Large-Eddy Simulation of the Shock/Turbulence Interaction

doi:10.1006/JCPH.1999.6238

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Large-Eddy Simulation of the Shock/Turbulence Interaction

Journal Article•DOI•

Large-Eddy Simulation of the Shock/Turbulence Interaction

F. Ducros, V Ferrand¹, Franck Nicoud, C Weber, D Darracq, C Gacherieu, Thierry Poinsot¹ - Show less +3 more•Institutions (1)

IM Flash Technologies¹

01 Jul 1999-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 152, Iss: 2, pp 517-549

TL;DR: In this article, the authors derive a shock capturing tool able to treat turbulence with minimum dissipation out of the shock for a large-eddy simulation (LES) of the interaction.

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About: This article is published in Journal of Computational Physics.The article was published on 1999-07-01. It has received 605 citations till now. The article focuses on the topics: K-omega turbulence model & K-epsilon turbulence model.

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Journal Article•DOI•

Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble

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Emile Touber¹, Neil D. Sandham¹•Institutions (1)

University of Southampton¹

22 May 2009-Theoretical and Computational Fluid Dynamics

TL;DR: In this paper, a large-eddy simulation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer is presented, which does not introduce any energetic low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system.

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Abstract: The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. We present here a large-eddy simulation investigation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer. Contrary to past large-eddy simulation investigations on shock/turbulent boundary layer interactions, we have used an inflow technique which does not introduce any energetically significant low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system. The large-eddy simulation has been run for much longer times than previous computational studies making a Fourier analysis of the low frequency possible. The broadband and energetic low-frequency component found in the interaction is in excellent agreement with the experimental findings. Furthermore, a linear stability analysis of the mean flow was performed and a stationary unstable global mode was found. The long-run large-eddy simulation data were analyzed and a phase change in the wall pressure fluctuations was related to the global-mode structure, leading to a possible driving mechanism for the observed low-frequency motions.

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455 citations

Cites methods from "Large-Eddy Simulation of the Shock/..."

...In addition, a variant of the standard total variation diminishing scheme is used for shock capturing [57], coupled with the Ducros sensor [10]....
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Journal Article•DOI•

Numerical Methods for High-Speed Flows

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Sergio Pirozzoli

04 Jan 2011-Annual Review of Fluid Mechanics

TL;DR: In this paper, the authors review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves.

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Abstract: We review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves. Ideal numerical methods should be accurate and free from numerical dissipation in smooth parts of the flow, and at the same time they must robustly capture shock waves without significant Gibbs ringing, which may lead to nonlinear instability. Adapting to these conflicting goals leads to the design of strongly nonlinear numerical schemes that depend on the geometrical properties of the solution. For low-dissipation methods for smooth flows, numerical stability can be based on physical conservation principles for kinetic energy and/or entropy. Shock-capturing requires the addition of artificial dissipation, in more or less explicit form, as a surrogate for physical viscosity, to obtain nonoscillatory transitions. Methods suitable for both smooth and shocked flows are discussed, and the potential for hybridization is highlighted. Examples of the application of advanced algorithms to DNS/LES of turbulent, compressible flows are presented.

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381 citations

Journal Article•DOI•

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

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Eric Johnsen¹, Johan Larsson¹, Ankit Bhagatwala², William H. Cabot³, Parviz Moin¹, Britton J. Olson², Pradeep S. Rawat⁴, Santhosh K. Shankar², Björn Sjögreen³, Helen C. Yee⁵, Xiaolin Zhong⁴, Sanjiva K. Lele² - Show less +8 more•Institutions (5)

Center for Turbulence Research¹, Stanford University², Lawrence Livermore National Laboratory³, University of California, Los Angeles⁴, Ames Research Center⁵

01 Feb 2010-Journal of Computational Physics

TL;DR: The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation, and the hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor.

