (micro-scale models) will be coupled with simulation codes for buildings in order to study the energy budgets of buildings. Therefore it is vital that predictions and thus underlying modelling assumptions are representative i.e. the thermal boundary layer representation. Data from controlled wind tunnel experiments to be conducted at the Meteorological Institute of the University of Hamburg hope to provide the basis to improve and optimize these models.

air-conditioning Froude number street canyon height (m) wall-air temperature difference (K) above-canyon wind speed (m/s) street canyon width (m)

INTRODUCTION The heating and cooling requirements of buildings are strongly associated with the micro-climatic conditions that develop within their vicinity, the incident solar radiation and the physical properties of the building e.g. building materials. In particular more solar radiation absorbed by a building façade results in greater total heat gain by the building and as a consequence, during the cooling period, to increased cooling requirements and thus larger air-conditioning (A/C) units. This in turn increases energy consumption of the building. In addition to heat radiated from the building wall due heating by the sun, external wall mounted A/C compressor unit also contributes as a heat source to further increase the outside air temperature. This collectively causes a reduction in the efficiency of the A/C system and hence increased energy consumption to compensate. As a consequence there is added waste heat from the air-conditioning system increasing further the outside temperature within the vicinity of the building thus resulting in yet more energy use by the A/C system to compensate and so the cycle continues. It is therefore important to understand the thermal convection around a building and its influence on local airflow patterns in order to fully assess the efficiency of an A/C system.

Preliminary wind tunnel experiments have been conducted, using a heated cube to assess the ability of modelling the thermal boundary layer on a vertically heated surface at model scale. The size and behaviour of the thermal layer is assessed using a laser light sheet technique and some preparatory temperature and velocity profile measurements made. Some results from this work will be presented at the conference in September 2003.

While there are numerous studies looking at influence of wind around buildings or the effects of urban heating on local microclimates (i.e. the Urban Heat Island effect), there is limited knowledge on specific influences of thermal effects, due to wall heating from direct solar radiation, on the flow regime within the vicinity of buildings. With only handful of numerical, field and experimental studies to date and

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component at the ground within a deep canyon is not strong enough therefore the maximum temperature axis acts towards the centre of the canyon with the thermal upward motion causing a split in the lowest vortex to form two adjacent counter-rotating vortices. For the leeward and windward wall heating cases the principle flow changes in canyons of H/W>3 tend to follow the examples of figure 1a-ii and 1b-ii respectively.

inconsistencies in their findings the influence of thermal effects on the flow field due wall heating remains unclear. This paper will highlight these works and the discrepancies between them and outline the work proposed in order to further investigate these effects and attempt to resolve some unanswered questions. While in most cases the studies reviewed are not directly comparable they may still be compared qualitatively provided the conditions of study are stated clearly.

Ambient wind flow direction

LITERATURE REVIEW To date numerical studies concerning the influence of thermal effects within a street canyon due to solar radiation show varying degrees of modification to the classic isothermal flow regimes (Ca et al, 1995; Louka, et al., 2001; Mestayer et al, 1995; Sini et al, 1996; Kim and Baik, 1999, 2001). The degree of flow modification was primarily dependent on the wall being heated and canyon aspect ratio H/W where W is the street width and H is the height of the building. The schematic drawings in figure 1 summarise the findings of Ca et al. (1995), Mestayer et al. (1995), Sini et al. (1996) and Kim and Baik, (1999), for a 2D street canyon with H/W=1 and H/W=2. The wall-air temperature difference was 5K and the above-canyon wind speed was ≥2.5m/s for full-scale conditions i.e. above the threshold value suggested by DePaul and Shieh (1986) for which a discernible cross-canyon circulation appears.

H/W=2

H/W=1 a-ii

a-i

HLW H

HLW

ea Heated leeward wall (HLW)

b-i

b-ii

HWW

HWW

Heated windward wall

In each heating case the thermally induced motion generated close to the heated surface was shown either to act with (to strengthen) or against (to alter) the mechanically induced flow field i.e. the cavity driven flow due to ambient isothermal conditions. For example for leeward wall heating and H/W=1 higher temperatures close to the wall induced an upward motion acting together with the mechanical induced circulation to strengthen the rotation of the single canyon vortex, figure 1a-i. Whereas for windward wall heating the thermally induced upward motion close to the wall worked in opposition to the mechanically driven downward flow creating two counter-rotating vortices from one single vortex at some height where the thermal and mechanical flows became balanced, figure 1b-i. For H/W=2, leeward wall heating resulted in multiple vortices combining to form one single vortex, figure 1a-ii and windward wall heating altered the relative size of the two existing contra-rotating vortices figure 1b-ii i.e. the thermally induced motion worked with the lower vortex to enhance it.

c-i

Heated ground

c-ii

Mechanically induced flow Thermally induced flow Resultant flow

Figure 1: Schematic diagrams from numerical predictions of flow pattern change due to wall heating within a 2D street canyon with different H/W (modified from Kim and Baik, 1999) Kim and Baik (2001) and Mestayer et al (1995) further reported that an increase in the wall-air temperature difference (max ∆T=16K) to reinforce and strengthen the already modified flow structure and in some cases lead to the formation of additional vortices within the flow field. These observations were made for only ground or windward wall heating.

For the ground-heated case the resultant flow structure was dependent on the magnitude of the horizontal velocity component close to the ground, which in turn was dependent on the H/W ratio. For both H/W=1 and H/W=2 the magnitude of this velocity component was sufficient to shift the high temperature axis towards the leeward wall with the thermally induced upward motion acting close to the wall in concert with the mechanically induced flow. As a consequence the existing flow field was strengthened or modified for H/W=1 and H/W=2 respectively, figure 1c-i/ii. It is further interesting to note that for deeper canyons H/W>3 the flow modification became more complex for the ground heated case. The horizontal velocity

The results presented by Ca et al (1995), Mestayer et al (1995), Sini et al (1996) and Kim and Baik (1999, 2001) clearly suggest an influence on the cross-canyon vortex structure due to canyon wall heating, the significance primarily dependent on the canyon wall being heated, H/W and ∆T. However validation of these numerical models against experimental or field data are limited. Kim and Baik (2001) used the wind tunnel results of Uehera et al (2000) to validate against only one

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condition i.e. H/W = 1 and ∆T = 2K and while their predictions of normalised potential temperature and horizontal velocity profiles were in fair agreement with the condition chosen it represented the least complex in terms of flow structure and modification due to thermal effects. It was therefore not appropriate to conclude that the model is suitable for simulating urban street-canyon flows and identifying changes in flow regimes due to street-bottom heating. Further validations against more conditions are clearly required. The thermal flow predictions of Ca et al (1995), Mestayer et al (1995), Sini et al (1996) and Kim and Baik (1999) remain invalidated. The underlying velocity fields for all the studies were however validated with the flow regimes characterised by in wind and field studies.

temperature stratification within the canyon (maximum ∆T=19K). It was unclear from the publication whether this referred to windward or leeward wall heating but with reference to figure 1a/b-ii these results would either agree (windward heating) or contradict the numerical predictions (leeward heating). Model-scale wind tunnel investigations show further inconsistency with the numerical predictions but are in themselves limited in their scope of study. Kovar-Panskus et al. (2001) and Huizhi et al, (2003) are the only studies to date concerned directly with wall heating and thermal effects within a street canyon. These studies are not comparable as KovarPanskus et al. (2001) used a wind tunnel and applied windward wall heating and Huizhi et al, (2003) used a towing tank and applied ground heating. Using a nominally two-dimensional cavity of H/W=1 Kovar-Panskus et al. (2001) observed the velocity field to be the driving force of the cross-canyon circulation with little influence due to windward wall heating and no significant alterations to the flow structure (U=0.5-1m/s and ∆T≈50K which equates to ∆T≈5K full-scale for H=20m). While the equivalent full scale ∆T is comparable to that applied in the numerical predictions figure 1b-i shows a modified flow structure for H/W=1 as a consequence of windward wall heating which is clearly not reflected by the experimental findings of Kovar-Panskus et al. (2001).

In a combined numerical and field study Louka et al (2001) reported the numerical model to over estimate the thermal effects for windward wall heating, predicting two counterrotating vortices when only one recirculation vortex was observed in the field (H/W = 1.4, ∆T=18K). The same numerical methods as applied by Mestayer et al (1995), Sini et al (1996) were used. It should further be noted however that the quantification of thermal effects on the airflow close to the wall (to within 1.5m) were complicated due to the absence of velocity measurements at the positions of the temperature measurements and the combined traffic effects within the street. During field measurements a steep horizontal temperature gradient of 10.7°C/2cm was measured within 2cm of the wall in direct solar radiation, the gradient remaining steep to within 20cm (2.9°C /20cm) and then dropping off significantly at distances farther than 20cm from the wall to just 0.7-1.2°C/m. These observations implied the presence a thin thermal boundary layer close to the wall and thermal effects significant to within only 20cm of the wall for a 14.85m width canyon.

Huizhi et al, (2003) also considered a 2D cavity and reported the cross-canyon flow field (H/W~1 max ∆T=5.8K at scale, to be driven entirely by thermal effects under zero wind conditions for ground heating. For a light ambient above canyon flow, equivalent to U=1m/s full-scale, a single mechanically induced cross-canyon vortex was enhanced by thermal convection. While this tends to reflect the predictions of figure 1c-i these observations were made primarily based on instantaneous flow vector maps captured using Particle Image Velocimetry (PIV) and therefore no definite conclusions regarding the influence on the mean flow field can be drawn at this time. Nevertheless the results indicate some influence on the cross-canyon flow due to thermal convection from ground heating but further study is clearly required.

Similar field studies by Nakamura and Oke (1988) and Santamouris et al (1999) further reported thermal effects to be confined close to the wall, typically to within 1/8 of the total canyon width, the actual distance dependent on the abovecanyon wind speed. In terms of flow modification Nakamura and Oke (1988) observed no change in flow direction within the canyon for H/W=1.4 and ∆T=12-14K but based on only one velocity-point measurement made at the centre, 1m above the canyon floor, information concerning the flow regime due to thermal stratification was limited. However during a period of leeward wall heating they did observe a change in magnitude of this single velocity measurement associating it with a strengthening of the cross-canyon vortex due to thermal convection. A single cross-canyon vortex was assumed based on a previous study of isothermal street canyon flow fields by Hussain and Lee (1980). A similar flow enhancement was also observed in the predictions of Ca et al. (1995), Mestayer et al. (1995), Sini et al. (1996) and Kim and Baik, (1999) figure 1a-i but notably with only ∆T=5K.

Ruck (1993) used a cylindrical building with square crosssection to investigate changes in the flow field within the vicinity of a single building due to surface heating (all surfaces heated). While this study did not address changes to crosscanyon flow regime it was concluded that buoyancy due to surface heating can alter the flow pattern around a building depending on 1/Fr, where Fr is Froude number,

Fr = U ∞2 gH[(Tw − T∞ ) / T∞ ]1: U ∞ is the mean free stream

velocity, g acceleration due to gravity, H is the model height, Tw wall temperature and T∞ is the temperature of the surrounding fluid far away from the heated surface. For moderate surface heating no significant change to the integral dimensions of the flow field were observed but for 1/Fr > 0.2 a shortening of the reattachment length and an enhancement of the rotational speed

During a field campaign in Athens Santamouris et al (1999) observed either one main vortex or a system of 2 counterrotating vortices within a street canyon of H/W=2.5 the occurrence of the double vortex almost always associated with

1

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Tw-T∞ ≡ ∆T © 2003 Firenze University Press

within the building recirculation region were noted. No significant change was observed in the flow field upwind of the building.

heat transfer close to the wall and the corresponding numerical grid resolution (Louka et al, 2000). The wall condition applied assumes a thick thermal layer close to the wall i.e. the thermal boundary layer, whereas results from the parallel field study clearly showed the problem to be concerned with a thin thermal boundary layer i.e. just 1.3% of the total canyon width. The numerical method applied was unable to resolve for such a thin layer based on the applied thermal wall functions and corresponding grid resolution close to the wall. A more accurate representation of the thermal characteristics in close proximity of a heated wall is clearly required.

Finally Uehera et al (2000) used simple block shapes to represent city street and investigate the effects of thermal stratification on wind flow patterns. While this study was not specifically designed to examine influences due to surface heating an increase in strength of a single canyon vortex was observed during unstable conditions induced by heating of the wind tunnel floor.

Within the scope of the ATREUS project similar numerical models (micro-scale models) will be coupled with simulation codes for buildings in order to study the energy budgets of buildings. Therefore it is imperative that the predictions and thus underlying modelling assumptions for these micro-scale models are as accurate as practically possible. Data from controlled experimentation can thus provide the basis to improve and optimise these models.

DISCUSSION The above review highlights not only the differences between numerical predictions and field and wind tunnel observations but also the sparseness in studies specifically concerned with the influence of thermal effects due to wall heating on flow regime within the vicinity of buildings. In a way it is due to this sparseness of data that lends to such inconsistencies between the studies. There is simply insufficient data and knowledge from field and experimental studies to fully understand these effects and consequently inadequate data to validate numerical models predicting these effects. A general difficulty when making the comparisons in the previous section was that data from several studies was either not well documented or insufficient to draw certain conclusions. For example Santamouris et al (1999) did associate a system of 2 counter-rotating vortices with temperature stratification but it was unclear whether this applied to windward or leeward wall heating and so qualitative comparison with the predictions was not possible.

PROPOSED EXPERIMENTAL PROGRAMME An experimental programme is proposed to investigate both the thermal effects close to and in the vicinity of a building with vertical wall heating. At this stage the intention is not to model in detail a street canyon but to examine the more fundamental aspects of the thermal effects. For this a basic cube will be used to represent a simplified building. This decision was also made for reasons of modelling simplicity. Two primary experimental tasks have been identified: Task 1: To investigate thermal effects close to a vertically heated wall

While observations of general flow strengthening due to wall heating were mirrored in the predictions, for example the observations of Nakamura and Oke (1988) changes in the flow regime were not observed, Louka et al (2000). In the field recorded values of ∆T tended to be 10-14K higher than that applied in the numerical models, the Froude number, Fr in the field being lower than in the predictions implying greater thermal influences i.e. buoyancy in the flow. However the numerical models tend to over predict the influences due to thermal effects despite lower ∆T i.e. higher Fr, less buoyancy. For example Nakamura and Oke (1988) observed that for little or no ambient wind thermally induced motion dominated the street canyon flow for ∆T=12-14K2 and that for an increased ambient wind speeds i.e. above threshold velocity (DePaul and Shieh, 1986) the effects became less influential and more confined to the canyon perimeter as the cross-canyon flow field strengthened. This observation, which is naturally logical, was totally contradicted by the numerical predictions for smaller ∆T

The thermal boundary layer structure along a vertical heated wall under both free- and forced convection will be examined. Profiles of mean velocity, temperature and heat flux to be determined closed to the heated surface that would allow for the derivation of a revised thermal law of the wall relating the wall sensible heat flux to the air temperature far from the wall. This would potentially allow for the application of much coarser grids in numerical models. Furthermore knowledge of the mean velocity and temperature profiles in the wall thermal boundary layer would allow for estimates of heat flux and transfer coefficient in terms of a thermal emission source from a building which would be useful when specifying boundary conditions for building energy simulations. Task 2: To investigate the influence of thermal effects on the flow field within the vicinity of a building.

U ∞ ≥ 2.5m/s. The over estimation in the numerical models is believed to be due to the wall functions applied in the description of the and

2

The significance of thermal effects due to wall heating on the flow field within the vicinity of a building will be investigated. Vertical profiles of mean and instantaneous velocity and temperature will be made far upstream, around and in the wake of the building to assess the significance of flow disturbances. Flow turbulent kinetic energy and heat fluxes are further determined from the measured profiles. The approach flow will

It was not possible to calculate exact Froude number from Nakamura and Oke

(1988) because U ∞ and ∆T were recorded on separate days.

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Huizhi, L., Bin, L., Fengrong, Z., Boyin, Z., and Jianguo, S. (2003): ‘A laboratory model for the flow in urban street canyons induced by bottom heating’ to appear in the Journal of Advances in Atmospheric Sciences, September 2003. Hussain, M. and Lee, B. E. (1980): ‘An investigation of wind forces on three-dimensional roughness elements in a simulated atmospheric boundary layer flow – Part II. Flow over large arrays of identical roughness elements and the effect of frontal and side aspect ratio variations. Report No. BS 56, Department of Building Sciences, University of Sheffield. Kim, J-J. and Baik, J-J (1999): ‘A numerical study of thermal effects on flow and pollutant dispersion in urban street canyons’ Journal of Applied Meteorology 38(8) pp.1249-1260. Kim, J-J. and Baik, J-J (2001): ‘Urban street-canyon flows with bottom heating’ Atmospheric Environment 35(20) pp.3395-3404. Kovar-Panskus, A., Moulinneuf, L., Robins, A., Savory, E. and Toy, N. (2001): ‘The influence of solar-induced wall heating on the flow regime within urban street canyons’, 3rd International Conference on Urban Air Quality, 19-23rd March, Loutraki, Greece. Louka, P., Vachon, G., Sini, J-F., Mestayer, P. G. and Rosant, J-M. (2001): ‘Thermal effects on the airflow in a street canyon – Nantes ’99 experimental results and model simulations’, accepted for publication by Journal of Water Air and Soil Pollution: Focus Mestayer, P. G., Sini, J-F. and Jobert, M. (1995): ‘Simulation of wall temperature influence on flow and dispersion within street canyons’, 3rd International Conference on Air Pollution, Proto Carras, Greece Vol. 1; Turbulence and Diffusion pp.109-116. Nakamura, Y. and Oke, T.R. (1988): ‘Wind, temperature and stability conditions in an east-west oriented urban canyon’, Atmospheric Environment 22(12) pp.2691-2700. Ruck, B. (1993): ‘Wind-tunnel measurements of flow field characteristics around a heated model building’, Journal of Wind Engineering and Industrial Aerodynamics, 50(1-3), pp.139-152. Sini, J-F., Anquetin, S., and Mestayer, P. G. (1996): ‘Pollutant dispersion and thermal effects in urban street canyons’, Atmospheric Environment 30(15) pp.2659-2677. Uehara, K., Murakami, S., Oikawa, S. and Wakamatsu, S. (2000): ‘Wind tunnel experiments on how thermal affects flow in and above urban street canyons’, Atmospheric Environment, 34(10), pp.1553-1562. VDI Guideline 3783/12 (2000), ‘ Physical modeling of flow and dispersion processes in the atmospheric boundary layer – application of wind tunnels’ Beuth Verlag, Berlin.

be modelled as a boundary layer flow in accordance with ESDU (1985) and in the German VDI guideline (2000). The experimental data will not only provide a greater understanding of thermal influences but also provide validation data and appropriate inflow boundary conditions for numerical simulations. Initially the study will focus on a single building but the hope is to extend this to a group of buildings in order to assess the significance of more global influences. RESULTS TO BE PRESENTED (SEPTEMBER 2003) Preliminary work is being undertaken to assess the feasibility of modelling the thermal boundary layer on a vertically heated surface at model scale. The work involves: § The design and test of a heating system to enable just one face of the model building to be heated i.e. a cube. § Visualisation of the thermal boundary layer using a laser light sheet technique to qualitatively assess its size and behaviour. This will be conducted for both free and forced convection. § Preparatory measurements of temperature and velocity profiles to assess the practicality of the measurement techniques to be applied. Notably Laser Doppler Anemometry (LDA) for the velocity measurements and thermocouples for the temperature. Presented at the conference scheduled for September 2003 will be results from this preliminary study detailing the design considerations for the cube i.e. modelling similarity laws and heating requirements, findings from the flow visualisation study and initial measurements of temperature and or velocity profiles. REFERENCES Ca, V. T., Asaeda, T., Ito, M. and Armfield, S. (1995): capabilities for prediction by physical modelling’, Atmospheric Environment 30(3) pp.393-401. DePaul, F. T. and Shieh, C. M. (1986): ‘Measurements of wind velocities, Atmospheric Environment, 33(24-25), pp.4143-4150. ESDU (1985), ‘Characteristics of atmospheric turbulence near the ground. Part II: Single point data for strong winds (neutral atmosphere)’ Engineering Sciences Data Unit, Item No. 85020, London.

