Simulation of laminar and turbulent concentric pipe flows with the isogeometric variational multiscale method

Abstract We present an application of the residual-based variational multiscale modeling methodology to the computation of laminar and turbulent concentric annular pipe flows. Isogeometric analysis is utilized for higher-order approximation of the solution using Non-Uniform Rational B-Splines (NURBS). The ability of NURBS to exactly represent curved geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through annular channels. We demonstrate the applicability of the methodology to both laminar and turbulent flow regimes.

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

[2]  Victor M. Calo,et al.  The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers , 2012 .

[3]  Victor M. Calo,et al.  Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls , 2012 .

[4]  G. Sangalli,et al.  A fully ''locking-free'' isogeometric approach for plane linear elasticity problems: A stream function formulation , 2007 .

[5]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .

[6]  Rickard Bensow,et al.  Vorticity–strain residual‐based turbulence modelling of the Taylor–Green vortex , 2007 .

[7]  Thomas J. R. Hughes,et al.  Multiscale and Stabilized Methods , 2007 .

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

[9]  Wolfgang A. Wall,et al.  Time-dependent subgrid scales in residual-based large eddy simulation of turbulent channel flow , 2010 .

[10]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[11]  Yuri Bazilevs,et al.  High-performance computing of wind turbine aerodynamics using isogeometric analysis , 2011 .

[12]  Charbel Farhat,et al.  A Variational Multiscale Method for the Large Eddy Simulation of Compressible Turbulent Flows on Unstructured Meshes - Application to vortex shedding , 2004 .

[13]  Victor M. Calo,et al.  Residual-based multiscale turbulence modeling: Finite volume simulations of bypass transition , 2005 .

[14]  Siamack A. Shirazi,et al.  Evaluation of Several Turbulence Models for Turbulent Flow in Concentric and Eccentric Annuli , 1998 .

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

[16]  K. Rehme Turbulence measurements in smooth concentric annuli with small radius ratios , 1975, Journal of Fluid Mechanics.

[17]  Thomas J. R. Hughes,et al.  An isogeometric analysis approach to gradient damage models , 2011 .

[18]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems , 1986 .

[19]  Thomas J. R. Hughes,et al.  Sensitivity of the scale partition for variational multiscale large-eddy simulation of channel flow , 2004 .

[20]  T. Hughes,et al.  Sensitivity of the scale partition for variational multiscale LES of channel flow , 2004 .

[21]  Giancarlo Sangalli,et al.  Variational Multiscale Analysis: the Fine-scale Green's Function, Projection, Optimization, Localization, and Stabilized Methods , 2007, SIAM J. Numer. Anal..

[22]  Tayfun E. Tezduyar,et al.  Finite element stabilization parameters computed from element matrices and vectors , 2000 .

[23]  R. Moser,et al.  Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity , 1994, Journal of Fluid Mechanics.

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

[25]  Victor M. Calo,et al.  Isogeometric Variational Multiscale Large-Eddy Simulation of Fully-developed Turbulent Flow over a Wavy Wall , 2012 .

[26]  Thomas J. R. Hughes,et al.  Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations , 2004 .

[27]  G. Haller An objective definition of a vortex , 2004, Journal of Fluid Mechanics.

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

[29]  Thomas J. R. Hughes,et al.  Patient-Specific Vascular NURBS Modeling for Isogeometric Analysis of Blood Flow , 2007, IMR.

[30]  Jamshid M. Nouri,et al.  Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli , 1993, Journal of Fluid Mechanics.

[31]  Victor M. Calo,et al.  A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high‐order B‐spline finite elements , 2012 .

[32]  C. Lawn,et al.  Fully Developed Turbulent Flow through Concentric Annuli , 1972 .

[33]  Xi-Yun Lu,et al.  Large eddy simulation of turbulent concentric annular channel flows , 2004 .

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

[35]  Alessandro Reali,et al.  Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) , 2007 .

[36]  T. Hughes,et al.  Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations , 2010 .

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

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

[39]  Thomas J. R. Hughes,et al.  Isogeometric Analysis for Topology Optimization with a Phase Field Model , 2012 .

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

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

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

[43]  T. Hughes Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[44]  F. Auricchio,et al.  The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations , 2010 .

[45]  Srinivas Ramakrishnan,et al.  Turbulence control simulation using the variational multiscale method , 2004 .

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

[47]  H. Sung,et al.  DIRECT NUMERICAL SIMULATION OF TURBULENT CONCENTRIC ANNULAR PIPE FLOW , 2002, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

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

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

[50]  Alessandro Reali,et al.  AN ISO GEOMETRIC ANALYSIS APPROACH FOR THE STUDY OF STRUCTURAL VIBRATIONS , 2006 .

[51]  W. Wall,et al.  An extended residual-based variational multiscale method for two-phase flow including surface tension , 2011 .

[52]  Thomas J. R. Hughes,et al.  The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence , 2001 .

[53]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[54]  Alessandro Reali,et al.  Duality and unified analysis of discrete approximations in structural dynamics and wave propagation : Comparison of p-method finite elements with k-method NURBS , 2008 .

[55]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[56]  M. P. Escudier,et al.  Flow of shear-thinning fluids in a concentric annulus , 1995 .

[57]  Victor M. Calo,et al.  Improving stability of stabilized and multiscale formulations in flow simulations at small time steps , 2010 .

[58]  Jesús Ildefonso Díaz Díaz,et al.  ON THE COMPLEX GINZBURG–LANDAU EQUATION WITH A DELAYED FEEDBACK , 2006 .

[59]  R. Codina,et al.  Time dependent subscales in the stabilized finite element approximation of incompressible flow problems , 2007 .

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

[61]  S. Collis,et al.  Monitoring unresolved scales in multiscale turbulence modeling , 2001 .

[62]  T. Hughes,et al.  Variational and Multiscale Methods in Turbulence , 2005 .