Methods for computation of flow-driven string dynamics in a pump and residence time

We present methods for computation of flow-driven string dynamics in a pump and related residence time. The string dynamics computations help us understand how the strings carried by a fluid interact with the pump surfaces, including the blades, and get stuck on or around those surfaces. The residence time computations help us to have a simplified but quick understanding of the string behavior. The core computational method is the Space–Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), a general-purpose NURBS mesh generation method for complex geometries, and a one-way-dependence model for the string dynamics. The ST-IGA with NURBS basis functions in space is used in both fluid mechanics and string structural dynamics. The ST framework provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the turbulent nature of the unsteady flow, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the pump geometry and increased accuracy in the flow solution. The IGA discretization also enables increased accuracy in the structural dynamics solution, as well as smoothness in the string shape and fluid dynamics forces computed on the string. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometry we have here. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small.

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

[2]  Victor M. Calo,et al.  YZβ discontinuity capturing for advection‐dominated processes with application to arterial drug delivery , 2007 .

[3]  Tayfun E. Tezduyar,et al.  SPACE–TIME VMS METHODS FOR MODELING OF INCOMPRESSIBLE FLOWS AT HIGH REYNOLDS NUMBERS , 2013 .

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

[5]  Tayfun E. Tezduyar,et al.  Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes , 2014 .

[6]  Yuri Bazilevs,et al.  Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment , 2014 .

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

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

[9]  Yuri Bazilevs,et al.  Wind turbine aerodynamics using ALE–VMS: validation and the role of weakly enforced boundary conditions , 2012 .

[10]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of compressible flows with the entropy and conservation variables formulations , 1993 .

[11]  Tayfun E. Tezduyar,et al.  Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces , 2007 .

[12]  Tayfun E. Tezduyar,et al.  Stabilized formulations for incompressible flows with thermal coupling , 2008 .

[13]  Alessandro Corsini,et al.  Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations , 2012 .

[14]  Alessandro Corsini,et al.  A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors , 2010 .

[15]  Tayfun E. Tezduyar,et al.  Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations , 1986 .

[16]  Yuri Bazilevs,et al.  Fluid–structure interaction modeling of wind turbines: simulating the full machine , 2012, Computational Mechanics.

[17]  Kenji Takizawa,et al.  Space–time computational analysis of MAV flapping-wing aerodynamics with wing clapping , 2015 .

[18]  Xiaowei Deng,et al.  Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines , 2017 .

[19]  Tayfun E. Tezduyar,et al.  SPACE–TIME FLUID–STRUCTURE INTERACTION METHODS , 2012 .

[20]  A. Korobenko,et al.  Novel structural modeling and mesh moving techniques for advanced fluid–structure interaction simulation of wind turbines , 2015 .

[21]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[22]  Thomas J. R. Hughes,et al.  Fluid–structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation , 2014, Computational Mechanics.

[23]  Tayfun E. Tezduyar,et al.  Special methods for aerodynamic-moment calculations from parachute FSI modeling , 2015 .

[24]  Tayfun E. Tezduyar,et al.  Modelling of fluid–structure interactions with the space–time finite elements: Solution techniques , 2007 .

[25]  Hitoshi Hattori,et al.  Computational analysis of flow-driven string dynamics in turbomachinery , 2017 .

[26]  Kenji Takizawa,et al.  Computer modeling techniques for flapping-wing aerodynamics of a locust , 2013 .

[27]  Thomas J. R. Hughes,et al.  Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations , 1984 .

[28]  Tayfun E. Tezduyar,et al.  Computational Methods for Parachute Fluid–Structure Interactions , 2012 .

[29]  Tayfun E. Tezduyar,et al.  METHODS FOR FSI MODELING OF SPACECRAFT PARACHUTE DYNAMICS AND COVER SEPARATION , 2013 .

[30]  Yuri Bazilevs,et al.  Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines , 2012 .

[31]  Kenji Takizawa,et al.  Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent , 2012, Computational Mechanics.

[32]  Tayfun E. Tezduyar,et al.  Enhanced-discretization Selective Stabilization Procedure (EDSSP) , 2006 .

[33]  A. Korobenko,et al.  FSI modeling of a propulsion system based on compliant hydrofoils in a tandem configuration , 2016 .

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

[35]  Tayfun E. Tezduyar,et al.  FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes , 2014 .

[36]  Pablo A. Kler,et al.  SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems , 2013 .

[37]  Tayfun E. Tezduyar,et al.  Space–time fluid mechanics computation of heart valve models , 2014 .

[38]  Tayfun E. Tezduyar,et al.  Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms , 2013 .

[39]  Tayfun E. Tezduyar,et al.  Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV , 2014 .

[40]  Yuri Bazilevs,et al.  Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling , 2012 .

[41]  Tayfun E. Tezduyar,et al.  Computation of Inviscid Supersonic Flows Around Cylinders and Spheres With the V-SGS Stabilization and YZβ Shock-Capturing , 2009 .