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ATMOSPHERIC BOUNDARY LAYER-LIKE FLOWS José Cataldo Instituto de Mecánica de los Fluidos e Ingeniería Ambiental, Facultad de Ingeniería, Universidad de la República Oriental del Uruguay

Valeria Durañona Instituto de Mecánica de los Fluidos e Ingeniería Ambiental, Facultad de Ingeniería, Universidad de la República Oriental del Uruguay

fp Iu k Lux m M n p Ru(τ) S U(z) u* Uδ u´ w´ x z zL z0 zR

ABSTRACT The physical modelling of atmospheric flows not related to extreme events like tornadoes, hurricanes, macro-cells, etc., or to convective conditions, can be developed in wind tunnels with natural or artificial methods. For the artificial methods, the comprehension of how certain types of obstacles modify the flow in a wind tunnel is of vital importance for the design of the simulation system. The artificial systems used for the generation of boundary layer-like flows generally consist of a grid of obstacles of vertical dimension similar to the depth of the target boundary layer, a rough floor selected in accordance with the characteristics of the flow to be modelled and a barrier with variable geometry. The interaction between the flow and the different components gives rise to flows similar to the atmospheric boundary layer. In this case, the simulated flows present a quasiequilibrium state -generation does not equal dissipation-, and in the position of the model inside the wind tunnel it should represent a homologue condition to the one to be studied, but at different downstream distances from the simulation system the flow presents qualitative differences. Changing the grid and maintaining the rough floor unchanged produces a change in the aerodynamic characteristics obtained from the analysis of the flow. Introducing additional properly designed obstacles, as screens, some flow characteristics could be amplified The Institute of Fluid Mechanics and Environmental Engineering (IMFIA) of the School of Engineering of the University of the Republic counts with an open circuit wind tunnel with a test section 2.25m wide, 2.1m high and 17m long, with a maximum speed of 30m/s. Experiments performed in this wind tunnel allowed some verifications of the characteristics already mentioned and the development of methodologies for the analysis of atmospheric flows. The simulation systems constructed for this purpose were those developed by Counihan, 1969 and Hunt, 1982. In this paper, the experimental results are presented for both types of simulation systems.

peak spectrum frequency value longitudinal turbulence intensity von Karman constant longitudinal turbulence integral scale empirical parameter z0 parameter screen mesh size index potential law screen porosity auto-correlation function spectral power density mean velocity at height z friction velocity mean velocity at height δ longitudinal turbulence component vertical turbulence componet horizontal distance height logarithmic sub-layer height roughness length roughness sub-layer height

greek symbols β δ σu

empirical parameter z0 dependent. atmospheric boundary-layer height root mean square of u

sub-index M P

model prototype

INTRODUCTION From long ago, the achievement of an adequate atmospheric boundary layer (ABL) simulation is known to be a necessary condition for the proper study of the interaction between the atmospheric flow and obstacles on the floor. Baines, 1965 showed the qualitative differences between the pressure field developed over a tall building model when the flow presents an uniform mean velocity profile or a boundarylayer like mean velocity profile. That study also showed those differences for the mean pressure field developed over a lowrise building. Lighter materials, more fearless architectural

NOMENCLATURE C empirical parameter z0 dependent d zero-plane displacement height d0 screen wire diameter eL model length scale f frecquency

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designs and very different exposure conditions gave rise to the necessity of more careful flow simulation conditions. When talking about atmospheric flow simulations, several things are involved. Firstly, a simulation system is considered, but also an analysis methodology is supposed. The simulation system must be selected in agreement with the flow condition to be modelled. When the mean pressure field over a tall building should be modelled, an adequate mean velocity profile simulation is sufficient. But, if it were necessary to simulate the peak pressure over the roof of a lowrise building, the simulation of other flow properties as energy of turbulence and spectrum would be essential. In other words, the simulation system should be able to simulate the significant magnitudes of the studied phenomenon. The analysis method is composed by a measurement system, a processing methodology and an interpretation model. Additionally, this method must be adequate to recognise the significant magnitudes. This paper presents a summary of the different atmospheric boundary layer like flow simulation methods and an analysis of their operation. Then, a methodology to analyse the simulation and a method to distort such flows are exposed.

Lateral view

Lateral view

Upstream view

Downstream view

Plan view Plan view

Figure 1 – Elliptical vortex generators

Figure 2 – Spires generators

The Counihan generators have a height equal to the boundary layer height, while the spires have the height of the wind tunnel test section. Both methods simulate the entire ABL. Another methods with the same objectives, as vertical jets (Blessmann, 1972) horizontal jet (Teunissen, 1975) and curved screens have been reported. When the model scales are so big that the modelled ABL could be deeper than the wind tunnel test section height, then a partial simulation must be implemented. Cook, 1973 and Hunt, 1982 report such methods. Figure 3 shows a sketch of the Hunt simulation method. In this case, only the logarithmic sub-layer is simulated.

SIMULATION SYSTEMS A first classification of the simulation system is in natural and artificial methods. In natural methods, the boundary layer is developed on a rough floor. The advantage of this method is the achievement of a flow in equilibrium in all position along the floor. What only needs to be selected is the aerodynamic roughness to be installed on the floor of the wind tunnel. Let suppose that a boundary layer 1.5m high should be obtained in the wind tunnel, corresponding to an atmospheric boundary layer at scale 1/400. Following White, 1974, a fetch between 51 and 57m with an adequate roughness would be enough to develop it, depending on the type of terrain (sea or urban). This consideration shows the necessity to develop other simulation system to obtain a flow similar to an ABL flow in a shorter distance. The turbulence production of the flow is then accelerated introducing some obstacles. Basically, such obstacles are grids and barriers. As examples, the Counihan method (Counihan, 1969, Robins, 1980) and the Spire method (Standen, 1969 and Irwin 1981) can be quoted. There exist several alternatives around these methods in the existent bibliography. The principal difference among these methods is the geometry of the grid elements. The named elliptical vortex generators (turbulence generators) of the first mentioned method are showed in figure 1, while the spires, corresponding to the grid elements of the second method, are showed in figure 2.

Figure 3 – Partial ABL simulation system. In this case, again, the system by a screen or grid, a barrier, and a rough floor is composed. When the energy in the significant spectrum component is too low or when the mean velocity profile is not adequate, it could be necessary to distort the modelled flow. The distortion of an ABL simulation can be achieved with additional grids or screens made. Examples of such distortions are reported in Tieleman, 1996 using spires and in Cataldo and Farell, 2001 using screens. These two papers present some results on the effect of the small scales of the turbulence on peak pressure values developed on low-rise buildings roofs. SOME QUALITATIVE TOPICS As it was mentioned before, an artificial simulation system is basically composed by with three components: a grid, a

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barrier and a rough floor. In the next paragraphs, a qualitative vision about the operation of this kind of systems is described. When the flow reaches the simulation system, it first interacts with the grid and then turbulence of high scale is produced. This turbulent flow is responsible for the extent of the simulated region and its biggest scales. Behind the grid, the flow develops over the rough floor and starts losing momentum near the floor. Such loss is dispersed towards up while the flow advances downstream. This region of the flow presents a relatively high turbulence, but of small scale. The aforementioned flow regions have very different characteristics. Their turbulence levels, turbulent scales and mean wind profiles are different from each other. Then, it is necessary to mix both, and this can be obtained if an intermediate turbulent scale is produced. This is the function of the barrier. The objective of this component of the simulation system is to produce a shear layer at the necessary height over the floor in order to obtain a flow with the required properties. Figure 4 shows the mean velocity profile if the barrier is forgotten.

18 16 14 12 10 8 6 4 2 0

Counihan 600mm Without generators

1

10

100

1000

Figure 5 – Mean velocity profile in three ABL simulations. From this picture, it can easily be seen that the roughness length is 2mm in the first case, 1mm in the second and 0.7mm in the third. MEAN FLOW ANALYSIS A logarithmic-potential analysis is proposed for the mean velocity profile. This method is based on the identification of three sub-layers in the boundary layer. Such sub-layers are the roughness sub-layer, the logarithmic sub-layer and the potential sub-layer, as it is presented in figure 6.

Mean velocity profile 1 0.9 0.8

U/Ud

Counihan 1200mm

0.7

Potential Sub-Layer

0.6 0.5

Outer Layer

0.4 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z/d

ZL

Logarithmic Sub-Layer Inner Layer

Figure 4 – Mean velocity profile without barrier

ZR

In this case, the mean velocity profile was obtained with the Counihan method without barrier, at 1/6000 model scale. A kink is observed at 48cm over the floor. The aerodynamic characteristics of the mean flow also change when the flow is developed over the same rough floor but with different grids. In these situations, the vortex structures present similar scales when the flow interacts with the same obstacles, but the turbulent scales of the leading flow are different and then, the power exchanged will also be different. As a consequence, the momentum loss will be different and therefore also the measured aerodynamic characteristics. As an example, figure 5 shows the mean velocity profile obtained for the same rough floor and three different grid designs: the first one corresponds to Counihan generators 1200mm high, the second one to Counihan generators 600mm high and the last one to the case without generators.

Roughness Sub-Layer

Figure 6 – Boundary-Layer structure In this figure, δ is the boundary layer height. The logarithmic sub-layer, deduced asymptotically from the inner and the outer layers, has a height equal to ZL and there, the mean velocity profile follows a logarithmic law as equation 1.

U (Z ) =

u*  Z −d   L k  Z 0 

(1)

U is the mean velocity at a height equal to Z, u* the friction velocity, k the von Karman constant (0.41), d the zerodisplacement plane height and Z0 the roughness length. The potential sub-layer extends from the logarithmic top up to the boundary layer top. In this region, the mean velocity profile follows a potential law as equation 2:

Z U (Z ) = U δ   δ  138

n

(2)


where β is an empirical parameter dependent on the roughness length (Simiu and Scanlan, 1986). In all cases, the intensity of turbulence law is adjusted to the data adjusting the value of a geometrical significant parameter as the boundary layer height. The spectral power density S(f) is basically presented in logarithmic scale in the two forms showed in figure 7.

where n is an empirical factor that depends on the aerodynamic floor characteristics. In the bibliography, (Counihan, 1975, Wieringa, 1993, Wang et al., 1996) different correlation between terrain characteristics, n and Z0 have been found. The flow in the roughness sub – layer is strongly dependent on obstacle geometry and it does not exist an universally accepted mean velocity law. When the mean velocity is measured in a boundary layer, its height is deduced from such measurements as the height where the mean velocity is 99% of that of the free flow. Then, for the complete description of the mean velocity profile in the boundary layer, the parameters u*, Z0, d, n, ZL and ZR must be determined. Figure 6 explains an usual methodology for this purpose. In this figure, the dots represent the measurement data, the continuous line shows the logarithmic law and the dashed line indicates the potential law. The drawing is made once a d value is selected. Then, the logarithmic law and the potential law are found by the least square method. For this d value and its corresponding approximation laws, ZL is selected in order to obtain the minimum mean square root error when the data are estimated with the laws. This process is repeated for different d values. Then, the parameters’ ensemble that gives the minimum mean square root error is selected.

2 u

S(0)

Zl

log(Z-d)

Zl

(b)

f

Figure 8 (a) is a dimensional form while figure 8 (b) is a dimensionless form. In both cases, the production range, the inertial range and the dissipation range can be identified. Some relevant characteristics are identified in figure 8. The S(0) value and the fP value (frequency value that corresponds to the maximum dimensionless power spectrum density value) can be used to estimate the longitudinal integral length scale as it will be shown below. Also, the inertial sub-layer is identified applying a power law as it is deduced with the Kolmogorov hypothesis. Finally, the smallest turbulent scale, associated to the right side of the inertial range, is quoted. This scale corresponds to the minimum turbulent structure modelled. The longitudinal integral turbulent scale, Lux, is defined from the auto-correlation function (Ru(τ))as:

log(Z-d)

Lux =

TURBULENCE ANALYSIS The analysis of the turbulence includes the power content, the power spectrum (distribution of the power content for different frequency components), the turbulent scales and the cross components. Among the last mentioned components, the most significant one is , where u´ and w´ are, respectively, the longitudinal and vertical turbulent components. This parameter must be similar to -u*2, as such component is proportional to the shear stress over the floor. The longitudinal intensity of turbulence profile could be verified with prototype experimental data, if it exists (see Harris, 1969 for rural data, ESDU, 1985), or compared with equation 3:

U ∞ ∫0 Ru (τ ).dτ ´2 < u´ >

(4)

using the named Taylor’s hypothesis. Simpler approximations for the estimation of the integral scale that use the power spectrum are suggested. Using the zero frequency spectrum value, the integral scale can be approximated as:

Lux = S (0).

U 4. < u´ 2 >

(5)

The integral scale Lux can also be estimated using fP, the frequency value that gives the maximum dimensionless power spectrum, as follows:

Lux =

β .k  Z −d   L  Z0 

fp

Figure 8 – Spectral power density sketch.

Figure 7 – Mean velocity profile

I u (Z ) =

f

(a)

log(U)

U

S(f) . f

S(f)

(3)

1 U 2π f p

(6)

Counihan, 1975 proposes a correlation law between the longitudinal turbulent integral scale at height Z and that height, as follows:

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Lux = C.Z m

therefore, to a prototype roughness length of 0.8m. On the other hand, the second case has a model scale of 1/1333 and then a prototype roughness length of 1.1m was obtained. Usually, the design of the rough floor is made using an integral turbulence model, as it is presented in Gartshore, 1973. In such case, the floor is selected according with the grid scale. But it must be noticed that if the grid scale is changed, then the aerodynamic characteristics of the floor and the modelled kind of terrain will be changed. The second case of study refers to the use of screens. As it was said before, once the model scale is estimated the smallest modelled turbulent structures can be determined. These turbulent structures will interact with those vortices produced on the building, as indicated in Tenekes and Lumley, 1972, whose scales are greater than 60% of the smallest turbulent scales of the incoming flow. If a description of the peak pressure field on a building or the flow around a tree that damages it is required, then very fine structures must be described. The adequate modelling of a flow structure implies to have the adequate energy in the corresponding spectral component of the turbulence that gives or removes power from such structure. Then, it could be necessary to have additional power in those scales. One possible method to achieve that is to introduce a screen in the flow as it is shown in figure 9.

(7)

where C and m are empirical parameters, correlated to the roughness length. Then, the longitudinal turbulent integral scale profile, equation (7), must be adjusted to fit the deduced profile obtained with equation (5) or (6). MODEL SCALE DEDUCTION The model scale eL to be used in a wind tunnel study must be deduced from the ABL simulation. Basically, the model scale can be deduced in three different ways. One possibility is to deduce it from the roughness length calculated from the mean velocity profile adjustment, as follows:

eL =

Z o, M Z 0, P

(8)

Here, the Z0,M value is deduced from the measurements, while Z0,P is a characteristic value of the modelled terrain. As it was said before, the intensity of turbulence profile measured in the wind tunnel at height Z, Iu,M (Z), could be made dimensionless using the modelled boundary layer height, δM, obtaining Iu,M (Z/δM). The prototype data could then be made dimensionless in a similar way using the homologue magnitude δP, and then the intensity of turbulence profile could be expressed as Iu,P (Z/δP). After obtaining a good adjustment between prototype and model data, the model scale can be deduced as:

eL =

δM δP

Screen Model

(9)

Figure 9 – Flow distorted by a screen The obtained distortion will depend on the screen dimensions and the distance between the model and the installed screen. Then, the selection of the screen dimensions and its position should be made taking into account the size of the turbulent scales to be powered. As an example, an ABL model was modified to study the pressure peak on a cube 250mm high, with the screen specified in table 1:

The third possible method for the calculation of the model scale is similar to the latter, but using the longitudinal integral turbulence scale profile. After performing the aforementioned calculations, it is possible to obtain three different values for the model scale. The final selection of the value of this important parameter, which will be used to model the studied situation, should be made taking into account the relevant parameters for such problem. Once the model scale is decided, the minimum modelled flow scale could then be calculated.

Distortion

M d0 x p x/M (mm) (mm) (mm) 1 39.1 8 1985 0.633 50.8 2 39.1 8 990 0.633 25.3 Table 1 – Screen used to distort an ABL model

MODIFYING THE ABL MODEL In the next paragraphs, two cases with modified boundary layers will be presented. The first one refers to the use of the same rough floor with different grids, as it was reported before. In this case, different aerodynamic floor characteristics are obtained. For the same rough floor, a Z0-value of 1.6mm was obtained when a grid was installed, while a value of 0.9mm was obtained without that grid. The first case corresponded to a model scale of 1/500 and

In both cases, the same screen was used but it was located at two different upstream distances from the model. A first change can be seen in the spectrum. Figure 10 shows the density power spectrum for the original ABL model. The inertial sub-layer extends up to 600Hz.

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Longitudinal component density power spectra at Z = 250mm

Mean velocity profiles 35

1.000

25

Mean velocity (m/s)

S(f).f/σ u

2

30

0.100 0.010 0.001 0.1

1

10

100

1000

f (Hz)

ABL Model

20

Distortion 1 15

Distortion 2

10

5

Figure 10 – Density power spectra of the ABL model

0 0

S(f)*f/σ u2

1 0.1

0.001

0.0001 100000

f (Hz)

Figure 11- Distorted ABL Flow. Distortion 1 Density power spectra at 1 Z=250mm, Distortion2 S(f).f/σ u2

800

1000

1200

CONCLUSIONS Different methodologies were presented for the physical simulation of ABL flows. All the described methods use a simulation system composed by a grid, a barrier and a rough floor. Each component has a definite function: the grid bounds the modelled region and introduces the biggest scales of the flow, the rough floor introduces the momentum loss near the floor needed to obtain the mean profile and produces small scale turbulence, while the barrier produces the shear layer required to mix both flows. A flow analysis method permits to obtain its characteristic parameters and estimate the model scale. Special situations can be modelled introducing some distortion in the ABL model, changing the grid or installing a screen.

0.01

1000

600

Figure 13 – Mean velocity profile in ABL model and distorted cases.

Density power spectra at Z=250mm, Distortion1

10

400

Height (mm)

Figures 11 and 12 show the density power spectrum for the two aforementioned distortions.

0.1

200

0.1

0.01

REFERENCES

0.001

Baines, W.D., “Effects of velocity distribution on wind loads and flow pattern on buildings”, Proceedings of Symposium No. 16 Wind Effects on buildings and structures, National Physical Laboratory, England, 1965. Blessmann, J., 1977. "The use of cross-jets to simulate wind characteristics", J. Wind Eng. Ind. Aerodyn., 2, 37-47. Cataldo, J. and Durañona, V., 1998. Open boundary-layer wind tunnel built in Uruguay”, Transactions of the Jubileum Conference on Wind Effects on Buildings and Structures, Gramado RS, Brazil, mayo 25-29 1998, ed. by Louredo-Souza. Cataldo, J. and Farell, C., (2001) “Vortex flow around bluff bodies”, Americas Conference on Wind Engineering – 2001, 3-6 June, 2002, Clemson, USA. Cook, N.J. (1973), “On simulating the lower third of the urban adiabatic boundary layer in a wind tunnel Atm. Env., 7, 691-705. Counihan, J., 1969. An improved method of simulating an atmospheric boundary layer in a wind tunnel, Atm. Env., 4, pp. 197-214. Counihan, J., (1975), “Adiabatic atmospheric boundarylayer: A review and analysis of data from the periods 18801972”, Atmospheric Environment, 9, pp. 871-905. ESDU, 1985. Characteristics of atmospheric turbulence

0.0001 0.1

1

10 100 f (Hz)

1000 10000

Figure 12 – Distorted ABL Flow. Distortion 2 In both cases, the inertial sub-layer was extended up to a frequency greater than 2000Hz. But some additional problems can occur. Figure 13 shows the mean velocity profile for the modelled ABL flow and for both distorted flows. It can be seen that up to 150mm, the mean flow does not almost change, but at 250mm, the mean profile presents a very great difference in the gradient. This magnitude can be very significant if separation occurs. Then, the distortion could be used up to 150mm.

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near the ground. Part II: single point data for strong winds (neutral atmosphere), Item Number 85020. Gartshore, I. S., (1973), “A relationship between roughness geometry and velocity profile shape for boundary-layers”, Report LTR-LA-140, Lab. Order NAE-1305, file 4011-2, National Establishment, Canada. Harris, I., 1969. Measurments of wind structure at heights up to 598ft. above ground level, Symposium on Wind Effects on Buildings and Structures Organized by Loughbourough University of Technology, National Physical Laboratory, Royal Aeronautical Society. Hunt, A., 1982. Wind-tunnel measurements of surface pressures on cubic building models at several scales, Journal of Wind Engineering and Industrial Aerodynamics, 10, pp. 137163. Irwin, H.P.A.H., (1981), “The design of spires for wind simulation”, Journal of Wind Engineering and Industrial Aerodynamics, 7, pp. 361-366. Simiu, E. and Scanlan, R.H., (1986), “Wind effects on structures”, John Wiley & Sons, 2nd ed., New York. Standen, N.M., 1972. "A spire array for generating thick turbulent shear layers for natural wind simulation in wind tunnels", National Aeronautical Establishment, Ottawa, Laboratory Technical Report LTR-LA-94. Tieleman,H.W. and Akins,R.E., (1996) "The effect of incident turbulence on the surface pressure of surface-mounted prism", Journal of Fluids and Structures, No. 10, pp.367-393. Tennekes, H. and Lumley, J.L., 1972. A first course in turbulence, MIT Press, Cambridge. Teunissen, HW., (1975), “Simulation of the planetary boundary-layer in a multiple-jet wind tunnel”, Atmospheric Environment, vol. 9, pp. 145-174. Wang, Z.Y., Plate, E.J., Rau, M. and Keiser, R. (1996), “Scale effects in wind tunnel modelling”, J. Wind Eng. Ind. Aerodyn., 61, 113-130. White, Frank M. (1974), Viscous fluid flow, McGraw-Hill, Inc., U.S.A. Wieringa, J., 1993. Representative roughness parameters for homogeneous terrain, Boundary Layer Meteorology., 63, pp. 323-363.

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PHYSICAL SIMULATION OF ATMOSPHERIC FLOW AND TURBULENCE E.Ferrero University of Piemonte Orientale, Alessandria, (It) M.Manfrin University of Torino, (It)

A.Longhetto University of Torino, (It)

L.Montabone University of Oxford (UK)

H.Didelle Laboratoire Coriolis-LEGI, Grenoble, (Fr) C.Giraud IFSI-CNR Torino, (It)

L.Mortarini University of Torino, (It)

J.Sommeria Laboratoire Coriolis-LEGI, Grenoble, (Fr)

D.Bertoni University of Torino, (It)

R.Forza University of Torino, (It)

turbulent flow in the whole ABL. (Nieuwstadt, 1984; Sorbjan, 1987 and 1995). The physical reason is that very often the atmospheric flows at different heights in the ABL exhibit significant uncoupling, which is enhanced by the Earth rotation and irregular topographic patterns. Notwithstanding this, the input data of most numerical and analytical models, applied for assessing space and time patterns of pollutant concentrations, still make use of parameters relevant to surface conditions. Then, it follows that seeking for reliable relationships, connecting easy of access surface turbulent scales with the Earth-rotation-governed dynamics of the whole ABL, still appears as a topical subject. A lot of efforts have been made in the past few decades in order to better account for the complex vertical structure of the atmospheric flow, due to the combined action of obstacles, topography and morphology of Earth surface (Yeh and Huang, 1975; Britter et al., 1981; Taylor et al., 1987; Tampieri, 1987; Zeman et al. 1987; Venkatram, 1988; Shar and Durran, 1997, Ferrero et al. 2002). As far as the influence of Earth rotation is concerned, several studies have been made regarding the effects on the dispersion due to both frictional wind turning (Ekman spiral) with the altitude inside the PBL depth (Csanady, 1972; Csanady and Shaw, 1980; Thompson and Flierl, 1993; Zhang et al., 1994), and of vortex tube strecting over obstacles (Hupper and Bryan, 1976). A very interesting theoretical approach to try to understand the direct influence of the Coriolis parameter on the diffusion mechanisms in the whole ABL has been instead worked out by Wippermann and Yordanov (1972). This effect of the rotation on the diffusion parameters, which operates independently of the distortions of the mean flow (even if it can be related to them), is not easily fit for being

ABSTRACT A laboratory experiment on the atmospheric boundary layer (ABL) is presented. It was carried out in the large rotating tank of the Coriolis-LEGI laboratory in Grenoble. An ABL was reproduced with different roughness lengths at reduced scale and measured. In order to generate a regular mean flow, both spin up and spin down techniques were adopted by varying the rotation period of the tank. A set of preliminary measurements was performed by means of acoustic probes in order to know the velocity trend generated in the tank. The mean velocity fields and the turbulence were measured using PIV (Particle Image Velocimetry) method which allows to obtain high resolution measurements in the simulated ABL. For each rotation period two vertical (nonsimultaneous) cross sections of the flow were obtained, and 3D velocity fields reconstructed from the two planar fields under convenient geometric (orthogonal) and physical assumptions (reproducibility of the flow). Preliminary results on the analysis of the collected data are presented and discussed. INTRODUCTION The space and time distributions of airborne pollutants released into the atmosphere either as hot plumes from elevated stacks of large industrial and power plants, or as extended surface emissions from urban regions marked by heat and moisture islands, depend, especially in complex terrain, on the whole depth, or a substantial fraction, of the atmospheric boundary layer (ABL) of the atmosphere. In these situations, the spread of pollutant plumes or clouds will not be determined any more entirely by atmospheric turbulence conditions near the surface, but new turbulence scales should be sought, based on local and non-local properties of the

143


particular, a wide range of low Rossby numbers can be investigated in such a facility, by conveniently changing its rotation speed.

organizable in the frame of a theory based on the primitive equations governing the turbulent dispersion into the ABL. It deserves then to be resumed also on the experimental point of view, because it could help reveal some reasons of many discrepancies, still unsolved, among field observations and model predictions. The main objective of this work is the establishment, through laboratory experiments in a large hydraulic rotating tank in dynamical similitude, of modified expressions of turbulent dispersion coefficients on spatial extents typical of the mesoscale (≈300 Km). These new coefficients would account for the variability with the altitude of the "cross-wind" concentration distribution of pollutants released as plumes or clouds into the atmosphere, and for the perturbations induced by the non-homogeneities and by the Earth rotation directly on the dispersion mechanisms within the whole depth of the PBL.

THE LABORATORY EXPERIMENT The research consists in a series of laboratory simulations of the dynamics of rotating turbulent ABL and their influence on the diffusive conditions of the atmosphere. The laboratory experiments took place on the hydrodynamic rotating tank of “Coriolis/LEGI” (Grenoble). The rotating speed of the tank can be continuously changed up to 5 revolutions per minute, allowing to achieve Rossby numbers typical of mesoscale circulations (10-1 zo (where Rossby number similarity exists in the PBL), is the following:

K x , y ,z =

k x , y ,z κ 2 u *2 / f

where kx,y,z is the dimensional coefficient of turbulent diffusion along the x,y,z directions respectively. Up to now, this last result has been checked with scarce and poor experimental observations. On the contrary, in laboratory experiments in rotating tank, all the above scales and parameters can be reproduced in a very accurate way. In

144


Figure 2 Two typical behaviors can be observed for all the curves, U corresponding to a turbulence regime, for > 0.8 and the U0

tU 0 < 10 2 (where H=30cm is the total fluid H depth) and to the laminar regime for lower velocity and longer times. In the case of a fully developed turbulence the friction can be written as: dU H = -u *2 dt where the friction velocity u* is proportional to the geostrophyc velocity U above the boundary layer, u*= αU. We have: 1 t 1 = -α 2 + U H U0 In Figure 3 this linear law for 1/U is verified for the same cases of Figure 2 and α=0.07. normalized time

Figure 1: Schematic picture of the experiments set-up The experiments were carried out with different values of the roughness length. In the first case no roughness elements were put in the tank, while in the second series of experiments cubicshaped roughness elements were put (glued) over the tank surface. PRELIMINARY RESULTS The main objective of the experiment is to investigate the turbulent PBL over a surface with and without roughness. A proper flow was created in tank by varying, in a very short time, the rotation period of the platform from T0 to T1. This variation produce a solid body rotations of the fluid in the tank with a velocity U=2π(1/T1-1/T0)r, proportional to the distance r from the axe (in our case r=5.1 m). Firstly a series of velocity measurements by using sound Doppler probes were carried out. They were aimed to obtain the friction as a function of the Reynolds number. The first condition to be satisfied is to create a turbulent PBL. The Ekman layer instability attains for Reynolds numbers Re=Uδ/ν (where δ=(νT1/2π)1/2 is the laminar layer depth) of the order of 55. The turbulence is fully developed for Reynolds numbers higher than this value. In order to assess the presence of well developed turbulence in the flow, we performed a series of experiments with different initial velocity (generated by choosing different value for T0 and T1), both accelerating (spin-up) and decelerating (spindown) the tank rotation. The results are shown in figure 2.

Figure 3 It can be see that the measured curves agree with the linear law for small time and large velocities. Moreover different trends

145


were found for spin-up (first three curves in the legend) and spin-down (second three cases). Analysing the corresponding experiments for the case with and without roughness, no differences were found. This fact is not surprising because the probes were positioned above the boundary layer and hence the measurements were not influenced by the turbulence developed inside of it. The turbulent boundary layer depth can be evaluated as of the order of: δt=0.4 u* /f,

(1)

where f=4π/T1. and u*=a U. Considering that U= 2π(1/T1-1/T0)r, we have:

Figure 5: Horizontal mean velocity component (cm s-1) as a function of the height z (cm) (Pos. 2)

δt =0.2 a (1-T1/T0) r

In Figure 6 the vertical profile of vertical velocity second order moment , for the two position are depicted. They demonstrate the presence of a turbulent layer whose height δt is of the order of 3.6 cm, according with the valued prescribed by equation (1).

which does not depend on the rotation period. In our experiments we have T1/T0=1/2, a = 0.07 and r=5.1 m and thus: δt = 3.6 cm The Reynolds number based on the laminar depth is Uδ/ν= (1- T1/T0)r(2π)1/2 ( ν T1)-1/2 =6390T1-1/2 In the experiments with values of T1 ranging from 30 s to 240 s we obtained Reynolds numbers ranging from 412 to 1166. These values refer to the initial velocity, then the velocity decrease and hence the Reynolds numbers are lower. The flow initially turbulent, after about 102 normalised times becomes laminar (see Figure 2). These results are confirmed by the analysis of the experiments measured through the PIV technique. The experiment refers to the case without roughness, with a free stream velocity of about 5.5 cm/s. Obtained by varying the rotation period from T0=120 s to T1=60 s. With this values of the parameters the Reynolds numbers is Re= 171.

Figure 6: Vertical momentum fluxes (cm2s-2) as a function of the height z (cm) (Pos. 1 and 2) The Figure 7 and 8 present the results about the momentum flux in term of vertical profile. Also in this case a turbulent layer is found in the layer below 4 cm. The plots also show that in lower layer (below about 2 cm) the results cannot considered satisfactory. This effect is probably due to the reflection of the laser light sheet on tank wall, which produce a noise in the images and does not allow to detect the velocity field close to the wall.

Figure 4: Horizontal mean velocity component (cm s-1) as a function of the height z (cm) (Pos. 1) Figure 4 and 5 show the horizontal velocity component vertical profile for Position 1 and 2 in Figure 1. It can be clearly observed the Ekman layer generated by the rotation.

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subsidences, and so on). Additional possibilities, could include a repetition of the experiments, for a weakly baroclinic PBL. ACKNOWLEDGMENTS This work has been carried out in the frame of the EU Programme “Transnational Access to major Research Infrastructures”. REFERENCES Bernero S. and H.E. Fiedler (2000): "Application of particle image velocimetry and a proper ortogonal decomposition to the study of jet in a counterflow" Experiments in Fluids, S274-S281 Britter R.E, J.C.R. Hunt and K.J. Richards (1981): "Flow over a two-dimensional hill: studies of velocity speed-up, roughness effects and turbulence" J.R. Meteorol. Soc., 107, 91-110 Csanady G.T.(1972): "Cross-wind shear effects on atmospheric diffusion" Atmospheric Environment, 6, 221-232 Csanady G.T. and P.T. Shaw (1980): "The evolution of a turbulent Ekman layer" J. Geophys. Res., 85, 1537-1547 Ferrero E., Loglisci N. and Longhetto A. (2002): "Numerical experiments of barotropic flow interaction with a 3-D obstacle", J. of the Atmos. Sci., Vol. 59, No. 22, 3239-3253 Fincham A.M. and G.R. Spedding (1997): "Low-cost, high resolution DPIV for measurement in turbulent fluid flows" Experiments in Fluids, 23, 449-462 Huppert H.E. and K. Bryan (1976): "Topographically generated eddies" Deep Sea Reserarch, 23, 655-679 Nieuwstadt F.T (1984): "The turbulent structure of the stable, nocturnal boundary layer" J. Atmos. Sci.,41,2202-2216 Schar C. and D.R. Durran (1997) "Vortex formation and vortex shedding in continuously stratified Flows past isolated topography" J. of the Atmospheric Sciences, 54, 534-554 Sorbjan Z.(1987): "An examination of local similarity theory in the stably stratified boundary layer" Bound-Layer Meteor., 38,63-71 Sorbjan Z.(1995): "Toward evaluation of heat fluxes in the CBL" Appl.Met., 34, 1092-1098 Tampieri F. (1987): "Separation features of Boundary layer flow over valleys" Bound.-Layer Meteorol., 40, 295-308 Taylor P.A., P.J. Mason and E.F. Bradley (1987): "Boundary layer flow over low hills (A review)" Bound.-Layer Meteorol., 39, 107-132 Thompson L. and G.R. Flierl (1993): "Barotropic flow over finite isolated topography: steady solutions on the betaplane and the initial value problem" J. of Fluid Mechanics, 250, 553-586 Venkatram A.(1988): "Topics applied dispersion modelling" in Lectures on Air Pollution Modelling, Venkatram A. and J.C. Wingaard Eds. - American Meteorological Society Wippermann F. and D. Yordanov (1972): "A note on the Rossby similarity for flows of barotropic planetary boundary layers" Atm. Env. Vol. 6, 877-888 Yeh G.T. and C.H. Huang (1975): "Three-dimensional air pollutant modelling in the lower atmosphere" Boundary Layer Met., 9, 381-390

Figure 7: Vertical momentum flux (cm2s-2) as a function of the height z (cm) (Pos. 1)

