Access by Xinjiang University

Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows

Victor Topalian^*, Todd A. Oliver^†, and Rhys Ulerich^‡

Robert D. Moser^§

Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA

Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA and Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA

^*Current address: Esgee Technologies, Austin, Texas 78746, USA; victopa@gmail.com
^†oliver@ices.utexas.edu
^‡Current address: Two Sigma Investments, L.P., New York, New York 10013, USA; rhys@twosigma.com
^§rmoser@ices.utexas.edu

PDF

Phys. Rev. Fluids 2, 084602 – Published 7 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084602

Abstract

A slow-growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow-growth modeling concepts to wall-bounded flows with complex physics. As in previous slow-growth approaches, the formulation assumes scale separation between the fast scales of turbulence and the slow evolution of statistics such as the mean flow. This separation enables the development of approaches where the fast scales of turbulence are directly simulated while the forcing provided by the slow evolution is modeled. The resulting model admits periodic boundary conditions in the streamwise direction, which avoids the need for extremely long domains and complex inflow conditions that typically accompany spatially developing simulations. Further, it enables the use of efficient Fourier numerics. Unlike previous approaches [Guarini, Moser, Shariff, and Wray, J. Fluid Mech. 414, 1 (2000); Maeder, Adams, and Kleiser, J. Fluid Mech. 429, 187 (2001); Spalart, J. Fluid Mech. 187, 61 (1988)], the present approach is based on a temporally evolving boundary layer and is specifically tailored to give results for calibration and validation of Reynolds-averaged Navier–Stokes (RANS) turbulence models. The use of a temporal homogenization simplifies the modeling, enabling straightforward extension to flows with complicating features, including cold and blowing walls. To generate data useful for calibration and validation of RANS models, special care is taken to ensure that the mean slow-growth forcing is closed in terms of the mean and other quantities that appear in standard RANS models, ensuring that there is no confounding between typical RANS closures and additional closures required for the slow-growth problem. The performance of the method is demonstrated on two problems: an essentially incompressible, zero-pressure-gradient boundary layer and a transonic boundary layer over a cooled, transpiring wall. The results show that the approach produces flows that are qualitatively similar to other slow-growth methods as well as spatially developing simulations and that the method can be a useful tool in investigating wall-bounded flows with complex physics.

Physics Subject Headings (PhySH)

Article Text

References (28)

J. A. Sillero, J. Jimenez, and R. D. Moser, One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $δ^{+} = 2000$ , Phys. Fluids 25, 105102 (2013).
P. Schlatter and R. Örlü, Assessment of direct numerical simulation data of turbulent boundary layers, J. Fluid Mech. 659, 116 (2010).
X. Wu, Inflow turbulence generation methods, Annu. Rev. Fluid Mech. 49, 23 (2017).
T. S. Lund, X. Wu, and K. D. Squires, Generation of turbulent inflow data for spatially-developing boundary layer simulations, J. Comput. Phys. 140, 233 (1998).
N. Nikitin, Spatial periodicity of spatially evolving turbulent flow caused by inflow boundary condition, Phys. Fluids 19, 091703 (2007).
J. W. Jewkes, Y. M. Chung, and P. W. Carpenter, Modifications to a turbulent inflow generation method for boundary-layer flows, AIAA J. 49, 247 (2011).
P. R. Spalart, Direct simulation of a turbulent boundary layer up to ${Re}_{θ} = 1410$ , J. Fluid Mech. 187, 61 (1988).
S. Guarini, R. Moser, K. Shariff, and A. Wray, Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5, J. Fluid Mech. 414, 1 (2000).
T. Maeder, N. A. Adams, and L. Kleiser, Direct simulation of turbulent supersonic boundary layers by an extended temporal approach, J. Fluid Mech. 429, 187 (2001).
P. R. Spalart, Numerical study of sink-flow boundary layers, J. Fluid Mech. 172, 307 (1986).
P. R. Spalart and A. Leonard, Direct numerical simulation of equilibrium turbulent boundary layers, in Turbulent Shear Flows 5: Selected Papers from the Fifth International Symposium on Turbulent Shear Flows, Cornell University, Ithaca, New York, USA, August 7–9, 1985, edited by F. Durst, B. E. Launder, J. L. Lumley, F. W. Schmidt, and J. H. Whitelaw (Springer, Berlin, Heidelberg, 1987), pp. 234–252
P. G. Huang, G. N. Coleman, and P. Bradshaw, Compressible turbulent channel flows: DNS results and modeling, J. Fluid Mech. 305, 185 (1995).
K. Sinha and G. Candler, Turbulent dissipation-rate equation for compressible flows, AIAA J. 41, 1017 (2003).
P. T. Bauman, R. Stogner, G. F. Carey, K. W. Schulz, R. Upadhyay, and A. Maurente, Loose-coupling algorithm for simulating hypersonic flows with radiation and ablation, J. Spacecr. Rockets 48, 72 (2011).
B. S. Kirk, R. H. Stogner, P. T. Bauman, and T. A. Oliver, Modeling hypersonic entry with the Fully-Implicit Navier–Stokes (FIN-S) stabilized finite element flow solver, Computers and Fluids 92, 281 (2014).
R. Stogner, P. T. Bauman, K. W. Schulz, R. Upadhyay, and A. Maurente, Uncertainty and parameter sensitivity in multiphysics reentry flows, In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (Paper No. 2011-764), January 2011.
F. M. White, Viscous Fluid Flow, Second Edition (McGraw-Hill, New York, 1991).
R. Ulerich, Reducing Turbulence- and Transition-Driven Uncertainty in Aerothermodynamic Heating Predictions for Blunt-Bodied Reentry Vehicles, Ph.D. thesis, The University of Texas at Austin, 2014.
M. Lee and R. D. Moser, Direct numerical simulation of turbulent channel flow up to ${Re}_{τ} \approx 5200$ , J. Fluid Mech. 774, 395 (2015).
M. V. Morkovin, Effects of compressibility on turbulent flows, Proc. Int. Symp. Mechanique de la Turbulence, edited by A. J. Favre (CNRS, Paris, 1962), pp. 367–380.
A. J. Smits and J.-P. Dussauge, Turbulent Shear Layers in Supersonic Flow (Springer, New York, 2006).
E. R. van Driest, Turbulent boundary layers in compressible fluids, J. Aeronaut. Sci. 18, 145 (1951).
P. Huang and G. N. Coleman, Van Driest transformation and compressible wall-bounded flows, AIAA J. 32, 2110 (1994).
A. Trettel and J. Larsson, Mean velocity scaling for compressible wall turbulence with heat transfer, Phys. Fluids 28, 026102 (2016).
Y. Sumitani and N. Kasagi, Direct numerical simulation of turbulent transport with uniform wall injection and suction, AIAA J. 33, 1220 (1995).
S. Pirozzoli, F. Grasso, and T. B. Gatski, Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at $M = 2.25$ , Phys. Fluids 16, 530 (2004).
E. R. van Driest, On turbulent flow near a wall, J. Aeronaut. Sci. 23, 1007 (1956).
T. Stevenson, A law of the wall for turbulent boundary layers with suction or injection, CoA Report Aero 166, The College of Aeronautics Cranfield, 1963.

Physical Review Fluids

Export citation

Export citation

Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows

Abstract

Physics Subject Headings (PhySH)

Article Text

References (28)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation