Proceedings of the 1st Thermal and Fluid Engineering Summer Conference, TFESC August 9-12, 2015, New York City, USA
TFESC-12935
ADVANCED STATISTICAL ANALYSIS OF THE COLLISION OF WALL JET WITH A BOUNDARY LAYER André R. R. Silva1*, Miguel R. O. Panão2, Jorge M. M. Barata1 1
Aerospace Sciences Department, University of Beira Interior, Rua Marques Avila e Bolama, 6201-001 Covilhã, Portugal 2
Department of Mechanical Engineering, University of Coimbra, Rua Luis Reis Santos, 3030-788 Coimbra, Portugal
ABSTRACT Laser-Doppler measurements of the velocity characteristics of a ground vortex flow resulting from the collision of a wall jet with a boundary layer are analyzed using advanced statistical tools. Namely, finite mixtures of probability density functions, which determine the best fitting using a Bayesian approach based on a Markov Chain Monte Carlo (MCMC) algorithm. This approach takes into account eventual multimodality and heterogeneities in velocity field distributions. Therefore, it provides more complete information about the probability density function of multimodal velocity distributions and allows the identification of characteristic velocities in the heterogeneous data. The experiments are performed for a wall jet-to-boundary layer velocity ratio of 2, and include mean and turbulent velocity characteristics along the two normal directions contained in planes parallel to the nozzle axis. The results, which have relevance to flows encountered by VSTOL aircraft, quantify the structure of the complex ground vortex flow. The results revealed that in the collision zone the rms velocity fluctuation appears to be overestimated for the horizontal component, probably due to the measured velocity range, oscillating between positive and negative values. The results revealed that finite mixture was able to accurately reconstruct a mathematical function describing the probability distribution obtained experimentally. ̅ and 𝑢′𝑟𝑚𝑠 rms provide an idea of the flow dynamics, their use is limited and an The results shows that 𝑈 important amount of information associated with the highly curved flow complexity is lost, preventing a more accurate description of turbulent structures emerging from the collision of wall jet with a boundary layer.
KEY WORDS: VSTOL, Ground Vortex, Wall Jet, Boundary Layer, Statistical Analysis, Finite Mixtures, Bayesian Approach, Markov Chain Monte Carlo
1. INTRODUCTION Highly curved flows are quite common in nature and are frequently originated by impermeable surfaces that deflect a flow (e.g. Castro and Bradshaw [1]). This type of complex flows is characterized by phenomena like extra rates of strain and enhanced turbulence production through the interaction of normal stresses with normal strains, which is typical of impingement cooling applications in industry, as well as of the flow beneath short/vertical take-off (VSTOL) aircraft while lifting off or landing with zero or small forward momentum. In this latter application, the impingement of lift jets on the ground results in the formation of a wall jet that flows radially from the impinging point along the ground surface, interacting strongly with the ground plane, thus resulting in: lift losses; enhanced entrainment close to the ground (suckdown); engine thrust losses following reingestion of the exhaust gases; and in possible aerodynamic instabilities caused by fountain impingement on the aircraft underside. The interaction of this wall jet with the free stream results in the formation of a highly curved flow (ground vortex) far upstream of the impinging jet that has a profound influence on the flow development.
*Corresponding Author:
[email protected]
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TFESC-12893 Measurements of this type of flow have only been reported in the context of a secondary flow within the impinging jet flow problem. Barata and Durão [2] found that the shape, size and location of the ground vortex were dependent on the ratio between the jet exit and the crossflow velocities, and two different regimes were identified. One is characterized by the contact between the ground vortex and the impinging jet, while another is detached upstream of the impinging zone. They also report that crossflow acceleration over the ground vortex was directly connected with the jet exit velocity, and the influence of the upstream wall jet was not confined to the ground vortex but spread upwards by a mechanism not very well known.
Fig. 1 Diagram of the ground vortex facility. Laser-Doppler measurements of velocity characteristics of two dimensional ground vortex flows resulting from the collision of a wall jet with a boundary layer (Fig. 1) were presented by several authors [3-7] and discussed with visualization results for wall jet to boundary layer velocity ratios (Uj/U0) of 1.6, 1.7 and 2. To avoid the influence of the impinging region, a plane wall jet was produced independently with a configuration previously used to study two-dimensional upwash flows [8]. The wall jet collides with the boundary layer produced by a conventional wind tunnel giving rise to a ground vortex [3-4], allowing to investigate different velocity ratios between the wall jet and crossflow. Using the theory of turbulent jets and the distance to the separation point, it is possible to establish a relation between the wall jet velocity and the velocity at the jet exit, and the results evidenced the existence of a small vortex flow located upstream the separation point, not yet reported before for this type of flows [9]. This secondary vortex has a very low broadband pulsating behavior, expanding and contracting, as it is observed in some impinging jet configurations with ground vortex flows [10]. In a first stage, the vortex is very small, but growing. The lower part of the boundary layer with anticlockwise vorticity seems to merge into the growing vortex. In a second stage, as the small vortex continues to grow, it becomes higher than the boundary layer thickness, and suddenly detaches, and convected upwards in the direction of the curved flow. In a third stage, a new small vortex appears and starts to grow, in a cyclic process restarting at stage 1. The secondary vortex growth cannot be attributed to the shear layer vortices, convected with the wall jet, since it cannot merge into the deflected flow resulting from the collision of the wall jet with the boundary layer. This is explained by the vertical velocity component that is always positive above the vortex [3-4]. The unsteadiness of the ground vortex reported before for the case of impinging jets in unconfined crossflows may also be associated with
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TFESC-12893 an additional small vortex upstream the separation point, but, due to its extreme small size, could not be observed so far, as in the case of very high jet-to-crossflow velocity ratios [7]. The particular ordered sequence that was identified from the visualization studies for the small recirculation zone that appears near the separation point can also be interpreted as an oscillation of the separation zone or of the virtual deflected flow origin, and can be confirmed by the bimodal histogram of the horizontal velocity measurements obtained in this zone [3-4]. In spite of the apparent organized sequence of the turbulent structure of the collision zone, the power spectra of the horizontal velocity component does not exhibit any evident particular peak for the same location [3-4]. Barata et al. [11] presented a detailed analysis of the turbulent structure of a ground vortex flow resulting from the collision of a wall jet with a boundary layer, following the work reported in Refs. [4-5, 8, 12-14], having detected a small recirculating zone located upstream the separation point not yet reported for this type of flows. The authors reproduced experimentally the ground vortex upstream of the stagnation point of an impinging jet under a crossflow for a high jet-to-crossflow velocity ratio relevant to V/STOL applications, and tested the hypothesis that the formation of a second (small) vortex should be due to a particular turbulent structure not yet analyzed or reported before. According to their hypothesis, a velocity ratio between the wall jet and the crossflow of 2.0 was used, corresponding to a regime where the small vortex is present. The mean ̅) and turbulent (u’) velocity components, as well as the Reynolds shear stress data is used to calculate the (𝑈 turbulent kinetic balances, in order to understand the complex flow in the collision zone. The turbulent kinetic energy balances reveal that, in the collision zone of the wall jet with the boundary layer, there is a local gain of energy by convection. In the region of the deflected flow, the convective term does not present any significant contribution to the loss or gain of turbulent kinetic energy. Results evidence that in the collision zone, the diffusive and dissipative terms, as well as the production term by shear stresses become predominant and the production of turbulent kinetic energy tends to balance the loss by diffusion and dissipation. In the same zone, near to the wall, the production of turbulent kinetic energy occurs by convection, normal and shear stresses. The small contribution of convective term to the production of turbulent kinetic energy is less than the production due to the normal and shear stresses. The collision zone between the wall jet and the boundary layer presents a behavior similar to a wall jet. Following the works of Barata et al. [3-7, 9, 11-14], this paper explores advanced statistical tools, such as finite mixtures of probability distribution functions to better describe velocity distributions obtained experimentally, and improve the physical interpretation of two dimensional ground vortex flows resulting from the collision of a wall jet with a boundary layer. Velocity distributions are acquired by a DANTEC Flow Lite dual-beam, backscatter laser anemometer, sensible to the flow direction provided by light-frequency shifting from acousticoptic modulation. The wall jet collides with the boundary layer produced by a conventional wind tunnel, thus forming a ground vortex, which can be made of different velocity ratios between the wall jet and crossflow. In the present study, a smaller velocity ratio between the wall jet and the boundary layer of UR =Uj/U0=2 is considered. In terms of the advanced statistical tools, the finite mixtures of probability density functions are determined by the best fitting with experimental data, using a Bayesian approach based on a Markov Chain Monte Carlo (MCMC) algorithm [15]. Recently Panão et al. [16] applied this advanced statistical tool to analyze the characteristics of secondary atomization resulting from the spray impact onto a flat surface under crossflow, and, for the first time, the characteristic size of droplets produced by a mechanism known as film stripping has been identified due to the application of this statistical tool. The present approach takes into account eventual multimodality and heterogeneities in velocity field distributions. Therefore, it provides a more detailed information about the probability density function describing multimodal velocity distributions, allowing the identification of characteristic velocities in the heterogeneous data, and improving the physical interpretation of the highly curved flow.
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Fig. 2 Photograph of the experimental rig the experimental facility [13].
2. EXPERIMENTAL METHOD The experimental setup has been detailed in Barata et al. [13] and only a brief summary is given here. The wind tunnel facility designed and constructed for the present study is illustrated in Fig. 1 and shown in Fig. 2. The recommendations of Metha and Bradshaw [17] for open circuit wind tunnels were followed throughout the design process, especially for the boundary layer part of the flow. A fan of 15KW nominal power drives a maximum flow of 3000m3/h through the boundary layer and the wall jet tunnels of 300x400mm and 40x400mm exit sections, respectively. The origin of the horizontal, X, and vertical, Y, coordinates is taken near the visual maximum penetration point. The X coordinate is positive in the wall jet flow direction and Y is positive upwards. The present results are obtained at the vertical plane of symmetry for a wall jet mean velocity of 13.7m/s and mean boundary layer velocity of 6.9m/s, corresponding to a wall jet-to-crossflow velocity ratio, UR, of 2. The velocity field is measured with a Laser-Doppler velocimeter (Dantec Flowlite 2D), comprising a 10 mW He-Ne and a 25 mW diode-pumped frequency doubled Nd:YAG lasers, the sensitivity to the flow direction is provided by frequency shifting a Bragg cell at fo=40MHz, and the transmission and backward-scattered light collection is made with a focal lens of 400mm. The half-angle between the beams is set to 2.8o and the calculated axis dimensions of the measurement volume at the e-2 intensity locations are 135x6.54x6.53μm and 112x5.46x5.45μm, for the He-Ne and Diode lasers, respectively. The principal characteristics of the laser-Doppler velocimeter are summarized in Table 1. The horizontal, U, and vertical V, mean and turbulent velocities together with the shear stress, ̅̅̅̅̅ 𝑢′𝑣′ were determined by a two-velocity channel Dantec BSA F60 processor. The seeding of the flow with glycerin particles of 0.1-5µm is produced with medical atomizers operating at 1.5 bar. The transmitting and collecting optics is mounted on a three-dimensional transversing unit, allowing the positioning of the control volume within 0.1mm. According to an information theory approach [18], Shannon information entropy can be used to assess the stabilization of entire velocity distribution in a Laser-Doppler measurement, ensuring that
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TFESC-12893 enough samples have been acquired for data processing. Therefore, it has been verified that the sample number set to 10,000 in each measurement point is above the minimum value given by the information theory approach, considering all measurements points, resulting in uncertainties lower than 4.4% according to Panão [18]. Table 1 Principal characteristics of the Laser-Doppler velocimeter. Wave length, λ [nm]
633 (He-Ne)
532 (Diode Laser)
Focal length of focusing lens, f [mm]
400
400
Beam diameter at e-2 intensity [mm]
1.35
1.35
Beam spacing, s [mm]
38.87
39.13
Calculated half-angle of beam intersection, θ
2.78
o
2.8o
Fringe spacing, δf [μm]
6.53
5.45
0.153
0.183
-1
Velocimeter transfer constant, K [MHz/ms ]
3. SATISTICAL METHOD The statistical method has been detailed in Panão and Radu [15] and only a brief summary is given here. There are several methods for finding the best mixture of probability distribution functions (pdf) fitting a discrete one obtained experimentally. The approach used in this work is a Bayesian one based on a Markov Chain Monte Carlo (MCMC) algorithm as described in Frühwirth-Schnatter [19]. The finite mixture is a weighted linear combination of several mathematical pdfs, each capturing a group of velocity with similar characteristics distributed by a Normal distribution function. In turbulent flows, the velocity is usually described by Normal distribution, given the approximation of the instantaneous velocity ̅) with a fluctuating one (u’). In defining the mathematical (u) with the sum of an average component (𝑈 functions comprising the finite mixture, the same assumption has been made. Furthermore, finding the true number of K mixed Normal distributions that best describe experimental data is also a problem in model specification, which relies on the evolution of the marginal likelihood (MLK) with K. In Panão and Radu [15], the criterion found is that either MLK stabilizes above a certain K, or attains a maximum value. A finite mixture of several probability distribution functions depends on the weight - 𝑤𝑖 – attributed to each cluster of values with similar characteristics, and the characteristic mean velocity and rms of a Gaussian distribution - 𝑓(𝜇𝑖 , 𝜎𝑖 ) - expressed as 𝑝𝑚𝑖𝑥 (𝑣) = ∑𝑁 𝑖=1 𝑤𝑖 ∙ 𝑓(𝜇𝑖 , 𝜎𝑖 )
(1)
where the number of probability density functions – N – depends on the result for best fitting. With this kind of detailed information provided, one has a more accurate picture of the collision of wall jet with a boundary layer, which is quite different from that given solely by the mean and rms velocities retrieved from the entire distribution, regardless of its eventual multimodality. It is noteworthy that the information contained in (𝜇𝑘 , 𝜎𝑘 , 𝜂𝑘 )𝑘=1,𝐾 allows the reconstruction of the velocity distribution as a mathematical function describing the discrete distribution obtained from experimental measurements, justifying the greater accuracy in the analysis of the flow compared to using mean quantities alone.
4. RESULTS AND DISCUSSION The present study explores the finite mixtures of probability distribution functions to better describe velocity distributions obtained experimentally from the collision of a wall jet with a boundary layer for a velocity ratio
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TFESC-12893 between the wall jet and the boundary layer of UR =Uj/U0=2. The finite mixtures of probability density functions are determined by the best fitting with experimental data, using a Bayesian approach based on a Markov Chain Monte Carlo algorithm. The present approach takes into account eventual multimodality and heterogeneities in velocity field distributions. ̅ , and vertical, 𝑉̅ , velocity components, as well as the Fig. 3 shows contours of the mean horizontal, 𝑈 corresponding streamlines, depicted to support the above description of the flow and provide the order of magnitude of mean flow characteristics in the collision zone (X = 0mm).
150
125
U mean (m/s) 8.000 6.625
100
Y (mm)
5.250 3.875
75
2.500 1.125 50
-0.250 -1.625
25
-3.000
0 -100
-50
0
50
100
X (mm)
(a) 150
125
V mean (m/s) 3.000 2.563
100
Y (mm)
2.125 1.688
75
1.250 0.813 50
0.375 -0.063
25
-0.500
0 -100
(b)
-50
0
50
100
X (mm)
̅; b) vertical Fig. 3 Contours of the measured average velocity for UR = 2: a) horizontal component, 𝑈 component, 𝑉̅ [3] The mean vertical velocity component is negative near the wall in the boundary layer side for Y 0, indicating the existence of a secondary vortex. However, while for -10mm < X < 0mm, the mean vertical velocity (black dots in Fig. 5b) points to a stagnation at X = 0mm, through finite mixtures, a vertical characteristic velocity is clearly identified as positive, approximately 0.75m/s, and has a weight in the distribution of 64.5%, which is considerably higher than the weights associated with the other two characteristic negative velocities of approximately -0.9m/s and -2.0m/s, having weights of 21% and 14.5%, respectively. The positive characteristic vertical velocity could be associated with the secondary vortex when it grows and becomes larger that the boundary layer, thus, being convected upwards in the direction of the curved flow. The lowest negative value of characteristic mean velocity of vertical component may be associated with an additional small vortex upstream separation point reported before [9], but difficult to observe so far due to its extreme small size, as in the case of very high jet-to crossflow velocity ratios.
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(a)
(b) Fig. 5 Characteristic mean velocity profiles at 12mm above the wall in the flow direction (X) for the horizontal (u) and vertical (v) components. Point size is proportional to the weight associated with each distribution function (wi). Fig. 6 portrays the horizontal characteristics of rms velocity fluctuation components obtained at 12 mm from the surface, with the black dots corresponding to the rms velocity of the flow at xi, and the bubble plot representing the characteristic fluctuation identified in a certain point, and the size is proportional to the weight distribution i has in the finite mixture. Furthermore, an important quantity for numerical simulations is the turbulence intensity in locations closer to the wall jet and boundary layer entries through the ratio between rms and average values. It is interesting to note tht a comparison between the characteristic velocity and fluctuation, and the average and rms values evidences their similarity, being the finite mixture approach validated, in a certain sense, relatively to a more established approach using mean and rms values. For |X| > 40mm, in both wall jet and boundary layer regions, the characteristic velocity fluctuations and the rms velocity fluctuation retrieved from measurements have similar behavior. Namely, in the boundary layer region, for X > 20mm, the similarity between characteristic and rms velocity fluctuations express the closeness to a near Gaussian distribution function to describe flow velocity. In the collision zone, -40mm < X < 20mm, the values for u’ and v’ present a distinct behavior relatively to the rms velocity fluctuation. Namely, the later appears overestimated for u, probably due to the measured velocity range, oscillating between positive and negative values, thus, presenting a typical bimodal histogram. In the ̅ and u' still provide a idea of the flow dynamics, but their use is collision region, it is possible to infer that 𝑈 limited and an important amount of information associated with the flow complexity is lost, preventing a more accurate description of turbulent structures emerging from the collision of wall jet with a boundary layer. This 2 ̅) and the levels of anisotropy (√𝑢̅′ 2 / can be better understood by considering the turbulence intensity (√𝑢̅′ /𝑈 ̅ 2 ) for example, at X = -20mm and -10mm. Using the average and rms values, the absolute values of √𝑣′ turbulence intensity are 3.06 and 46 for the u-component, and 3.25 and 16 for the v-component, respectively. Considering finite mixtures, the absolute values for the u-component are in the range of 0.53-0.59, and for the vcomponent 0.57-0.6, for X = -20, -10 mm, respectively. The maximum values of the horizontal velocity fluctuations are observed in the collision zone where the mean horizontal velocity is zero giving rise to extremely high local turbulence intensity values, meanwhile for same location consider mixture finites distributions the turbulence intensity never exceeds the value of. 0.6. Relatively to the anisotropy values, without finite mixtures, the results are 2.43 (-20mm) and 2.2 (-10mm), thus, experiments indicate ill conditioning for
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TFESC-12893 numerically simulate the flow at the collision region. However, in Silva et al. [9], numerical simulations were able to capture the collision region, where experiments point otherwise. In fact, following a finite mixture approach, where the anisotropy is based on the weighted sum of characteristic fluctuation values, the results are 1.25 (-20mm) and 1.46 (-10mm), evidencing the underlying physical reason in favor of a close to anisotropic field that endorses the possibility of being simulated numerically.
(a)
(b) Fig. 6 Characteristic rms fluctuation velocity profiles at 12mm above the wall in the flow direction (x) for the horizontal (u) and vertical (v) components. Point size is proportional to the weight associated with each distribution function (wi).
