Development of turbulence models for shear flows by a double expansion technique
Abstract
Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK̄/■̄) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.
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The RNG model shows excellent results for homogeneous shear flow and flow over a backward-facing step.
“This model shows excellent results for the case of homogeneous shear flow and flow over a backward-facing step.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [222]
The RNG model is a two-equation eddy viscosity model equal to the k-# model but with different constants.
“The result is a two-equation eddy viscosity model that is equal to the previously discussed k -# model but with different constants.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [222]
Cites
The numerical computation of turbulent flows
Launder, B. E., & SPALDING, D. B. (1974) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(74)90029-2 · Cited by 12,898 · see citing works
Tennekes, H., & Lumley, J. L. (1972) · The MIT Press eBooks · doi:10.7551/mitpress/3014.001.0001 · Cited by 8,361 · see citing works
Renormalization group analysis of turbulence. I. Basic theory
Yakhot, V., & Orszag, S. A. (1986) · Journal of Scientific Computing · doi:10.1007/bf01061452 · Cited by 4,281 · see citing works
Self-citationProgress in the development of a Reynolds-stress turbulence closure
Launder, B. E., Reece, G., & Rodi, W. (1975) · Journal of Fluid Mechanics · doi:10.1017/s0022112075001814 · Cited by 4,014 · see citing works
Wilson, K. G. (1971) · Physical review. B, Solid state · doi:10.1103/physrevb.4.3174 · Cited by 2,341 · see citing works
Statistical Fluid Mechanics: The Mechanics of Turbulence
Monin, A. S., & Yaglom, A. M. (1999) · doi:10.21236/ada398728 · Cited by 1,949 · see citing works
Renormalization-Group Analysis of Turbulence
Yakhot, V., & Orszag, S. A. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.1722 · Cited by 1,717 · see citing works
Self-citationThe renormalization group and critical phenomena
Wilson, K. G. (1983) · Reviews of Modern Physics · doi:10.1103/revmodphys.55.583 · Cited by 1,685 · see citing works
Equations of turbulent motion in an incompressible fluid
Kolmogorov, A. N. (1941) · Cited by 1,295 · see citing works
Computational Modeling of Turbulent Flows
Lumley, J. L. (1979) · Advances in applied mechanics · doi:10.1016/s0065-2156(08)70266-7 · Cited by 1,234 · see citing works
Turbulence models for near-wall and low Reynolds number flows - A review
Patel, V. C., Rodi, W., & Scheuerer, G. (1985) · AIAA Journal · doi:10.2514/3.9086 · Cited by 1,133 · see citing works
A Reynolds stress model of turbulence and its application to thin shear flows
Hanjalić, K., & Launder, B. E. (1972) · Journal of Fluid Mechanics · doi:10.1017/s002211207200268x · Cited by 1,067 · see citing works
On nonlinear K-l and K -ε models of turbulence
Speziale, C. G. (1987) · Journal of Fluid Mechanics · doi:10.1017/s0022112087001319 · Cited by 665 · see citing works
Self-citationAnalytical Methods for the Development of Reynolds-Stress Closures in Turbulence
Speziale, C. G. (1991) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fl.23.010191.000543 · Cited by 596 · see citing works
Self-citationThe renormalization group, the ?-expansion and derivation of turbulence models
Yakhot, V., & Smith, L. M. (1992) · Journal of Scientific Computing · doi:10.1007/bf01060210 · Cited by 526 · see citing works
Self-citationTavoularis, S., & Corrsin, S. (1981) · Journal of Fluid Mechanics · doi:10.1017/s0022112081002930 · Cited by 511 · see citing works
Bardino, J., Ferziger, J. H., & Reynolds, W. C. (1983) · Stanford Univ. Report · Cited by 411 · see citing works
Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step
