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The Use of Wall Functions for Simulating the Turbulent Thermal Boundary Layer

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Abstract

An important problem in the numerical simulation of turbulent heat exchange in fluids is accurate prediction of hydrodynamic characteristics of the flow in the boundary layer, which requires a fine grid near rigid surfaces. In applications, it is not always possible to have a fine grid and the use of a coarser grid results in significant loss of accuracy. A well-known approach to improving the accuracy of the numerical simulation of the boundary layer is the use of universal wall functions for computing the friction and thermal flux. In this paper, we consider the known wall functions for computing the thermal flux. The accuracy of these functions in problems of turbulent nonisothermal flow of fluid is studied. These are the flow in a plane channel, Couette flow, and flow along a heated plate. Each of these problems is solved on grids with various near wall resolutions. The results of solving these problems provide a basis for estimating the accuracy of the wall functions used for solving them. It is shown that the wall functions considered in this study yield nonmonotonic convergence of the results as the grid is refined.

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REFERENCES

  1. H. Schlichting, Boundary Layer Theory, 6th ed. (McGraw-Hill, New York, 1968).

  2. A. Yu. Snegirev, High-Performance Computations in Physics: Numerical Simulation of Turbulent Flows (Politekhnicheskii Univ., St. Petersburg, 2009) [in Russian].

    Google Scholar 

  3. P. R. Spalart, “Strategies for turbulence modeling and simulations,” Heat Fluid Flow 21, 252–263 (2000).

    Article  Google Scholar 

  4. A. S. Kozelkov, O. L. Krutyakova, V. V. Kurulin, S. V. Lashkin, and E. S. Tyatyushkina, “Application of numerical schemes with singling out the boundary layer for the computation of turbulent flows using eddy-resolving approaches on unstructured grids,” Comput. Math. Mat. Phys. 57, 1036–1047 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. S. Kozelkov, V. V. Kurulin, S. V. Lashkin, R. M. Shagaliev, and A. V. Yalozo, “Investigation of supercomputer capabilities for the scalable numerical simulation of computational fluid dynamics problems in industrial applications,” Comput. Math. Mat. Phys. 56, 1506–1516 (2016).

  6. I. A. Belov and S. A. Isaev, Simulation of Turbulent Flows: A Texbook (Baltic State Technical Univ. St. Petersburg, 2001) [in Russian].

    Google Scholar 

  7. A. S. Kozelkov, Yu. N. Deryugin, Yu. A. Tsibereva, A. V. Kornev, O. V. Denisova, D. Yu. Strelets, A. A. Kurkin, V. V. Kurulin, I. L. Sharipova, D. P. Rubtsova, M. A. Legchanov, E. S. Tyatyushkina, S. V. Lashkin, A. V. Yalozo, S. V. Yatsevich, N. V. Tarasova, R. R. Ginniyatullin, M. A. Sizova, and O. L. Krutyakova, “The minimal set of benchmarks for validating methods of numerical simulation of turbulent lows of viscous incompressible fluid,” Trudy Nizh. Gos. Tech. Univ., No. 4 (106), 21–69 (2014).

  8. B. E. Launder and D. B. Spalding, “The numerical computation of turbulent flows,” Comput. Meth. Appl. Mech. Eng. 3, 269–289 (1974).

    Article  MATH  Google Scholar 

  9. A. S. Kozelkov, V. V. Kurulin, O. L. Puchkova, and S. V. Lashkin, “Simulation of turbulent flows using the algebraic Reynolds stress model with universal near-wall functions,” Vychisl. Mekh. Sploshnykh Sred 7 (1), 40–51 (2014).

    Google Scholar 

  10. L. I. Zaichik, “Wall functions for simulation of turbulent flows and heat transfer, High. Temp. 35, 385–390 (1997).

    Google Scholar 

  11. S. A. Isaev, P. A. Baranov, A. G. Sudakov, and I. A. Popov, “Verification of the standard model of shear stress transport and its modified version that takes into account the streamline curvature and estimation of the applicability of the Menter combined boundary conditions in calculating the ultralow profile drag for an optimally configured cylinder–coaxial disk arrangement,” Tech. Phys. 61, 1151–1161 (2016).

    Article  Google Scholar 

  12. B. A. Kader, “Temperature and concentration profiles in fully turbulent boundary layers,” Int. J. Heat Mass Transfer 24, 1541–1544 (1981).

    Article  Google Scholar 

  13. P. L. Kirillov, Yu. S. Yur’ev, and V. P. Bobkov, Handbook of Heat and Hydraulic Computations (Nuclear Reactors, Heat Exchangers, and Steam Generators) (Energoatomizdat, Moscow, 1990) [in Russian].

    Google Scholar 

  14. W. M. Kays and M.E. Crawford, Convective Heat and Mass Transfer (McGraw-Hill, New York, 1994).

    Google Scholar 

  15. J. Kim and P. Moin, Transport of Passive Scalars in a Turbulent Channel Flow, Vol. VI (Springer, Berlin, 1989).

    Book  Google Scholar 

  16. F. R. Menter, M. Kuntz, and R. Langtry, “Ten years of experience with the SST turbulent model,” Turbulence, Heat and Mass Transfer 4, ed. by K. Hanjalic, Y. Nagano, and M. Tummers (Begell House Inc, 2003).

  17. K. Wieghardt and W. Tillmann, “On the turbulent friction layer for rising pressure,” NACA TM-1314 (1951).

  18. E. M. Smirnov and D. K. Zaitsev, “Modification of wall boundary conditions for low-Re k-w turbulence models aimed at grid sensitivity reduction,” Proc. of the Europ. Conf. for Aerospace Sci., Moscow, 2005 (EUCASS 2005), ID 2.09.06.

  19. J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics (Springer, Berlin, 2001).

    MATH  Google Scholar 

  20. A. S. Kozelkov, “Implementation of a method for the computation of viscous incompressible fluid using the multigrid method and the SIMPLE algorithm in the software package LOGOS,” Voprosy Atom. Nauki Tekhn., Ser. Math. Model. Phys. Proc. No. 4 (2013).

  21. K. N. Volkov, A. S. Kozelkov, S. V. Lashkin, N. V. Tarasova and A. V. Yalozo, “A parallel implementation of the algebraic multigrid method for solving problems in dynamics of viscous incompressible fluid,” Comput. Math. Mat. Phys. 57, 2030–2046 (2017).

  22. A. S. Kozelkov, A. A. Kurkin, V. V. Kurulin, M. A. Legchanov, E. S. Tyatyushkina, and Yu. A. Tsibereva, “Investigation of the application of RANS turbulence models to the calculation of nonisothermal low-Prandtl-number flows,” Fluid Dyn. 50, 501–513 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  23. E. U. Repik and Yu. P. Sosedko, Turbulent Boundary Layer: Methodology and Experimental Results (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

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FUNDING

The results of were obtained within the state research program, project nos. 5.4568.2017/6.7 and 5.1246.2017/4.6. The work was also supported by the Presidential program of Support of Leading Scientific Schools, project no. NSh-2685.2018.5; by the Presidential program of support of young Russian doctors of science, project no. MD-4874.2018.9; and by the Russian Foundation for Basic Research, project no. 16-01-00267.

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Authors and Affiliations

  1. Instrument Design Bureau, 300001, Tula, Russia

    V. R. Efremov

  2. Russian Federal Nuclear Center—All-Russia Institute of Experimental Physics, 607189, Sarov, Nizhegorodskaya oblast, Russia

    V. V. Kurulin, A. S. Kozelkov & D. A. Utkin

  3. Nizhny Novgorod State Technical University, 603950, Nizhny Novgorod, Russia

    A. S. Kozelkov & A. A. Kurkin

Authors
  1. V. R. Efremov
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  2. V. V. Kurulin
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  3. A. S. Kozelkov
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  4. A. A. Kurkin
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  5. D. A. Utkin
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Correspondence to V. R. Efremov, V. V. Kurulin, A. S. Kozelkov, A. A. Kurkin or D. A. Utkin.

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Translated by A. Klimontovich

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Efremov, V.R., Kurulin, V.V., Kozelkov, A.S. et al. The Use of Wall Functions for Simulating the Turbulent Thermal Boundary Layer. Comput. Math. and Math. Phys. 59, 1006–1014 (2019). https://doi.org/10.1134/S0965542519060058

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  • DOI: https://doi.org/10.1134/S0965542519060058

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