Keywords: Mean pressure; Fluctuating pressure; Shear Stress Transport (SST) model; Full scale data; TTU building.

Transcription

1 EACWE 5 Florence, Italy 19 th 3 rd July 9 Flying Sphere image Museo Ideale L. Da Vinci CFD modeling of wind induced mean and fluctuating eternal pressure coefficients on the Teas Technical University building 1 st T.K.Guha, nd R.N.Sharma, 3 rd P.J.Richards 1 st Ph.D. Candidate - tguh1@aucklanduni.ac.nz - Department of Mechanical Engineering nd Senior Lecturer - r.sharma@auckland.ac.nz - Department of Mechanical Engineering 3 rd Associate Professor - p.richards@auckland.ac.nz - Department of Mechanical Engineering The University of Auckland, Private Bag 919, Auckland, New Zealand Keywords: Mean pressure; Fluctuating pressure; Shear Stress Transport (SST) model; Full scale data; TTU building. ABSTRACT This par considers the possibility of predicting both eternal mean and fluctuating wind pressures on buildings by using a finite volume based CFD method in conunction with an advanced k- ω based two equation turbulence model called Shear Stress Transport (SST) model. The building studied in this case is the low rise Teas Technical University (TTU) building located at Lubbock, Teas, USA. Results from the computer model are compared with the results obtained for the same building configuration using standard k-ε model, RNG k-ε model and full scale data. The Kato-Launder (KL) modification was incorporated in all turbulence models for the production limiter. The SST model gives improved rformance in terms of predicting the windward edge roof top separation and reattachment compared to other models. The fluctuating rms pressure coefficients were calculated using the equations proposed by Paterson and Holmes, Selvam and Richards and Wanigaratne. While all the three equations under predict the windward wall centre-line fluctuating pressure coefficients, the equation proposed by Richards and Wanigaratne provides conservative results in the centre-line leeward and roof top reattachment planes in comparison to full scale data. Contact rson: 1 st T.K.Guha, Department of Mechanical Engineering, The University of Auckland, Private Bag 919, Auckland, New Zealand, Tel.: , fa: , tguh1@aucklanduni.ac.nz

2 1. INTRODUCTION The United States National Science Foundation sponsored Colorado State University/Teas Technical University Coorative Program on Wind Engineering provided valuable insights into wind effects on Teas Tech University (TTU) erimental building, a typical eample of a low rise structure. The study involved field tests on the high plains of Lubbock, Teas and 1:1 scale model studies in the Meteorological Wind Tunnel (MWT) at Colorado State University [Yeatts & Mehta (1993)]. Since then a number of wind tunnel simulations and numerical studies have been conducted on the flow around the TTU building using different turbulence models by researchers with TTU field data as benchmark. Selvam (199, 1996 and 1997) computed pressures around the TTU building using standard k-ε, Kato-Launder k-ε and Large Eddy Simulation (LES) turbulence models. While the computed pressure coefficients and velocity field were in good agreement over the centre plane of the building for both standard k- ε and Kato-Launder k- ε models, the computed turbulence kinetic energy from standard k- ε model were much higher than the Kato-Launder k- ε model on the windward side of the building. The standard k- ε model led to higher values of turbulence eddy viscosities in the stagnation point region thereby preventing roof top separation of flow at leading windward edge of the building roof. The LES model on the other hand predicted mean pressures in good agreement with the field data. Three different techniques were used to generate inflow turbulent velocity fluctuations, namely 1) by means of random number generation with riodic lateral boundary conditions ) by means of Gaussian distribution using random numbers with inflow and outflow lateral boundary condition and 3) turbulence generated using measured field data with inflow and outflow lateral boundary condition. However, ak pressures resulting from these approaches were not in good agreement with full scale data, with the latter of the three ak pressure sets being closest to full scale. He & Song (199 and 1997) used LES to compute the pressures on a cube without using inflow turbulence and with on boundary conditions. Simulation of roof corner delta wing vortices of TTU building using LES showed poor agreement of the fluctuating pressures due to inclusion of only resolvable part due to large scale eddies of size comparable to the local mesh dimensions. Refining the mesh in the region of interest (roof corners) resulted in better agreement of computed and measured rms values. Mochida et al. (1993) used turbulence generated for a channel flow with riodic boundary conditions as inflow while other boundaries as outflow or on for simulating the flow field around TTU building using LES. Bekele and Hangan () questioned the ustification of using LES for practical wind engineering applications citing that the significantly higher computing resources required for LES should be ustified by showing the inadequacy of RANS turbulence models to handle particular ascts of the flow field around sharp edged bluff bodies. They used a second order moment closure Reynolds Stress Model (RSM) which simulated the phase averaged fluctuating pressures and by combining it with modeling of the small scale random pressure field, they produced total instantaneous pressures. While the model predicted the pressure field on the roof of TTU slightly better than the wind tunnel data, there were significant deviations from erimental data in the impingement and wake regions. The RSM model also posed significant limitations in the roof corner region associated with the highly comple and turbulent delta wing vortices. Of late Senthooran et al. (4) had proposed a computational approach to predict the flow induced pressure fluctuations based on a stochastic model to generate plausible velocity fluctuations (synthetic turbulence) that satisfy the mean turbulent quantities. The mean flow quantities were however solved by employing the standard k-ε and Kato-Launder k-ε turbulence models to the discretized Navier Stokes equation. The fluctuating pressure field was obtained by solving the Poisson equation. The computed rms values showed good agreement with the erimental results. This par scifies the computational work done using commercial computational fluid dynamics package CFX to simulate the flow field around TTU using standard k-ε model, RNG k-ε model and an advanced k-ω based two equation turbulence model called the Shear Stress Transport (SST) model develod by Menter (1994). The main reason for using the SST turbulence model lies in the limitation of standard two equation turbulence models to accurately predict the onset and etent of flow separation under adverse pressure gradient conditions. The SST model is designed to overcome

3 these limitations by inclusion of transport effects into the formulation of eddy-viscosity [Ansys CFX help manual (7)] and can be used with success for boundary layer simulations. The SST model is a zonal k-ω model identical to k-ε model in the free shear region and includes a blending function as a function of wall distance to enable smooth transition to wall functions or low-re near wall k-ω formulation based on mesh refinement. This provides maor advantages allowing automatic switch from wall-functions to a low-re near wall k-ω formulation as the mesh is refined. In the present work, angle of attack corresponding to wind flowing rndicular to the shorter wall containing the door has been investigated. The results from numerical computation are compared with the full scale data considering the average of all measured data within ± 1 degree of the intended angle of attack. While all the turbulence models are found to predict the windward wall mean pressure coefficients fairly accurately, the SST model is found to most accurately predict the leading edge roof separation bubble and reattachment and hence mean roof pressure coefficients. The leeward wall pressure coefficients are found to be sensitive to mesh variations with all the models under predicting mean pressure coefficients. The fluctuating rms pressure coefficients calculated using the equations proposed by Paterson & Holmes (1989), Selvam (199) and Richards & Wanigaratne (1993) show that while all the three equations under-predict the windward wall fluctuating pressure coefficients, the equation proposed by Richards & Wanigaratne (1993) provides conservative results in the leeward and roof top reattachment zone in comparison to full scale data.. MATHEMATICAL FORMULATION OF THE SST MODEL The SST model takes the advantage of robustness and accuracy of k-ω model in the near wall region and the free stream indendence of k-ε model in the outer part of boundary layer. To achieve this, k-ε model is transformed into a k-ω formulation. The original k-ω model is multiplied by a blending function F 1 and the transformed k-ε model is multiplied by (1- F 1 ), and both added together. The function F 1 is designed to be one in the near wall region and zero away from the surface. A modification to the eddy viscosity is introduced to account for the importance of the transport of the principal turbulent shear stress in the prediction of adverse pressure gradient flows. The transport equations of k and ω in tensor notation [Menter (1994)] take the following form resctively as: u ρ k * i = τ i D Dt Dρω γ = Dt ν t τ i β u i ρωk + βρ ω ( μ + ) + σ k μ t k ( μ + ) σ ω μ t ω + ( 1 F ) 1 σ 1 k ρ ω ω The last term on the right hand side of equation () is an additional cross diffusion term besides the original terms in the transport equation of ω in k-ω model. If φ 1 represents any constant in the original k-ω model and φ represents any constant in the transformed k-ε model, then φ, the corresponding constant in the SST model can be written as: ϕ = F ϕ + ( 1 1 F 1)ϕ (3) 1 The constants of φ 1, φ and the denominations of symbols used in equations (1) and () along with relevant details of SST model have been defined in Menter (1994). ω (1) ()

4 3. COMPUTER MODELLING The CAD model was develod in Ansys Design Modeller (Version 11., 7). The unstructured tetrahedral mesh systems were generated using the Ansys Mesh program in Ansys Workbench. The computational modeling of wind load and associated flow pattern were rformed using commercial computational fluid dynamics package Ansys CFX (Version 11., 7). 3.1 Modelling of the Atmospheric Boundary Layer (ABL) in CFX The modeling of atmospheric boundary layer in CFX is based on scifying appropriate inlet and wall boundary conditions. The inlet boundary conditions were scified based on recommendations by Richards & Hoey (1993). Equations 4 through 6 were used to define the inlet boundary conditions in terms of stream wise velocity (u) component, turbulent kinetic energy (k) and turbulent eddy dissipation (ε) such that the desired logarithmic velocity profile entered the fluid domain. u * z u = ln + 1 (4) K u C * z k = (5) μ 3 u* ( z + z ) ε = (6) K where K =.4 is the Von Karman s constant, u * is the wall friction velocity, = height above the ground, z = roughness height which dends on the prevailing terrain condition and C μ =.9 a constant. In the present work, average aerodynamic roughness length (z ) used in the CFD analysis was 17 mm (Jensen Number = 4), consistent with the average TTU site data as reported by Levitan et al. (1991). The ground was treated as a rough wall boundary using sand grain roughness. The equivalent sand grain roughness (k s ABL ) corresponding to an aerodynamic roughness length of z = 17 mm was obtained by first order matching of the ABL velocity profile and wall function velocity profile in the centre point of the wall adacent cell as r Blocken et al. (7) as: z (.17). m k = 9.6 = 9.6 = 477 (7) sabl Care was taken during meshing to put the first element node adacent to the wall outside k s ABL (=.477 m) as suggested by Ansys CFX (Version 11., 7). This combination of inlet condition and the rough wall boundary condition resulted in an equilibrium boundary layer which in the absence of the building gave outlet conditions almost identical to that at the inlet. Figures 1 (a) and (b) show the characteristics of the approach flow through the empty computational domain. The rms velocity of approach flow (u rms ) was estimated as the square root of turbulence kinetic energy i.e. u rms k and thus embodies some information of the turbulent state of flow. While the velocity profiles at all the three positions namely inlet, outlet and centre of the domain show fairly good agreement as in figure 1 (a), the computed turbulent intensities values are, however, slightly lower [figure 1 (b)] than what is reported in the field data and are possibly associated with the choice of C μ =.9 and K =.4, the implications of which are eplained in Richards & Hoey (1993).

