Abstract
Large eddy simulation (LES) seeks to predict the dynamics of the organized structures in the flow, that is, local spatial averages
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
Some integral formulas have been used in the derivation and the analysis of the friction coefficients. It holds,
where erf(.) is the error function. Recall that
and
The derivative of the error function is easily computed from Eq. (14) as follows,
References
[1] K. S. Abbot and D. E. Kline, “Experimental investigations of subsonic turbulent flow over single and double backward-facing steps,” Trans. ASME, Ser. D, vol. 84, pp. 317–325, 1962. https://doi.org/10.1115/1.3657313.Suche in Google Scholar
[2] W. F. Bradshaw and P. Wong, “The reattachment and relaxation of a turbulent shear layer,” J. Fluid Mech., vol. 52, pp. 113–135, 1972. https://doi.org/10.1017/s002211207200299x.Suche in Google Scholar
[3] J. Kim, S. J. Kline, and J. P. Johnston, “Investigation of a reattaching turbulent shear layer: flow over a backward-facing step,” J. Fluid Eng., vol. 102, pp. 302–308, 1980. https://doi.org/10.1115/1.3240686.Suche in Google Scholar
[4] F. Durst and C. Tropea, “Turbulent, backward-facing step flows in two-dimensional ducts and channels,” in Proceedings of the Fifth International Symposium on Turbulent Shear Flows, Davis, Cornell University, 1981, pp. 181–185.Suche in Google Scholar
[5] B. F. Armaly, F. Durst, J. C. F. Pereira, and B. Schönung, “Experimental and theoretical investigation of backward-facing step flow,” J. Fluid Mech., vol. 127, pp. 473–496, 1983. https://doi.org/10.1017/s0022112083002839.Suche in Google Scholar
[6] J. J. Adams and E. W. Johnston, “Effects of the separating shear layer on the reat- tachment flow structure. part 1: pressure and turbulence quantities. part 2: reattachment length and wall shear stress,” Exp. Fluid, vol. 6, pp. 400493–408499, 1988. https://doi.org/10.1007/bf00196485.Suche in Google Scholar
[7] S. Jovic and D. Driver, “Backward-facing step measurements at low Reynolds number,” NASA Tech. Memorand., p. 108807, 1994.Suche in Google Scholar
[8] P. G. Spazzini, G. Iuso, M. Oronato, N. Zurlo, and G. M. Di Cicca, “Unsteady behaviour of back-facing step flow,” Exp. Fluid, vol. 30, pp. 551–561, 2001. https://doi.org/10.1007/s003480000234.Suche in Google Scholar
[9] S. Yoshioka, S. Obi, and S. Masuda, “Turbulence statistics of periodically perturbed separated flow over backward-facing step,” Int. J. Heat Fluid Flow, vol. 22, pp. 393–401, 2001. https://doi.org/10.1016/s0142-727x(01)00079-0.Suche in Google Scholar
[10] S. D. Hall, M. Behnia, C. A. J. Fletcher, and G. L. Morrison, “Investigation of the secondary corner vortex in a benchmark turbulent backward-facing step using cross- correlation particle imaging velocimetry,” Exp. Fluid, vol. 35, pp. 139–151, 2003. https://doi.org/10.1007/s00348-003-0626-9.Suche in Google Scholar
[11] A. M. R. Friedrich, “Analysing turbulent backward-facing step flow with the lowpass-filtered Navier-Stokes equations,” J. Wind Eng. Ind. Aerod., vol. 35, pp. 101–228, 1990. https://doi.org/10.1016/0167-6105(90)90212-u.Suche in Google Scholar
[12] A. Silveira Neto, D. Grand, O. Metais, and M. Lesieur, “A numerical investigation of the coherent vortices in turbulence behind a backward-facing step,” J. Fluid Mech., vol. 256, pp. 1–25, 1993. https://doi.org/10.1017/s0022112093002691.Suche in Google Scholar
[13] L. C. Berselli, W. J. Layton, and T. Iliescu, Mathematics of Large Eddy Simulation of Turbulent Flows, Berlin, Springer, 2006.Suche in Google Scholar
[14] P. Sagaut, Large eddy Simulation for Incompressible Flows, Berlin, Springer-Verlag, 2001.10.1007/978-3-662-04416-2Suche in Google Scholar
[15] U. Piomelli and E. Balaras, “Wall-layer models for large-eddy simulations,” Annu. Rev. Fluid Mech., vol. 34, pp. 349–374, 2002. https://doi.org/10.1146/annurev.fluid.34.082901.144919.Suche in Google Scholar
[16] H. Werner and H. Wengle, “Large eddy simulation of turbulent flow around a cube in a plane channel,” in Selected Papers From the 8th Symp. on Turb. Shear Flows, F. Durst, B. Launder, U. Schumann, and J. Whitelaw, Eds., New York, Springer, 1993, pp. 155–168.10.1007/978-3-642-77674-8_12Suche in Google Scholar
[17] J. W. Deardoff, “A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers,” J. Fluid Mech., vol. 41, pp. 453–480, 1970.10.1017/S0022112070000691Suche in Google Scholar