Figure 8 Vertical momentum flux (cm2s-2) as a function of the height z (cm) (Pos. 2) CONCLUSIONS This work focused on the laboratory simulation of simple conditions of barotropic boundary layers over regular and flat terrain. Specific algorithms, devoted to turn the information provided by the PIV methodology into eulerian fields of flow velocity at different levels of the turbulent rotating ABL, were used. The eulerian velocity field were used to calculate turbulent quantities as turbulent kinetic energy and Reynolds stress. The eulerian kinematic flow fields provided by the PIV analysis and the reconstruction of the concentration fields of released dye tracers can provide the coefficients of turbulent diffusion. The ensemble of all the above mentioned experimental information of mean and turbulent flow patterns and of tracer dispersion obtained under strictly controlled laboratory conditions might let one foresee, in perspective, a promising up-grade of numerical dispersion models of airborne pollutants, before they are applied to simulate natural dispersion processes in actual conditions of the natural prototype at meso-scale, through: i) - adimensionalization with the proper scales; ii) calibration of their parameters; and, iii) - validation of their predictions, obtained with the same boundary conditions adopted in the rotating tank, against the relevant results of the laboratory experiments. As a future work, the experiments will go be extended to barotropic ABL over a few typologies of complex terrain (schematic two-and three-dimensional obstacles, terrain

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Zeman O. and N.O. Jensen (1987): "Modification of turbulence characteristics in flow over hills" Quart. J. R. Meteor. Soc., 113, 55-80

Zhang X, D.S. McGuiness and D.L. Boyer (1994) "Narrow barotropic current impinging on an isolated seamount" J. Geophysical of Research, 99, 22,707-22,724

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PHYSICAL MODEL RESULTS FROM DISPERSION EXPERIMENTS WITH GROUND-LEVEL SOURCES B.Leitl Meteorological Institute, University of Hamburg Bundesstraße 55, 20146 Hamburg, Germany Email: [email protected]

M.Schatzmann Meteorological Institute, University of Hamburg Bundesstraße 55, 20146 Hamburg, Germany Email: [email protected]

ABSTRACT Sponsored by the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety, experiments in the wind tunnel laboratory of Hamburg University were carried out. A neutrally stratified boundary layer flow above open terrain was modelled at a scale of 1:450. After carefully measuring and completely documenting the simulated boundary layer, three idealized ground level sources were installed flash to the wind tunnel floor. Subsequently, the dispersion of a passive tracer released from a point source, a line source (perpendicular to the wind) and from an area source (rectangular, same width as the line source) was studied. In the resulting plumes, lateral and vertical concentration profiles were measured at several source distances. A completely documented validation data set has been compiled from the measurements and will be made available to the scientific community on the CEDVAL homepage. Subsequently the results of the wind tunnel study will be presented and discussed.

experiments can be used as a reference. For basic model testing, results from experiments in a boundary layer wind tunnel should be preferred to field data because they overcome some of the specific limitations field data have (Schatzmann et al, 2003). For instance, in a wind tunnel the boundary conditions with respect to wind profile, wind speed and atmospheric turbulence can be controlled and can be kept constant over a sufficiently long period of time. Atmospheric flow and dispersion problems can be replicated under “quasistationary” conditions, enabling the wind tunnel modeller to generate data that completely match the situation simulated in corresponding numerical model runs (Schatzmann and Leitl, 2002). Furthermore, complete sets of input data required to configure a numerical simulation can be provided. No further assumptions are needed in setting up the model run. A small number of completely documented reference data sets are already available (see www.mi.unihamburg.de/cedval). These data sets comprise highly idealised urban-type geometries but are, for some types of applications (e.g. Gaussian or Lagrangian model testing) already too complex. Therefore, additional wind tunnel experiments were carried out with momentum-free ground-level releases into flat uniform terrain. A variety of practical dispersion problems can be assigned to ground-level sources such as pollutant dispersion from waste dumps, radon releases from mining relics or odour releases from farmland fertilized with liquid manure.

NOMENCLATURE All variables are defined in the text. INTRODUCTION Numerical modelling of atmospheric pollutant transport is widely used for immission control and air quality management. A variety of different modelling approaches ranging from simple mass conserving box models to complex CFD codes are applied to practical pollutant dispersion problems. It is well known that different models may deliver different results. Depending on the type of problem, the results from numerical dispersion models may even vary significantly (Ketzel et al., 2001). Model validation is required in order to test the accuracy of a model and to identify the limits of its applicability.

REQUIREMENTS FOR VALIDATION DATA SETS There are some basic requirements for a validation data set: The data set must be complete in that all boundary and input conditions are clearly defined. In other words, the degree of freedom a numerical modeller has in setting up a test run should be minimized. The data set should comprise a sufficiently large number of individual cases in which the most important input parameters are varied in a systematic way over the whole range of interest. If a model successfully replicates all of these, it can be assumed

In principle, data from field measurements as well as highresolution laboratory data from systematic wind tunnel

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the boundary layer was 1:450. Only values transformed to full scale will be reported in this paper.

that it would correctly predict also cases that were not covered in the test runs. The data set should be sufficiently large in that it allows the assessment of whether or not a model is able to replicate complete fields of the variables. Models that show good agreement with measurements at one or two locations might fail to do so at the third. Above all when a property of interest is expected to show significant local variation, the density of measurement points must be large. The data itself must be of known quality. This means the data set must come with a documentation, which includes not only a clear description of the experimental set-up but also a quantification of the uncertainties inherent to the data.

Figs. 1 to 3 show a selection of properties of the wind tunnel boundary layer. Shown are normalised vertical profiles of the mean wind velocity at positions upstream from the sources and at the end of the test section (Fig.1).

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Field experiments are seldom able to match the requirements stated above. Basic model testing is therefore predominantly carried out with wind tunnel data.

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EXPERIMENTS A number of completely documented reference data sets are already available for simplified urban-type dispersion problems (see for instance the CEDVAL data bank (Leitl, 2000) under www.mi.uni-hamburg.de/cedval), but hardly any laboratory data have been published for momentum-free ground-level releases in flat uniform terrain. The only exception we are aware of is the study by Snyder (1991) who made experiments with a point source and several area sources. The lack of such data is contrasted by a variety of practical dispersion problems that can be assigned to ground-level sources. Such problems include the dispersion of gases emitted from waste dumps or radon releases from mining relics. In order to remedy the lack of qualified reference data, the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety recently sponsored a number of systematic experiments in the wind tunnel laboratory of Hamburg University.

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In the environmental wind tunnel ‘BLASIUS’ a neutrally stratified boundary layer flow over flat and open terrain was modelled. After carefully measuring and completely documenting the modelled boundary layer, three idealized ground level sources were set into the tunnel floor. Passive tracer gas was emitted from (1) a point source, (2) a line source oriented perpendicular to the wind and (3) a rectangular area source with a width identical to that of the line source. The resulting tracer plumes downwind from the sources were measured for several lateral and vertical profiles. At present the wind tunnel data are being processed. They will soon be made available to the scientific community via the CEDVAL data bank. The boundary layer was generated through a combination of vortex generators and roughness elements. Velocity time series were measured in several heights above ground and turbulent macro scales determined. The macro scales in combination with the roughness length (determined from the logarithmic wind profile) led to the conclusion that the scale of

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The roughness length of the boundary layer was determined to be 0.1m and the power law exponent to be 0.18. In Fig. 2 the turbulence intensities (defined by Ii = σi(z)/U(z), with σi the standard deviation of velocity fluctuations of wind component i ) are given. Over the lowest 40 m above ground the wind tunnel data fits well to the reference curves derived from measurements in the real atmosphere. Above this height some deficits in the Iw –profile were observed which could have rectified by further adjustments of the vortex generators and roughness elements. Since the dispersing clouds keep close to the ground, additional effort to improve the agreement was not taken.

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The longitudinal power spectrum measured at 20 m above ground is given in Fig 3. It compares reasonably well with the curves determined by Kaimal, v.Karman or Simiu and Scanlan (1986) in corresponding field experiments. Fig. 4 shows a sketch of the 3 sources that were investigated. As can be seen in Fig.5 the sources were set flash into the tunnel floor. The source design deserves mentioning. In order to assure an emission flux absolutely homogeneous over the complete source area, the sources were made up by numerous hypodermic needles with an inner diameter between 0.2 and 0.3 mm. A steady and continuous tracer flow through the needles was ensured by maintaining a large pressure drop over the length (70 mm) of the needles (Meroney et al., 1996). The needles were distributed in regular arrays over the source cross section The largest distance between 2 needles was 5 mm (area source).

Fig. 5: View into the wind tunnel equipped with the area source.

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Due to the large number of needles, the source flows were virtually free of vertical momentum (The exit velocity varied between 0.03m/s (area source) and 0.45 m/s (line source)). Flow visualisation experiments and test measurements proved that the plumes remained at ground for these velocities.

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as functions of distance from the source (x), distance from the centreline (y) or distance from the ground (z). C stands for concentrations; the velocity Uref refers to a reference height of 10 m above ground (anemometer height) and Q is the tracer release volume flux in m³/s.

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Figs. 6 and 7 show normalised ground level concentrations for each of the 3 sources at identical downstream positions and Fig. 8 concentration fields in vertical cross sections perpendicular to the wind. The comparison of results reveals that with increasing source distance the lateral profiles of the 3 plumes become more and more identical. The specific source configuration is in the near field of the plume of significance only. The longitudinal concentration decay in the far field of the plumes follows the -2/3 – law known from Berljands (1982) analytical solution for point sources. It is also in agreement with Snyders (1991) point source results. More details will be presented in the talk.

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Fig. 7: Lateral ground level concentration profiles for several source distances ACKNOWLEDGEMENTS The authors are grateful for financial support from the German federal ministry for the environment, nature conservation and nuclear safety through a grant from the federal agency for radiation protection. Fig. 6: Ground level concentration decay with source distance at the plume centre-line for the three sources investigated.

REFERENCES Berljand, M. E. 1982: Moderne Probleme der atmosphärischen Diffusion und der Verschmutzung der Atmosphäre, Akademie-Verlag, Berlin 1982.

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Ketzel, M., Louka, P., Sahm, P., Guilloteau,E., Sini, J.-F., and Moussiopoulos, N., 2001: Inter-comparison of numerical urban dispersion models - Part II: Street canyon in Hanover, Germany. Proc. 3rd Int. Conf. on Urban Air Quality, Loutraki/Greece. Leitl, B., 2000: Validation Data for Microscale Dispersion Modelling. EUROTRAC Newsletter, 22, 28-32. Meroney, R.N., Pavageau, M, Rafailidis, S. and Schatzmann, M. 1996: Study of Line Source Characteristics for 2-d-Physical Modelling of Pollutant Dispersion in Street Canyons. Journ. Wind Eng. and Ind. Aerodynamics, 62, 37-56. Schatzmann, M., and Leitl, B. 2002: Validation and application of obstacle resolving urban dispersion models. Atmospheric Environment,.36, 4811-4821. Schatzmann, M., Grawe, D., Leitl, B., and Müller, W.J., 2003: Data from an urban street monitoring station and its application in model validation. Proc. 26th NATO/CCMS Int. Techn. Meeting on Air Poll. Mod. and its Appl., Istanbul/Turkey. Simiu, E., Scanlan, R. H. 1986: Wind Effects on Structures – Part A: The Atmosphere. Wiley & Sons Inc. Snyder, W.H. 1991: Wind-Tunnel Simulation of Dispersion from Superfund Area Sources. Report, US Environmental Protection Agency, Research Triangle Park, NC 27711.

point source at X = 225 m 2

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CHEMICALLY REACTIVE DISPERSION INTO ATMOSPHERIC BOUNDARY LAYER C.Aguirre University of Entre Ríos, Road N° 11, Km 10 , Oro Verde Entre-Rios, Argentine. [email protected]

S. Simoëns Laboratoire de Mecanique des Fluides et d’Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon 69 131, Ecully Cedex, France simoë[email protected]

M. Ayrault Laboratoire de Mecanique des Fluides et d’Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon 69 131, Ecully Cedex, France

plants and cars burning fossile fuels. Consequently, the nitrogen oxides composition of many in situ stack plumes has been investigated and several reacting plume models have been developed by different authors. The objective of the present work is to apply a combination of Large Eddy Simulation (LES) (as it is now admitted that prediction of scalar dispersion into atmospheric boundary layer requires the knowledge of large eddy turbulent motion) to continuous Lagrangian stochastic modelling for environmental studies. For this aim the small scale turbulent mixing is approximated by a classic one particle and one time scale lagrangian stochastic model coupled with a deterministic and continuous diffusion model which can be seen as an extension of the CD model of Curl [1]. The principal reason of this last choice is that it can achieve continuous mixing in order that the extent of the mixing to be controlled at the particle level. This work is concerned with a rapid chemical reaction modeling of species spreading into Atmospheric Boundary Bayer (ABL) from a chemney. We have used the work by Fackrell and Robins [2] (FR82) in order to validate our simulations concerning velocity and concentration fields evolution. Concerning chemical reactions of some species inside the ABL we have not found experimental data basis wellenough described in order to support our simulation. We have thus substitute chemical reactant species to the previous passive scalar for the previous case of FR82. First we will present LES and subgrid scale modelling and the velocity field results, the lagrangian stochastic model and the diffusion model and the concentration field evolution results. A comparison with experimental results by FR82 is also presented. Finally we will apply it to a rapid chemical reaction (a source of nitrogen monoxide NO emitted from plume chemney inside ABL charged of ozone O3 ).

ABSTRACT The objective of the present work is to apply a complete modelling taking into account for large turbulent scales, inertial turbulent scales and micromixing for dispersion of species chemically reactant. For this a Large Eddy simulation, continuous Lagrangian stochastic modelling and coalescence dispersion modelling are combined for the environmental study. The Large Eddy simulation is necessary to take into account for large scales which modify the well established Kolmogoroff cascade. The turbulent mixing for the scales corresponding to the inertial zone of the Kolmogoroff cascade is approximated by a classic one particle and one time scale lagrangian stochastic model satisfying the well-mixed condition and the molecular diffusion by a deterministic and continuous in time pairing particle exchange model which is an extension of the coalescence-dispersion (CD) model of Curl (1963). This model enables to reach many statistical quantities to be predicted. In this paper we present the effectiveness of the model to predict a second order rapid chemical reaction between two species. A fictive experiment of a reactive plume in a reference atmospheric boundary layer case is simulated. A point source of nitrogen monoxide NO is dispersed inside a boundary layer containing ozone O3 dispersed homogeneously. Dynamical and concentration statistical results display good agreement with experimental data. Chemical reaction produce realistic data. Keywords : Lagrangian, stochastic, turbulence, mixing, diffusion, chemical reaction. INTRODUCTION During the last decade, people has become sensitive to air quality, especially through the greater knowledge of deseases linked to pollution. A notable example is breathing system mysfunctionings due to excessive levels of ozone. The main chemical source of this component in the troposphere is the photolysis of nitrogen dioxide that is mainly produced by power

DYNAMICAL MODELLING

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All details can be found in Michelot [7] or Simoëns et al. [8]. Modifications are realised here to substitute small scale fluctuations to Reynolds fluctuations. One question still exists is the difference between Eulerian parameters issued from LES filtering and corresponding Lagrangian parameters issued from Reynolds decomposition.

LES subgrid modeling We used Large-Eddy-simulation (LES) in order to calculate the large scales evolution whereas the small scales are modeled by a subgrid scale model. For the velocity subgrid < < T = u u −  u u  ij i j  i j

stress

0.05. close to the wall the energy is not correct and is responsible for the small discrepencies of the mean concentration close to the wall (figure 2). Such problems are due to not correct comportment of the simple Smagorinsky model close to the wall and in the inhomogeneous direction, and may be due also to the wall law comportment.

MODEL PREDICTIONS AND DISCUSSION

Passive scalar case FR82 provide data concerning a boundary layer of δ = 1,2 m depth and the spreading of a source of propane of 8,5 mm indiameter was disposed at an altitude of Zs = 0,228 m from the ground. They present concentration measurements about a length L = 6,52 .δ = 7,824 m. The external velocity was Ue = 4,0 m/s with a friction velocity u* = 0,047*Ue = 0,188 m/s. The rugosity parameter was Z0 = 2,4.10-4 .δ = 2,88.10-4 m and no pressure gradient inside the boundary layer exists. For concentration we will present two vertical profiles X1= 1,152m and X2 = 2,304 m. To simulate this case we used a grid of Nx = 49 x Ny = 11x Nz = 60 meshes with spatial steps ∆x, ∆y equal to 0,135 m and ∆z variable in function of the altitude. Our statistics are obtained for a same profile with 84 samples spaced of ∆t = 0.25s. We have a good agreement with the data of FR82 both for mean velocity and kinectic energy as shown on figures 1a and 1b. We present also (Figure 2) the mean concentration vertical profiles for the stations presented in FR82. We can note that we have a good agreement at the different levels greater than Z=0.1. Such profiles are obtained with only LES (1) combined to Stochastic Lagrangian modelling (2) without reaction and diffusion part (equation (3)). 50 000 passive particles are injected during the simulation. It can be noticed that it exists a small departures with the results of FR82. Out of the dynamic discrepencies such difference is due to diffusion process which is not correctly simulated here whereas in the chemical reactant case with model (3) (Figure 3) it is.

On figure 2 the concentration results are in good agreement with FR82 results, in spite of discrepencies of the turbulent kinetic energy close to the wall. This signify that mean flow (and thus large scales) is mainly responsible for dispersion of scalar. It can be noticed that mean concentration peak is thinner certainly due to the fact that we have not used model (3) and thus the diffusion process. In figure 3 we see that such differences disapears. The presented results concern with the mean mixture fraction C − CO3 + CO0 3 ( < F >= NO ) that has, as expected, the same 0 CO03 + CNO comportment as a passive scalar. The improvment compared to figure 2 is due to the fact that diffusion process are here taken into account (model (3)). For the gases such effect is not neglectible. This signifies that reactive species comportments are correct and that our modelisation with its three different parts is robust enough to simulate more complex pollution events as those detailed in this conference by Simoëns et al. [14] For the street canyon situation. CONCLUSIONS A combined LES/Lagrangian stochastic/diffusion modelling has been applied to the simulation of atmospheric turbulent chemical reacting flows. The turbulent mixing is approximated by a classic inhomogeneous one particle and one time scale lagrangian stochastic model that we have translate to substitute LES filtering on a mesh to classic Reynolds average. The diffusion is modelised by a deterministic and continuous pairing particle exchange model. Large scale movement which are responsible for breaking a well-established turbulence are took into account by LES.

Chemical reactant case It is still difficult to find a fundamental case well enough described in order to validate our numerical approach. Thus we used the FR82 experimental case and we substitute the passive scalar emitted from the chemney by Nitrogen monoxyde (NO) and the main flow (BL) containing ozone (O3) diluted in air

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fluctuations in grid-generated turbulence”, Phys. Fluifs A4, 2292. [12] Hsu, A.T. and Tchen, J.Y.: 1991, “A continuous mixing model for pdf simulations at its applications to combusting shear flows”, Eight symposium on turbulent shear flows, 22.4.1.

We have to improve the LES model with at least the use of dynamical smagorinsky model. An inhomogeneous and adapted to small scales fluctuations version of the Generalised Lagrangian Stochastic modelling of Haworth and Pope [15] could also be implemented. Nevertheless to calibrate all constant of such model is a huge work. Concerning the diffusion part we have to introduce more explicitely the Schmidt and Dahmkoler number dependances. By now our global model is strong enough to simulate pollution transferts from urban canopy (as street canyon case) to external boundary layer.

[13] Li, J.D. and Bilger, R.W.: 1996, “The diffusion of conserved and reactive scalars behind line sources in homogeneous turbulence”, J. Fluid Mech., 316, 339-372. [14] Simoens, S., Ayrault, M., Wallace, J., “Pollutant fluxes from 2D line source between 2D obstacles into atmospheric boundary layer”, Physical Modelling of Flow and Dispersion Phenomena, 3-5 September 2003, Prato, Italy. [15] Haworth D.C. and Pope S. B.,”A generalised Langevin model for turbulent flows”, Phys. Of Fluids, 29(2), pp 387-405, February 1986.

REFERENCES [1] Curl, R.L.”Disperse phase mixing : Theory and effects in simple reactors”, AIChEJ (9), 175-181, 1963. [2] Fackrel J.E. and Robins A.,”Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer”, J.F.M., vol. 117, pp 1-26, 1982. [3] Deardorff, J.W., :”Stratocumulus-capped mixed layers derived from a three-dimensional model”, Boundary layer Meteorology 18, pp 495-527, 1980. [4] Kobayashi T., Taniguchi N., Tsubokura M. And Kogaki Tetsuya, “The verification of the SGS model of LES to a practical engineering problem”, Advances in Turbulence Research, pp 1-26, Korea Univ. Seoul, May 17, 1996. [5] Thomson, D.J., 1987, “Criteria for the selection of stochastic models of particle trajectories in turbulent flows”, J. Fluid Mech. 180, 529. [6] Thomson, D.J.”A stochastic model for the motion of particle pairs in isotropic high Reynolds number turbulence and it’s application to the problem of concentration variance”, J.F.M. 210,1993. [7] Michelot, C.: 1996, “Developpement d’un modele stochastique lagrangian - Application a la dispersion et a la chimie de l’atmosphere”, These de Doctorat, Ecole Centrale de Lyon. [8] Simoens, S., Michelot, C, Ayrault, M. and Méjean P., "Dispersion of continuous releases over a two-dimensional obstacle", Int. Conf. and Workshop on Modelling and Mitigating the consequences of Accidental releases of hazardous Materials, New-Orleans, AICHE, pp 851-858, 26-29 Sept. 1995. [9] Simoëns, S., Michelot, C, Ayrault, M. and Sabelnikov, V.: 1997, “Modele stochastique de diffusion continu en temps : approximation differentielle de l’equation d’evolution de la densite de probabilite de la concentration et sa solution asymptotique dans le cas d’une turbulence homogene” C.R.Acad.Sci. Paris, t.324, Serie Iib, 667-678. [10] Pope, B.S.: 1985, “Pdf methods for turbulent reactive flows”, Prog. Energy Combust. Sci. 11, 119. [11] Jayesh and Warhaft, Z.: 1992, “Probability distribution, conditional dissipation and transport of passive temperature

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Proceedings of PHYSMOD2003: International Workshop on Physical Modeling of Flow and Dispersion Phenomena 3-5 September 2003, Prato, Italy

WIND TUNNEL EXPERIMENTS FOR LNG TERMINAL SITING Jerry Havens Chemical Hazards Research Center Chemical Engineering Department University of Arkansas Fayetteville, Arkansas 72701, USA

Tom Spicer Chemical Hazards Research Center Chemical Engineering Department University of Arkansas Fayetteville, Arkansas 72701, USA

ABSTRACT Experiments are being conducted in the Chemical Hazards Research Center (CHRC) Ultra-Low-Speed Wind Tunnel to validate computational fluid dynamics models for application to LNG terminal siting consequence analyses. Area-source ground-level releases of carbon dioxide gas in the wind tunnel provide physical simulation of near-field dispersion of cold natural gas vapors. Extensive measurements of turbulence parameters and gas concentration are compared with model predictions. Current emphasis is on the effects upon dispersion due to obstacles, such as tank and dike structures, as well as surface roughness arrays that simulate suburban housing.

Wendy Sheppard Chemical Hazards Research Center Chemical Engineering Department University of Arkansas Fayetteville, Arkansas 72701, USA

The CHRC Wind Tunnel is an ultra-low-speed boundary layer wind tunnel capable of producing airflows that simulate the constant stress layer of the atmospheric boundary layer. It was designed and constructed specifically for the study of atmospheric dispersion of dense gases at wind speeds below 2 m/s (Havens et al., 1994). Figure 1 depicts the floor plan of the CHRC Wind Tunnel.

INTRODUCTION The Gas Research Institute (GRI) sponsored research conducted at the CHRC to develop and verify alternative model approaches, such as the DEGADIS (Dense Gas Dispersion) and FEM3A models to account for LNG vapor buoyancy, directional diversion by topography, holdup in vapor detention systems (dikes or fences), wake turbulence, or (earth) surfaceto-cloud heat transfer in the determination of vapor cloud safety exclusion zones around LNG storage and transfer facilities. (Havens et al., 1987; Havens and Spicer, 1990; Havens et al., 1994; Spicer and Havens, 1996). Currently, GTI and the University of Arkansas are jointly conducting a continuing a research program to provide for continued evaluation, development, and standardization of the DEGADIS and FEM3A vapor dispersion models for application to a wide range of catastrophic hazardous material release scenarios required to support siting decisions, for effective management of the hazards associated with such facilities, and to develop a national focal point for LNG safety research and technical dissemination.

Figure 1. Floor plan of CHRC Wind Tunnel As shown in the diagram, the wind tunnel is centered laterally in a larger room in order to ensure a symmetrical return space for the re-circulating air on both sides, under, and over the tunnel. An isolated control/observation room is situated adjacent to the wind tunnel housing data acquisition systems and control instrumentation. During the course of an experiment, the tunnel room is isolated so as to prevent extraneous effects that would disrupt the tunnel flow and the variables being measured. The re-circulating airflow is provided by two 75-horsepower, 72-inch diameter adjustable pitch vane-axial fans

EXPERIMENTAL DETAILS CHRC Wind Tunnel 159


side-length dike dimensions were 0.943 m and 0.636 m respectively for the low-dike and high-dike designs. The dike heights were 0.02 m and 0.037 m respectively for the low-dike and high-dike designs. Cut aluminum angles functioning as surface roughness elements were installed later on the floor to "roughen" the floor for experiments that studied the effects of surface roughness. The details of the surface roughness elements are also illustrated in Figure 2. These surface roughness elements were made up of a square base of 3.81 cm in length on all sides with another square of the same dimensions extended perpendicularly from one edge of the base. They were arranged in a staggered array at a distance of 30.5 cm between subsequent elements in the downwind as well as the lateral directions.

manufactured by Buffalo Forge Company. These fans, working as master-and-slave, are outfitted with Fenner M-Trim speed controllers that regulate the rotational speed in revolutions-per-minute (rpm) as directed by a computer-based control system in the control room. The airflow produced by the fans passes through a circularto-rectangular transition from the fans to the working area of the wind tunnel. The working area is 7 ft high, 20 ft wide and 80 ft long, and is divided into two regions: § Boundary-layer generation region follows immediately after the circular-to-rectangular transition. A uniform airflow across the cross-sectional area of the wind tunnel is generated when the airflow flows through a honeycomb with ½-inch cells and a series of four seamless nylon screens placed after the honeycomb. Fourteen Irwin spireshaped turbulence generators (13.2 cm base, and 92.7 cm height; refer to Figure 2), positioned at 30 cm downwind from the last seamless screen with 46.3 cm between adjacent spires, were employed to induce an approximately 1 m high turbulent boundary layer. § Measurement region begins at six spire heights (approximately 18 ft) downwind from the last screen. This region also consists of the modeling system as well as instrumentations for data acquisition purposes (refer to discussions later in this section). The wind tunnel floor was tiled with smooth rubber matting. Another seamless screen and a back-pressure device consisting of vertical Plexiglass strips (3 inches in width and ¼ inch in thickness spaced 3-3/16 inches apart) were installed at the end of the working section of the wind tunnel.

Velocity Measurement Measurements of wind-tunnel velocity and turbulence statistics utilized constant temperature thermal anemometry, (CTA), specifically the miniature cylindrical two-sensor "X"film probes (Model Number 1248A-10 by TSI Inc.). Figure 3 shows a side view illustration of the constant-temperature hotwire anemometer probe mounted in the CHRC Wind Tunnel. The X-probe simultaneously measures two components of the velocity vector. By orienting the probe in two different perpendicular directions via a micro-electric motor in the control room, the probe is enabled to measure velocities in the x-y and x-z directions.

Figure 3. Side view of XWA mounted in CHRC. Experiments acquiring velocity and turbulence statistics were conducted with the fans running at 90 rpm. The fans were run for approximately an hour prior to the commencement of measurements. Meanwhile, calibration of the XWA (conducted for each experiment performed) was conducted. The calibration involved centering the probe in a calibration tube (0.5 in. diameter and 30 in. long Plexiglass tube) to which breathing-grade bottled air was fed. The laminar centerline velocities in the calibration tube detected by the XWA sensor were consequently twice the value of the average velocities. The specific flow rates used in the calibration were designed to provide laminar flows through the tube that spanned the range of the wind velocities studied in the experiments. The fans were momentarily turned off during the calibration to eliminate external effects during the calibration of the XWA. The XWA was calibrated by decoupling it as if it were two single probes, and the data were acquired by using the

Figure 2. Details of turbulence generators and surface roughness.

Modeling System The tank and dike configurations used in the tunnel for experimental work were of 150:1 scale. The tank was 31 cm in diameter, cylindrical in shape, and had a spherical-section “dome” top. The height of the tank measured to the top of the dome was 28.3 cm. The tank was located in the center of areas enclosed by square dikes, on a platform topped with a mesh screen that was flush with the tunnel floor surface. The inner 160


D. Low momentum area source CO2 release – rough floor. E. Low momentum area source CO2 release with high dike and tank – rough floor. The fans were also run at 90 rpm for approximately an hour

acquisition function of the IFA 300 ThermoPro software by TSI. Each data point in the calibration stage was taken at 1 kilo-Hertz (kHz) and for 60 seconds. Ten voltage outputs (calibration points) were obtained corresponding to flow rates between 0.5 and 2.3 slpm with a 0.2 slpm increment between two subsequent flow rates. The yaw calibration was achieved by pivoting the calibration tube from 30-degrees right to 30degrees left (with increments of 6-degrees) about the centerline location of the XWA, thus yielding eleven yaw calibration points. Following computer processing of the raw data files, the voltages with their corresponding flow rates for the velocity calibration were then entered into the software to generate two separate calibration curves, one for each single wire. Meansquare-errors for both curves were also shown as an indication of the deviation of the calibration curve from a fourth-order polynomial. The voltages from the yaw calibration were also entered into the software to calculate the yaw coefficients. A typical calibration curve generated as a result of calibration of the XWA is shown in Figure 4.

Figure 5. Side view of FID mounted in CHRC before any experimental work was conducted during which the FID was lit and allowed to stabilize. As before, the wind tunnel area was isolated to prevent external disturbances of the flow in the tunnel. The fans were turned off momentarily for calibration. Calibration of the FID entailed generating a five-point calibration curve. A calibration line “diffuser” was constructed from a 6 in. long, 1 in. diameter Plexiglass tube fitted with a cotton or porous foam filter which dampened pressure fluctuations in the calibration gas supply. Data for each calibration point, also acquired by the IFA 300 ThermoPro, were sampled at 1 kHz for 60 seconds for air-CO2 mixtures (using propane tracer) corresponding to carbon dioxide concentrations of 0%, and other concentrations catering to the specifics of the different experiment configurations. The 0% point was taken in the room air at the beginning of each experiment, so as to measure concentrations relative to the initial room gas air mixture (of air, carbon dioxide, and minor hydrocarbon contaminants). Subsequent data points were measured by inserting the sampling tube into the calibration diffuser (perpendicular to the flow in the diffuser). A typical calibration curve is shown in Figure 6. Following calibration, the fans were started again (90 RPM), and gas flow to the source box under the wind tunnel floor was started. The flow for all experiments was set at 33.4 slpm carbon dioxide traced with 0.5 slpm (~1.5%) propane. The gas concentration measurements began after the gas flow downwind of the source box reached steady state in approximately 30 minutes.

Figure 4. Typical XWA Probe Calibration. The fans were started again upon completion of the calibration. The probe was positioned at an elevation of 0.5 (+/- 0.1) cm above the tunnel for all measurements in vertical velocity profiles in this study. The turbulence statistics were determined for all data points from data sampled at 1 kHz for 2 minutes. Gas Concentration Measurement The gas concentration measurements were performed by a High Frequency Response (HFR) 400 Fast Flame-IonizationDetector (FID) by Cambustion Limited. This application is based on the premise that an electrical signal (which would be converted into voltage output) is generated proportional to the number of negative ions produced when a hydrocarbon sample is burned, thus making it possible to detect hydrocarbon tracer in the sample gas. Figure 5 depicts the FID sampling chamber. The five experiment configurations studied in the gas concentration measurements are listed as follows: A. Low momentum area source CO2 release – smooth floor. B. Low momentum area source CO2 release with low dike and tank – smooth floor. C. Low momentum area source CO2 release with high dike and tank – smooth floor.

Figure 6. Typical FID Probe Calibration. 161


Lateral profiles of gas concentration spanning the entire gas cloud were made at pre-assigned downwind locations. All such measurements were made at 0.5 cm elevation. In selected experiments, vertical gas concentration profiles were measured on the wind tunnel centerline at 0.5 cm vertical intervals from the floor so as to span (vertically) the gas cloud down to concentrations of approximately 1%. Flow Visualization Visualization tests were conducted prior to the experimental measurement phase to ensure that the gas flow was down the center of the wind tunnel, thus demonstrating the symmetry of the flow in the tunnel. This was accomplished by adding Rosco fog (theater) fluid to the carbon dioxide at the entrance to the gas source box under the tunnel. Fog fluid addition was at the same rate, as nearly as could be approximated, for all tests. A video camera was mounted near the center of the tunnel ceiling so as to give an oblique view of the gas flowing in the downwind direction. Camera position and angle of view was the same for all tests. Figures 7 - 11 show captured video frames from the five configurations represented by cases A - E, respectively.

Figure 9: Case C: Low momentum area source release with high dike – smooth floor

Figure 10. Case D: Low momentum area source release – rough floor.

Figure 7. Case A: Low momentum area source release – smooth floor.

Figure 11. Case E: Low momentum area source release with high dike – rough floor. The results as shown above were considered satisfactory. EXPERIMENTAL RESULTS Figure 8. Case B: Low momentum area source release with low dike – smooth floor

Velocity and Turbulence Statistics The measurements made for cases A-C had been completed more than three years before any measurements were undertaken for cases D and E. In order to ensure repeatability, measurements of selected velocity and turbulence statistics for case A (which were identical for cases A-C) were performed prior to any measurements made for cases D-E. Measurements for the vertical profiles of mean velocity and turbulence statistics were made at the centerline of the wind tunnel immediately upwind of the gas source box at the fan 162


speed of 90 rpm for all cases. These data were used to determine the mean velocity at the (model) elevation corresponding to 10 meters of elevation at field scale (1000 cm / 150 = 6.67 cm) as well as to determine the friction velocity. Figure 12 shows the vertical velocity profiles over the smooth floor taken over three years apart (representing the measurement periods when cases A-C were completed and when cases D-E were completed). Ambient conditions were not identical, but were similar since the wind tunnel and its enclosure are climate-controlled. The repeatability of the velocity measurements, particularly in the range of such low tunnel operating speeds, is very good, thus indicating the exceptional control of the flow in the CHRC ULS wind tunnel. Figure 13 shows measurements of the vertical velocity profile over the rough floor (cases D and E) with the smooth floor velocity profile (cases A - C) indicated for comparison.

parameters are required for simulation of the wind tunnel experiments with FEM3A. Floor Smooth Rough

Friction velocity, m/s 0.0264 0.035

Surface roughness, m 0.000063 0.00072

Table 1. Velocity profile characteristics for smooth and rough floors. Concentration Measurements Due to the three year lapse between cases A-C and cases D-E, concentrations measurements were made again for case A conditions before any measurements over the rough floor began in order to ensure repeatability. Figure 14 compares the measurements made for case A (Low momentum area source CO2 release - smooth floor) with recent measurements under identical (as nearly as possible) wind tunnel and gas release conditions. The repeatability was excellent.

Figure 12. Verification of repeatability of velocity measurements.

Figure 14. Verification of concentration measurement repeatability. The lateral profiles, all at 0.5 cm elevation, were made at various designated downwind distances for each of the cases AE in order to ensure accurate determination of the distances associated with the concentrations representing the upper flammable limit (UFL), the lower flammable limit (LFL), and the one-half of the lower flammable limit (LFL/2). Also, in some cases the location of the measurement distances had to be varied slightly to avoid the concentration sensor touching a roughness element or the dike. Table 2 shows the downwind locations of the lateral profiles of concentration (all at elevation 0.5 cm) for cases A-E. The maximum gas concentrations measured at that downwind distance, some of which are off-centerline, are also indicated.

Figure 13. Smooth and rough floor velocity profiles.

Case A

Table 1 indicates the values of surface roughness and friction velocity, derived from the data shown in Figure 13, for the smooth floor (cases A-C) and rough floor (cases D-E). These

Downwind location (cm) 60 150 250 350 450 550 650 750 850 Maximum concentration (%) 24.3 12.1 7.2 5.5 4.4 3.8 3.4 2.7 2.4

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Case B Downwind location (cm) Maximum concentration (%)

50 150 7.6 3.8

250 350 2.1 1.5

400 1.2

450 500 1.1 0.92

Case C Downwind location (cm) Maximum concentration (%)

60 150 250 300 5.2 2.6 1.6 1.2

350 400 450 1.1 0.92 0.86

Case D Downwind location (cm) 55 88 175 236 357 Maximum concentration (%) 24.0 18.9 4.9 2.8 1.5

Case E Downwind location (cm) Maximum concentration (%)

84 175 236 357 4.0 2.2 1.6 0.85

Table 2. Downwind locations of lateral concentrations with observed maximum values. Figures 15 - 19 show lateral profiles (0.5 cm elevation) of gas concentration (top) and iso-concentration contours (bottom) of carbon dioxide concentrations which correspond to methane UFL, LFL, and LFL/2 concentration levels, for Cases A-E, respectively: UFL LFL LFL/2

Methane (%) 15 5 2.5

Carbon Dioxide (%) 6 1.9 0.09

Figure 16. Case B - lateral profiles (top) and iso-countours (bottom), 0.5 cm elevation.

Figure 17. Case C - lateral profiles (top) and iso-contours (bottom), 0.5 cm elevation.

Figure 15. Case A - lateral profiles (top) and iso-contours (bottom), 0.5 cm elevation

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CONCLUSION ! The experimental results described above provide a large wind tunnel data collection which can be used for continuing verification of computational models. !

Five experimental configurations have been studied:

- Cases A - C provide additional data contributing toward the verification of the models for dike designs which span current U.S. practice. - Cases D - E were performed to study the combined effects of tank/dike obstacles and earth surface roughness. The roughness, approximately 10 cm at field scale (150:1) was intended to be representative of regularly arranged suburban housing. ! The results indicate an important reduction in downwind hazard extent due to the presence of a tank/dike system alone, surface roughness alone, and to their combination. It is noted that the surface roughness studied may be greater than that which characterizes most large LNG installations in the United States (since urban or suburban housing is not normally found immediately adjacent to the facility). Consequently, the apparent small additional reduction in hazard distance due to the tank and dike in the presence of the high surface roughness is probably not typical.

Figure 18. Case D - lateral profiles (top) and iso-contours (bottom), 0.5 cm elevation.

•

These experiments show that further important reductions in the downwind hazard extent are possible with judicious dike/tank designs. ! These experiments indicate that the concentration of gas flowing over the dike appears to be determined by the dike height, thus indicating the potential for further reduction by the use of vapor fences.

•

The data provided here exemplify the best, most costeffective methodology available for validation of computer based dispersion models: carefully scaled physical models that can be used to directly evaluate the numerical models by comparison of experimental data with numerical simulation. REFERENCE Arthur D. Little, Inc., “Evaluation of LNG Vapor Control Methods”, Report to the American Gas Association, October, 1974. Havens, J. A., T. O. Spicer, and P. J. Schreurs, “Evaluation of 3-D Hydrodynamic Computer Models for Prediction of LNG Vapor Dispersion in the Atmosphere,” Final Report to GRI on Contract No. 5083-252-0788, August, 1987.

Figure 19. Case E - lateral profiles (top) and iso-contours (bottom), 0.5 cm elevation.

Havens, Jerry and Tom Spicer, “LNG Vapor Dispersion Prediction with the DEGADIS Dense Gas Dispersion Model,” Topical Report to GRI on Contract No. 5086-252-1287, 165


September, 1990. Havens, Jerry, Tom Spicer, and Heather Walker, "Regulatory Application of Wind Tunnel Models and Complex Mathematical Models for Simulating Atmospheric Dispersion of LNG Vapor," Gas Research Institute Report No. 92-0257, August 1994. Havens, Jerry, Tom Spicer, and Heather Walker, "Evaluation of Mitigation Methods for Accidental LNG Releases: Volume 1/5--Wind Tunnel Experiments and Mathematical Model Simulations to Study Dispersion of a Vapor Cloud Formed following LNG Spillage into a Diked Area Surrounding a Storage Tank," Topical Report for Gas Research Institute, November 1996. Havens, Jerry, Tom Spicer, and Heather Walker, "Evaluation of Mitigation Methods for Accidental LNG Releases: Volume 2/5--Wind Tunnel Experiments and Mathematical Model Simulations to Study Heat Transfer from a Flat Surface to a Cold Nitrogen Cloud in a Simulated Atmospheric Boundary Layer," Topical Report for Gas Research Institute, November 1996. Havens, Jerry, Tom Spicer, and Heather Walker, "Evaluation of Mitigation Methods for Accidental LNG Releases: Volume 3/5--Wind Tunnel Experiments for Mitsubishi Heavy Industries, Ltd.," Topical Report for Gas Research Institute, November 1996. Havens, Jerry, Tom Spicer, and Heather Walker, "Evaluation of Mitigation Methods for Accidental LNG Releases: Volume 4/5--Wind Tunnel Experiments for Osaka Gas Company," Topical Report for Gas Research Institute, November 1996. Spicer, Tom, Jerry Havens, and Heather Walker, "Evaluation of Mitigation Methods for Accidental LNG Releases: Volume 5/5--Using FEM3A for LNG Accident Consequence Analysis," Topical Report for Gas Research Institute, December 1996.

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ATMOSPHERIC DISPERSION IN NON-HOMOGENEOUS CONDITIONS – SIMULATION OF A WIND TUNNEL TRACER EXPERIMENT S. Trini Castelli Istituto di Scienze dell’Atmosfera e del Clima, CNR, Torino, Italy

E. Ferrero Dipartimento di Scienze e Tecnologie Avanzate, Univ. Piemonte Orientale, Alessandria, Italy and ISAC/CNR, Torino, Italy

D. Anfossi Istituto di Scienze dell’Atmosfera e del Clima, CNR, Torino, Italy

is effective in correctly predicting concentration in complex terrain. Here we compare simulations produced using two different turbulence closure models, the Mellor Yamada level 2.5, already present in RAMS, and a standard E-l turbulence closure, implemented in RAMS.

ABSTRACT One of the RUSVAL EPA wind tunnel tracer experiments is simulated by our modelling system RMS (RAMS-MIRSSPRAY). We analyse, in particular, the effects of two closure schemes on the prediction of mean flow, turbulence and concentration fields in this complex terrain configuration. We considered two closure models, the Mellor Yamada level 2.5, already present in RAMS, and the turbulence closure E-l, implemented in RAMS by us. The input quantities needed to the Lagrangian stochastic model SPRAY are computed from RAMS turbulence fields trough the interface code MIRS. The tracer dispersion simulations are performed with SPRAY. The resulting 3-D concentration fields are compared to the measured ones. It resulted that the simulation with the turbulence closures E-l overcame those with the classical closure. Furthermore, the predicted fields of mean flow, velocity standard deviations and Lagrangian time scales demonstrated to be able to take into account the nonhomogeneities due to the valley.

THE MODEL SYSTEM The RMS modelling system is based on an off-line interface between the meteorological model RAMS (Pielke et al. 1992), the parameterisation code MIRS (Trini Castelli and Anfossi, 1997, Trini Castelli, 2000) and the Lagrangian stochastic particle model SPRAY (Tinarelli et al., 1994; Tinarelli et al., 2000). RAMS is a widely known model designed to simulate the atmospheric flows from local and regional to the synoptic scale, so that phenomena from the micro to the large scale can be studied. RAMS atmospheric model performs the actual simulations by solving a full set of ensemble averaged equations for the atmospheric motion and a closure model for the Reynolds stresses. In the version of RAMS used in the RMS system, the standard E-l and E-ε turbulence closure models were implemented (Trini Castelli et al., 2001, Ferrero et al., 2001) as alternative to the closures already available in the original version (Mellor and Yamada, 1982, level 2.5 closure, for instance). We recall that the E-l closure model solves the dynamical equation for the turbulent kinetic energy E, while its dissipation rate ε is defined by the Kolmogorov relationship: c E 3/ 2 ε= ε (1) ld

INTRODUCTION Wind tunnel experiments are a useful tool for investigating the Atmospheric Boundary Layer structure and the dispersion phenomena, particularly in complex terrain. Besides yielding experimental evidence of the main physical processes governing the airborne pollutant dispersion, they may also produce accurate data sets for numerical flow and dispersion model validation. With reference to this aspect, in this work we present the simulation of one of the RUSVAL wind tunnel tracer experiments with our modelling system RMS (RAMSMIRS-SPRAY). RUSVAL experiment was carried out in the Environment Protection Agency Laboratory (USA). A neutral flow over a two-dimensional smooth valley, was reproduced and tracer was released and sampled (Khurshudyan et al., 1990). Since the obtained data set is rich and complete, it allows a significant comparison to be made. In particular it is possible to investigate how a proper description of turbulence

where l d is the dissipation length scale. Assuming that the mixing length l coincides with l d ( l d = l ), the diffusion coefficient Km is given according to the Prandtl-Kolmogorov hypothesis:

167


SPRAY is a Lagrangian stochastic one-particle model based on a 3D form of the Langevin equation for the random velocity (Thomson, 1987). The velocity and the displacement of each particle are given by the following equations: dui = ai (x,u)dt + bij (x,u)dW j (6)

K m = cµ E 1 / 2 l , (2) and the diffusion coefficients for heat and turbulent kinetic energy are proportional to it. The values for the closure empirical constants were specifically estimated and used for the EPA-RUSVAL experiment in previous works, Trini Castelli et al., (2001) and Ferrero et al. (2001), as cµ = 0.42 and c ε = 0.08 . For the mixing length here we used the Blackadar (1962) formulation, with a scaled value of Ying (1992) asymptotic mixing length. The RAMS output meteorological fields are ingested by MIRS: topography, wind speed and potential temperature are the minimum information requested, then turbulent kinetic energy, diffusion coefficients and surface fluxes are treated when available. MIRS has several options to calculate the boundary layer parameters and turbulence quantities needed for modelling atmospheric dispersion. Surface layer parameters, like friction velocity u∗ , temperature scale θ∗ and MoninObukhov length L , are calculated on the basis of the similarity theory, from the surface fluxes or, when these last are not available, by the Louis (1979) parameterisation. Alternative methods are available for determining the PBL height zi (see Trini Castelli, 2000), and consequently to estimate the convective velocity scale w∗ . Then, different options are available in MIRS to calculate the turbulence parameters for the dispersion model SPRAY, that is the variances of the wind

and

dx = (U + u )dt , (7) where i, j = 1,2,3 , x is the displacement vector, U is the mean wind velocity vector, u is the Lagrangian velocity vector, ai ( x, u)dt is a deterministic term, bij ( x, u)dWi (t ) is a stochastic term and the quantity dW j is the incremental Wiener process. The deterministic coefficient depends on the Eulerian probability density function (PDF), PE ( x, u ) , of the turbulent velocity and is determined from the Fokker-Planck equation. The diffusion coefficient bij ( x, u) is obtained from the Lagrangian structure function and is related to the Kolmogorov constant, C0 , for the inertial sub-range and to the ensemble-average rate of dissipation of turbulent kinetic energy ε. bij ( x, u) can be also determined from the variances of the velocity fluctuations and the Lagrangian time scale. The model allows to study the dispersion of passive pollutants in 3D complex conditions (characterised by the inhomogeneity of the variables that determine the dispersion process), emitted from single or multiple sources of different geometries (point, line and area). Besides the meteorological input file supplied by MIRS, the source characteristics and the numerical parameters of the simulation are directly provided to SPRAY by configuration files managed by the user. The RMS modelling system has been already applied to EPA-RUSVAL wind tunnel experiments (Ferrero et al., 2003) and to real-case studies, as in Kerr et al. (2000) and Carvalho et al. (2002).

velocity fluctuations σ i2 = u i ' 2 (i=1,2,3) and the Lagrangian time scales TLi . When available, E, Km and ε fields can be used. In particular, when Mellor and Yamada (1982) closure is adopted in RAMS simulation, the velocity standard deviations are calculated in MIRS on the basis of the formulations proposed by them, as: σ u2 = (1 − 2γ )q 2 , σ v2 = γq 2 , σ 2w = γq 2 (3) where q 2 = 2 E , γ ≡

A 1 −2 1 3 B1

and A1, B1 are empirical

constants. When the E-l closure is used in RAMS, wind variances can be calculated in MIRS on the basis of the K-theory formulation as follows: ∂u 2 σ i2 = − 2 K m i + E . (4) ∂xi 3 The Lagrangian timescale values can be obtained, in both the models, from the diffusion coefficients, (Km) as: K TLi = m2 . (5) σi In alternative to use E and Km fields, other parameterisations selected from literature can be chosen (i.e. Hanna, 1982, Degrazia et al., 2000). When necessary, also the third (Chiba, 1978) and fourth (Ferrero and Anfossi, 1998) moments of the vertical velocity component can be estimated in MIRS. Subsequently, MIRS processes the flow and turbulence data so to prepare the input meteorological file in the appropriate format and with the temporal sequence of interest to be used by SPRAY.

THE WIND TUNNEL EXPERIMENT The EPA-RUSVAL data set here used, was collected in wind tunnel experiments (Khurshudyan et al., 1990, Busuoli et al., 1993), carried out at the Environment Protection Agency Laboratory (USA). In these experiments a neutral flow over a two dimensional (2D) valley was reproduced. The wind tunnel was characterised by a roughness length z0 = 0.16 10-3 m, a friction velocity u∗ = 0.19 ms-1 and free stream velocity u∞ = 4 ms-1. The three diagonal components of the Reynolds stress tensor, measured in the surface layer on flat terrain in the same 1/ 2

wind tunnel, were  u' 2   

1/ 2

= 2.5u∗,  v' 2   

= 1.8u∗ and

1/ 2

 w' 2  = 1.2u ∗.   Among the various experiments, here we consider a valley characterized by a maximum depth of H=0.117 m and a width of 2a, where a = 0.936 m, hence having an aspect ratio a/H = 8. Other valleys were characterized by aspect ratios equal to 5 and 3. The parametric equation modelling the valley shape is the following:

168


x val =

(

The 3D meteorological fields needed by SPRAY were simulated on a horizontal domain of 8000x1000 m2, with grid size ∆x=∆y=50 m. Such a high horizontal resolution is needed to detail the scaled valley with a satisfactory number of grid points. In the vertical direction a stretched grid is used in order to improve the resolution in the lower layer. The minimum vertical grid size is 10 m and the maximum 60 m. The total vertical extension of the numerical domain is 2h. The simulation time step is 0.3 s. In MIRS the surface layer parameters are calculated from the RAMS surface fluxes and the constant value of h = 600 m is set for the height of the neutral boundary layer. The parameterisations for standard deviations and Lagrangian time scales are calculated for the alternative closures as described above. In SPRAY Gaussian PDFs, determined according to the prescribed wind velocity standard deviations, are adopted both in the vertical and horizontal directions, since neutral conditions characterised the wind-tunnel experiment. We compared the results of the numerical RMS simulations with the measured mean flow, turbulence and concentration fields.

 1  a2 ξ 1 + 2  2 2 2 2  ξ + m a − ξ 

(

)

)

  a2 1 − 2 2 2 2   ξ + m a − ξ  for ξ ≤ a and z val = 0 elsewhere. x is directed along the flow direction (x=0 corresponds to the centre of the valley), z is the vertical coordinate, ξ is an arbitrary parameter and 1 z val = − m a 2 − ξ 2 2

1

(

2

)

1

2 1 H  H  2  m= +   +1 . a  a     Vertical profiles of mean wind velocity u , v and Reynolds

stress components σ i2 = u i′ 2 and − u'w' were measured at 15 different positions along the x axis upwind, inside and downwind the valley. It can be noticed that the flow was essentially twodimensional because of the symmetry with respect to the x-z plane. The velocity component along the y direction (crosswind direction) is assumed to be zero. Several non-buoyant tracer experiments, from sources placed in different locations and characterised by different heights, were performed. Here we considered a source placed in the centre of the valley at a height of 0.029 m. We stress that the emission height is about ¼ of the valley depth, so fully inside the valley, and represents a challenging diffusion situation. Both horizontal (along X and Y directions) and vertical normalized concentration profiles were available. The normalized measured mean concentrations χ were Cu ∞ hc2 estimated as χ = , where C is the concentration Q corrected subtracting the background, Q is the tracer flow rate and hc is a convenient length scale of the experiment.

RESULTS AND DISCUSSION In Figures 1-3 vertical sections of the along-wind speed are presented respectively for the observed data and simulations with E-l and Mellor and Yamada (MY82 hereafter) closures. We notice that E-l closure fairly well reproduces the observed mean flow structure over the valley and clearly overcomes the result obtained with MY82 model. While E-l predicts the same speed values as measurements, MY82 produces a large decrease of the speed inside the valley and the effect of the valley is smoothed immediately above it, as showed by the 3.0 ms-1 isoline. Considering that the tracer source is placed at the bottom of the valley, this different wind pattern will affect the tracer concentration simulation.

NUMERICAL SIMULATIONS For the numerical simulations, the wind tunnel experiment was reported to the dimension of an actual atmospheric boundary layer (Trini Castelli et al., 2001, Ferrero et al., 2003). A scaling factor of 600 for lengths is chosen since the wind tunnel boundary layer height (h=1 m) was corresponding to an actual neutral ABL depth of 600 m (Khurshudyan et al., 1981). This scaling makes the maximum depth of the valley H=70.2 m, the roughness length z0=0.096 m and the source height equal to 17.4 m. The scaling factor for time and for length is the same since in neutral conditions the similarity theory prescribes a logarithmic law for the wind profile: considering its nondimensional form, it must be equal both in the tunnel and in the actual prototype. The free stream velocity is then maintained u∞ = 4 ms-1. To perform the numerical simulations, we used RAMS in its non-hydrostatic version. At the boundaries, KlempWilhelmson condition is used for the normal velocity component, while for the other variables a zero-gradient is considered. At the top of the vertical domain a rigid lid with a thin Rayleigh friction layer is adopted.

Figure 1: observed data, speed (ms-1)

169


turbulence, as a consequence, the choice of a proper turbulence closure is of great importance (refer also to Trini Castelli et al, 2001, and Ferrero et al., 2003).

