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Large eddy simulation of dispersion around an isolated cubic building: evaluation of localized dynamic \(k_\mathrm{SGS}\)-equation sub-grid scale model

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Abstract

In the present study, the prediction accuracy of a dynamic one-equation sub-grid scale model for the large eddy simulation of dispersion around an isolated cubic building is investigated. For this purpose, the localized dynamic \(k_\mathrm{SGS} \)-equation model (LDKM) is employed and the results are compared with the available experimental data and two other classic sub-grid scale models, namely, standard Smagorinsky–Lilly model (SSLM) and dynamic Smagorinsky–Lilly model (DSLM). It is shown that the three SGS models give results in good agreement with experiment. However, near the ground level of the leeward wall, dimensionless time-averaged concentration, \(\langle K\rangle \), profile is not quite similar to the experimental data. It is also demonstrated that the LDKM predicts the values of \(\langle K\rangle \) on the roof, leeward and side walls more acceptably than the SSLM and DSLM. Whereas, the streamwise elongation of time-averaged structures of the plume shape is more over-estimated with the LDKM than with the other two SGS models. In terms of numerical difficulty, the LDKM is found to be stable and computationally reasonable. In addition, it does not suffer from a flow dependent constant such as the Smagorinsky coefficient employed in the SSLM model.

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Abbreviations

\(\langle \;\rangle \) :

Time-averaged value

c:

Concentration

\(C_D\) :

Dynamic coefficient in dynamic Smagorinsky–Lilly model

\(C_\mu =0.09\) :

Constant

\(C_s\) :

Smagorinsky model constant

\(C_\tau \) :

Dynamic coefficient in localized dynamic \(k_\mathrm{SGS} \)-equation model

CFL:

Courant–Friedrichs–Lewy number

\(D_m\) :

Molecular diffusion coefficient

\(D_\mathrm{SGS}\) :

Sub-grid scale turbulent diffusivity

\(\overline{c}\) :

Filtered Concentration

I:

Turbulence intensity

\(J_j^\mathrm{SGS}\) :

SGS scalar flux

k:

Turbulence kinetic energy

K:

Dimensionless concentration

\(k_\mathrm{SGS} \) :

Sub-grid scale turbulence kinetic energy

\(L_{ij}\) :

Leonard stress tensor

\(Q_x^C =\langle \overline{u} _i \rangle \langle \overline{c} \rangle \) :

Convective flux in streamwise direction

\(Q_x^T =\langle \overline{{u}'} _i \overline{{c}'} \rangle +J_i^\mathrm{SGS}\) :

Turbulent flux in streamwise direction

\(S_{ij}\) :

Rate of strain tensor

\(Sc_\mathrm{SGS}\) :

Sub-grid scale turbulent Schmidt number

\(t^*=t / T, T={H_b } /U_b\) :

Dimensionless time

\(T_{ij} \) :

Subtest scale stress tensor

\({u}',\;{v}'\) and \({w}'\) :

Velocity fluctuation components

\(u_\tau \) :

Friction velocity

\(U_b =3.3\, \mathrm{m/s}\) :

Velocity at the building height

\(U_e =0.63\, \mathrm{m/s}\) :

Velocity of effluent

\(U_\infty =4.5 \, \mathrm{m/s} \) :

Free stream velocity (mean velocity at \(y=\delta )\)

\(y^+\) :

Dimensionless wall distance

\(y_p^+\) :

\(y^+\) At the first point from the wall

\(\kappa =0.41\) :

Von Karman constant

\(\Delta \) :

Grid filter width

\(\widehat{\Delta }\) :

Test filter width

\(\varepsilon \) :

Turbulence dissipation rate

\(\lambda _{uu-z}\) :

Integral length scale based on streamwise velocity fluctuation in z direction

\(\lambda _{vv-z}\) :

Integral length scale based on normal velocity fluctuation in z direction

\(\lambda _{ww-z}\) :

Integral length scale based on spanwise velocity fluctuation in z direction

\(\lambda _{ww-x}\) :

Integral length scale based on spanwise velocity fluctuation in x direction

\(\upsilon _\mathrm{SGS}\) :

Sub-grid scale eddy viscosity

\(\tau _{ij}\) :

SGS stress tensor

\(\xi =x^A-x^B\) :

Separation distance between points A and B

\('\) :

Fluctuation component

C:

Convective flux

T:

Turbulent flux

rms:

Root-mean-squared

SGS:

Sub-grid scale

test:

Test filter

x :

Streamwise direction

y :

Normal direction

z :

Spanwise direction

\(-\) :

Filtered

\(\widehat{a}\) :

Test filtered

References

  1. Li W-W, Meroney RN (1983) Gas dispersion near a cubical model building. Part I. Mean concentration measurements. J Wind Eng Ind Aerodyn 12:15–33

    Article  Google Scholar 

  2. Tominaga Y, Stathopoulos T (2010) Numerical simulation of dispersion around an isolated cubic building: model evaluation of RANS and LES. Build Environ 45:2231–2239

    Article  Google Scholar 

  3. Meng T, Hibi K (1998) Turbulent measurements of the flow field around a high-rise building. J Wind Eng 76:55–64

    Google Scholar 

  4. Gousseau P, Blocken B, van Heijst GJF (2011) CFD simulation of pollutant dispersion around isolated buildings: on the role of convective and turbulent mass fluxes in the prediction accuracy. J Hazard Mater 194:422–434

    Article  Google Scholar 

  5. Tominaga Y, Stathopoulos T (2009) Numerical simulation of dispersion around an isolated cubic building: comparison of various types of k-\(\varepsilon \) models. Atmos Environ 43:3200–3210

    Article  Google Scholar 

  6. Lateb M, Masson C, Stathopoulos T, Bédard C (2010) Numerical simulation of pollutant dispersion around a building complex. Build Environ 45:1788–1798

    Article  Google Scholar 

  7. Blocken B, Stathopoulos T, Carmeliet J, Hensen J (2011) Application of CFD in building performance simulation for the outdoor environment: an overview. J Build Perform Simul 4:157–184

    Article  Google Scholar 

  8. Blocken B, Stathopoulos T, Saathoff P, Wang X (2008) Numerical evaluation of pollutant dispersion in the built environment: comparisons between models and experiments. J Wind Eng Ind Aerodyn 96:1817–1831

    Article  Google Scholar 

  9. Shao J, Liu J, Zhao J (2012) Evaluation of various non-linear k-\(\varepsilon \) models for predicting wind flow around an isolated high-rise building within the surface boundary layer. Build Environ 57:145–155

    Article  Google Scholar 

  10. Salim SM, Cheah SC, Chan A (2011) Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: comparison between RANS and LES. Build Environ 46:1735–1746

    Article  Google Scholar 

  11. Tominaga Y, Stathopoulos T (2012) CFD modeling of pollution dispersion in building array: evaluation of turbulent scalar flux modeling in RANS model using LES results. J Wind Eng Ind Aerodyn 104–106:484–491

    Article  Google Scholar 

  12. Blocken B, Persoon J (2009) Pedestrian wind comfort around a large football stadium in an urban environment: CFD simulation, validation and application of the new Dutch wind nuisance standard. J Wind Eng Ind Aerodyn 97:255–270

    Article  Google Scholar 

  13. Köse DA, Fauconnier D, Dick E (2011) ILES of flow over low-rise buildings: influence of inflow conditions on the quality of the mean pressure distribution prediction. J Wind Eng Ind Aerodyn 99:1056–1068

    Article  Google Scholar 

  14. Tominaga Y, Stathopoulos T (2007) Turbulent Schmidt numbers for CFD analysis with various types of flowfield. Atmos Environ 41:8091–8099

    Article  Google Scholar 

  15. Bazdidi-Tehrani F, Jadidi M, Khalili H, Karami M (2011) Investigation of effect of sub-grid scale turbulent schmidt number on pollutant dispersion. 22nd International Symposium on Transport Phenomena. Delf, The Netherlands.

  16. Yoshie R, Jiang G, Shirasawa T, Chung J (2011) CFD simulations of gas dispersion around high-rise building in non-isothermal boundary layer. J Wind Eng Ind Aerodyn 99:279–288

    Article  Google Scholar 

  17. Cheng WC, Liu C-H (2011) Large-eddy simulation of turbulent transports in urban street canyons in different thermal stabilities. J Wind Eng Ind Aerodyn 99:434–442

    Article  Google Scholar 

  18. Chavez M, Hajra B, Stathopoulos T, Bahloul A (2011) Near-field pollutant dispersion in the built environment by CFD and wind tunnel simulations. J Wind Eng Ind Aerodyn 99:330–339

    Article  Google Scholar 

  19. Iizuka S, Kondo H (2004) Performance of various sub-grid scale models in large-eddy simulations of turbulent flow over complex terrain. Atmos Environ 38:7083–7091

    Article  Google Scholar 

  20. Huang S, Li QS, Xu S (2007) Numerical evaluation of wind effects on a tall steel building by CFD. J Constr Steel Res 63:612–627

    Google Scholar 

  21. Huang S, Li QS (2010) A new dynamic one-equation subgrid-scale model for large eddy simulations. Int J Numer Method Eng 81:835–865

    Google Scholar 

  22. Gousseau P, Blocken B, van Heijst GJF (2013) Quality assessment of large-eddy simulation of wind flow around a high-rise building: validation and solution verification. Comput Fluids 79:120–133

    Article  Google Scholar 

  23. Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge

  24. Sagaut P (2010) Large eddy simulation for incompressible flows: an introduction. Springer, Berlin

  25. Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York

  26. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91:99–164

    Article  Google Scholar 

  27. Moin P, Kim J (1982) Numerical investigation of turbulent channel flow. J Fluid Mech 118:341–377

    Article  Google Scholar 

  28. Davidson L (2011) Fluid mechanics, turbulent flow and turbulence modeling. Chalmers University of Technology, Goteborg

  29. Germano M, Piomelli U, Moin P, Coboy WH (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3:1769–1775

    Google Scholar 

  30. Lilly D (1992) A proposed modification of the Germano subgrid-scale closure method. Phys Fluids A 4:633–635

    Google Scholar 

  31. Kim W-W, Menon S (1997) Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows. AIAA 1997-210

  32. Tominaga Y, Mochida A, Yoshie R, Kataoka H, Nozu T, Yoshikawa M et al (2008) AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J Wind Eng Ind Aerodyn 96:1749–1761

    Article  Google Scholar 

  33. Davidson L (2009) Large eddy simulations: how to evaluate resolution. Intern J Heat Fluid Flow 30:1016–1025

    Article  Google Scholar 

  34. Davidson L (2011) How to estimate the resolution of an LES of recirculating flow. In: Salvetti MV, Geurts B, Meyers J, Sagaut P (Eds) Quality and reliability of large-eddy simulations II. Springer, Netherlands, p 269–286.

  35. Werner H, Wengle H (1993) Large-eddy simulation of turbulent flow over and around a cube in a plate channel. In: Durst FRF, Launder B, Schmidt F, Schumann U, Whitelaw J, (Eds) Turbulent shear flows. Munich, Germany, p 155–168

  36. Sergent E (2002) Vers une méthodologie de couplage entre la simulation des grandes échelles et LES modèles statistiques. L’Ecole Centrale de Lyon, Lyon

    Google Scholar 

  37. OPENFOAM, the open source CFD tool box, user guide, Version 2.2, 2013, www.openfoam.org

  38. Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson Education Limited, Harlow

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Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Farzad Bazdidi-Tehrani & Mohammad Jadidi

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  1. Farzad Bazdidi-Tehrani
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  2. Mohammad Jadidi
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Correspondence to Farzad Bazdidi-Tehrani.

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Bazdidi-Tehrani, F., Jadidi, M. Large eddy simulation of dispersion around an isolated cubic building: evaluation of localized dynamic \(k_\mathrm{SGS}\)-equation sub-grid scale model. Environ Fluid Mech 14, 565–589 (2014). https://doi.org/10.1007/s10652-013-9316-1

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