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Sharath S Girimaji - One of the best experts on this subject based on the ideXlab platform.
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lower dimensional manifold algebraic representation of Reynolds Stress closure equations
Theoretical and Computational Fluid Dynamics, 2001Co-Authors: Sharath S GirimajiAbstract:For complex turbulent flows, Reynolds Stress closure modeling (RSCM) is the lowest level at which models can be developed with some fidelity to the governing Navier–Stokes equations. Citing computational burden, researchers have long sought to reduce the seven-equation RSCM to the so-called algebraic Reynolds Stress model which involves solving only two evolution equations for turbulent kinetic energy and dissipation. In the past, reduction has been accomplished successfully in the weak-equilibrium limit of turbulence. In non-equilibrium turbulence, attempts at reduction have lacked mathematical rigor and have been based on ad hoc hypotheses resulting in less than adequate models.¶In this work we undertake a formal (numerical) examination of the dynamical system of equations that constitute the Reynolds Stress closure model to investigate the following questions. (i) When does the RSCM equation system formally permit reduced representation? (ii) What is the dimensionality (number of independent variables) of the permitted reduced system? (iii) How can one derive the reduced system (algebraic Reynolds Stress model) from the full RSCM equations? Our analysis reveals that a lower-dimensional representation of the RSCM equations is possible not only in the equilibrium limit, but also in the slow-manifold stage of non-equilibrium turbulence. The degree of reduction depends on the type of mean-flow deformation and state of turbulence. We further develop two novel methods for deriving algebraic Reynolds Stress models from RSCM equations in non-equilibrium turbulence. The present work is expected to play an important role in bringing much of the sophistication of the RSCM into the realm of two-equation algebraic Reynolds Stress models. Another objective of this work is to place the other algebraic Stress modeling efforts in the lower-dimensional modeling context.
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development of algebraic Reynolds Stress model for non equilibrium turbulence
1999Co-Authors: Sharath S GirimajiAbstract:For over 20 years, the Rodi (1976) weak-equilibrium assumption has been invoked to derive algebraic Reynolds Stress model from its transport equation. In this paper, we describe a more general procedure for formal development of an algebraic Reynolds Stress model in non-equilibrium turbulence. In this approach, the departure from equilibrium of anisotropy (b ij ) is parameterized in terms of the departure from equilibrium of relative strain rate (ω = e/SK, where S is some characteristic strain rate). An algebraic solution of the Reynolds Stress anisotropy transport equation in non-equilibrium turbulence is derived analytically for the case of two-dimensional mean flows employing quasilinear pressure-strain correlation model. The present model is compared with the full Reynolds Stress closure model against direct numerical simulation (DNS) data and rapid distortion theory (RDT) resulting in good agreement.
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a galilean invariant explicit algebraic Reynolds Stress model for turbulent curved flows
Physics of Fluids, 1997Co-Authors: Sharath S GirimajiAbstract:A Galilean invariant weak-equilibrium turbulence hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to a fully explicit algebraic expression for Reynolds Stress in terms of the mean velocity field and kinetic energy and dissipation of turbulence. The model is tested in curved homogeneous shear flow which is a homogeneous idealization of the circular streamline flow. The agreement is excellent with Reynolds Stress closure model and adequate with available experimental data.
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A GALILEAN INVARIANT EXPLICIT ALGEBRAIC Reynolds Stress MODEL FOR CURVED FLOWS
1996Co-Authors: Sharath S GirimajiAbstract:A Galilean invariant weak-equilibrium hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to an algebraic Reynolds Stress model for curved flows that is fully explicit and self-consistent. The model is tested in curved homogeneous shear flow: the agreement is excellent with Reynolds Stress closure model and adequate with available experimental data.
Arne V. Johansson - One of the best experts on this subject based on the ideXlab platform.
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algebraic Reynolds Stress modeling of turbulence subject to rapid homogeneous and non homogeneous compression or expansion
Physics of Fluids, 2016Co-Authors: Igor Grigoriev, Geert Brethouwer, Stefan Wallin, Olof Grundestam, Arne V. JohanssonAbstract:A recently developed explicit algebraic Reynolds Stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds Stress model for compressible turbulent flow with significant me ...
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engineering turbulence models and their development with emphasis on explicit algebraic Reynolds Stress models
2002Co-Authors: Arne V. JohanssonAbstract:Single-point turbulence models will be discussed from a somewhat analytical point of view. The lowest level of modelling considered here is that of eddy-viscosity-based two-equation models, but particular attention is given to explicit algebraic Reynolds Stress models (and explicit algebraic scalar flux models). Some new trends in models based directly on the Reynolds Stress transport equations are also discussed.
Fujihiro Hamba - One of the best experts on this subject based on the ideXlab platform.
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higher order realizable algebraic Reynolds Stress modeling based on the square root tensor
arXiv: Fluid Dynamics, 2019Co-Authors: Kazuhiro Inagaki, Taketo Ariki, Fujihiro HambaAbstract:In this study, realizable algebraic Reynolds Stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds Stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds Stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds Stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.
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euclidean invariance and weak equilibrium condition for the algebraic Reynolds Stress model
Journal of Fluid Mechanics, 2006Co-Authors: Fujihiro HambaAbstract:Taking into account the frame-invariance of a model expression under arbitrarily rotating transformations, Weis & Hutter (J. Fluid Mech. vol. 476, 2003, p. 63) proposed a Euclidean-objective weak-equilibrium condition for the algebraic Reynolds Stress model (ARSM). However, Gatski & Wallin (J. Fluid Mech. vol. 518, 2004, p. 147) pointed out that the weak-equilibrium condition proposed is not correct in actual rotating flows such as a rotating channel flow and showed that a non-objective weak-equilibrium condition extended to curved and rotating flows should be assumed. The frame-invariance is an important issue not only for the ARSM but also for general nonlinear eddy-viscosity models. By introducing the corotational derivative of the Reynolds Stress, the transport equation for the Reynolds Stress can be written to be frame-invariant. It is shown that a frame-invariant expression is desirable as a general model by comparing the error of model expressions in different rotating frames. The extended weak-equilibrium condition of Gatski & Wallin is examined to show that it is in reality objective and it does not contradict a frame-invariant model expression for the Reynolds Stress.
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nonlocal analysis of the Reynolds Stress in turbulent shear flow
Physics of Fluids, 2005Co-Authors: Fujihiro HambaAbstract:An exact expression for the Reynolds Stress is derived using the response function for the velocity fluctuation. The nonlocal eddy viscosity in the expression represents a contribution to the Reynolds Stress by the mean velocity gradient at remote points in space and time. A direct numerical simulation of channel flow is conducted to validate the nonlocal expression. The transport equations for the velocity and the response function are numerically solved to evaluate the nonlocal eddy viscosity; it is shown that the nonlocal expression is accurate for both normal and shear Stresses. A local expression for the Reynolds Stress is also evaluated and reveals that the local approximation is not accurate enough near the wall. Analysis using the nonlocal expression is shown to be useful for obtaining a better understanding of turbulent shear flow.
Stefan Wallin - One of the best experts on this subject based on the ideXlab platform.
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algebraic Reynolds Stress modeling of turbulence subject to rapid homogeneous and non homogeneous compression or expansion
Physics of Fluids, 2016Co-Authors: Igor Grigoriev, Geert Brethouwer, Stefan Wallin, Olof Grundestam, Arne V. JohanssonAbstract:A recently developed explicit algebraic Reynolds Stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds Stress model for compressible turbulent flow with significant me ...
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explicit algebraic and differential Reynolds Stress model application to homogeneously sheared and compressed turbulence
15th European Turbulence Conference ETC 2015 25 August 2015 through 28 August 2015, 2015Co-Authors: Igor Grigoriev, Stefan Wallin, Geert Brethouwer, Anders JohanssonAbstract:An explicit algebraic and differential Reynolds Stress models (EARSM and DRSM) are used to investigate the influence of homogeneous shear and compression on the behaviour of turbulence in the limit ...
Igor Grigoriev - One of the best experts on this subject based on the ideXlab platform.
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algebraic Reynolds Stress modeling of turbulence subject to rapid homogeneous and non homogeneous compression or expansion
Physics of Fluids, 2016Co-Authors: Igor Grigoriev, Geert Brethouwer, Stefan Wallin, Olof Grundestam, Arne V. JohanssonAbstract:A recently developed explicit algebraic Reynolds Stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds Stress model for compressible turbulent flow with significant me ...
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explicit algebraic and differential Reynolds Stress model application to homogeneously sheared and compressed turbulence
15th European Turbulence Conference ETC 2015 25 August 2015 through 28 August 2015, 2015Co-Authors: Igor Grigoriev, Stefan Wallin, Geert Brethouwer, Anders JohanssonAbstract:An explicit algebraic and differential Reynolds Stress models (EARSM and DRSM) are used to investigate the influence of homogeneous shear and compression on the behaviour of turbulence in the limit ...
