Simulation of stably stratified turbulent channel flow using residual-based variational multiscale method and isogeometric analysis

Abstract Stably stratified turbulent channel flow (STCF) is a canonical flow that is representative of shear-driven boundary mixing processes in geophysical settings. We examine the performance of a turbulence modeling framework composed of residual-based variational multiscale method (RBVMS) and isogeometric analysis (IGA) applied to STCF at friction Reynolds number R e τ = 180 . The framework is implemented with two augmentation companion features, namely weak imposition of Dirichlet boundary conditions (WD) and a new subgrid-scale (SGS) model. The performance of the modeling framework, as well as its interaction with the two companion features, are assessed in both weakly and strongly stratified regimes. In comparison to existing direct numerical simulation (DNS) data, our study reveals that RBVMS–IGA framework is able to faithfully capture the flow structures and one-point statistics in STCF simulation with relatively coarse grid resolution. The framework also demonstrates its capability of replicating intermittent flow dynamics under strong stratification. Such characteristics dynamics are reproduced robustly when the modeling framework is enhanced with WD and the new SGS model, features that are shown to generally improve numerical accuracy of simulations for the cases tested. Our results confirm the computational efficiency as well as the robustness of RBVMS–IGA framework in modeling wall-bounded stratified flows.

[1]  Thomas J. R. Hughes,et al.  Large eddy simulation of turbulent channel flows by the variational multiscale method , 2001 .

[2]  T. Hughes,et al.  ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES , 2006 .

[3]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[4]  Thomas J. R. Hughes,et al.  n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method , 2009 .

[5]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[6]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[7]  B. Grisogono,et al.  Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain , 2018 .

[8]  L. H. Thomas.  THE STABILITY OF PLANE POISEUILLE FLOW , 1952 .

[9]  Tayfun E. Tezduyar,et al.  Space–Time Variational Multiscale Isogeometric Analysis of a tsunami-shelter vertical-axis wind turbine , 2020, Computational Mechanics.

[10]  Thomas J. R. Hughes,et al.  What are C and h ?: inequalities for the analysis and design of finite element methods , 1992 .

[11]  Yuri Bazilevs,et al.  Computational and experimental investigation of free vibration and flutter of bridge decks , 2018, Computational Mechanics.

[12]  Tayfun E. Tezduyar,et al.  Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization , 2018, Computational Mechanics.

[13]  T. Hughes,et al.  Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes , 2010 .

[14]  R. Tailleux.  Available Potential Energy and Exergy in Stratified Fluids , 2013 .

[15]  Yuri Bazilevs,et al.  Isogeometric divergence-conforming variational multiscale formulation of incompressible turbulent flows , 2017 .

[16]  Tayfun E. Tezduyar,et al.  Turbocharger turbine and exhaust manifold flow computation with the Space–Time Variational Multiscale Method and Isogeometric Analysis , 2019, Computers & Fluids.

[17]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[18]  J. Riley,et al.  Fluid Motions in the Presence of Strong Stable Stratification , 2000 .

[19]  Manuel García-Villalba,et al.  Turbulence modification by stable stratification in channel flow , 2011 .

[20]  Yuki Ueda,et al.  A node-numbering-invariant directional length scale for simplex elements , 2019, Mathematical Models and Methods in Applied Sciences.

[21]  P. Moin,et al.  A numerical method for large-eddy simulation in complex geometries , 2004 .

[22]  Vincenzo Armenio,et al.  An investigation of stably stratified turbulent channel flow using large-eddy simulation , 2002, Journal of Fluid Mechanics.

[23]  Victor M. Calo,et al.  The role of continuity in residual-based variational multiscale modeling of turbulence , 2007 .

[24]  J. R. Taylor,et al.  The intermittency boundary in stratified plane Couette flow , 2015, Journal of Fluid Mechanics.

[25]  T. Tezduyar.  Computation of moving boundaries and interfaces and stabilization parameters , 2003 .

[26]  K. S. Gage,et al.  The stability of thermally stratified plane Poiseuille flow , 1968, Journal of Fluid Mechanics.

[27]  Thomas J. R. Hughes,et al.  NURBS-based isogeometric analysis for the computation of flows about rotating components , 2008 .

[28]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[29]  Tayfun E. Tezduyar,et al.  Multiscale space-time methods for thermo-fluid analysis of a ground vehicle and its tires , 2015 .

[30]  Steven A. Orszag,et al.  Large Eddy Simulation of Complex Engineering and Geophysical Flows , 2010 .

[31]  Victor M. Calo,et al.  Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow , 2008 .

[32]  Tayfun E. Tezduyar,et al.  Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations , 2018 .

[33]  Ming-Chen Hsu,et al.  A residual-based variational multiscale method with weak imposition of boundary conditions for buoyancy-driven flows , 2019, Computer Methods in Applied Mechanics and Engineering.

[34]  Carl Wunsch,et al.  VERTICAL MIXING, ENERGY, AND THE GENERAL CIRCULATION OF THE OCEANS , 2004 .

[35]  Ming-Chen Hsu,et al.  Immersogeometric fluid-structure interaction modeling and simulation of transcatheter aortic valve replacement. , 2019, Computer methods in applied mechanics and engineering.

[36]  Yuri Bazilevs,et al.  Heart valve isogeometric sequentially-coupled FSI analysis with the space–time topology change method , 2020 .

[37]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[38]  R. Kerswell,et al.  A prediction for the optimal stratification for turbulent mixing , 2009, Journal of Fluid Mechanics.

[39]  A. Korobenko,et al.  FSI Simulation of two back-to-back wind turbines in atmospheric boundary layer flow , 2017 .

[40]  Victor M. Calo,et al.  Weak Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows , 2007 .

[41]  Tayfun E. Tezduyar,et al.  Anatomically realistic lumen motion representation in patient-specific space–time isogeometric flow analysis of coronary arteries with time-dependent medical-image data , 2020, Computational Mechanics.

[42]  P. Mason.  Large‐eddy simulation: A critical review of the technique , 1994 .

[43]  Tayfun E. Tezduyar,et al.  Space–time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle , 2019, Computational Mechanics.

[44]  Yuri Bazilevs,et al.  Large-eddy simulation with near-wall modeling using weakly enforced no-slip boundary conditions , 2015 .

[45]  P. Linden,et al.  Diapycnal mixing in layered stratified plane Couette flow quantified in a tracer-based coordinate , 2017, Journal of Fluid Mechanics.

[46]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[47]  A. Scotti,et al.  The Mixing Efficiency of Stratified Turbulent Boundary Layers , 2016 .

[48]  John R. Taylor,et al.  Self-similar mixing in stratified plane Couette flow for varying Prandtl number , 2017, Journal of Fluid Mechanics.

[49]  Yuri Bazilevs,et al.  Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method , 2020 .

[50]  A. Korobenko,et al.  A new variational multiscale formulation for stratified incompressible turbulent flows , 2017 .

[51]  Tore Andreas Helgedagsrud,et al.  A variational multiscale framework for atmospheric turbulent flows over complex environmental terrains , 2020 .

[52]  M. G. Gelder,et al.  In Reply: BEHAVIOUR THERAPY , 1965 .

[53]  I. Akkerman,et al.  Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method , 2010, J. Comput. Phys..

[54]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[55]  A. Korobenko,et al.  ALE–VMS formulation for stratified turbulent incompressible flows with applications , 2015 .

[56]  Yuri Bazilevs,et al.  Computational Fluid-Structure Interaction: Methods and Applications , 2013 .

[57]  P. Moin,et al.  The basic equations for the large eddy simulation of turbulent flows in complex geometry , 1995 .

[58]  A. W. Vreman.  An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications , 2004 .

[59]  Tayfun E. Tezduyar,et al.  Element length calculation in B-spline meshes for complex geometries , 2020, Computational Mechanics.

[60]  Tayfun E. Tezduyar,et al.  Tire aerodynamics with actual tire geometry, road contact and tire deformation , 2018, Computational Mechanics.

[61]  A. Oberai,et al.  A mixed large eddy simulation model based on the residual-based variational multiscale formulation , 2010 .

[62]  G. Zimmermann,et al.  Mycopathogens of soil insects , 1989 .

[63]  T. Hughes,et al.  Large Eddy Simulation and the variational multiscale method , 2000 .

[64]  K. Trenberth,et al.  The atmospheric energy budget and implications for surface fluxes and ocean heat transports , 2001 .

[65]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[66]  Branko Kosovic,et al.  Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers , 1997, Journal of Fluid Mechanics.

[67]  A. Bayram,et al.  Variational multiscale framework for cavitating flows , 2020 .

[68]  W. Tang,et al.  Reynolds number dependence of an upper bound for the long-time-averaged buoyancy flux in plane stratified Couette flow , 2004, Journal of Fluid Mechanics.

[69]  Thomas J. R. Hughes,et al.  Weak imposition of Dirichlet boundary conditions in fluid mechanics , 2007 .

[70]  Joel H. Ferziger,et al.  Stably stratified turbulent channel flows. I. Stratification regimes and turbulence suppression mechanism , 2000 .

[71]  J. Koseff,et al.  Density Stratification, Turbulence, but How Much Mixing? , 2008 .

[72]  W. Munk,et al.  Abyssal recipes II: energetics of tidal and wind mixing , 1998 .

[73]  Jinhui Yan,et al.  Residual-based variational multi-scale modeling for particle-laden gravity currents over flat and triangular wavy terrains , 2019, Computers & Fluids.

[74]  Tayfun E. Tezduyar,et al.  Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change , 2020, Computational Mechanics.