[18] U. Schumann, “Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli,” J. Comput. Phys., vol. 18, pp. 376–404, 1975. https://doi.org/10.1016/0021-9991(75)90093-5.Suche in Google Scholar
[19] G. Grötzbach, “Direct numerical and large eddy simulation of turbulent channel flows,” in Encyslopedia of Fluid Mechanics, N. Cheremisinoff, Ed., West Orange, NJ, Gulf, 1987.Suche in Google Scholar
[20] U. Piomelli, P. Moin, and J. Kim, “New approximate boundary condition for large eddy simulation of wall-bounded flows,” Phys. Fluids A, vol. 1, pp. 1061–1068, 1989. https://doi.org/10.1063/1.857397.Suche in Google Scholar
[21] W. H. Cabot, “Large-eddy simulations with wall models,” in Annual Research Briefs, Stanford, Center for Turbulence Research, 1995, pp. 41–58.Suche in Google Scholar
[22] W. H. Cabot, “Near-wall models in large eddy simulations of flow behind a backward-facing step,” in Annual Research Briefs, Stanford, Center for Turbulence Research, 1996, pp. 199–210.Suche in Google Scholar
[23] T. Bagwell, “Stochastic estimation of Near Wall Closure in Turbulence Models,” PhD thesis, University of Illinois at Urbana-Champaign, 1994.Suche in Google Scholar
[24] T. G. Bagwell, R. D. Moser, and J. Kim, “Improved approximation of wall shear stress boundary conditions for large eddy simulation,” Near-Wall Turbulent Flows, New York, Elsevier Science, 1993.Suche in Google Scholar
[25] I. Marusic, G. J. Kunkel, and F. Porte-Agel, “Experimental study of wall boundary conditions for large-eddy simulation,” J. Fluid Mech., vol. 446, pp. 309–320, 2001. https://doi.org/10.1017/s0022112001005924.Suche in Google Scholar
[26] S. Bose and P. Moin, “A dynamic slip boundary condition for wall-modeled large-eddy simulation,” Phys. Fluids, vol. 26, no. 1, p. 015104, 2014. https://doi.org/10.1063/1.4849535.Suche in Google Scholar
[27] E. Boström, “Boundary Conditions for Spectral Simulations of Atmospheric Boundary Layers,” PhD thesis, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden, 2017.Suche in Google Scholar
[28] A. T. Anum Shafiq and Z. Hammouch, “Impact of radiation in a stagnation point flow of Walters? B fluid towards a riga plate,” Therm. Sci. Eng. Prog., vol. 6, pp. 27–33, 2018. https://doi.org/10.1016/j.tsep.2017.11.005.Suche in Google Scholar
[29] Z. Hammouch, M. Amkadni, and A. Azzouzi, “On the exact solutions of laminar mhd flow over a stretching flat plate,” Commun. Nonlinear Sci. Numer. Simulat., vol. 13, pp. 359–368, 2008.10.1016/j.cnsns.2006.04.002Suche in Google Scholar
[30] M. C. Lombardo and M. Sammartino, “Nonlocal Boundary Conditions for the Navier–Stokes Equations,” in Waves and Stability in Continuous Media, 2006, pp. 340–345.10.1142/9789812773616_0047Suche in Google Scholar
[31] Y. Cao, Global Classical Solutions to the Compressible Navier-Stokes Equations with Navier-type Slip Boundary Condition in 2d Bounded Domains, 2021, arXiv:2102.10235v2.Suche in Google Scholar
[32] J. Leray, “Sur le mouvemennt d’un fluide visquex emplissant l’espace,” Acta Math., vol. 63, pp. 193–248, 1934. https://doi.org/10.1007/bf02547354.Suche in Google Scholar
[33] E. O. A. Cheskidov, D. Holm, and E. Titi, On a Leray-Alpha Model of Turbulence, Royal Society London, Mathematical, Physical and Engineering Sciences, 2005, pp. 629–649.10.1098/rspa.2004.1373Suche in Google Scholar
[34] G. Galdi and W. Layton, “Approximation of the larger eddies in fluid motion ii: a model for space filtered flow,” Math. Model Methods Appl. Sci., vol. 10, pp. 343–350, 2000. https://doi.org/10.1142/s0218202500000203.Suche in Google Scholar
[35] N. Sahin, “Derivation, Analysis and Testing of New Near Wall Models for Large Eddy Simulation,” PhD thesis, Department of Mathematics, Pittsburgh University, 2003.Suche in Google Scholar
[36] W. Layton, V. John, and N. Sahin, “Derivation and analysis of near wall models for channel and recirculating flows,” Comput. Math. Appl., vol. 28, pp. 1135–1151, 2004.10.1016/j.camwa.2004.10.011Suche in Google Scholar
[37] S. Pope, Turbulent Flows, New York, Cambridge University Press, 2000.10.1017/CBO9780511840531Suche in Google Scholar
[38] C. Navier, “Memoire sur les lois du movement des fluiales,” Mem. Acad. R. Sci., vol. 6, pp. 389–440, 1823.Suche in Google Scholar
[39] J. Maxwell, “On stresses in rarefied gases arising from inequalities of temperature,” Philos. Trans. R. Soc., vol. 170, pp. 249–256, 1879.10.1098/rstl.1879.0067Suche in Google Scholar