[42]  Kenji Takizawa,et al.  Computational engineering analysis with the new-generation space–time methods , 2014 .

[43]  Thomas J. R. Hughes,et al.  Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations , 1983 .

[44]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems , 1987 .

[45]  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..

[46]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics , 2011 .

[47]  Alessandro Corsini,et al.  A variational multiscale method for particle-cloud tracking in turbomachinery flows , 2014 .

[48]  Yuri Bazilevs,et al.  Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS , 2012 .

[49]  Tayfun E. Tezduyar,et al.  Stabilization and shock-capturing parameters in SUPG formulation of compressible flows , 2004 .

[50]  Tayfun E. Tezduyar,et al.  Multiscale space–time fluid–structure interaction techniques , 2011 .

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

[52]  Kenji Takizawa,et al.  Computational thermo-fluid analysis of a disk brake , 2016 .

[53]  Yuri Bazilevs,et al.  CHALLENGES AND DIRECTIONS IN COMPUTATIONAL FLUID–STRUCTURE INTERACTION , 2013 .

[54]  Yuri Bazilevs,et al.  An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. , 2015, Computer methods in applied mechanics and engineering.

[55]  A. Marsden,et al.  A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations , 2011 .

[56]  Yuri Bazilevs,et al.  Aerodynamic and FSI Analysis of Wind Turbines with the ALE-VMS and ST-VMS Methods , 2014 .

[57]  Tayfun E. Tezduyar,et al.  Space–Time Computational Analysis of Tire Aerodynamics with Actual Geometry, Road Contact, and Tire Deformation , 2018 .

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

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

[60]  Alessandro Corsini,et al.  Computer Modeling of Wave-Energy Air Turbines With the SUPG/PSPG Formulation and Discontinuity-Capturing Technique , 2012 .

[61]  Tayfun E. Tezduyar,et al.  Modeling of fluid–structure interactions with the space–time finite elements: contact problems , 2008 .

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

[63]  Yuri Bazilevs,et al.  Engineering Analysis and Design with ALE-VMS and Space–Time Methods , 2014 .

[64]  Tayfun E. Tezduyar,et al.  New Directions in Space–Time Computational Methods , 2016 .

[65]  T. Tezduyar,et al.  Particle tracking and particle–shock interaction in compressible-flow computations with the V-SGS stabilization and $$YZ\beta $$YZβ shock-capturing , 2015 .

[66]  Tayfun E. Tezduyar,et al.  Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: Applications to transient convection-diffusion problems , 1986 .

[67]  Tayfun E. Tezduyar,et al.  Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters , 2011 .

[68]  Alessandro Corsini,et al.  Stabilized finite element computation of NOx emission in aero‐engine combustors , 2011 .

[69]  Xiaowei Deng,et al.  Fluid–Structure Interaction Modeling of Vertical-Axis Wind Turbines , 2014 .

[70]  Kenji Takizawa,et al.  Space–time interface-tracking with topology change (ST-TC) , 2014 .

[71]  Kenji Takizawa,et al.  ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling , 2014 .

[72]  Tayfun E. Tezduyar,et al.  Space–time VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method , 2017 .

[73]  Yuri Bazilevs,et al.  Computational fluid–structure interaction: methods and application to a total cavopulmonary connection , 2009 .

[74]  Tayfun E. Tezduyar,et al.  Massively parallel finite element simulation Of compressible and incompressible flows , 1994 .

[75]  Thomas J. R. Hughes,et al.  Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device , 2009 .

[76]  Yuri Bazilevs,et al.  Modeling of a hydraulic arresting gear using fluid-structure interaction and isogeometric analysis , 2017 .

[77]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades , 2011 .

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

[79]  A. Korobenko,et al.  Fluid–Structure Interaction Modeling for Fatigue-Damage Prediction in Full-Scale Wind-Turbine Blades , 2016 .

[80]  A. Korobenko,et al.  STRUCTURAL MECHANICS MODELING AND FSI SIMULATION OF WIND TURBINES , 2013 .

[81]  A. Korobenko,et al.  Computational free-surface fluid–structure interaction with application to floating offshore wind turbines , 2016 .

[82]  Alessandro Corsini,et al.  A Multiscale Finite Element Formulation With Discontinuity Capturing for Turbulence Models With Dominant Reactionlike Terms , 2009 .

[83]  Yuri Bazilevs,et al.  Experimental and numerical FSI study of compliant hydrofoils , 2015 .

[84]  Tayfun E. Tezduyar,et al.  Computation of Inviscid Supersonic Flows Around Cylinders and Spheres with the SUPG Formulation and YZβ Shock-Capturing , 2006 .

[85]  Tayfun E. Tezduyar,et al.  Space–Time method for flow computations with slip interfaces and topology changes (ST-SI-TC) , 2016 .

[86]  Tayfun E. Tezduyar,et al.  Finite Element Methods for Fluid Dynamics with Moving Boundaries and Interfaces , 2004 .

[87]  T. Tezduyar,et al.  Computation of inviscid compressible flows with the V‐SGS stabilization and YZβ shock‐capturing , 2007 .

[88]  Tayfun E. Tezduyar,et al.  Space-Time Computational Techniques for the Aerodynamics of Flapping Wings , 2012 .

[89]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[90]  A. Korobenko,et al.  Recent Advances in ALE-VMS and ST-VMS Computational Aerodynamic and FSI Analysis of Wind Turbines , 2018 .

[91]  T. Tezduyar,et al.  Space–time computation techniques with continuous representation in time (ST-C) , 2014 .

[92]  Tayfun E. Tezduyar,et al.  FSI modeling of the Orion spacecraft drogue parachutes , 2015 .

[93]  Hitoshi Hattori,et al.  Space–time VMS method for flow computations with slip interfaces (ST-SI) , 2015 .

[94]  Tayfun E. Tezduyar,et al.  SUPG finite element computation of inviscid supersonic flows with YZβ shock-Capturing , 2007 .

[95]  Yuri Bazilevs,et al.  Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulation , 2011 .

[96]  Tayfun E. Tezduyar,et al.  Space–time finite element computation of complex fluid–structure interactions , 2010 .

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

[98]  Tayfun E. Tezduyar,et al.  Ram-air parachute structural and fluid mechanics computations with the Space-Time Isogeometric Analysis (ST-IGA) , 2016 .

[99]  Tayfun E. Tezduyar,et al.  A Geometrical-Characteristics Study in Patient-Specific FSI Analysis of Blood Flow in the Thoracic Aorta , 2016 .

[100]  Tayfun E. Tezduyar,et al.  Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity , 2017 .

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

[102]  Tayfun E. Tezduyar,et al.  Space–time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle , 2012 .

[103]  Tayfun E. Tezduyar,et al.  Aorta flow analysis and heart valve flow and structure analysis , 2018 .

[104]  Alessandro Corsini,et al.  Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD) , 2007 .

[105]  Kenji Takizawa,et al.  Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity , 2013 .

[106]  Yuri Bazilevs,et al.  Free-Surface Flow and Fluid-Object Interaction Modeling With Emphasis on Ship Hydrodynamics , 2012 .

[107]  Yuri Bazilevs,et al.  ALE-VMS AND ST-VMS METHODS FOR COMPUTER MODELING OF WIND-TURBINE ROTOR AERODYNAMICS AND FLUID–STRUCTURE INTERACTION , 2012 .

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

[109]  Tayfun E. Tezduyar,et al.  Heart valve flow computation with the integrated Space–Time VMS, Slip Interface, Topology Change and Isogeometric Discretization methods , 2017 .

[110]  Tayfun E. Tezduyar,et al.  Space–time VMS computation of wind-turbine rotor and tower aerodynamics , 2014 .

[111]  Yuri Bazilevs,et al.  Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models , 2015, Computational mechanics.

[112]  Ming-Chen Hsu,et al.  Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms , 2010, Biomechanics and modeling in mechanobiology.

[113]  T. Tezduyar,et al.  Stabilized space–time computation of wind-turbine rotor aerodynamics , 2011 .

[114]  Tayfun E. Tezduyar,et al.  Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity , 2012 .

[115]  Yuri Bazilevs,et al.  A fully-coupled fluid-structure interaction simulation of cerebral aneurysms , 2010 .

[116]  Tayfun E. Tezduyar,et al.  Heart Valve Flow Computation with the Space–Time Slip Interface Topology Change (ST-SI-TC) Method and Isogeometric Analysis (IGA) , 2018 .

[117]  Yuri Bazilevs,et al.  Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics , 2011 .

[118]  Tayfun E. Tezduyar,et al.  Space–time techniques for computational aerodynamics modeling of flapping wings of an actual locust , 2012 .

[119]  Yuri Bazilevs,et al.  Fluid–structure interaction simulation of pulsatile ventricular assist devices , 2013, Computational Mechanics.

[120]  Yuri Bazilevs,et al.  Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk , 2014 .

[121]  Yuri Bazilevs,et al.  Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells , 2013 .

[122]  Hitoshi Hattori,et al.  Turbocharger flow computations with the Space-Time Isogeometric Analysis (ST-IGA) , 2017 .

[123]  T. Tezduyar,et al.  A parallel 3D computational method for fluid-structure interactions in parachute systems , 2000 .

[124]  A. Korobenko,et al.  Aerodynamic Simulation of Vertical-Axis Wind Turbines , 2014 .

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

[126]  Tayfun E. Tezduyar,et al.  A General-Purpose NURBS Mesh Generation Method for Complex Geometries , 2018 .

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

[128]  Yuri Bazilevs,et al.  New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods , 2015 .

[129]  Kenji Takizawa,et al.  FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta , 2014 .

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

[131]  T. Tezduyar,et al.  Improved Discontinuity-capturing Finite Element Techniques for Reaction Effects in Turbulence Computation , 2006 .

[132]  A. L. Marsden,et al.  Computation of residence time in the simulation of pulsatile ventricular assist devices , 2014 .