Abstract
We present a generalised treatment of the wall boundary conditions for RANS computation of turbulent flows and heat transfer. The method blends the integration up to the wall (ItW) with the generalised wall functions (GWF) that include non-equilibrium effects. Wall boundary condition can thus be defined irrespective of whether the wall-nearest grid point lies within the viscous sublayer, in the buffer zone, or in the fully turbulent region. The computations with fine and coarse meshes of a steady and pulsating flow in a plane channel, in flow behind a backward-facing step and in a round impinging jet using the proposed compound wall treatment (CWT) are all in satisfactory agreement with the available experiments and DNS data. The method is recommended for computations of industrial flows in complex domains where it is difficult to generate a computational grid that will satisfy a priori either the ItW or WF prerequisites.
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Chieng, C.C., Launder, B.E.: On the calculation of turbulent heat transport downstream from an abrupt pipe expansion. Numer. Heat Transf. 3, 189–207 (1980)
Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E.: Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160 (2002)
Jayatilleke, C.L.V.: The influence of Prandtl number and surface roughness on the resistance of the laminar sublayer to momentum and heat transfer. Prog. Heat Mass Transf. 1, 193 (1969)
Esch, T., Menter, F.R.: Heat transfer predictions based on two-equation turbulence models with advanced wall treatment. Turbul. Heat Mass Transf. 4, 633–640 (2003)
Kalitzin, G., Medic, G., Iaccarino, G., Durbin, P.: Near-wall behaviour of RANS turbulence models and implications for wall functions. J. Comput. Phys. 204, 265–291 (2005)
Craft, T.J., Gant, S.E., Iacovides, H., Launder, B.E.: A new wall function strategy for complex turbulent flows. Numer. Heat Transf., Part B 45, 301–317 (2004)
Kader, B.A.: Temperature and concentration profiles in fully turbulent boundary layers. Int. J. Heat Mass Transfer 24, 1541–1544 (1981)
Hanjalic, K., Popovac, M., Hadziabdic, M.: A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD. Int. J. Heat Fluid Flow 25, 1047–1051 (2004)
Durbin, P.A.: Near-wall turbulence closure modelling without ‘damping functions’. Theor. Comput. Fluid Dyn. 3, 1–13 (1991)
Speziale, C.G., Sarkar, S., Gatski, T.: Modelling the pressure-strain correlation of turbulence: an invariant system dynamic approach. J. Fluid Mech. 227, 245–272 (1991)
Laurence, D.R., Uribe, J.C., Utyuzhnikov, S.V.: A robust formulation of the v2-f model. Flow Turbul. Combust. 73, 169–185 (2005)
Hanjalić, K., Laurence, D., Popovac, M., Uribe, C.: (v2/ k – f) turbulence model and its application to forced and natural convection. In: Rodi, W., Mulas, M. (eds.) Engineering Turbulence Modelling and Experiments, vol. 6, pp. 67–76. Elsevier, Amsterdam, The Netherlands (2005)
Durbin P.A.: On the k-ε stagnation-point anomaly. Int. J. Heat Fluid Flow 17, 89–90 (1996)
Ng, E.Y.K., Tan, H.Y., Lim, H.N., Choi, D.: Near-wall function for turbulence closure models. Comput. Mech. 29, 178–181 (2002)
Popovac, M.: Ph.D. thesis, Delft University of Technology, Delft, The Netherlands (2006)
Reichardt, H.: Vollstaendige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen. ZAMM 31, 208–219 (1951)
Spalding, D.B.: A single formula for the law of the wall. ASME J. Appl. Mech. 28, 444–458 (1961)
Musker, A.J.: Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J. 17, 655–657 (1979)
Liakopoulos, A.: Explicit representations of the complete velocity profile in a turbulent boundary layer. AIAA J. 22, 844–846 (1984)
Shih, T., Povinelli, L., Liu, N.: Application of generalised wall functions for complex turbulent flows. In: Rodi, W., Fueyo, N. (eds.) Engineering Turbulence Modelling and Experiments, vol. 5, pp. 177–186. Elsevier, Amsterdam, The Netherlands (2002)
Tanahashi, M., Kang, S.-J., Miyamoto, S., Shiokawa, S., Miyauchi, T.: Scaling law of fine scale eddies in turbulent channel flows up to Re τ =800. Int. J. Heat Fluid Flow 25, 331–340 (2004)
Brohmer, A., Mehring, J., Scheider, J., Basara, B., Tatschl, R., Hanajlic, K., Popovac, M.: Progress in the 3D-CFD calculation of gas- and water-side heat transfer in IC-Engines. In: Eichlseder, H. (ed.) 10. Tagung der Arbeitsprozess der Verbrebubgsmotors, Techniche Universität Graz, Austria, 22–23 September 2005
Cooper, D., Jackson, D.C., Launder, B.E., Liao, G.X.: Impinging jet studies for turbulence model assessment – I. Flow-filed experiments. Int. J. Heat Mass Transfer 36, 2675–2684 (1993)
Scotti, A., Piomelli, U.: Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13, 1367–1384 (2001)
Vogel, J.C., Eaton, J.K.: Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step. ASME J. Heat Transfer 107, 922–929 (1985)
Baughn, J., Shimizu, S.: Heat transfer measurements from a surface with uniform heat flux and an impinging jet. ASME J. Heat Transfer 111, 1096–1098 (1989)
Baughn, J., Hechanova, W.E., Yan, X.: An experimental study of entrainment effects on the heat transfer from a flat surface to a heated circular impinging jet. ASME J. Heat Transfer 113, 1023–1025 (1991)
Tatschl, R., Basara, B., Schneider, J., Hanjalic, K., Popovac, M., Brohmer, A., Mehring, J.: Advanced turbulent heat transfer modeling for IC-engine applications using AVL FIRE. In: Int. Multidimensional Engine Modelling, User’s Group Meeting, Detroit, MI, 2 April 2006
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Popovac, M., Hanjalic, K. Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer. Flow Turbulence Combust 78, 177–202 (2007). https://doi.org/10.1007/s10494-006-9067-x
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DOI: https://doi.org/10.1007/s10494-006-9067-x