Kim, J., Kline, S. J., & Johnston, J. P. (1980) · Journal of Fluids Engineering · doi:10.1115/1.3240686 · Cited by 311 · see citing works
Effect of rotation on isotropic turbulence: computation and modelling
BARDINA, J., Ferziger, J. H., & Rogallo, R. S. (1985) · Journal of Fluid Mechanics · doi:10.1017/s0022112085001550 · Cited by 245 · see citing works
Nonlinear Reynolds stress models and the renormalization group
Rubinstein, R., & Barton, J. M. (1990) · Physics of Fluids A Fluid Dynamics · doi:10.1063/1.857595 · Cited by 204 · see citing works
Extending hydrodynamics via the regularization of the Chapman-Enskog expansion
Rosenau, P. (1989) · Physical Review A · doi:10.1103/physreva.40.7193 · Cited by 203 · see citing works
Viscoelastic properties of fine-grained incompressible turbulence
Crow, S. C. (1968) · Journal of Fluid Mechanics · doi:10.1017/s0022112068002314 · Cited by 188 · see citing works
Fundamentals of Turbulence for Turbulence Modeling and Simulation
Reynolds, W. C. (1987) · Cited by 166 · see citing works
On the Yakhot–Orszag renormalization group method for deriving turbulence statistics and models
Smith, L. M., & Reynolds, W. C. (1992) · Physics of Fluids A Fluid Dynamics · doi:10.1063/1.858310 · Cited by 150 · see citing works
Turbulent flow past a backward-facing step - A critical evaluation of two-equation models
Thangam, S., & Speziale, C. G. (1992) · AIAA Journal · doi:10.2514/3.11066 · Cited by 129 · see citing works
Self-citationLocal Anisotropy in Strained Turbulence at High Reynolds Numbers
Durbin, P. A., & Speziale, C. G. (1991) · Journal of Fluids Engineering · doi:10.1115/1.2926540 · Cited by 112 · see citing works
Self-citationEquations of Turbulent Motion in an Incompressible Fluid
Tikhomirov, V. М. (1991) · Springer eBooks · doi:10.1007/978-94-011-3030-1_48 · Cited by 57 · see citing works
An analysis of RNG-based turbulence models for homogeneous shear flow
Speziale, C. G., Gatski, T. B., & Fitzmaurice, N. (1991) · Physics of Fluids A Fluid Dynamics · doi:10.1063/1.857963 · Cited by 36 · see citing works
Self-citationScaling laws for homogeneous turbulent shear flows in a rotating frame
Speziale, C. G., & Mhuiris, N. M. G. (1989) · Physics of Fluids A Fluid Dynamics · doi:10.1063/1.857446 · Cited by 30 · see citing works
Self-citationSmagorinsky (1963) · doi:10.1175/1520-0493(1963)091
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Luzi, G., & McHardy, C. (2022) · Energies · doi:10.3390/en15113966 · Cited by 44 · see citing works
Frosting in a heat pump evaporator part B: Numerical analysis
Popovac, M., Emhofer, J., & Reichl, C. (2021) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2021.117488 · Cited by 26 · see citing works
- Authors
- Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B., & Speziale, C. G.
- Affiliations
- Langley Research Center (US)
- Princeton University (US)
- ORCID
- Gatski, T. B.
- Venue
- Physics of Fluids A: Fluid Dynamics
- Publisher
- AIP Publishing
- Published
- 1992-07-01
- Volume
- 4
- Issue
- 7
- Pages
- 1510-1520
- ISSN
- 0899-8213 (ISSN-L)
- OpenAlex
- W1983708969
- Cited by
- 2,832
- References
- 30
- Citations by year
- 2026: 158 · 2025: 160 · 2024: 170 · 2023: 201 · 2022: 178 · 2021: 178 · 2020: 163 · 2019: 141 · 2018: 155 · 2017: 133 · 2016: 126 · 2015: 106 · 2014: 102 · 2013: 113 · 2012: 85
- FWCI
- 23.67
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physics of Fluids A Fluid Dynamics (publishedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
- Physical Sciences › Engineering › Computational Mechanics › Computational Fluid Dynamics and Aerodynamics
- Physical Sciences › Engineering › Computational Mechanics › Combustion and flame dynamics
- Keywords
- turbulence modeling, turbulent shear flow, Reynolds stress, two-equation turbulence model, Reynolds stress model, homogeneous shear flow, backward-facing step
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