Numerical study on turbulent mixed convection in a vertical plane channel using hybrid RANS/LES and LES models

doi:10.1016/j.cjche.2019.04.007

Abstract

Abstract: Two Delayed-Detached Eddy Simulation (DDES) models, and a Large-Eddy Simulation (LES) model are used to investigate the turbulent flows and mixed convection between a hot plate and a cold plate via the software FLUENT. The two DDES models include Production-limited DDES (PL-DDES) and Improved DDES (IDDES) models. The Wall-Adapting Local Eddy-Viscosity (WALE) model is the used LES model. The numerical computations are performed at Reynolds number Re_b=4494 and different Richardson numbers Ri=0.025, 0.048, 0.1. The comparing data is from the Direct Numerical Simulation (DNS) at Re_b=4494 and Ri=0.048. The comparison reveals that the two DDES models have better performance in predicting time-averaged parameters than the WALE model in the aiding flow. The best predicted time-averaged results are obtained by the PL-DDES model in the opposing flow. Furthermore, the results of different Ri obtained by the PL-DDES model agree well with the DNS data.

Key words: Turbulent mixed convection, Hybrid RANS/LES model, PL-DDES model, WALE model, Vertical plane channel

摘要： Two Delayed-Detached Eddy Simulation (DDES) models, and a Large-Eddy Simulation (LES) model are used to investigate the turbulent flows and mixed convection between a hot plate and a cold plate via the software FLUENT. The two DDES models include Production-limited DDES (PL-DDES) and Improved DDES (IDDES) models. The Wall-Adapting Local Eddy-Viscosity (WALE) model is the used LES model. The numerical computations are performed at Reynolds number Re_b=4494 and different Richardson numbers Ri=0.025, 0.048, 0.1. The comparing data is from the Direct Numerical Simulation (DNS) at Re_b=4494 and Ri=0.048. The comparison reveals that the two DDES models have better performance in predicting time-averaged parameters than the WALE model in the aiding flow. The best predicted time-averaged results are obtained by the PL-DDES model in the opposing flow. Furthermore, the results of different Ri obtained by the PL-DDES model agree well with the DNS data.

关键词: Turbulent mixed convection, Hybrid RANS/LES model, PL-DDES model, WALE model, Vertical plane channel

Puxian Ding, Shuangfeng Wang, Kai Chen. Numerical study on turbulent mixed convection in a vertical plane channel using hybrid RANS/LES and LES models[J]. Chinese Journal of Chemical Engineering, 2020, 28(1): 1-8.

Puxian Ding, Shuangfeng Wang, Kai Chen. Numerical study on turbulent mixed convection in a vertical plane channel using hybrid RANS/LES and LES models[J]. 中国化学工程学报, 2020, 28(1): 1-8.

References

[1] M.H. Bahmani, G. Sheikhzadeh, M. Zarringhalam, O.A. Akbari, A.A. Alrashed, G.A.S. Shabani, M. Goodarzi, Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger, Adv. Powder Technol. 29(2) (2018) 273-282.
[2] H. Alipour, A. Karimipour, M.R. Safaei, D.T. Semiromi, O.A. Akbari, Influence of Tsemi attached rib on turbulent flow and heat transfer parameters of a silver-water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel, Physica E 88(2017) 60-76.
[3] G. Yang, Y. Huang, J. Wu, L. Zhang, G. Chen, R. Lv, A. Cai, Experimental study and numerical models assessment of turbulent mixed convection heat transfer in a vertical open cavity, Build. Environ. 115(2017) 91-103.
[4] Y.Y. Huang, G. Yang, J.Y. Wu, Large eddy simulation and experimental study of turbulent mixed convection inside a cavity with large Rayleigh number:Effect of buoyancy, Build. Environ. 151(2019) 268-279.
[5] H. Sun, R. Li, E. Chénier, G. Lauriat, J. Padet, Optimal plate spacing for mixed convection from an array of vertical isothermal plates, Int. J. Therm. Sci. 55(2012) 16-30.
[6] D. Roeleveld, D. Naylor, W. Leong, Free convection in asymmetrically heated vertical channels with opposing buoyancy forces, J. Heat Transf. 136(6) (2014), 062502.
[7] I. Zavala-Guillen, J. Xaman, C. Salinas, K. Ismail, I. Hernández-Pérez, I. HernandezLopez, Optical thickness effect on natural convection in a vertical channel containing a gray gas, Int. J. Heat Mass Transf. 107(2017) 510-519.
[8] B. Metais, E.R.G. Eckert, Forced, mixed, and free convection regimes, J. Heat Transf. 86(2) (1964) 295.
[9] A.D. Carr, M.A. Connor, H.O. Buhr, Velocity, temperature, and turbulence measurements in air for pipe flow with combined free and forced convection, J. Heat Transf. 95(4) (1973) 445.
[10] J.P. Easby, The effect of buoyancy on flow and heat transfer for a gas passing down a vertical pipe at low turbulent Reynolds numbers, Int. J. Heat Mass Transf. 21(6) (1978) 791-801.
[11] N. Masamoto, F. Keisuke, Buoyancy effects on turbulent transport in combined free and forced convection between vertical parallel plates, Int. J. Heat Mass Transf. 23(10) (1980) 1325-1336.
[12] J. Wang, J. Li, J.D. Jackson, A study of the influence of buoyancy on turbulent flow in a vertical plane passage, Int. J. Heat Fluid Flow 25(3) (2004) 420-430.
[13] M.S. Shadloo, A. Hadjadj, F. Hussain, Temperature-invariant scaling for compressible turbulent boundary layers with wall heat transfer, Heat Transfer Eng. 39(11) (2018) 923-932.
[14] S. Sharma, M. Shadloo, A. Hadjadj, Effect of thermo-mechanical non-equilibrium on the onset of transition in supersonic boundary layers, Heat Mass Transf. (2018) 1-13.
[15] N. Kasagi, M. Nishimura, Direct numerical simulation of combined forced and natural turbulent convection in a vertical plane channel, Int. J. Heat Fluid Flow 18(1) (1996) 88-99.
[16] J. You, J.Y. Yoo, H. Choi, Direct numerical simulation of heated vertical air flows in fully developed turbulent mixed convection, Int. J. Heat Mass Transf. 46(9) (2003) 1613-1627.
[17] M. Niemann, R.A.B. Navarro, V. Saini, J. Fröhlich, Buoyancy impact on secondary flow and heat transfer in a turbulent liquid metal flow through a vertical square duct, Int. J. Heat Mass Transf. 125(2018) 722-748.
[18] O.A. El-Samni, H.S. Yoon, H.H. Chun, Direct numerical simulation of turbulent flow in a vertical channel with buoyancy orthogonal to mean flow, Int. J. Heat Mass Transf. 48(7) (2005) 1267-1282.
[19] J.H. Bae, J.Y. Yoo, H. Choi, Direct numerical simulation of turbulent supercritical flows with heat transfer, Phys. Fluids 17(10) (2005) 105104.
[20] X. Chu, E. Laurien, D.M. Mceligot, Direct numerical simulation of strongly heated air flow in a vertical pipe, Int. J. Heat Mass Transf. 101(2016) 1163-1176.
[21] J. Yin, B.C. Wang, D.J. Bergstrom, Large-eddy simulation of combined forced and natural convection in a vertical plane channel, Int. J. Heat Mass Transf. 50(19) (2007) 3848-3861.
[22] A. Keshmiri, M.A. Cotton, D. Laurence, Turbulence models and large eddy simulations applied to ascending mixed convection flows, Flow Turbul. Combust. 89(3) (2012) 407-434.
[23] C. Kath, C. Wagner, DNS and LES of turbulent mixed convection in the minimal flow unit, New Results in Numerical and Experimental Fluid Mechanics IX, Springer 2014, pp. 123-131.
[24] J. Wang, J. Li, S. He, J.D. Jackson, Computational simulations of buoyancy-influenced turbulent flow and heat transfer in a vertical plane passage, ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 1989-1996(vols 203-210), 218(11) 2004, pp. 1385-1397.
[25] C. Balaji, M. Hölling, H. Herwig, Entropy generation minimization in turbulent mixed convection flows, Int. J. Heat Mass Transf. 34(5) (2007) 544-552.
[26] W.S. Kim, S. He, J.D. Jackson, Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection, Int. J. Heat Mass Transf. 51(5) (2008) 1293-1312.
[27] M. Shahraeeni, M. Raisee, Investigation of turbulent mixed convection of air flow in vertical tubes using a zonal turbulence model, Int. J. Heat Fluid Flow 31(2) (2010) 179-190.
[28] F. Dehoux, Y. Lecocq, S. Benhamadouche, L.E. Brizzi, Algebraic modeling of the turbulent heat fluxes using the elliptic blending approach-Application to forced and mixed convection regimes, Flow Turbul. Combust. 88(1-2) (2012) 77-100.
[29] D. Vanpouille, B. Aupoix, E. Laroche, Development of an explicit algebraic turbulence model for buoyant flows-Part 1:DNS analysis, Int. J. Heat Fluid Flow 43(7) (2013) 170-183.
[30] H. Gopalan, S. Heinz, M.K. Stöllinger, A unified RANS-LES model:Computational development, accuracy and cost, J. Comput. Phys. 249(2013) 249-274.
[31] C. Speziale, Turbulence modeling for time-dependent RANS and VLES:A review, AIAA J. 36(2) (1998) 173-184.
[32] X. Han, S. Krajnović, An efficient very large eddy simulation model for simulation of turbulent flow, Int. J. Numer. Methods Fluids 71(11) (2013) 1341-1360.
[33] S.S. Girimaji, Partially-averaged Navier-Stokes model for turbulence:A Reynoldsaveraged Navier-Stokes to direct numerical simulation bridging method, J. Appl. Mech. 73(3) (2006) 413-421.
[34] F. Pereira, G. Vaz, L. Eça, S. Girimaji, Simulation of the flow around a circular cylinder at Re=3900 with partially-averaged Navier-Stokes equations, Int. J. Heat Fluid Flow 69(2018) 234-246.
[35] F.R. Menter, M. Kuntz, Adaptation of Eddy-Viscosity Turbulence Models to Unsteady Separated Flow Behind Vehicles, Springer Berlin Heidelberg, Berlin, Heidelberg, 2004339-352.
[36] P.R. Spalart, S. Deck, M.L. Shur, K.D. Squires, M.K. Strelets, A. Travin, A new version of detached-eddy simulation, resistant to ambiguous grid densities, Theor. Comput. Fluid Dyn. 20(3) (2006) 181.
[37] M.S. Gritskevich, J. Schütze, F.R. Menter, Development of DDES and IDDES formulations for the k-ω shear stress transport model, Flow Turbul. Combust. 88(3) (2012) 431-449.
[38] P. Ding, S. Wang, K. Chen, Production-limited delayed detached eddy simulation of turbulent flow and heat transfer, Can. J. Chem. Eng. (2019)https://doi.org/10.1002/cjce.23453.
[39] J. Liu, J. Niu, C.M. Mak, Q. Xia, Detached eddy simulation of pedestrian-level wind and gust around an elevated building, Build. Environ. 125(2017) 168-179.
[40] M.V. Masterov, M.W. Baltussen, J.A.M. Kuipers, Numerical simulation of a square bubble column using Detached Eddy Simulation and Euler-Lagrange approach, Int. J. Multiphase Flow 107(2018) 275-288.
[41] J. Hu, H.B. Xuan, K.C.S. Kwok, Y. Zhang, Y. Yu, Study of wind flow over a 6 m cube using improved delayed detached Eddy simulation, J. Wind Eng. Ind. Aerodyn. 179(2018) 463-474.
[42] H. Gopalan, R. Jaiman, Numerical study of the flow interference between tandem cylinders employing non-linear hybrid URANS-LES methods, J. Wind Eng. Ind. Aerodyn. 142(2015) 111-129.
[43] G. Kumar, A. De, H. Gopalan, Investigation of flow structures in a turbulent separating flow using hybrid RANS-LES model, Int. J. Numer. Methods Heat Fluid Flow 27(7) (2017) 1430-1450.
[44] G. Kumar, S.K. Lakshmanan, H. Gopalan, A. De, Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS-LES models for predicting flow fields with separation and reattachment, Int. J. Numer. Methods Fluids 83(12) (2017) 917-939.
[45] C. He, Y. Liu, A dynamic detached-eddy simulation model for turbulent heat transfer:Impinging jet, Int. J. Heat Mass Transf. 127(2018) 326-338.
[46] S. Ruck, F. Arbeiter, Detached eddy simulation of turbulent flow and heat transfer in cooling channels roughened by variously shaped ribs on one wall, Int. J. Heat Mass Transf. 118(2018) 388-401.
[47] F. Nicoud, F. Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow Turbul. Combust. 62(3) (1999) 183-200.
[48] O. Ben-Nasr, A. Hadjadj, A. Chaudhuri, M. Shadloo, Assessment of subgrid-scale modeling for large-eddy simulation of a spatially-evolving compressible turbulent boundary layer, Comput. Fluids 151(2017) 144-158.
[49] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32(8) (1994) 1598-1605.
[50] H. Jasak, H.G. Weller, A.D. Gosman, High resolution NVD differencing scheme for arbitrarily unstructured meshes, Int. J. Numer. Methods Fluids 31(2) (1999) 431-449.