Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-kfj7r Total loading time: 0.533 Render date: 2022-12-05T23:50:49.252Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Toward the large-eddy simulation of compressible turbulent flows

Published online by Cambridge University Press:  26 April 2006

G. Erlebacher
Affiliation:
ICASE, NASA Langley Research Center, Hampton, VA 23665, USA
M. Y. Hussaini
Affiliation:
ICASE, NASA Langley Research Center, Hampton, VA 23665, USA
C. G. Speziale
Affiliation:
ICASE, NASA Langley Research Center, Hampton, VA 23665, USA
T. A. Zang
Affiliation:
NASA Langley Research Center, Hampton, VA 23665, USA

Abstract

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 963 grid using Fourier collocation methods. Extensive comparisons between the direct and modelled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence – conducted on a coarse 323 grid – is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

Type
Research Article
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abarbanel, S., Dutt, P. & Gottlieb, D. 1989 Splitting methods for low Mach number Euler and Navier-Stokes equations. Computers & Fluids 17, 112.Google Scholar
Arfken, G. 1970 Mathematical Methods for Physicists. Academic.
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1983 Improved subgrid-scale models based on large-eddy simulation of homogeneous, incompressible, turbulent flows. Stanford University Rep. TF-19.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Biringen, S. & Reynolds, W. C. 1981 Large-eddy simulation of the shear-free turbulent boundary layer. J. Fluid Mech. 103, 5363.Google Scholar
Blaisdell, G. A., Mansour, N. N. & Reynolds, W. C. 1991 Numerical Simulations of Compressible Homogeneous Turbulence. Stanford University Rep. TF-50.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 116.Google Scholar
Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated, isotropic turbulence. J. Fluid Mech. 48, 273337 (referred to herein as CBC).Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453480.Google Scholar
Eidson, T. M. 1985 Numerical simulation of the turbulent Rayleigh-Bénard problem using numerical subgrid modeling. J. Fluid Mech. 158, 245268.Google Scholar
Erlebacher, G., Hussaini, M. Y., Kreiss, H. O. & Sarkar, S. 1990 The analysis and simulation of compressible turbulence. Theor. Comput. Fluid Dyn. 2, 7395.Google Scholar
Feiereisen, W. J., Reynolds, W. C. & Ferziger, J. H. 1981 Numerical simulation of compressible, homogeneous, turbulent shear flow. Stanford University Rep. TF-13.Google Scholar
Frisch, U. & Orszag, S. A. 1990 Turbulence: challenges for theory and experiment. Phys. Today 43, 2432.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hussaini, M. Y., Speziale, C. G. & Zang, T. A. 1990 Comment on the potential and limations of direct and large-eddy simulations. In Lecture Notes in Physics, vol. 357 (ed. J. L. Lumley), pp. 354368.
Hussaini, M. Y. & Zang, T. A. 1987 Spectral methods in fluid dynamics. Ann. Rev. Fluid Mech. 19, 339368.Google Scholar
Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic, numerical turbulence. J. Fluid Mech. 153, 3158.Google Scholar
Leonard, A. 1974 On the energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237248.Google Scholar
Lumley, J. L. 1983 Turbulence modeling. Trans. ASME E: J. Appl. Mech. 50, 10971103.Google Scholar
McMillan, O. J. 1980 Tests of new subgrid-scale models in strained turbulence. AIAA Paper 80–1339; in AIAA 13th Fluid and Plasma Dynamics Conf. Snowmass. Co.
McMillan, O. J. & Ferziger, J. H. 1979 Direct testing of subgrid-scale models. AIAA J. 17, 13401346.Google Scholar
Passot, T. & Pouquet, A. 1987 Numerical simulation of compressible homogeneous flows in the turbulent regime. J. Fluid Mech. 181, 441466.Google Scholar
Piomelli, U., Ferziger, J. H. & Moin, P. 1987 Models for large-eddy simulations of turbulent channel flows including transpiration. Stanford University Tech. Rep. TF-32.Google Scholar
Piomelli, U., Zang, T. A., Speziale, C. G. & Hussaini, M. Y. 1990 On the large-eddy simulation of transitional wall-bounded flows. Phys. Fluids A 2, 257265.Google Scholar
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183208.Google Scholar
Rogallo, R. S. & Moin, P. 1984 Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech. 16, 99137.Google Scholar
Sarkar, S., Erlebacher, G., Hussaini, M. Y. & Kreiss, H. O. 1991 The analysis and modeling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473493.Google Scholar
Schumann, U. 1975 Subgrid scale models for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376404.Google Scholar
Speziale, C. G. 1985 Galilean invariance of subgrid-scale stress models in the large-eddy simulation of turbulence. J. Fluid Mech. 156, 5262.Google Scholar
Speziale, C. G., Erlebacher, G., Zang, T. A. & Hussaini, M. Y. 1988 The subgrid-scale modeling of compressible turbulence. Phys. Fluids 31, 940942.Google Scholar
Tennekes, H. & Lumley, J. L. 1972. A First Course in Turbulence. MIT Press.
Voke, P. R. & Collins, M. W. 1983 Large-eddy simulation: retrospect and prospect. PhysicoChem. Hydrodyn. 4, 119161.Google Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 21522164.Google Scholar
Zang, T. A., Dahlburg, R. B. & Dahlburg, J. P. 1992 Direct and large-eddy simulations of compressible Navier-Stokes turbulence. Phys. Fluids A 4, 127140.Google Scholar
532
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Toward the large-eddy simulation of compressible turbulent flows
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Toward the large-eddy simulation of compressible turbulent flows
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Toward the large-eddy simulation of compressible turbulent flows
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *