Effect of inlet conditions for numerical modelling of the

Effect of inlet conditions for numerical modelling of the urban boundary layer Renata Gnatowska

Citation: AIP Conference Proceedings 1922, 110008 (2018); View online: https://doi.org/10.1063/1.5019111 View Table of Contents: http://aip.scitation.org/toc/apc/1922/1 Published by the American Institute of Physics

Effect of Inlet Conditions for Numerical Modelling of the Urban Boundary Layer Renata Gnatowska1, a) 1

Faculty of Mechanical Engineering and Computer Science, Czestochowa University of Technology Al. Armii Krajowej 21, 42-200 Cz stochowa, Poland a)

Corresponding author: [email protected]

Abstract. The paper presents the numerical results obtained with the use of the ANSYS FLUENT commercial code for analysing the flow structure around two rectangular inline surface-mounted bluff bodies immersed in a boundary layer. The effects of the inflow boundary layer for the accuracy of the numerical modelling of the flow field around a simple system of objects are described. The analysis was performed for two concepts. In the former case, the inlet velocity profile was defined using the power law, whereas the kinetic and dissipation energy was defined from the equations according to Richards and Hoxey [1]. In the latter case, the inlet conditions were calculated for the flow over the rough area composed of the rectangular components.

INTRODUCTION The application of Computational Fluid Dynamics (CFD) in the urban boundary layer wind environment has been significantly increased in last decades [2-4]. Therefore a large number of codes employing a variety of solution strategies are now available. Furthermore, the atmospheric boundary layer develops along the roughened surface. Currently used of codes are based on trends in the introduction of simple alternatives to the classical logarithmic law for smooth walls that are inappropriate, even outside the detachment, and certainly wrong in the immediate vicinity of obstacles. It is known that the standard logarithmic law fails in such regions. However, the accurate reproduction of the physical nature of the boundary conditions around and on the object is not decisive for the correctness of calculations. Significant changes of parameters of the flow near the wall do not affect substantially the qualitative nature of the simulation results and only slightly impacts on the quantitative results, at least in the case of calculation prescribed. This is due to the fact that pressure and velocity fields are dominated by the large-scale movements generated by the obstacle [5-6]. It is important, however, to properly model the inlet layer mundane, and it requires a careful mutual fit of model parameters of turbulence and roughness conditions in the boundary layer [7-9]. Preliminary calculations without considering obstacles are necessary to validate a simulation of inlet conditions. Most of the published comparisons between calculations and experiment do not describe these types of tests. This problem becomes mainly important for uRANS or LES methods. Among the various developed techniques of modelling inlet conditions [10, 11], none of them is not easy to apply in the external flows. The evaluation of the results among various turbulence models and simulation of inlet conditions for the wind environment can benefit the selection of turbulence models and improves the accuracy of simulations [3, 12, 13]. In the present study, based on the wind tunnel tests with buildings models, the author investigated the performance of several RANS models, mainly including the most widely used turbulence models in industrial CFD. This study was aimed to evaluate the improvement of modelling of the characteristics of the velocity field formed at the inlet to the calculation area and its effect on the flow around a simple arrangement of objects. The analysis was performed according to two concepts. The first of them was definition of the velocity profile using the power law U(z)=U0(z/ ) , whereas the kinetic energy (k) and dissipation energy ( ) was defined from the equations according to Richards and Hoxey [1]: k=u*2/Cµ 0.5, (z)=u*2/ z, where Cµ =0.09, is von Karman constant equal 0.41 and friction velocity is u*=0.04U0. The second concept assumes modelling of inlet conditions through the Computer Methods in Mechanics (CMM2017) AIP Conf. Proc. 1922, 110008-1–110008-6; https://doi.org/10.1063/1.5019111 Published by AIP Publishing. 978-0-7354-1614-7/$30.00

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development of the layer profile by means of the calculation of the flow over the rough area composed of the rectangular cuboid components [7]. Modelling of the structure of the boundary layer corresponding to the parameter = 0.16 was obtained through modelling of the flow over the components at the height h=B/6 on the section x/h=400.

COMPUTATIONAL AND EXPERIMENTAL DETAILS The geometry of the analysed case of two rectangular in-line surface-mounted square cylinders immersed in a boundary layer are sketched in Fig. 1. The measurements were carried out for configuration of two elements with different height, aligned in one line and the distance between them was S/B=1.5. The results presented in this work relate to a fixed ratio of object height H1/H2=0.6 and value of their “immersion” in boundary layer H2/ =1.

FIGURE 1. Scheme of considered flow around system of bluff-bodies

The program of the study consists of wind-tunnel experiments and numerical simulations. In the frame of the numerical study, the three-dimensional steady RANS simulations have been carried out using a commercial CFD code, FLUENT v. 17.2, with two turbulence models: RSM and k- RNG. According to the literature [3, 4, 13], these models are widely used for analysis of flows for different configurations of buildings. The dimensions of the computational domain were chosen based on the best practice guidelines by Tominaga et al. [13]. The upstream computational domain length is 6.25H, and the downstream one is 16.7H. The computational grid was created using the pre-processor Gambit 2.4.6, resulting in structured grids with 191 x 85 x 69 resolution (fine grid). For computation purposes, the flow domain is divided into a number of hexahedral cells. The mesh is nonuniform in all the three directions. The grid is clustered near the object and the spacing is increased to a proper ratio of 1.2 away from the object surface. The first cell adjacent to the walls has been set with respect to the criteria required for the individual near-wall treatment. Hence, using a two-layer approach, the width of the near-wall cell has been 0.003H1, which corresponds to 1 < y+ < 3. The SIMPLE algorithm was used for pressure correction and velocity implicitly, pressure interpolation was second order and second-order discretization schemes were used for both the convection terms and the viscous terms of the governing equations. Convergence was assumed to obtain when all the scaled residuals leveled off and reached a minimum of 10-6 for x-, y- and z-velocity, and 10-4 for k, and continuity. Normalized time step defined as t* = t U0/B was chosen at level of 0.15. In this relationship U0 is the free stream velocity and t is the actual length of time step estimated from the dominant frequency in the flow, representing 1% value of one period of oscillation T. Comparison of the distribution of mean (U) and fluctuation of velocity (Urms) for two concepts of modelling of inlet conditions with the experimental data with single-sensor miniature probe CTA was presented in the Fig. 2ab. In addition Fig. 2c presents the distribution of dissipation energy by comparison of the two methods of modelling of this value at the inlet of calculation area. Comparison of the inlet velocity distributions in the layer shows a very good consistency between the profile defined by means of the power law (U(z)= U0(z/δ) ) and velocity profile obtained through modelling of the flow over the group of rectangular cuboid components. Therefore, it can be assumed that the velocity profile generated according to the second concept of modelling of inlet conditions can be described with sufficient accuracy by means of the power law at a specific exponent . Modelling of the layer

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profile through rough components is also very well reflected by the experimental distribution of velocity fluctuation at the inlet. In this case, the value of the parameter corresponds to the characteristics of flat land with low plants [14]. The undisturbed velocity U0 in the tunnel and in CFD simulations was 12m/s, and the Reynolds number based on the length of the edge of the object B=0.04m was equal ReB = 2.7 104. The parameter of submerging objects in the flow was intended as δ/H2 = 1.524.

(a)

(b)

(c) FIGURE 2. The distributions of the reduced mean (a) and fluctuation velocity (b), and energy dissipation (c) for two concepts of modelling of inlet conditions

RESULTS The above presented concepts of modelling of inlet conditions were subjected to further verification in a traverse x/B = -1.0 (Fig. 3). The traverse x/B = -1.0 was located one length of the edge of the base from the frontal plane of the first object (see Fig. 1). Comparison of the distributions of velocity in profile x/B = -1.0 does not reveal the effect of the method to generate the inlet conditions on the velocity field. However, the insignificant difference in the shape of velocity profiles was observed for the profiles obtained from calculations and experimental profile visible in the range z/H1 = 0.2 ÷ 1.0. It can be assumed that the deformation of the experimental profile represents the effect of objects in the forward direction of the flow.

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(b)

FIGURE 3. The distributions of the reduced mean velocity (a) and fluctuation velocity (b) for traverse x/B = -1.0, y/B = 0 for two concepts of modelling of inlet conditions

The diagram on Fig. 4 shows a numerical velocity profile in range x/B = -1.0 ÷ -0.7. In order to ensure reliable comparison of the results, one should reduce the values of velocity and velocity fluctuation with the values measured at objects location. In the present analysis, the reference values were provided by the values of velocity (Uref) and velocity fluctuation (Urms,ref) recorded for the height z/H1=1 of the flow without objects in their location. The numerical results for traverse x/B = -0.7 point to both local maximum in the central part of the layer and just at the surface. Proper evaluation of the effect of the method to generate inlet conditions and the turbulence model used on the correctness of modelling of the flow structure requires that the analysis of the velocity field around the system of objects is made, especially for the detachment zone behind the system. It is noticeable that with the reduction in the distance to the object, the velocity profile is becoming more similar in its shape to the experimental profile. The shape of the velocity profile which is similar to the experimental profile (x/B = -1.0) is observed for the traverse x/B = -0.7. This means that the potential effect of objects in the forward direction in the numerical modelling is slightly weaker than in the reality. As can be observed, the method to model conditions at the inlet has a substantial effect on the distribution of velocity fluctuation (Fig. 4b). The velocity fluctuation obtained through the development of the layer structure by means of the rough area (II concept) is more consistent with the experimental distribution than the fluctuation profile obtained through flow modelling as suggested Richard and Hoxey [1]. In the latter case, the effect of inlet conditions is being observed.

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(b)

FIGURE 4. The distributions of the reduced mean velocity (a) and fluctuation velocity (b) for traverses x/B = -1.0 ÷ -0.7 for the second concept of modelling of inlet conditions

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Figure 5 presents the distributions of the reduced velocity obtained in the traverse x/B = 4.5. No effect of the method of generation of inlet conditions on the velocity field in the aerodynamic wake of the system of objects was found. The change in the turbulence model from k- RNG to RSM does not lead to the significant differences in the description of the velocity distribution. The numerical results are well consistent with the experimental results outside the area z/H2 = 0.75. Below the height z/H2 = 0.75, i.e. below the shear layer that represents the boundary between the stable top flow and the zone of strong recirculation of the flow in a direct neighbourhood of the second object, the numerical results point to the stronger reverse flow compared to the experimental data. It seems that underestimation of the velocity in this area results from the measurement methodology. On the one hand, the CTA probe measures the velocity in the direction that is normal to the probe wire i.e. not always along the flow. On the other hand, in the case of the reverse flow, the probe support inhibits the flow and is likely to generate strong disturbances. The lack of the difference between the modelling results for different concepts of implementation of the inlet conditions does not result from the lack of the effect of the method of model conditions at the inlet but rather from a strong effect of the system on the flow. This observation is also supported by the comparative analysis of the distribution of velocity fluctuation in the traverse x/B = 4.5 (Fig. 5b). Some discrepancies in the fluctuation distribution, which result from adoption of the different method to generate inflow conditions are noticeable only over the height z/H2 = 2, where the effect of the object disappears. Comparison of the numerical with the experimental results reveals only a qualitative consistency of velocity fluctuation. Additionally, numerical analysis of the flow structure using the RSM model (at least in the flow recirculation zone, below z/H2 = 0.75) shows much better correlation with the experimental results compared to the use of the k- RNG model. However, the limitations of CTA measurement quality in the area of the reverse flow made should be taken into account.

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FIGURE 5. The distributions of the reduced mean (a) and fluctuation (b) velocity obtained in the traverse x/B = 4.5, y/B = 0

As mentioned before, due to the areas of flow recirculation in the aerodynamic wake of the objects, measurement with the CTA wire probe does not seem entirely reliable. Therefore, verification of the numerical calculations was additionally conducted through comparison of the distribution of shear stresses. For the purpose, several measurements were conducted using the surface probe type flush-mounted (CTA FM). This comparison is critical since the focus of interest of this study is on the analysis of the flow structure at the level of the pedestrian who is located in the direct closeness to the ground (z/H1 = z/D = 0.01), whereas the measurement of the shear stresses allows for a better verification of the calculation methodology and helps evaluate the reliability of the flow structure modelling. The qualitative evaluation of the level of stress around the object is also facilitated by oil visualization that allows for detection of the areas of stagnation and areas that are characterized by elevated speed of the medium near the base. This information results from the direct relation of the shape of the surface current lines with the presence of circular movements that occur in different areas, including the horseshoe vortex that is formed around the obstacles and the phenomenon of detachment and adherence of the flow to the ground. In the areas where the

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surface stresses and velocity are close to zero, the thicker layer of oil mixture is formed, whereas in the location of high velocity, the oil mixture is washed out.

CONCLUSIONS This article evaluated the effect of the method to model inlet conditions and turbulence model on the accuracy of numerical modelling of the structure of the flow around the objects. No significant differences resulting from the method of inlet conditions modelling were found in the aerodynamic wake for the system of objects (see also [1520]). Since it was necessary to model inflow conditions, especially the distribution of velocity fluctuation in the space before the object, further analysis was based on the methodology of modelling of the inflow layer by means of the initial calculations conducted over the surface with rough elements. Numerical analysis using the RSM turbulence model, which takes into account the anisotropy of velocity fluctuations, should lead to the more accurate mapping of the flow structure than calculations using the k- model in RNG version especially in the stagnation region where the assumption of isotropic turbulence is not right. For flow in the close vicinity to the ground, which is important for the wind comfort, the better efficiency representation of experimental result was obtained for the model k- RNG.

ACKNOWLEDGMENTS The work was partially supported by National Science Centre, Poland (Narodowe Centrum Nauki) under grant number NCN 2017/01/X/ST8/00076.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

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