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357 citations

Journal Article•DOI•

Large Eddy Simulation of Flow Around an Airfoil Near Stall

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Ivan Mary, Pierre Sagaut

01 Jan 2002-AIAA Journal

TL;DR: In this paper, a large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x 10 6 is performed and compared with wind-tunnel experiments.

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Abstract: A large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x 10 6 is performed and compared with wind-tunnel experiments. This configuration still constitutes a challenging test case for Reynolds-averaged Navier-Stokes (RANS) simulation and LES as a result of the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment, and a turbulent separation near the trailing edge. To handle this high-Reynolds-number flow with LES on available supercomputers, a local mesh-refinement technique and a discretization of the convective fluxes are developed in a block-structured finite volume code to reduce the total number of grid points and the numerical dissipation acting on the small scales, respectively. Influence of subgrid scale modeling (SGS) is assessed through the comparisons of explicit selective mixed scale model (SMSM) and implicit monotone-integrated LES model results. Moreover, the solution sensitiveness to grid refinement and spanwise extent is investigated

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334 citations

Journal Article•DOI•

A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations

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Christophe Bogey¹, Nicolas de Cacqueray¹, Christophe Bailly¹•Institutions (1)

École centrale de Lyon¹

30 Mar 2009-Journal of Computational Physics

TL;DR: A shock-capturing methodology is developed for non-linear computations using low-dissipation schemes and centered finite differences that allows in particular to distinguish shocks from linear waves, and from vortices when it is performed from dilatation rather than from pressure.

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329 citations

Cites background from "Large-Eddy Simulation of the Shock/..."

...[41], a possibility is to take into account the local property of compressibility....
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...[41] also proposed a modified version of the Jameson detector taking into account the local property of compressibility, which is capable of discriminating between turbulent fluctuations and shocks [40,42]....
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References

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Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

[...]

Antony Jameson¹, Wolfgang Schmidt², Eli Turkel³•Institutions (3)

Princeton University¹, Dornier Flugzeugwerke², Tel Aviv University³

01 Jun 1981

TL;DR: In this paper, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.

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Abstract: A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free stream value.

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4,220 citations

"Large-Eddy Simulation of the Shock/..." refers methods in this paper

...Equations (5)‐(13) refer to the classical Jameson scheme as described in [ 42 ]....
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...For the present study where unsteady calculations are considered, the underlying numerical method consists of an explicit finite volume second-order centered scheme, augmented with a blending of second- and fourth-order artificial dissipation [ 42 ] for the space discretization....
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...Fourth-order dissipation is used to damp high-frequency modes developing in all centered schemes even in smooth regions of the fluid flow field [ 42 , 43]....
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Journal Article•DOI•

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

[...]

Parviz Moin¹, Kyle D. Squires, William H. Cabot, Sangsan Lee¹•Institutions (1)

Ames Research Center¹

01 Nov 1991-Physics of Fluids

TL;DR: Germano et al. as discussed by the authors generalized the dynamic subgrid-scale (SGS) model for the large eddy simulation (LES) of compressible flows and transport of a scalar.

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Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

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1,588 citations

"Large-Eddy Simulation of the Shock/..." refers background or methods in this paper

...Although a priori tests conducted on DNS of compressible turbulence suggest that the contribution of the trace of the subgrid scale tensor may be neglected [29], other works propose a model for this trace, either based on original work [30], or on an analog of Bardina’s model [31] or on the dynamic procedure of Germano [24]....
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...[24] using the dynamic model, although the dynamic model predicts an equilibrium value of the constant comparable to the value of Smagorinsky constant obtained using isotropic turbulence [24]....
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...3, the dynamic coefficient brought up by the modeling of the trace of the subgrid scale tensor can exceed the dynamic coefficient obtained for its anisotropic part: this finding is followed by the fact that the gradients of resolved pressure and of SGS kinetic energy are of the same order [24, 32]....
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...Although this approximation is neither supported by the hypothesis of passive scalar for temperature in compressible turbulence, nor by the results of [24], we chose it for its simplicity in this first approach....
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...[24]....
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Book•

Turbulence in fluids

[...]

Marcel Lesieur

01 Jan 1990

TL;DR: In this article, the transition from transition to Turbulence in fluid mechanics is described as follows: "Basic Fluid Dynamics, Transition to Turbence, Shear Flow Turbulence, Fourier Analysis of Homogeneous Turburbence, Isotropic Turbulences: Phenomenology and Simulations".

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Abstract: to Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards "Real World Turbulence".

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1,463 citations

Journal Article•DOI•

New Trends in Large-Eddy Simulations of Turbulence

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Marcel Lesieur, Olivier Métais

01 Jan 1996-Annual Review of Fluid Mechanics

TL;DR: In this article, a large-eddy simulation (LES) formalism, along with various subgrid-scale models developed since Smagorinsky's model, is presented, with an emphasis on the generation of coherent vortices.

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Abstract: The paper presents large-eddy simulation (LES) formalism, along with the various subgrid-scale models developed since Smagorinsky’s model. We show how Kraichnan’s spectral eddy viscosity may be implemented in physical space, yielding the structure-function model. Recent developments of this model that allow the eddy viscosity to be inhibited in transitional regions are discussed. We present a dynamic procedure, where a double filtering allows one to dynamically determine the subgrid-scale model constants. The importance of backscatter effects is discussed. Alternatives to the eddy-viscosity assumption, such as scale- similarity models, are considered. Pseudo-direct simulations in which numerical diffusion replaces subgrid transfers are mentioned. Various applications of LES to incompressible and compressible turbulent flows are given, with an emphasis on the generation of coherent vortices

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1,101 citations

"Large-Eddy Simulation of the Shock/..." refers methods in this paper

...An interpretation of high-order dissipative operators in terms of subgrid scale modeling is proposed by [ 39 ] within the formulation in physical space of a spectral eddy viscosity accounting for a cusp behaviour near kc....
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...chosen for„t is the filtered structure function model [38, 39 ]....
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Journal Article•DOI•

Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence

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Geneviève Comte-Bellot¹, Stanley Corrsin²•Institutions (2)

École centrale de Lyon¹, Johns Hopkins University²

28 Jul 1971-Journal of Fluid Mechanics

TL;DR: In this paper, the Eulerian time correlation coefficient of turbulent velocities passed through matched narrow-band niters shows a strong dependence on nominal filter frequency (∼ wave-number at these small turbulence levels).

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Abstract: Space-time correlation measurements in the roughly isotropic turbulence behind a regular grid spanning a uniform airstream give the simplest Eulerian time correlation if we choose for the upstream probe signal a time delay which just ‘cancels’ the mean flow displacement. The correlation coefficient of turbulent velocities passed through matched narrow-band niters shows a strong dependence on nominal filter frequency (∼ wave-number at these small turbulence levels). With plausible scaling of the time separations, a scaling dependent on both wave-number and time, it is possible to effect a good collapse of the correlation functions corresponding to wave-numbers from 0·5 cm−1, the location of the peak in the three-dimensional spectrum, to 10 cm−1, about half the Kolmogorov wave-number. The spectrally local time-scaling factor is a ‘parallel’ combination of the times characterizing (i) gross strain distortion by larger eddies, (ii) wrinkling distortion by smaller eddies, (iii) convection by larger eddies and (iv) gross rotation by larger eddies.

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991 citations

"Large-Eddy Simulation of the Shock/..." refers methods in this paper

...The energy of the initial purely solenoidal velocity field is contained in the large resolved scales and peaks up at ki LrefD 3. For the three remaining simulations (referred from CBC-1 to CBC-3), the initial conditions consist of a divergence-free velocity field with the same three-dimensional energy spectrum as in the Comte-Bellot and Corrsin experiment at the station tU0=MD42 (see [ 48 , 24])....
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