Figure 2: E-l simulation, speed (ms-1)

Figure 4: observed data, σu (ms-1)

Figure 3: MY82 simulation, speed (ms-1) As far as the turbulence field is concerned, in Figures 46 the along-wind standard deviations of wind velocity fluctuations are plotted again in the same sequence of Figures 1-3. Even in this case, the results of the two closures are quite different, both inside the valley and at the higher levels. E-l satisfactorily simulates the observed σu, whereas MY82 largely underestimates the effect of the valley on the isoline pattern and the σu values are much lower, ranging from 30 to 50 % of observations. The same behaviour is found for the vertical standard deviation σw, where the ratio between the values predicted by the two models is more than a factor of two, as clear from Figures 7 and 8. The results here presented clearly prove that, even a smooth valley like the one considered, is able to significantly perturb the structure both of flow and

Figure 5: E-l simulation, σu (ms-1)

170


The consequences of the different performances of the turbulence closures on the tracer dispersion, simulated by SPRAY, using as input the turbulence parameters calculated in MIRS from the two closures, can be assessed looking at Figure 9. The cumulative frequency distribution of concentration is plotted for the observations, solid line, the E-l closure, dotted line, and the MY82 closure, dashed line.

Figure 6: MY82 simulation, σu (ms-1)

Figure 9: Cumulative frequency distribution (c.f.d.) of normalized mean concentrations ?. Observed data: solid line; RMS with E-l closure: dotted line; RMS with MY82 closure: dashed line It can be observed that the dispersion simulation performed by using MY82 turbulence closure in RAMS and MIRS, produces a large underestimation of the higher concentrations. This unsatisfactory result is related both to the slowing down of the simulated flow, with respect to the observations, and to the small values of the standard deviations of wind velocity fluctuations, particularly within the valley. As a consequence both the transport and diffusion of the tracer are affected, so that the shape of the plume is not correctly reproduced and both vertical and horizontal spreads are substantially different from the observed ones. This causes a consistent difference in the distribution of the concentration field, particularly evident for the high values. While the most of normalized concentration values produced with MY82 lay in the range between 1 and 10, about the 60% of observed concentrations is greater than 10. Better results are obtained in the simulation performed by using the E-l model, since its frequency distribution curve fits satisfactorily the observed one. The underestimation of the higher concentration values is largely reduced with respect to MY82 case. This can be expected considering the better agreement between the observations and the mean flow and standard deviations values calculated by E-l turbulence model. These results are confirmed by the statistical analysis presented in Ferrero et al. (2003). We recall here, for instance, that the correlation coefficient and Normalised Mean Square Error are respectively 0.91 and 0.97 for E-l simulation, 0.40 and 5.40 for MY82 simulation.

Figure 7: E-l simulation, σw (ms-1)

Figure 8: MY82 simulation; σw (ms-1) 171


Kerr A., Anfossi D., Trini Castelli S. and Nascimiento S., 2000, ‘Investigation of inhalable aerosol dispersion at Cubatão by means of a modelling system for complex terrain’, Hybrid Methods in Enginnering, 2, 389-407 Khurshudyan L.H., Snyder W.H. and Nekrasov I.V., 1981, ‘Flow and dispersion of Pollutants within Two-Dimensional Hills’, EPA REPORT No. -6000/4-81/067 Khurshudyan L.H., Snyder W.H., Nekrasov I.V., Lawson R.E., Thompson R.S, Schiermeier F.A., 1990, ‘Flow and Dispersion of Pollutants within Two-Dimensional Valleys’, Summary Report on Joint Soviet-American Study, EPA REPORT No. -600/3-90/025 Hanna S.R., 1982 ‘Application in air pollution modeling’, in F.T.M. Nieuwstadt and H. van Dop, (Editors) Atmospheric Turbulence and Air Pollution Modelling, Beidel, Dordrecht, Ch. 7. Mellor G.L e Yamada T., 1982, ‘Development of a Turbulence Closure Model for Geophysical Fluid problems’, Rev. Geopys. and Space Physics, 20 , 851-875 Pielke R.A., Cotton W.R., Walko R.L., Tremback C.J., Lyons W.A., Grasso L.D., Nicholls M.E., Moran M.D., Wesley D.A., Lee T.J. and Copeland J.H., 1992, ‘A Comprehensive Meteorological Modeling System -RAMS’, Meteorology and Atmospheric Physics, 49, 69-91 Thomson D.J., 1987, ‘Criteria for the selection of stochastic models of particle trajectories in turbulent flows’, J. Fluid Mech., 180, 529-556 Tinarelli G., Anfossi D., Brusasca G., Ferrero E., Giostra U., Morselli M.G., Moussafir J., Tampieri F., Trombetti F., 1994, ‘Lagrangian particle simulation of tracer dispersion in the lee of a schematic two-dimensional hill’, Journal of Applied Meteorology, 33, N. 6, 744-756. Tinarelli G., Anfossi D., Bider M., Ferrero E., Trini Castelli S., 2000, ‘A new high performance version of the Lagrangian particle dispersion model SPRAY, some case studies’, Air Pollution Modelling and its Application XIII, Gryning S.E. and Batchvarova E. Eds, Plenum Press New York, 499-506 Trini Castelli S. and Anfossi D., 1997, ‘Intercomparison of 3D turbulence parameterisations for dispersion models in complex terrain derived from a circulation model’, Il Nuovo Cimento, 20 C, n. 3, 287-313 Trini Castelli S., 2000, ‘MIRS: a turbulence parameterisation model interfacing RAMS and SPRAY in a transport and diffusion modelling system’. Rap. Int. ICGF/CNR No 412/2000, Torino, Italy Trini Castelli S., Ferrero E., Anfossi D., 2001, ‘Turbulence Closures in Neutral Boundary Layer over Complex Terrain’, Boundary-Layer Meteorology, 100, 405-419 Ying R.,1992, ‘Research program aiming at establishing the turbulence parameters necessary to achieve a fluidodynamic code’. Progress report N.2,NASA-GISS.

CONCLUSIONS In this paper we showed how wind tunnel experiments, able to provide detailed information both of flow and turbulence fields in the vertical and along-wind directions, can be advantageously used for studying the atmospheric boundary layer structure and the dispersion phenomena. This is particularly important in complex terrain, since the controlled conditions of the wind tunnel and its spatial detail of measurements allow obtaining an amount of information which is difficult to achieve in field experiments. We used the EPA-RUSVAL dataset as a validation test case for numerical modelling with our system RMS, for simulating the flow, turbulence and diffusion over a 2D valley. In particular, it was possible to highlight the importance of a proper turbulence closure scheme in correctly reproducing the transport and dispersion of tracer in a neutral boundary layer. REFERENCES Blackadar, A., K., 1962, ‘The vertical distribution of wind and turbulent exchange in a neutral atmosphere’, J. Geophys. Res., 67, 3095-3102 Busuoli M., Trombetti F., and Tampieri F., 1993, ‘Data set for Studies of Flow and Dispersion in Complex Terrain: II) The “RUSVAL” Wind Tunnel Experiment (Flow Data)’, Technical Paper No. 3 - FISBAT - TP - 93/1 Carvalho J.C., Anfossi D., Trini Castelli S. and Degrazia G. A., 2002, ‘Application of a model system for the study of transport and diffusion in complex terrain to the tract experiment’, Atmospheric Environment, 36, 1147-1161 Chiba, O., 1978, ‘Stability dependence of the vertical wind velocity skewness in the atmospheric surface layer’, J. Met. Soc. Japan, 56, 140-142 Degrazia, G.A., Anfossi, D., Carvalho, J.C., Mangia, C., Tirabassi, T. and Campos Velho, H.F. (2000), ‘Turbulence parameterization for PBL dispersion models in all stability conditions’, Atmos. Environ., 34, 3575-3583. Ferrero E, Anfossi D., 1998, ‘Comparison of PDFs closure schemes and turbulence parameterizations in Lagrangian stochastic models’, Int. Jour. of Environment and Pollution, 9, n. 4, 384-410 Ferrero E., Trini Castelli S., Anfossi D., Finardi S. and Di Lisi E., 2001, ‘Study of different turbulence closure models simulating a neutral wind tunnel flow’, Hybrid Methods in Engineering, 3, no. 1, 11-23 Ferrero E., Trini Castelli S., Anfossi D., 2003, ‘Turbulence fields for atmospheric dispersion models in horizontally non-homogeneous conditions’, Atmospheric Environment, 37, n. 17, 2305-2315 Louis J.F., 1978, ‘A parametric model of the vertical eddy fluxes in the atmosphere’, Boundary-Layer Meteorology, 17, 187-202

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NOTES ON WEDGE-SHAPED BUOYANT PLUMES FROM SLITS OF FINITE WIDTH David M. Webber Integral Science and Software Ltd 484 Warrington Rd, Culcheth, WA3 5RA, UK

Torstein K. Fanneløp E+E Flow Analysis Utsikten 6, N-3179 Aasgaardstrand, Norway

auto- or airplane engines. The similarity solution of line plumes is also used to describe the late phase of bent plumes in wind. It is typical of these applications and of many familiar observations of line plumes, that the flow near the source is obscure or ill defined. The “true” initial conditions have been either ignored or considered to be of minor importance. The “error” is often corrected by use of an “effective” height or distance from the source, most often obtained by extrapolating the plume contour to the point or line where the plume width is zero (virtual source). The effects of a finite velocity and width as well as strong density variations in the source region are not taken into account. The loss in accuracy is not likely to be of concern in predicting environmental flows, but it could be important in certain technical applications. For visible round plumes from area sources, a converging flow region is often observed just above the source. The full plume consists of both converging and diverging flow regions separated by a minimum cross-section or “neck”. This type of flow has been analyzed recently by Fanneløp and Webber (2003). Similar flow phenomena are likely to exist also in the case of plumes originating from long slits of finite width, feeding buoyant material into a stagnant environment. In certain ventilation problems heated or cooled fresh air is often released, from the floor or ceiling respectively, through slits or perforated panels of high aspect ratio. For low momentum releases the initial flow will accelerate and converge towards a neck. The distance source-to-neck could represent a considerable fraction of the total room height, and it will be of interest to analyze the plume flow in detail. We are not aware of any experiments designed to explore such flows and for support of our theoretical results we have to refer to the analogous case of round plumes.

ABSTRACT Wedge-shaped buoyant plumes from low-momentum sources are often encountered both in nature and in technical applications. In the analysis of such plumes, the real initial conditions are either ignored or they are idealized as line sources that in the limit z=0 have zero initial width and infinite velocity. This allows similar solutions in powers of z to be found and these solutions give a good description of the flow as the distance from the source becomes large. For sources of finite width, it is usual to postulate an effective source height measured from a virtual source. This in turn is found by extrapolating the asymptotic (similar) solution to a point upstream where the radius is zero. This represents an engineering “fix” but the true initial conditions at the real source, are not satisfied. The present paper considers an alternative; a direct integration of the plume equations taking account of all initial conditions. We have obtained analytical and numerical results for the source region demonstrating both a region of accelerating flow and a “neck”. No experiments are available for comparison, a rather surprising situation in view of the many interesting applications. INTRODUCTION Wedge-shaped plumes represent a classical problem in applied fluid mechanics, perhaps older than the related problem of plumes from point sources. Round plumes are more common and more extensively studied. Examples are fire plumes and exhaust plumes, with visible outline from the smoke generated by the combustion process. Plumes from line sources were of interest in solving important problems in WW II. During the Battle of Britain lines of kerosene burners were used to produce upward rising plumes of hot air over aircraft runways, thereby lifting the fog and allowing the safe return of combat aircraft. In planning the Normandy invasion, it was proposed to use line bubble plumes, produced by perforated air pressure lines on the sea bed, as artificial breakwaters. These plumes also generate an outward moving surface current capable of damping oncoming waves. Professor G.I. Taylor appears to have inspired both proposals, for details see “Scientific Papers” (1958/60). Plumes from line sources have become important also in other situations where they occur naturally. Plumes of hot air are known to develop over runways and highways subject to strong solar radiation. This contributes to the dilution of fumes from

THE SIMPLEST CASE OF SMALL DENSITY DIFFERENCES AND A CALM ATMOSPHERE For illustration we will consider first the simplest case of isothermal flow and weak buoyancy force. The lighter fluid is released in a steady process through a narrow slit into a large stagnant reservoir. The plume half width b and velocity w are both functions of a single variable z of undetermined origin located near the level of the open slit. Similarity is implied here, by analogy with the case of round plumes discussed in many texts on buoyant flows (Turner 1973, Fanneløp 1994). The governing equations imply volume conservation

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(continuity), momentum and buoyancy conservation in this “Boussinesq” case. Cont:

d/dz ( b w) = α w

Mom:

d/dz ( b w2 ) = F/ w

z=

The nomenclature is common; w = velocity, b= half width, F = buoyancy parameter and V the total volume flow rate per unit length. The indices “a” and “g” indicate ambient and light gas respectively. New fluid is entrained into the plume from both sides at a rate proportional to the rise velocity w and an empirical coefficient α The particular formulation used here is often associated with the names Morton, Taylor and Turner (1956) and denoted MTT-entrainment. To solve the problem it is usual to assume a power-law solution in z for both b and w and one obtains the classic result:

The result shows that consideration of realistic initial conditions changes the solution near the source, but that at large heights (z >> z0 and m >> m0), we recover the classic solution for line plumes. In many practical problems the initial half width of the slit or opening, is a known quantity together with the buoyancy and volume fluxes. The entrainment coefficient in the near-source regime is uncertain as detailed experiments are not known to exist. Another simple solution, the non-entraining “plume”, will be useful in the source region. Consider two semi-infinite volumes of fluid of different densities separated by a membrane containing a narrow slit of width 2bs. Let the lighter fluid be located below so that it flows upwards through the slit, driven by gravity. Consider the narrow rising “plume” a unidirectional flow of velocity w (z) and the outer fluid as stagnant. The hydrostatic pressures are assumed to be balanced at each height z. The velocity of rise follows from Bernoulli.

b = α z and w = (F / α) 1/3 It predicts a wedge-shaped plume of constant velocity where the width grows linearly with z. The implication of a finite velocity, also at z=0, is obviously unrealistic and an indication that the true initial conditions are violated. The “engineering fix” is to apply the result only above the level where b equals the initial half width b0 of the slit. The point z =0, is considered the location of a “virtual source”. Alternatively one can adjust the origin so as to produce the right buoyancy flux through the slit and ignore other initial conditions. A satisfactory result near the source can not be obtained by such fixes, but the predictions for very large values of z will nevertheless be accurate and useful. We can improve the solution by integrating the equations directly without assuming a power-law solution.

w2 = 2 g’ (z – z0 )

d m /d z = α k / m and d k / d z = F m /k

b = Vg / 2

( 2 g’ (z – z0))

2

dm/dk=αk /Fm

On considering z0 to be the origin where w = 0, we see that the half width b is infinite at this point. It is located below the slit, but the distance will be small in practice. The flow predicted between the slit and z= z0 will be fictitious, but the solution is useful in understanding the real flow with negligible or very small entrainment just above the slit.

Rearranging and integrating one obtains: m2 d m = ( α / F) k2 d k or m3 = (α / F) k3 + C The constant C is specified by the initial value of the volume flux per unit length, denoted m0. 3

with g’ = g ( ρa - ρg ) / ρg

As before the indices stand for ambient and (light) gas respectively. Assume that the volume flow of light gas through the slit is known; Vg = 2 bsws ( per unit length). As this flow rate is constant, it follows that

Denote: m = b w and k = b w2 so that the equations can be written

On eliminating d z:

k d k / [ m03 + (α / F) k3 ] 1/3

The solution presented is new and it satisfies both the full equations and the initial conditions. It may be a bit awkward for practical use in view of the hypergeometric function produced by the integral for z. It eliminates the need for finding a “virtual origin” and similar artifices. For practical applications it may be more convenient to integrate the plume equations numerically, taking account of the true initial conditions. These are identified here by the index “0”. (Below z=0, one can refer to a fictitious source at z = z0, where w-> 0 and b-> oo in such a way that m = m0 remains finite. This is part of the nonentraining solution discussed in what follows.)

Buoyancy: F = constant with 2 F = Vg (1 - ρg / ρa ) g

2

(1/F) ∫

Denoting z0 the source depth, the velocity through the slit will be ws= (2 g’ z0 )

3 1/3

It follows: m = [m0 + (α / F) k ]

and also equal to ws = Vg / 2 bs . On combining these expressions, we obtain

The height above the source can be evaluated from the momentum relation

z0 = (Vg / 2 bs) 2 / 2 g’

dz/dk = k/Fm

The value of this source depth will be small in practice.

On integration:

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The derivation makes use of the Bernoulli equation and the boundary defining b(z) represents a streamline. In terms of the plume problem considered, it corresponds to the case with no entrainment. In fact, by letting α = 0, we can derive the same solution from the plume equations. In terms of flow geometry, it presents a “counterpoint” to the classical plume; i.e. the width is infinite at the source, it converges for increasing z and vanishes as z-> oo. In the classic line plume, the width is zero at the source and increases linearly with z. The two solutions combined will give a converging plume near the source, narrowing to a neck and increasing again for large z-values at a linear rate.

The quantity d m / d k = α k2 / F m2 is given by one of our governing equations. Another known result is m = [m03 + (α / F) k3] 1/3 and it is used to express k in terms of m. On combining we obtain: d b/d k = (m/k)2 [ 1 – 2 (m0 /m)3 ] The “neck” occurs when the expression in the bracket vanishes. Denoting the corresponding value of m with index b, we obtain: mb = 2 1/3 m0. The corresponding minimum half width becomes bmin = mb2 / kb

Let us see if a converging-diverging flow is possible also above the slit, i.e. in a region with finite but small entrainment rate. In the analogous problem of an area source (Fanneløp & Webber, 2003), we have found both a minimum cross section (a “neck”) and peak velocity in the region above the source. One or both of these phenomena would be expected in a region where an initially accelerating flow is followed by a retarded flow as the flow character is increasingly dominated by entrainment. Stationary values of w and b will occur at some values of z if these phenomena are present. It is convenient to study their rate-of-change with k as this variable has been demonstrated to be “z-like”

where

kb3 = (F/α) [ mb3 – m03 ] = (F/α) m03 bmin = 2 2/3 (α/F)1/3 m0

In practice the prediction of plumes resulting from a source of buoyancy in the form of a long and narrow porous surface or slit, will be concerned most often with small density differences. Examples are ventilation flows through slits or hot plumes from heated surfaces such as runways or highways. The simplified “Boussinesq” solution given here would be sufficiently accurate for most applications. An exception could be line fires but these are often associated with moving sources. Accidental releases of light gases are more likely to occur from area sources although line ruptures of long natural gas lines have been reported in the past when brittle steel qualities were used in pipelines.