(a)
(b) Fig. 7 Characteristic mean velocity profiles at 90mm (a) and 60 mm (b) above the wall in the flow direction (X) for the horizontal (u) component. Point size is proportional to the weight associated with each distribution function (wi). Fig. 7 depicts the characteristic mean velocity results obtained 90mm (a) and 60mm (b) from the surface, the black dots correspond to the average velocity of the flow at xi, but the bubble plot represents the characteristic
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TFESC-12893 velocities identified in a certain point, and the size is proportional to the weight distribution i has in the finite mixture. The horizontal profiles of horizontal characteristic mean velocity component at Y = 60mm (Fig. 7b) and 90mm (Fig. 7a) are according to the horizontal profile to 12mm above the wall, exhibiting a similar behavior. The horizontal velocity component shows two groups of distributions with characteristics mean velocity distinct, one group distribution shows a positive characteristic mean velocity while the other group distribution evidences a negative characteristic mean velocity. The group distribution with a positive characteristic mean velocity is associated with the wall jet, while the group distribution that evidences a negative characteristic mean velocity is related with the boundary layer. For Y = 60mm (Fig. 7b), the horizontal characteristic mean velocity is positive for -120mm < X < 40mm and negative -40mm < X < 120mm, so with the finite mixture approach allow observe the influence of the wall jet extends until X =40 mm, meanwhile at X = -40mm is yet possible observe the influence of the boundary layer. Therefore, the finite mixture distributions lets to identify the region of collision of wall jet and the boundary that is comprised between X = -40mm and X = 20 mm, for Y = 60mm. In the case of the horizontal profile farthest away from the wall, Y = 90mm (Fig. 7a), region of collision of wall jet and the boundary is comprised between X = -60mm and X = 70mm.
(a)
(b) Fig. 8 Characteristic rms fluctuation velocity profiles at 90mm (a) and 60mm (b) above the wall in the flow direction (x) for the horizontal (u) component. Point size is proportional to the weight associated with each distribution function (wi). Fig. 8 describes the horizontal characteristics rms fluctuation velocity components obtained 90mm (a) and 60mm (b) from the surface, the black dots correspond to the rms velocity of the flow at xi, and the bubble plot represents the characteristic fluctuation identified in a certain point, and the size is proportional to the weight distribution i has in the finite mixture. As the characteristic mean velocity (Fig. 7), the horizontal profiles of horizontal characteristic rms velocity fluctuation component at Y = 60mm (Fig. 8a) and 90mm (Fig. 8b) are according to the horizontal profile to 12mm above the wall, exhibiting a similar behavior. In the collision zone, for Y = 60mm and 90mm, the values for u’ present a distinct behavior relatively to the rms velocity fluctuation. The horizontal rms velocity fluctuation appears overestimated probably due to the measured velocity range, oscillating between positive and negative values, thus, presenting a typical bimodal histogram.
5. CONCLUSIONS Laser-Doppler measurements of the velocity characteristics of a ground vortex flow resulting from the collision of a wall jet with a boundary layer were presented and discussed using advanced statistical tools for a wall jet-toboundary layer velocity ratio of 2.
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TFESC-12893 The finite mixtures of probability density functions, which determine the best fitting using a Bayesian approach based on a Markov Chain Monte Carlo (MCMC) algorithm, taken into account eventual multimodality and heterogeneities in velocity field distributions. Therefore, it provides more complete information about the probability density function of multimodal velocity distributions and allows the identification of characteristic velocities in the heterogeneous data. The results shown different types of histograms were identified with bimodal pattern occurring in the collision zone. Also, the results expose that normal cumulative distribution based on the average velocity and corresponding fluctuation was far from the measured one. The finite mixture distributions allowed observe the influence of the wall jet is extended upstream of the separation point, while the influence of the boundary layer is still exerted clearly downstream of the separation point. The results revealed that in the collision zone the rms velocity fluctuation appears to be overestimated for the horizontal component, probably due to the measured velocity range, oscillating between positive and negative values. The results revealed that finite mixture was able to accurately reconstruct a mathematical function describing the ̅ and 𝑢′𝑟𝑚𝑠 rms provide an idea of the probability distribution obtained experimentally. The results shows that 𝑈 flow dynamics, their use is limited and an important amount of information associated with the highly curved flow complexity is lost, preventing a more accurate description of turbulent structures emerging from the collision of wall jet with a boundary layer.
ACKNOWLEDGMENT The present work was performed under the scope of the LAETA – Laboratório Associado em Energia, Transportes e Aeronáutica – activities.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Castro, I.P.; Bradshaw, P. “The Turbulence Structure of a Highly Curved Mixing Layer”, J. Fluid Mech, 73(2), pp.265-304, (1976). Barata, J.M.M. and Durão, D.F.G., “Laser-Doppler Measurements of Impinging Jets Through a Crossflow”, Experiments in Fluids, 36(5), pp.117-129, (2004). Silva, R. R., Durão, D. F. G., Barata, J. M. M., Santos, P., Ribeiro, S., “Laser-Doppler Analysis of the Separation Zone of a Ground Vortex Flow”, 14th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, (2008). Silva, A.R.R., Durão, D.F.G., Barata, J.M.M., Santos, P.J.T., Ribeiro, S.D.G., “Laser-Doppler Analysis of the Separation Zone of a Ground Vortex”, International Review of Aerospace Engineering (I.R.E.A.S.E), 2(3), pp.167-174, (2009). Barata, J.M.M., Ribeiro, S., Santos, P., Silva, A.R.R., Silvestre, M.A., "Experimental Study of Instabilities and Secondary Effects of a Ground Vortex Flow," 46th Aerospace Sciences Meeting and Exhibit, Paper AIAA 2008-0343, Reno, NV, (2008). Barata, J.M.M., Ribeiro, S.D.G., Santos, P.J.C.T. e Silva, A.R.R., “Experimental Study of the Collision Zone of a Boundary Layer with a Wall Jet,” 47th Aerospace Sciences Meeting and Exhibit, Paper AIAA 2009-0335, Orlando, FL, (2009). Barata, J.M.M., Santos, P., Silva, A.R.R., “Experimental Study of a Ground Vortex: The Effect of the Crossflow Velocity”, Journal of Aircraft, 50(1), pp. 298-302, (2013). Gilbert, B.L., “Detailed Turbulence Measurements in a Two-Dimensional Upwash”, AIAA 16th Fluid and Plasma Dynamics Conference, AIAA paper 83-1678, (1983). Silva, A. R., Barata, J. M. M., Nunes, R. B., Santos, P. J., Durão, D. F. G., “Unsteadiness of a Ground Vortex Flow”, 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, Orlando, Florida, (2009). Cimbala, J.M., Billet, M.L., Glaubomme, D.P. and Ofelein, J.C., “Experiments on the Unsteadiness Associated with a Ground Vortex”. Journal of Aircraft, 28(4), pp. 261-267, (1991). Barata, J.M.M., Santos, P.J.C.T., Silva, A.R.R., Durão, D.F.G., “Turbulent Energy Budgets of a Ground Vortex Flow”, Journal of Mechanics Engineering and Automation, 3(5), pp. 311-324, (2013). Barata, J.M.M. and Durão, D.F.G., “Laser-Doppler Measurements of a Highly Curved Flow”. AIAA Journal, 43(12), pp. 26522655, (2005). Barata, J.M.M., Ribeiro, S., Santos, P., Silva, A.R.R., “Experimental Study of a Ground Vortex”, Journal of Aircraft, 46(12),
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TFESC-12893 pp. 1152-1159, (2009). [14] Barata, J.M.M., Santos, P.J.C.T., Silva, A.R.R., “The Turbulent Structure of a Ground Vortex”, 48th Aerospace Sciences Meeting, Paper, AIAA-2010-1051, Orlando, FL, (2010). [15] Panão, M.R.O., Radu, L., “Advanced statistics to improve the physical interpretation of atomization processes”, International Journal of Heat and Fluid Flow, 40, pp. 151–164, (2013). [16] Panão, M.R.O., Moreira, A.L.N., Durão, D.F.G., “Statistical analysis of spray impact to assess fuel mixture preparation in IC engines”, Fuel Processing Technology, 107, pp. 64–70, (2013) [17] Metha R.D., and Bradshaw P., “Design Rules for Small Low-Speed Wind Tunnels”, The Aeronautical Journal of the Royal Aeronautical Society, (1979). [18] Panão, M.R.O., “Assessment of measurement efficiency in laser- and phase-Doppler techniques: an information theory approach”, Measurement Science and Technology, 23, 125304 (2012) [19] S. Frühwirth-Schnatter, Finite mixture and Markov switching models, Springer, (2006).
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