5 Figure 1: (a) Approach flow stream-wise velocity profiles and (b) Approach flow stream- wise turbulence intensity profiles through empty CFD domain 3. Computational Modelling of the Eternal Flow field around a full scale building in Atmospheric Boundary Layer The Teas Technical University full scale test building is located at the Wind Engineering Research Field Laboratory (WERFL) in the high planes of Lubbock, Teas, USA. The terrain surrounding the site is flat and on, with the intermediate encircling land being primarily used for agriculture. Strong winds are common to the area year round. The TTU building is a full scale rotatable prefabricated metal building with average dimensions of m long by 9. m wide and 3.91 m high and contains a door of dimensions.13 m high by.91 m wide on one small wall and a.86 m square window on the other. The building roof has a slo of 1 degree. The building can be rotated on a turn table allowing the azimuth of the wind to be controlled [Yeatts & Mehta (1993)]. The TTU building was modeled as a rectangular block placed inside the bigger rectangular domain of dimensions 3 H (i.e. building height) stream wise, 3 H transverse and 1 H high. The domain was meshed using three different unstructured mesh formats consisting of tetrahedral cells as shown in Table 1 to study in particular the sensitivity of the solution to different mesh configurations. The TTU building skeleton was removed out of the domain to reduce computational overhead since our interest is limited to the flow around the building. Mesh Setup Mesh Ty Number of Elements Number of Nodes 1 Unstructured Unstructured Unstructured Table 1: Mesh configurations investigated A steady state solution for flow field around the building was obtained for different mesh setups and turbulence models namely SST model, k-ε model and RNG k-ε model for angle of attack for a ridge height velocity of 3 m/s and compared with full scale data. Convergence was considered to be achieved when the maimum residual for each transported quantity was less than 1-4. A high resolution scheme (Version 11., 7) was used to discretize the advection terms. This scheme though nd order accurate is also bounded since it only reduces to first order near discontinuities. Kato- Launder modification was incorporated for the production limiter term for all the turbulence models investigated. The production limiter (P k ) with Kato-Launder modification can be epressed as follows:

6 P = S k ν t Ω (8) where ν t is the turbulent eddy viscosity of the fluid, S is the strain rate scale defined as: S = u u + 1 i (9) i and Ω is the vorticity scale given by: Ω = u u 1 i (1) i where u is the velocity and is the distance. The value of Ω is zero near the stagnation point as the flow is nearly irrotational. Thus, the turbulent energy generation in the vicinity of stagnation point using Kato-Launder modification is reduced to great etent and improves the results compared to standard k-ε model [Senthooran et al. (4)]. 4. RESULTS AND DISCUSSIONS 4.1 Mean Pressure Coefficients The computed mean eternal pressures ) are represented in terms of mean pressure ( p ) (C referenced to the ridge height dynamic pressure (q) as: p p C = = (11) q 1 ρ uh where u h is the mean ridge height velocity of flow. Figures (a), (b) and (c) show the centre-line mean windward, roof and leeward pressure coefficients resctively for mesh setup 1(see Table 1) for different turbulence models in comparison with full scale data. As can be seen from the plots, while the windward mean pressure coefficients are predicted fairly accurately by all the models for the given mesh configuration, the high mean suction pressures on the windward roof centre-line due to separation bubble at the leading edge is best predicted by the SST turbulence model. The k-ε based models over-predict the rooftop suction pressure due to ecessive production of turbulent kinetic energy resulting in little or no roof top separation. However, they produce conservative results form a designer s point of view. The leeward wall pressure coefficients are significantly under-predicted by all models irresctive of the mesh density.

7 Figure : (a) Windward wall (b) Roof and (c) Leeward wall centre-line mean pressure coefficient for mesh setup 1 A systematic mesh sensitivity study was carried out using the method outlined in the editorial policy of Journals of Fluids Engineering and used by Celik and Karatekin (1997). Figure 3 (a) shows the sensitivity of roof centre-line pressure coefficients to different mesh configurations and subsequent comparison with full scale data. Richardson etrapolation was used to work out the etrapolated solution using data from the mesh setups investigated. The global average order of accuracy is 3. and oscillatory convergence occurs at 38% of the 391 points on the roof top centre-line. The maimum fine grid convergence inde (GCI) is 16% corresponding to a discretization uncertainty of C =.9. The average relative and etrapolated errors are 1.5% and % resctively. The GCI values are plotted in the form of discretization error bars for mesh setup 3 corresponding to the finest grid in Figure 3 (b). The leeward wall mean pressure coefficients also show some mesh sensitivity, all models however under predict the leeward wall pressure coefficients; the average deviation ( δ C ) being.1. The deviations are more prominent in the lower part of the leeward wall. Figure 3: (a) Roof centre-line pressure coefficients for different mesh setups using SST model in comparison with full scale data and (b) Fine-grid (Mesh setup 3, Table 1) solution of roof centre-line pressure, with discretization error bars (GCI) 4. Fluctuating Pressure Coefficients The fluctuating (rms) pressure coefficients ( ~ C ) are calculated using the equations suggested by Paterson & Holmes (1989), Selvam (199) and Richards & Wanigaratne (1993) since there are no direct equations to solve for rms pressure coefficients in k-ε and k-ω based models or their variants. However, since both the models (and their variants) solve for the transport equation of turbulence

8 kinetic energy (k), the rms pressure coefficients are computed using the following equations suggested by Paterson & Holmes (1989), Selvam (199) and Richards & Wanigaratne (1993) resctively: ~ k C = C u k u (1) h 3 ~ = (13) C ~ C = C E k ( u k k ) h h h u ( + ) ( 1 F ) u σ u E k h F C u + u + k In these equations, C and k are the local mean pressure coefficient and turbulent kinetic energy on the building surface, u and k are the velocity and turbulent kinetic energy in the approach flow at the height of interest; u h and k h are the velocity and turbulent kinetic energy in the approach flow at the building height; σ u k ; E is a constant taken as.5 and F is a correlation factor taken as.64. Equation (14) assumes the azimuthal gradient of mean pressure coefficient ( θ ) to be zero h.5 C along the centre-line plane rndicular to the shorter edge of the building. Figures 4 (a), (b) and (c) give the centre-line fluctuating pressure coefficient ( ~ C ) for the building windward, roof and leeward side resctively for mesh setup 1 calculated using the proposed equations. (14) Figure 4: (a) Windward wall (b) Roof and (c) Leeward wall centre-line fluctuating pressure coefficient for mesh setup 1 While all the three equations under-predict the windward rms pressure coefficients, the equation by Richard & Wanigaratne (1993) gives conservative estimates of rms pressure coefficients in the centre-line roof top re-attachment and leeward wall region. The equation was derived using Bernoulli s equation following the work of Patterson & Holmes (1989) by assuming that the pressure erienced on the building surfaces reflect the condition of mean streamlines originating at height similar to the mean stagnation streamline a short distance upstream of the surfaces,. The equation proposed by Selvam (199) on the other hand is found to produce a better estimate of fluctuating pressures on the roof separation bubble zone of TTU building. However, its applicability to other full scale scenarios is yet to be established. Figures 5 (a), (b) and (c) show the vector plots of the computed flow field along the central longitudinal plane of the TTU building for angle of attack using k-ε model, RNG k-ε model and SST model resctively. While the vector plot using k-ε model barely shows any roof top separation,