Consider first w = k/m. Differentiation gives d w/d k = 1/m - (k / m2) d m /d k On inserting the value dm/dk from the governing equation, we obtain

NUMERICAL EXAMPLE The physical parameters are chosen to demonstrate the nature of the solution and do not present a practical case or application. The value of the entrainment parameter in particular, is uncertain. We have chosen to use a typical value, valid in the asymptotic flow region far from the source. This choice gives reasonable results, in agreement with experiments, in the analogous axisymmetric case.

d w/d k = (1/m) [ 1 - ( α / F ) (k 3/m3) ] A stationary value would be possible when the value inside the bracket vanishes so that (kw / mw )3 = F / α The indices are used to denote the particular values of k and m associated with the stationary value of w.

Parameters: Buoyancy: F=2.0 m^2/s^2, entrainment: σ= 0.08, density: (ρg / ρa) = 0.59

We have also derived: mw = [m03 + (α / F) k w 3] 1/3

half width: b0 = 1.0 m,

On substituting for (kw/mw)3 we obtain the condition of interest:

velocity: w0=0.5 m/s

The results for m(z) and k(z) are shown in Figures 1a and 1b, respectively, as calculated and plotted by means of Maple 7. The more interesting results, for plume width b(z) and velocity w(z), are illustrated in Figure 2. The neck occurs at a distance from the source about equal to the source half width, but its location will in general depend on the flow parameters. The velocity is seen to accelerate rapidly towards its asymptotic value of about 2.9 m/s. For all practical purposes the asymptote is reached within the z-range of the plots, i.e. 0-5 m. By extrapolating the width b down to the point where b=0, we find the “virtual source” to be located about 2.5 m below the true source.

3

(m0 / mw) = 0 This can only occur as z -> oo. For large values of z, we know the asymptotic character of both b (grows linearly with z) and w (approaches a constant value). Let us now check if a “neck” can occur in the source region. This would imply a minimum width 2b and the condition db /dz = 0. From the definitions we know b = m2 / k and also that db/dz=0 implies db/dk =0. From results already derived: d b/d k = - m2 / k2 + 2 (m/k) d m/d k

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Fanneløp, T.K. (1994) Fluid Mechanics for Industrial Safety and Environmental Protection. Elsevier

REFERENCES Taylor, G.I. (1955) The action of a surface current used as breakwater. Proc. Roy. Soc. A 231 pp466-78

Morton,B.R.,Taylor, G.I. and Turner,J.S. (1956) Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234 pp1-23

Taylor, G.I. (1958-1960) Scientific Papers , (Ed. G. Batchelor), Cambridge University Press.

Fanneløp, T.K. and Webber, D.M. (2003) On buoyant plumes rising from area sources in a calm environment (submitted).

Turner, J.S. (1973) Buoyancy Effects in Fluids. Cambridge University Press

Figure 2 Variation of plume width and velocity with height Figure 1 a. Variation of the flow parameter m = b w.

Figure 1b. Variation of the flow parameter k = bw2

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TWO-PLUME MIXING: TRAJECTORIES AND CONCENTRATION DISTRIBUTIONS Alan Robins EnFlo School of Engineering, University of Surrey Guildford, GU2 7XH Surrey, UK

Daniele Contini Istituto di Scienze dell’Atmosfera e del Clima Consiglio Nazionale delle Ricerche Str. Prv. Lecce-Monteroni km 1,2 73100 Lecce, Italy ABSTRACT In this paper the mixing of two identical plumes into a neutral cross-flow is investigated in terms of plume trajectories and plume shapes by using water tank experiments. The analysis refers to a couple of identical stacks releasing into a neutral cross-flow with different orientations and different stack separations. Small scale model measurements have been carried out to specifically investigate extra-rise E and trajectories during the mixing phase as well as modification of the plume shape induced by the interaction during the merging of the two plumes. Results obtained allow to evaluate E for different stack separation and different wind directions with respect to the source axis and to compare it with available empirical and semi-empirical models. Results show that the extra-rise can also be negative (a sort of downwash effect) as a consequence of the slow and inefficient mixing of vortex of opposite vorticity and this happens when the two plumes are rising almost side-by-side. Point concentration measurements show the changes in the cross-sectional distribution of concentration into the plume core (i.e. the plume shape) as a consequence of the merging phase. The results indicate that the plume becomes strongly asymmetric when the misalignment φ between the flow and the sources is increased and, for large values of φ, an accumulation of plume material at the bottom of the plume lowers the centre of mass of the combined plume causing the downwash effect. Instead when the emissions are almost aligned with the cross-flow the double vortex structure “guide” the lower plume into the middle of the upper plume, the mixing is efficient and the accumulation of plume material is not generated. The shape of the combined plume can be therefore significantly different with respect to the shape of single plume with no interaction even though the average dilution over the entire cross-section at a fixed distances from the source is, for large misalignments, basically the same.

x,y,z φ ρa ρs Q Ua

INTRODUCTION Understanding the different phases of the mixing process of multiple interacting identical plumes and evaluating how the mixing process influences their average path and spread is a matter of considerable interest in environmental impact studies, in developments of analytical and numerical codes for pollution diffusion and in basic studies of plume dynamics. Multiple emissions are often present in industrial sites and in power plants and their interaction should be taken into account if a correct simulation of dispersion is needed. The mixing of these emissions generates strong interactions, especially under favourable wind directions that create distortions of the plume cross-sectional shape and extra-rise or “downwash” effect with respect to the single source cases with zero interaction. As matter of fact the interaction that modifies both the plume trajectories and the plume shapes is due to three different contributions: the partial entrainment of plume material, instead of fresh air, when plumes originating from different source get in contact; the modification of the entrainment rate due to changes in speed relatively to the cross-flow and to changes in plume shape during the mixing phase; the shielding effect on downwind emissions due to the presence of upwind emissions [Contini & Robins 2001, MacDonald et al 2002]. Reliable analytical plume rise models exist for single plumes (e.g. Briggs, 1974; 1975; 1975b), as well as integral models that, in order to evaluate the plume trajectories, relate the plume mass and momentum fluxes to the forces acting on a plume and the entrainment rate of external fluid (e.g. Ooms & Mahieu, 1981; Robins & Aspley, 1994, Schatzmann 1979). This class of model has been widely tested against full scale data, as well as wind tunnel and water tank results. However, multiple, interacting plume configurations are considerably less well

NOMENCLATURE Symbol B d D I(x,z)

Cartesian co-ordinate centered in the upwind stack Average height of the plume Angle of the line joining the sources with respect to the cross-flow Density of the water in the tank (constant) Density of the emission at the source Emission flow-rate through a single stack Uniform towing speed referred to as flow speed

Definition Non dimensional buoyancy parameter Stack separation Stack diameter Pixel intensity profile

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are extracted from the final image and the plume average trajectory (x) is evaluated as a weighted average:

understood in theoretical terms and less studied experimentally. It is therefore necessary a deeper comprehension of the different aspects of the interaction of plumes starting from the schematic case of a couple of identical sources. In this work the mixing phase of two identical sources is studied for different stack separations and different orientation φ of the sources with respect to the flow. The maximum interaction is present when φ=0 (sources aligned with the cross-flow) and this is known to generate positive extra rise (at a distance downwind greater than 2-3 times the separation between the stacks) in the combined plume. However when φ≠0 the situation changes and the extra-rise quickly decreases because the mixing process become less and less efficient and the merging of the two emissions is becoming slower and slower. In this conditions the extra-rise E is practically disappearing when φ is about 30° in good agreement with the results of Overcamp and Ku (1988). If the value of φ is increased beyond this limit the extra-rise becomes negative indicating a sort of “downwash” effect as mentioned, relatively to experiments in different physical conditions, by MacDonald et al (2002). Our results allow to infer that this phenomenon is related to the inefficiency of mixing of vortex with opposite vorticity that creates an accumulation of plume material at the bottom of the combined plume lowering the centre of mass of the diffusing cloud and therefore its trajectory. Our results have been compared with available models in literature for φ=0 using different definition of the extra-rise.

∞

∫ zI(x, z)dz . ∞ ∫0 I(x, z)dz

< z > (x) = 0

A detailed description of the system and of the postprocessing is given in Contini and Robins (2001). Local concentration measurements into the plume core have been performed by using a colorimeter system usually calibrated once-a-day with a solution of known concentration of the same dye used as tracer. The effect of salt on measured concentrations has been evaluated and corrected in the calculations. Repeatability of trajectory evaluation furnishes a standard deviation of about 3% and repeatability on concentration measurements is about 15%. TRAJECTORIES AND EXTRA-RISE In Figure 1 final plume images are reported for a configuration with two identical emissions, stack separation d equal to 22, stack diameters D=7 mm, each stack releasing the buoyant mixture at a flow-rate Q equal to 1 l/min. The source buoyancy parameter B = ρ s − ρ a was equal to 9.7%. The ρa resulting plume has been recorded for different flow angles φ with respect to the line connecting the two sources. The flow speed was 8.86 cm/s. In the figure, two single source cases are also included as references. One (the no interaction case) is a single stack case that has the same physical and geometrical properties as used in the two source experiments and the other (the maximum interaction case) is a single stack case in which the combined emission of the two sources are emitted by a doubled area stack (i.e. a 9.9 mm source diameter) with the same relative density difference with respect to the surrounding fluid. These two cases represent, from a theoretical point of view, the two limiting trajectories, the lowest and the highest. The plume images show three different phases of the plume development, a first phase in which the two plumes develop independently of each other, as if they were emitted from isolated sources, a second phase in which the mixing process takes place and a third phase in which the mixing is basically complete and the two plumes have merged into one that interacts with the cross-flow, eventually re-establishing a characteristic vortex structures (i.e. the counter rotating vortex pair) as it is clear from the cross-sectional maps that will be described later on. It has to be mentioned that when φ exceeds 45° (for the stack separations analyzed) - the plume development involves the mixing of vortex structures with opposite vorticity, this process is slow and the geometrical extension of the second phase of the plume development becomes quite large. In this case the shape of the combined plume can be complicated showing an accumulation of plume material at the bottom of the plume itself. This accumulation can also make the plume asymmetric and it modifies the average trajectory of the centre of mass.

Cross-sectional concentration maps allow to put in evidence and to explain the behaviours that are characteristic to the mixing phase. In particular the results reported explain in details the nature of the deficit in the rise of the combined plume rise and put in evidence the strong asymmetries in the plume shape that are consequence of the mixing phase for φ≠0.

EXPERIMENTAL SET-UP AND METHODOLOGY Measurements have been carried out at the EnFlo water tank facility (University of Surrey, UK) by using both quantitative plume visualizations and local concentration detections. The different plumes simulated rise in a neutral environment being the tank filled with fresh water with density ? a. A water-salt solution is released up-side-down at the top of the tank containing a small quantity of a vegetable blue dye used as tracer. The salt is used to produce buoyant plumes with a density at the source ? s grater than ? a. The tip of the stacks are immerse in the tank for about 5 stack diameters and they are towed at constant speed Ua referred in the paper as flow speed. For plume visualizations measurements the emissions are backlit with diffused neon light and a digital film is recorded showing the side-view of the plumes during the time of a tow (typically 15 s long). The different images of the film are averaged and the average background image, obtained by a similar film without emissions, is subtracted in order to obtain a final image. The final plume image is used to retrieve quantitative information about the average path of the plume filmed. Pixel coordinates are converted to geometrical coordinates (x,z) by using the image of a regular grid placed in the focal plane of the camera. The pixel intensity profiles I(x,z)

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No interaction

Maximum interaction

483 mm

483 mm 890 mm

890 mm 45 degrees

15 degrees

483 mm

483 mm

890 mm

890 mm 60 degrees

90 degrees

483 mm

483 mm 890 mm

890 mm

Fig. 1) Final plume images for the case with d=22D; stack diameter D=7mm, Ua=8.86 cm/s, emission flow rate 1 l/min through each stack, relative density difference at the source 9.7%. The images show the two reference plume with maximum and no interaction and cases with φ = 15°, 45°, 60°, 90° alignments In Figure 2(a) the plume trajectories, evaluated by postprocessing the images, as described previously, are reported for a double source configuration with φ=0 and for several stack separations. Emission flow-rate was 1 litre per minute, B=9.7% and D=7 mm and Ua=8.86 cm/s. The values of the downwind distance X are calculated starting from the upwind stack. Single stack trajectories for the case with no interaction and the trajectory of a single plume representing the maximum interaction are included in the figure. Comparisons of the pixel intensity profiles extracted from the final images of the plume with the surface weighted integral of the cross-sectional maps obtained by point concentration measurements give very similar results showing negligible effects on trajectory

evaluations due to distortions in final images for the typical ranges of X analyzed. In figure 2(b) are reported plume trajectories referring to d=12D for different values of φ; in figure 2(c) are reported plume trajectories referring to d=22D for several values of φ. In both cases Q=1 litre per minute, B=9.7% and Ua=8.86 cm/s. It should be noted that the maximum interaction is present when the sources are aligned with the flow (φ=0) and its effects on trajectories is decreasing when d is increased. For large values of φ the two plumes come into contact when they are already quite diluted and the entrainment of low density plume material is therefore reduced with respect to the cases of small values of φ; what is more the shielding effect progressively reduces when φ is increased; in these situations the trajectories can be lower than the zerointeraction cases.

179


220

(a) Ua=8.86 cm/s; φ=0

200 180 160 Plume rise (mm)

140 120

F u ll in t e r a c t i o n

100

N o interaction

80

d=4D

60

d=6D

40

d=10D

20

d=22D

0

Plume rise (mm)

0

260 240 220 200 180 160 140 120 100 80 60 40 20 0

50

(b)

150 200 250 Downwind distance X (mm)

300

350

400

d= 22 diameters

Maximum interaction No interaction 0° 30° 60° 90°

0

Plume rise (mm)

100

50

260 240 220 200 180 160 140 120 100 80 60 40 20 0

(c)

100

150

200 250 300 350 400 450 Downstream distance X (mm)

500

550

600

650

d= 12 diameters

M aximum interaction No interaction 0° 20° 30° 45° 90°

0

50

100 150 200 250 300 350 400 450 500 550 600 650 Downwind distance X (mm)

Fig. 2) Plume trajectories for different physical and geometrical conditions. (a) refers to φ=0, B=9.7%, Ua=8.86 cm/s, D=7mm and Q= 1l/min for different stack separation. (b) refers to B=9.7%, Ua=8.86 cm/s, D=7mm, Q= 1l/min and d=22D for different flow angles. (c) refers to B=9.7%, Ua=8.86 cm/s, D=7mm, Q= 1l/min and d=12D for different flow angles.

180


reduced effectiveness of the mixing process when it requires a disruption of the vortex systems in the plumes; and the third is the progressive reduction of the shielding effect of the upwind stack that modifies the flow field actually experienced by the second plume and thus contributing to the extra rise. If a larger number of stacks are aligned with the cross-flow it is possible to have a wake generation that partially entrap the plume generating a downwash effect opposed to the effect of the momentum shield. However in the data referred to a two-stack configuration this effect has not been observed.

The complicated shape of the trajectory near the sources (x 11,000)

§

Stack Reynolds number (Res=weds/ν > 2000)


§

Figure 5 shows the variation of K on the roof of Building A in the along-wind direction for the Aug. 12 tests (x/L=0.08). Near the stack, the field values are significantly larger than the wind tunnel values. In particular, for the low M case (Mfield = 2.3), the field K is almost ten times as large as the wind tunnel value. This discrepancy may be due to incorrect modeling of the model stack exhaust. For this case, the exhaust flow was laminar and consequently, the plume rise may have been too large in the wind tunnel. Note, however, that even for M~5, the field K exceeds the wind tunnel value by a factor of 4. In this latter case, the model exhaust flow was turbulent.

Similar stack momentum ratio (M=we/UH)

where ν is the kinematic viscosity of the air, Wb is the nominal building dimension and ds is the stack diameter. It should be noted that the stack Reynolds number criterion was not always satisfied. At the minimum M-value, the model exhaust velocity was approximately 7.6 ms-1. Thus, the minimum Res value was approximately 1000. Concentration data are expressed in terms of the nondimensional concentration coefficient, K, which is defined as: K = CUHHA2(10-6)/QSF6

Figure 6 shows the variation of K with x for the Oct. 1 test when the stack location was near the center of the roof (x/L = 0.43) and the stack height was 1m. In this case, the field values near the stack were approximately two times the wind tunnel values. These discrepancies may again be attributable to excessive plume rise in the wind tunnel simulation. However, it should be noted that much better agreement between wind tunnel and field values was obtained at locations near the windward and leeward edges of the building.

where C is the measured concentration in ppb and QSF6 is the emission rate of SF6 in m3s-1. RESULTS AND DISCUSSION In the following analysis, the field data are 50-minute mean values derived from the ten 5-minute samples. This averaging time is larger than the value of 10 min. that is typically assumed for wind tunnel mean concentrations [Petersen and Wilson (1989)]. However, it is assumed that the effect of averaging time should be small for an emission source in the wake of a building.

Vertical distributions of K on the leeward wall of Building B are shown in Figure 7 for the Aug. 26 tests. The stack location in this case was near the windward edge (x/L=0.08) and the stack height was 3 m. The exhaust momentum ratio was 1.7 in the first test and 3.9 in the second test. K values obtained on the wall of Building B in the wind tunnel were significantly larger than the field values in both cases. Near the roof of Building B, the wind tunnel K values are 2 to 3 times larger than the field values. Both the field and wind tunnel results show that an increase in M by a factor of 2 caused a similar reduction in K values on the leeward wall.

Figure 4 shows wind tunnel and field K distributions on the roof of Building A for the tests conducted on Aug. 12. K values measured near the top of the leeward wall of Building B are also shown. The stack location was near the windward edge of Building A (x/L=0.08) and the stack height was 1 m. During the first test, the exhaust speed of 18.0 ms-1 produced a relatively high M-value of 4.9. In the second test, the exhaust speed was reduced to 8.8 ms-1, which corresponds to an Mvalue of 2.3

Similar results are shown in Figure 8 for the Oct. 1st tests for which x/L=0.43, hs=1 m. Values of M during the first and second test were 2.0 and 3.7, respectively. As with the Aug. 26 test, the maximum K occurs near the roof of Building B and the wind tunnel values are larger than the field values. However, the values are less than those obtained with the upwind stack used in the Aug. 26 test. For example, the maximum K value obtained in the wind tunnel with the central stack (370) was two to three times less than the values obtained with the upwind stack (750

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