[40] K. R. Mahmud, “Sensitivity analysis of near-wall turbulence modeling for large eddy simulation of incompressible flows,” Master’s thesis, Master Programme in Computer simulation for Science and Engineering, Royal Institute of Technology, School of Engineering Sciences, Stockholm, Sweden, 2014.Suche in Google Scholar
[41] T. Knopp, “Finite-element simulation of buoyancy-driven turbulent flows,” PhD thesis, Univ. of Göttingen, Germany, 2003.Suche in Google Scholar
[42] V. John, “Slip with friction and penetration with resistance boundary conditions for the Navier-Stokes equations-numerical tests and aspects of the implementation,” J. Comput. Appl. Math., vol. 147, pp. 287–300, 2002. https://doi.org/10.1016/s0377-0427(02)00437-5.Suche in Google Scholar
[43] H. Schlichting, Boundary-Layer Theory, New York, McGraw-Hill, 1979.Suche in Google Scholar
[44] G. Barenblatt and A. Chorin, “New perspectives in turbulence: scaling laws, asymptotic, and intermittency,” SIAM Rev., vol. 40, pp. 265–291, 1998. https://doi.org/10.1137/s0036144597320047.Suche in Google Scholar
[45] R. G. Hill, “Benchmark testing the alpha-models of turbulence,” Master’s thesis, The Graduate School of Clemson University, 2010.Suche in Google Scholar
[46] P. F. Hecht and O. K. Ohtsuka, Freefem++ Manual, 2021.Suche in Google Scholar
[47] O. Ilhan, “Turbulansli Sinir Tabakasi icin Duvar Kenari Modeli ve Modelin Logaritmik Kanunla Testleri,” PhD thesis, Mugla Sitki Kocman University, Institute of Science, 2018.Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Testing of logarithmic-law for the slip with friction boundary condition
- A new clique polynomial approach for fractional partial differential equations
- The modified Rusanov scheme for solving the phonon-Bose model
- Delta-shock for a class of strictly hyperbolic systems of conservation laws
- The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
- Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
- The simulation of two-dimensional plane problems using ordinary state-based peridynamics
- Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
- Simulation of the crystallization processes by population balance model using a linear separation method
- PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
- Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
- Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
- The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
- Intelligent controller for maximum power extraction of wind generation systems using ANN
- A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
- Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
- A study on solvability of the fourth-order nonlinear boundary value problems
- Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
- Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
- Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
- Carleman framework filtering of nonlinear noisy phase-locked loop system
- Corrigendum
- Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Testing of logarithmic-law for the slip with friction boundary condition
- A new clique polynomial approach for fractional partial differential equations
- The modified Rusanov scheme for solving the phonon-Bose model
- Delta-shock for a class of strictly hyperbolic systems of conservation laws
- The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
- Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
- The simulation of two-dimensional plane problems using ordinary state-based peridynamics
- Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
- Simulation of the crystallization processes by population balance model using a linear separation method
- PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
- Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
- Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
- The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
- Intelligent controller for maximum power extraction of wind generation systems using ANN
- A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
- Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
- A study on solvability of the fourth-order nonlinear boundary value problems
- Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
- Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
- Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
- Carleman framework filtering of nonlinear noisy phase-locked loop system
- Corrigendum
- Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon