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Large-eddy simulation of flow turbulence in clarification systems

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Abstract

Prediction of turbulent flow is required for design and assessment of clarifier systems that have been implemented throughout history to treat water in the urban water cycle through physical clarification. Yet, turbulent flow modeling is a relatively new tool that has not existed until the last half-century and can be, and often is, a tenuous component in a computational fluid dynamics simulation of unit operations and processes. Common Reynolds-averaged Navier–Stokes equation (RANS) approaches can be inadequate to obtain consistent and accurate flow solutions. In contrast, this study presents an application of large-eddy simulations (LES) for a clarification system with a high-order spectral element method employing 48 million degrees of freedom. Turbulent and unsteady flow characteristics are investigated, and statistics are examined for such a system. Simulation results are compared with laser Doppler anemometry measurements for mean flow velocity, turbulence kinetic energy, and Reynolds shear stress. LES results agree well with measurements, and the differences between LES and measurements are generally less than the reported measurement error. LES results capture the transition behavior from a jet-like flow at the near-inlet region to an open-channel flow at the downstream end of the system. Furthermore, LES results reveal that the widely adopted log-law of a classical turbulent boundary layer is not established in the system even at the most downstream location. Preliminary examination of commonly used RANS models identifies the challenges in application of RANS to such systems. The results from this study provide a benchmark for turbulence modeling of common water clarification systems.

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References

  1. Achari, A.M., Das, M.K.: Application of various RANS based models towards predicting turbulent slot jet impingement. Int. J. Therm. Sci. 98, 332–351 (2015). https://doi.org/10.1016/j.ijthermalsci.2015.07.018

    Article  Google Scholar 

  2. Adams, E.W., Rodi, W.: Modeling flow and mixing in sedimentation tanks. J. Hydraul. Eng. 116(7), 895–913 (1990). https://doi.org/10.1061/(ASCE)0733-9429(1990)116:7(895)

    Article  Google Scholar 

  3. Ahlman, D., Brethouwer, G., Johansson, A.V.: Direct numerical simulation of a plane turbulent wall-jet including scalar mixing. Phys. Fluids 19(6), 065102 (2007). https://doi.org/10.1063/1.2732460

    Article  MATH  Google Scholar 

  4. AlSammarraee, M., Chan, A.: Large-eddy simulations of particle sedimentation in a longitudinal sedimentation basin of a water treatment plant. Part 2: the effects of baffles. Chem. Eng. J. 152(2–3), 315–321 (2009). https://doi.org/10.1016/j.cej.2009.01.052

  5. Al-Sammarraee, M., Chan, A., Salim, S.M., Mahabaleswar, U.S.: Large-eddy simulations of particle sedimentation in a longitudinal sedimentation basin of a water treatment plant. Part I: particle settling performance. Chem. Eng. J. 152(2–3), 307–314 (2009). https://doi.org/10.1016/j.cej.2009.04.062

  6. Aref, H., Balachandar, S.: A First Course in Computational Fluid Dynamics. Cambridge University Press, Cambridge (2018). https://doi.org/10.1017/9781316823736

  7. Asgharzadeh, H., Firoozabadi, B., Afshin, H.: Experimental investigation of effects of baffle configurations on the performance of a secondary sedimentation tank. Sci. Iran. 18(4B), 938–949 (2011). https://doi.org/10.1016/j.scient.2011.07.005

    Article  Google Scholar 

  8. Bardina, J.E., Huang, P.G., Coakley, T.J.: Turbulence modeling validation. In: 28th Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics Inc, AIAA (1997). https://doi.org/10.2514/6.1997-2121

  9. Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2000). https://doi.org/10.1017/CBO9780511800955

  10. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid dynamics. Springer, Berlin (1988). https://doi.org/10.1007/978-3-642-84108-8

  11. Chakraborty, P., Balachandar, S., Adrian, R.J.: On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214 (2005). https://doi.org/10.1017/S0022112005004726

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, H.C., Patel, V.C.: Near-wall turbulence models for complex flows including separation. AIAA J. 26(6), 641–648 (1988). https://doi.org/10.2514/3.9948

    Article  Google Scholar 

  13. Craft, T.J., Iacovides, H., Yoon, J.H.: Progress in the use of non-linear two-equation models in the computation of convective heat-transfer in impinging and separated flows. Flow Turbul. Combust. 63(1), 59–80 (2000). https://doi.org/10.1023/A:1009973923473

    Article  MATH  Google Scholar 

  14. Eaton, J.K.: Turbulent flow reattachment: an experimental study of the flow and structure behind a backward-facing step. Stanford University Report, pp. MD-39 (1980)

  15. Fischer, P., Mullen, J.: Stabilisation par filtrage pour la méthode des éléments spectraux. Comptes Rendus de l’Academie des Sciences-Series I: Mathematics (2001). https://doi.org/10.1016/S0764-4442(00)01763-8

    Article  Google Scholar 

  16. Fischer, P.F.: An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations. J. Comput. Phys. 133(1), 84–101 (1997). https://doi.org/10.1006/jcph.1997.5651

    Article  MathSciNet  MATH  Google Scholar 

  17. Fornari, W., Zade, S., Brandt, L., Picano, F.: Settling of finite-size particles in turbulence at different volume fractions. Acta Mech. 230(2), 413–430 (2019). https://doi.org/10.1007/s00707-018-2269-1

    Article  MathSciNet  Google Scholar 

  18. Fröhlich, J., Mellen, C.P., Rodi, W., Temmerman, L., Leschziner, M.A.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005). https://doi.org/10.1017/S0022112004002812

    Article  MathSciNet  MATH  Google Scholar 

  19. Gao, H., Stenstrom, M.K.: Evaluation of three turbulence models in predicting the steady state hydrodynamics of a secondary sedimentation tank. Water Res. (2018). https://doi.org/10.1016/j.watres.2018.06.067

    Article  Google Scholar 

  20. Garofalo, G., Sansalone, J.J.: Transient elution of particulate matter from hydrodynamic unit operations as a function of computational parameters and runoff hydrograph unsteadiness. Chem. Eng. J. 175(1), 150–159 (2011). https://doi.org/10.1016/j.cej.2011.09.086

    Article  Google Scholar 

  21. Garofalo, G., Sansalone, J.J.: Urban drainage clarifier load-response as a function of flow, unsteadiness, and baffling. J. Environ. Eng. 144(3), 04017108 (2018). https://doi.org/10.1061/(ASCE)EE.1943-7870.0001283

    Article  Google Scholar 

  22. Goodarzi, D., Lari, K.S., Alighardashi, A.: A large eddy simulation study to assess low-speed wind and baffle orientation effects in a water treatment sedimentation basin. Water Sci. Technol. 2017(2), 412–421 (2017). https://doi.org/10.2166/wst.2018.171

    Article  Google Scholar 

  23. Hinterberger, C., Fröhlich, J., Rodi, W.: 2D and 3D turbulent fluctuations in open channel flow with Re \(\tau \) = 590 studied by large eddy simulation. Flow Turbul. Combust. 80(2), 225–253 (2008). https://doi.org/10.1007/s10494-007-9122-2

    Article  MATH  Google Scholar 

  24. Hussain, A.K.M.F., Reynolds, W.C.: The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41(2), 241–258 (1970). https://doi.org/10.1017/S0022112070000605

    Article  Google Scholar 

  25. Imam, E., McCorquodale, J.A.: Simulation of flow in rectangular clarifiers. J. Environ. Eng. 109(3), 713–730 (1983). https://doi.org/10.1061/(ASCE)0733-9372(1983)109:3(713)

    Article  Google Scholar 

  26. Imam, E., McCorquodale, J.A., Bewtra, J.K.: Numerical modeling of sedimentation tanks. J. Hydraul. Eng. 109(12), 1740–1754 (1983). https://doi.org/10.1061/(ASCE)0733-9429(1983)109:12(1740)

    Article  Google Scholar 

  27. Jamshidnia, H., Firoozabadi, B.: Experimental investigation of baffle effect on the flow in a rectangular primary sedimentation tank. Sci. Iran. 17(4) (2010)

  28. Jaramillo, J.E., Pérez-Segarra, C.D., Rodriguez, I., Oliva, A.: Numerical study of plane and round impinging jets using RANS models. Numer. Heat Transf. Part B Fund. 54(3), 213–237 (2008). https://doi.org/10.1080/10407790802289938

    Article  Google Scholar 

  29. Kaltenbach, H.J., Janke, G.: Direct numerical simulation of flow separation behind a swept, rearward-facing step at Re(H) = 3000. Phys. Fluids 12(9), 2320–2337 (2000). https://doi.org/10.1063/1.1287338

    Article  MATH  Google Scholar 

  30. Karpinska, A.M., Bridgeman, J.: CFD-aided modelling of activated sludge systems–a critical review. Water Res. 88, 861–879 (2016). https://doi.org/10.1016/j.watres.2015.11.008

    Article  Google Scholar 

  31. Kim, D., Kim, D.I., Kim, J.H., Stoesser, T.: Large eddy simulation of flow and tracer transport in multichamber ozone contactors. J. Environ. Eng. 136(1), 22–31 (2010). https://doi.org/10.1061/(ASCE)EE.1943-7870.0000118

    Article  Google Scholar 

  32. Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low reynolds number. J. Fluid Mech. 177, 133–166 (1987). https://doi.org/10.1017/S0022112087000892

    Article  MATH  Google Scholar 

  33. Kolmogorov, A.N.: Dissipation of energy in the locally isotropic turbulence. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 434(1890), 15–17 (1991). https://doi.org/10.1098/rspa.1991.0076

  34. Komminaho, J., Skote, M.: Reynolds stress budgets in Couette and boundary layer flows. Flow Turbul. Combust. 68(2), 167–192 (2002). https://doi.org/10.1023/A:1020404706293

    Article  MATH  Google Scholar 

  35. Launder, B., Spalding, D.: The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3(2), 269–289 (1974). https://doi.org/10.1016/0045-7825(74)90029-2

    Article  MATH  Google Scholar 

  36. Le, H., Moin, P., Kim, J.: Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374 (1997). https://doi.org/10.1017/S0022112096003941

    Article  MATH  Google Scholar 

  37. Li, H., Sansalone, J.J.: CFD as a complementary tool to benchmark physical testing of PM separation by unit operations. J. Environ. Eng. 146(11), 04020122 (2020). https://doi.org/10.1061/(ASCE)EE.1943-7870.0001803

    Article  Google Scholar 

  38. Li, H., Sansalone, J.J.: CFD model of PM sedimentation and resuspension in urban water clarification. J. Environ. Eng. 146(3), 04019118 (2020). https://doi.org/10.1061/(ASCE)EE.1943-7870.0001649

    Article  Google Scholar 

  39. Li, H., Sansalone, J.J.: Multi-scale physical model simulation of particle filtration using computational fluid dynamics. J. Environ. Manag. 271, 111021 (2020). https://doi.org/10.1016/j.jenvman.2020.111021

    Article  Google Scholar 

  40. Liu, B., Ma, J., Luo, L., Bai, Y., Wang, S., Zhang, J.: Two-dimensional LDV measurement, modeling, and optimal design of rectangular primary settling tanks. J. Environ. Eng. 136(5), 501–507 (2010). https://doi.org/10.1061/(ASCE)EE.1943-7870.0000186

    Article  Google Scholar 

  41. Liu, K., Lakhote, M., Balachandar, S.: Self-induced temperature correction for inter-phase heat transfer in Euler-Lagrange point-particle simulation. J. Comput. Phys. 396, 596–615 (2019). https://doi.org/10.1016/j.jcp.2019.06.069

    Article  MathSciNet  MATH  Google Scholar 

  42. Liu, K., Zgheib, N., Balachandar, S.: On the spreading of non-canonical thermals from direct numerical simulations. Phys. Fluids 32(2), 026602 (2020). https://doi.org/10.1063/1.5138981

    Article  Google Scholar 

  43. Liu, X., García, M.H.: Three-dimensional numerical model with free water surface and mesh deformation for local sediment scour. J. Waterw. Port Coast. Ocean Eng. 134(4), 203–217 (2008). https://doi.org/10.1061/(asce)0733-950x(2008)134:4(203)

    Article  Google Scholar 

  44. Liu, X., García, M.H.: Computational fluid dynamics modeling for the design of large primary settling tanks. J. Hydraul. Eng. 137(3), 343–355 (2011). https://doi.org/10.1061/(ASCE)HY.1943-7900.0000313

    Article  Google Scholar 

  45. Liu, X., Zhang, J.: Computational fluid dynamics: applications in water, wastewater, and stormwater treatment: EWRI computational fluid dynamics task committee. American Society of Civil Engineers (2019). https://books.google.com/books?id=cwDBwgEACAAJ

  46. Lyn, D.A., Einav, S., Rodi, W., Park, J.H.: A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder. J. Fluid Mech. 304, 285–319 (1995). https://doi.org/10.1017/S0022112095004435

    Article  Google Scholar 

  47. Lyn, D.A., Rodi, W.: Turbulence measurements in model settling tank. J. Hydraul. Eng. 116(1), 3–21 (1990). https://doi.org/10.1061/(ASCE)0733-9429(1990)116:1(3)

    Article  Google Scholar 

  48. Marchioli, C.: Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches. Acta Mech. 228(3), 741–771 (2017). https://doi.org/10.1007/s00707-017-1803-x

    Article  Google Scholar 

  49. Menter, F.R., Kuntz, M., Langtry, R.: Ten years of industrial experience with the SST turbulence model. Turbul. Heat Mass Transf. 4(1), 625–632 (2003)

    Google Scholar 

  50. Naqavi, I.Z., Tyacke, J.C., Tucker, P.G.: Direct numerical simulation of a wall jet: flow physics. J. Fluid Mech. 852, 507–542 (2018). https://doi.org/10.1017/jfm.2018.503

    Article  MathSciNet  MATH  Google Scholar 

  51. Ouro, P., Fraga, B., Viti, N., Angeloudis, A., Stoesser, T., Gualtieri, C.: Instantaneous transport of a passive scalar in a turbulent separated flow. Environ. Fluid Mech. 18(2), 487–513 (2018). https://doi.org/10.1007/s10652-017-9567-3

    Article  Google Scholar 

  52. Peng, L., Nielsen, P.V., Wang, X., Sadrizadeh, S., Liu, L., Li, Y.: Possible user-dependent CFD predictions of transitional flow in building ventilation. Build. Environ. 99, 130–141 (2016). https://doi.org/10.1016/j.buildenv.2016.01.014

    Article  Google Scholar 

  53. Pereira, J.C., SchöNung, B.: Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 473–496 (1983). https://doi.org/10.1017/S0022112083002839

    Article  Google Scholar 

  54. Pont-Vílchez, A., Trias, F.X., Gorobets, A., Oliva, A.: Direct numerical simulation of backward-facing step flow at Re \(\tau \) = 395 and expansion ratio 2. J. Fluid Mech. 863, 341–363 (2019). https://doi.org/10.1017/jfm.2018.1000

    Article  MathSciNet  MATH  Google Scholar 

  55. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000). https://doi.org/10.1017/CBO9780511840531

  56. Razmi, A., Bakhtyar, R., Firoozabadi, B., Barry, D.: Experiments and numerical modeling of baffle configuration effects on the performance of sedimentation tanks. Can. J. Civ. Eng. 40(2), 140–150 (2013). https://doi.org/10.1139/cjce-2012-0176

    Article  Google Scholar 

  57. Rodi, W.: Comparison of LES and RANS calculations of the flow around bluff bodies. J. Wind Eng. Ind. Aerodyn. 69–71, 55–75 (1997). https://doi.org/10.1016/S0167-6105(97)00147-5

    Article  Google Scholar 

  58. Rodi, W., Ferziger, J.H., Breuer, M., Pourquié, M.: Status of large eddy simulation: results of a workshop. J. Fluids Eng. Trans. ASME 119(2), 248–262 (1997). https://doi.org/10.1115/1.2819128

    Article  MATH  Google Scholar 

  59. Saeedi, E., Behnamtalab, E., Salehi Neyshabouri, S.A.A.: Numerical simulation of baffle effect on the performance of sedimentation basin. Water Environ. J. (2018). https://doi.org/10.1111/wej.12454

  60. Salinas, J., Balachandar, S., Shringarpure, M., Fedele, J., Hoyal, D., Cantero, M.: Soft transition between subcritical and supercritical currents through intermittent cascading interfacial instabilities. Proc. Natl. Acad. Sci. (2020). https://doi.org/10.1073/PNAS.2008959117

    Article  Google Scholar 

  61. Schäfer, F., Breuer, M., Durst, F.: The dynamics of the transitional flow over a backward-facing step. J. Fluid Mech. 623, 85–119 (2009). https://doi.org/10.1017/S0022112008005235

    Article  MATH  Google Scholar 

  62. Schlatter, P., Stolz, S., Kleiser, L.: LES of transitional flows using the approximate deconvolution model. Int. J. Heat Fluid Flow 25(3), 549–558 (2004). https://doi.org/10.1016/j.ijheatfluidflow.2004.02.020

    Article  Google Scholar 

  63. Stamou, A.I.: On the prediction of flow and mixing in settling tanks using a curvature-modified k-\(\epsilon \) model. Appl. Math. Model. (1991). https://doi.org/10.1016/0307-904X(91)90060-3

    Article  MATH  Google Scholar 

  64. Stamou, A.I., Adams, E.W., Rodi, W.: Numerical modeling of flow and settling in primary rectangular clarifiers. J. Hydraul. Res. 27(5), 665–682 (1989). https://doi.org/10.1080/00221688909499117

    Article  Google Scholar 

  65. Stolz, S., Adams, N.A.: An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11(7), 1699–1701 (1999). https://doi.org/10.1063/1.869867

    Article  MATH  Google Scholar 

  66. Tamayol, A., Firoozabadi, B., Ahmadi, G.: Effects of inlet position and baffle configuration on hydraulic performance of primary settling tanks. J. Hydraul. Eng. 134(7), 1004–1009 (2008). https://doi.org/10.1061/(ASCE)0733-9429(2008)134:7(1004)

    Article  Google Scholar 

  67. Taylor, G.I.: The spectrum of turbulence. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 164(919), 476–490 (1938). https://doi.org/10.1098/rspa.1938.0032

  68. Tsukahara, T., Seki, Y., Kawamura, H., Tochio, D.: DNS of turbulent channel flow at very low Reynolds numbers. In: TSFP Digital Library Online. Begel House Inc. (2005)

  69. Wang, H., Falconer, R.: Simulating disinfection processes in chlorine contact tanks using various turbulence models and high-order accurate difference schemes. Water Res. 32(5), 1529–1543 (1998). https://doi.org/10.1016/S0043-1354(98)80014-6

    Article  Google Scholar 

  70. Wilcox, D.C.: Turbulence Modeling for CFD, 3rd edn. DCW Industries (2006)

  71. Wolfshtein, M.: The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. Int. J. Heat Mass Transf. 12(3), 301–318 (1969). https://doi.org/10.1016/0017-9310(69)90012-X

    Article  Google Scholar 

  72. Wu, X.: Inflow turbulence generation methods. Annu. Rev. Fluid Mech. 49(1), 23–49 (2017). https://doi.org/10.1146/annurev-fluid-010816-060322

    Article  MathSciNet  MATH  Google Scholar 

  73. Yildiz, M.A., Yuan, H., Merzari, E., Hassan, Y.: Numerical simulation of isothermal flow across slant five-tube bundle with spectral element method code Nek5000. Nucl. Technol. 206(2), 296–306 (2020). https://doi.org/10.1080/00295450.2019.1626176

    Article  Google Scholar 

  74. Zhang, J., Tejada-Martínez, A.E., Zhang, Q.: Developments in computational fluid dynamics-based modeling for disinfection technologies over the last two decades: a review (2014). https://doi.org/10.1016/j.envsoft.2014.04.003

    Article  Google Scholar 

  75. Zhang, J., Tejada-Martínez, A.E., Zhang, Q., Lei, H.: Evaluating hydraulic and disinfection efficiencies of a full-scale ozone contactor using a RANS-based modeling framework. Water Res. 52, 155–167 (2014). https://doi.org/10.1016/J.WATRES.2013.12.037

    Article  Google Scholar 

  76. Zhiyin, Y.: Large-eddy simulation: past, present and the future (2015). https://doi.org/10.1016/j.cja.2014.12.007

  77. Zhou, J., Adrian, R.J., Balachandar, S., Kendall, T.M.: Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396 (1999). https://doi.org/10.1017/S002211209900467X

    Article  MathSciNet  MATH  Google Scholar 

  78. Zhou, S., McCorquodale, J.A.: Modeling of rectangular settling tanks. J. Hydraul. Eng. 118(10), 1391–1405 (1992). https://doi.org/10.1061/(ASCE)0733-9429(1992)118:10(1391)

    Article  Google Scholar 

  79. Zwick, D., Balachandar, S.: A scalable Euler-Lagrange approach for multiphase flow simulation on spectral elements. Int. J. High Perform. Comput. Appl. 34(3), 316–339 (2020). https://doi.org/10.1177/1094342019867756

    Article  Google Scholar 

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Li, H., Balachandar, S. & Sansalone, J. Large-eddy simulation of flow turbulence in clarification systems. Acta Mech 232, 1389–1412 (2021). https://doi.org/10.1007/s00707-020-02914-1

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