9 the predictions are much better using RNG k-ε model. The most accurate flow pattern consisting of roof top separation and consequent re-attachment are, however, achieved using the SST model. In order to achieve a similar distinctive roof top separation using k-ε model or its variants, a very fine mesh around the roof will be required to resolve the fine turbulent structures, as over prediction of turbulent kinetic energy (and hence eddy viscosity) in the windward wall stagnation region tends to cause miing of turbulent structures preventing windward edge roof top separation. The SST model can thus, give more accurate flow predictions for wind flows around bluff bodies like the TTU building using significantly low computational overheads (mesh setup 1) compared to more popular and frequently used k-ε based models. Figure 5: Flow vector along the centreline plane of TTU building using (a) k-ε (b) RNG k-ε and (c) SST model for mesh setup 1. Notice the distinct visibility of windward edge rooftop flow separation in figure 5 (c). 5. CONCLUSIONS The mean and fluctuating eternal wind pressures on the TTU building is successfully simulated using computational fluid dynamics (CFD) in conunction with an advanced two equation based turbulence model called the SST model. Comparisons with standard k-ε and RNG k-ε models show that the SST model gives improved results for the roof top separation and reattachment for the particular angle of attack investigated. However, the leeward wall pressures are slightly under-predicted by all models including the SST model as compared to full scale data and needs further investigation. A systematic mesh sensitivity analysis carried out shows that the etrapolated result compares well with the full scale data with a maimum discretization uncertainty of 16%. The fluctuating (rms) pressure coefficients calculated using the equation proposed by Selvam (199) produces better agreement with full scale data in the windward edge rooftop separation zone but the equation by Richards & Wanigaratne is found to provide conservative, hence better estimates of fluctuating pressures in the centre-line roof top re-attachment and leeward regions. REFERENCES Yeatts B. B., Mehta K. C. (1993). Field eriments for building aerodynamics, Journal of Wind Engineering and Industrial Aerodynamics, vol. 5, Selvam R. P. (199). Computation of Pressures on Teas Tech Building, Journal of Wind Engineering and Industrial Aerodynamics, vol , Selvam R. P. (1996). Computation of flow around Teas Tech building using k-ε and Kato-Launder k-ε turbulence model, Engineering Structures, vol. 18 (11), Selvam R. P. (1997). Computation of pressures on Teas Technical University building using large eddy simulation, Journal of Wind Engineering and Industrial Aerodynamics, vol. 67 & 68, He J., Song Charles C. S. (199). Computation of turbulent shear flow over a surface mounted obstacle, Journal of Engineering Mechanics, ASCE, vol. 118, 8-97.

10 He J., Song Charles C. S. (1997). A numerical study of wind flow around the TTU building and the roof corner vorte, Journal of Wind Engineering and Industrial Aerodynamics, vol. 67 & 68, Mochida A., Murakami S., Shoi M., Ishida Y. (1993). Numerical simulation of flowfield around Teas Tech building by large eddy simulation, Journal of Wind Engineering and Industrial Aerodynamics, vol. 46 & 47, Bekele S. A., Hangan H. (). A comparative investigation of the TTU pressure envelo. Numerical versus laboratory and full scale results, Wind and Structures, vol. 5 (-4), Senthooran S., Dong-Dae Lee, Parameswaran S. (4). A computational model to calculate the flow-induced pressure fluctuations on buildings, Journal of Wind Engineering and Industrial Aerodynamics, vol. 9, Menter F. R. (1994). Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, vol. 3(8), Ansys CFX help manual (7), Ansys CFX-11., ANSYS Inc. Paterson D. A., Holmes J. D. (1989). Computation of Wind Flow Around the Teas Tech Building, Proceedings, Workshop on Industrial Fluid Dynamics, Heat Transfer and Wind Engineering, CSIRO-DBCE, Highett, Victoria, Australia, Richards, P. J., Wanigaratne B. S. (1993). A comparison of computer and wind-tunnel models of turbulence around the Silsoe Structures Building, Journal of Wind Engineering and Industrial Aerodynamics, vol. 46 & 47, ANSYS Design Modeller 11. (7), ANSYS, Inc. Richards P. J., Hoey R. P. (1993). Appropriate boundary conditions for computational wind engineering models using the k-ε turbulence model, Journal of Wind Engineering and Industrial Aerodynamics, vol. 46 & 47, Levitan M. L., Mehta K. C., Vann W. P. (1991). Field measurements of pressures on the Teas Tech Building, Journal of Wind Engineering and Industrial Aerodynamics, vol. 38, Blocken B., Stathopoulos T., Carmeliet J. (7). CFD simulation of atmospheric boundary layer-wall function problems, Atmospheric Environment, vol. 41 (), Celik I., Karatekin O. (1997). Numerical Eriments on Application of Richardson Etrapolation with Nonuniform Grids, ASME Journal of Fluid Engineering, vol. 119,