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Title: Efficient implicit LES method for the simulation of turbulent cavitating flows

Abstract

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flow field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.

Authors:
 [1];  [1];  [1];  [2];  [1]
  1. Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, Boltzmannstr. 15, Garching bei München (Germany)
  2. (Netherlands)
Publication Date:
OSTI Identifier:
22572325
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 316; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAVITATION; COMPRESSIBLE FLOW; DESIGN; ERRORS; FUNCTIONS; HOMOGENEOUS MIXTURES; INTERFACES; LARGE-EDDY SIMULATION; LAYERS; LIQUID FLOW; LIQUIDS; LTE; MIXING; MULTIPHASE FLOW; SCALE MODELS; SENSORS; SHOCK WAVES; STANDARDS; TURBULENCE

Citation Formats

Egerer, Christian P., E-mail: christian.egerer@aer.mw.tum.de, Schmidt, Steffen J., Hickel, Stefan, Aerodynamics Group, Faculty of Aerospace Engineering, Technische Universiteit Delft, P.O. Box 5058, 2600 GB Delft, and Adams, Nikolaus A. Efficient implicit LES method for the simulation of turbulent cavitating flows. United States: N. p., 2016. Web. doi:10.1016/J.JCP.2016.04.021.
Egerer, Christian P., E-mail: christian.egerer@aer.mw.tum.de, Schmidt, Steffen J., Hickel, Stefan, Aerodynamics Group, Faculty of Aerospace Engineering, Technische Universiteit Delft, P.O. Box 5058, 2600 GB Delft, & Adams, Nikolaus A. Efficient implicit LES method for the simulation of turbulent cavitating flows. United States. doi:10.1016/J.JCP.2016.04.021.
Egerer, Christian P., E-mail: christian.egerer@aer.mw.tum.de, Schmidt, Steffen J., Hickel, Stefan, Aerodynamics Group, Faculty of Aerospace Engineering, Technische Universiteit Delft, P.O. Box 5058, 2600 GB Delft, and Adams, Nikolaus A. 2016. "Efficient implicit LES method for the simulation of turbulent cavitating flows". United States. doi:10.1016/J.JCP.2016.04.021.
@article{osti_22572325,
title = {Efficient implicit LES method for the simulation of turbulent cavitating flows},
author = {Egerer, Christian P., E-mail: christian.egerer@aer.mw.tum.de and Schmidt, Steffen J. and Hickel, Stefan and Aerodynamics Group, Faculty of Aerospace Engineering, Technische Universiteit Delft, P.O. Box 5058, 2600 GB Delft and Adams, Nikolaus A.},
abstractNote = {We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flow field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.},
doi = {10.1016/J.JCP.2016.04.021},
journal = {Journal of Computational Physics},
number = ,
volume = 316,
place = {United States},
year = 2016,
month = 7
}
  • Cited by 9
  • Numerical approximation of the five-equation two-phase flow of Kapila et al. [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002–3024] is examined. This model has shown excellent capabilities for the numerical resolution of interfaces separating compressible fluids as well as wave propagation in compressible mixtures [A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics 202(2) (2005) 664–698; R. Abgrall, V. Perrier, Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flows, SIAMmore » Journal of Multiscale and Modeling and Simulation (5) (2006) 84–115; F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214–2248]. However, its numerical approximation poses some serious difficulties. Among them, the non-monotonic behavior of the sound speed causes inaccuracies in wave’s transmission across interfaces. Moreover, volume fraction variation across acoustic waves results in difficulties for the Riemann problem resolution, and in particular for the derivation of approximate solvers. Volume fraction positivity in the presence of shocks or strong expansion waves is another issue resulting in lack of robustness. To circumvent these difficulties, the pressure equilibrium assumption is relaxed and a pressure non-equilibrium model is developed. It results in a single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms. It fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them. This formulation considerably simplifies numerical resolution. Following a strategy developed previously for another flow model [R. Saurel, R. Abgrall, A multiphase Godunov method for multifluid and multiphase flows, Journal of Computational Physics 150 (1999) 425–467], the hyperbolic part is first solved without relaxation terms with a simple, fast and robust algorithm, valid for unstructured meshes. Second, stiff relaxation terms are solved with a Newton method that also guarantees positivity and robustness. The algorithm and model are compared to exact solutions of the Euler equations as well as solutions of the five-equation model under extreme flow conditions, for interface computation and cavitating flows involving dynamics appearance of interfaces. In order to deal with correct dynamic of shock waves propagating through multiphase mixtures, the artificial heat exchange method of Petitpas et al. [F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214–2248] is adapted to the present formulation.« less
  • Numerical approximation of the five-equation two-phase flow of Kapila et al. [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10) (2001) 3002-3024] is examined. This model has shown excellent capabilities for the numerical resolution of interfaces separating compressible fluids as well as wave propagation in compressible mixtures [A. Murrone, H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics 202(2) (2005) 664-698; R. Abgrall, V. Perrier, Asymptotic expansion of a multiscale numerical scheme for compressible multiphase flows, SIAMmore » Journal of Multiscale and Modeling and Simulation (5) (2006) 84-115; F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214-2248]. However, its numerical approximation poses some serious difficulties. Among them, the non-monotonic behavior of the sound speed causes inaccuracies in wave's transmission across interfaces. Moreover, volume fraction variation across acoustic waves results in difficulties for the Riemann problem resolution, and in particular for the derivation of approximate solvers. Volume fraction positivity in the presence of shocks or strong expansion waves is another issue resulting in lack of robustness. To circumvent these difficulties, the pressure equilibrium assumption is relaxed and a pressure non-equilibrium model is developed. It results in a single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms. It fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them. This formulation considerably simplifies numerical resolution. Following a strategy developed previously for another flow model [R. Saurel, R. Abgrall, A multiphase Godunov method for multifluid and multiphase flows, Journal of Computational Physics 150 (1999) 425-467], the hyperbolic part is first solved without relaxation terms with a simple, fast and robust algorithm, valid for unstructured meshes. Second, stiff relaxation terms are solved with a Newton method that also guarantees positivity and robustness. The algorithm and model are compared to exact solutions of the Euler equations as well as solutions of the five-equation model under extreme flow conditions, for interface computation and cavitating flows involving dynamics appearance of interfaces. In order to deal with correct dynamic of shock waves propagating through multiphase mixtures, the artificial heat exchange method of Petitpas et al. [F. Petitpas, E. Franquet, R. Saurel, O. Le Metayer, A relaxation-projection method for compressible flows. Part II. The artificial heat exchange for multiphase shocks, Journal of Computational Physics 225(2) (2007) 2214-2248] is adapted to the present formulation.« less
  • Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data ofmore » the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.« less
  • We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k{sup D{minus}1} in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger`s equation and two-dimensional incompressible MHD flows.