Introduction to Computational Fluid Dynamics CFD Tao Xing and Fred Stern IIHR Hydroscience Engineering C Maxwell Stanley Hydraulics Laboratory The University of Iowa 58 160 Intermediate Mechanics of Fluids http css engineering uiowa edu me 160 August 30 2006 Outline 1 2 3 4 5 6 7 8 What why and where of CFD Modeling Numerical methods Types of CFD codes CFD Educational Interface CFD Process Example of CFD Process 58 160 CFD Labs 2 What is CFD CFD is the simulation of fluids engineering systems using modeling mathematical physical problem formulation and numerical methods discretization methods solvers numerical parameters and grid generations etc Historically only Analytical Fluid Dynamics AFD and Experimental Fluid Dynamics EFD CFD made possible by the advent of digital computer and advancing with improvements of computer resources 500 flops 1947 20 teraflops 2003 3 Why use CFD Analysis and Design 1 Simulation based design instead of build test More cost effective and more rapid than EFD CFD provides high fidelity database for diagnosing flow field 2 Simulation of physical fluid phenomena that are difficult for experiments Full scale simulations e g ships and airplanes Environmental effects wind weather etc Hazards e g explosions radiation pollution Physics e g planetary boundary layer stellar evolution Knowledge and exploration of flow physics 4 Where is CFD used Where is CFD Aerospace used Aerospace Automotive Biomedical Biomedical Chemical Processing HVAC Hydraulics Marine Oil Gas Power Generation Sports F18 Store Separation Automotive Temperature and natural convection currents in the eye following laser heating 5 Where is CFD used Chemical Processing Where is CFD used Aerospacee Automotive Biomedical Chemical Processing HVAC Hydraulics Marine Oil Gas Power Generation Sports Polymerization reactor vessel prediction of flow separation and residence time effects Hydraulics HVAC Streamlines for workstation ventilation 6 Where is CFD used Marine movie Sports Where is CFD used Aerospace Automotive Biomedical Chemical Processing HVAC Hydraulics Marine Oil Gas Power Generation Sports Oil Gas Flow of lubricating mud over drill bit Power Generation Flow around cooling towers 7 Modeling Modeling is the mathematical physics problem formulation in terms of a continuous initial boundary value problem IBVP IBVP is in the form of Partial Differential Equations PDEs with appropriate boundary conditions and initial conditions Modeling includes 1 Geometry and domain 2 Coordinates 3 Governing equations 4 Flow conditions 5 Initial and boundary conditions 6 Selection of models for different applications 8 Modeling geometry and domain Simple geometries can be easily created by few geometric parameters e g circular pipe Complex geometries must be created by the partial differential equations or importing the database of the geometry e g airfoil into commercial software Domain size and shape Typical approaches Geometry approximation CAD CAE integration use of industry standards such as Parasolid ACIS STEP or IGES etc The three coordinates Cartesian system x y z cylindrical system r z and spherical system r should be appropriately chosen for a better resolution of the geometry e g cylindrical for circular pipe 9 Modeling coordinates z z Cartesian x y z Cylindrical r z z Spherical r z y x x General Curvilinear Coordinates r y x y r General orthogonal Coordinates 10 Modeling governing equations Navier Stokes equations 3D in Cartesian coordinates 2u 2 u 2u u u u u p u v w 2 2 2 t x y z x y z x 2v 2v 2v v v v v p u v w 2 2 2 t x y z y y z x 2 w 2 w 2 w w w w w p u v w 2 2 2 t x y z z y z x Local acceleration Convection Piezometric pressure gradient Viscous terms u v w 0 Continuity equation t x y z p RT D 2 R 3 DR 2 pv p R Dt 2 2 Dt L Equation of state Rayleigh Equation 11 Modeling flow conditions Based on the physics of the fluids phenomena CFD can be distinguished into different categories using different criteria Viscous vs inviscid Re External flow or internal flow wall bounded or not Turbulent vs laminar Re Incompressible vs compressible Ma Single vs multi phase Ca Thermal density effects Pr Gr Ec Free surface flow Fr and surface tension We Chemical reactions and combustion Pe Da etc 12 Modeling initial conditions Initial conditions ICS steady unsteady flows ICs should not affect final results and only affect convergence path i e number of iterations steady or time steps unsteady need to reach converged solutions More reasonable guess can speed up the convergence For complicated unsteady flow problems CFD codes are usually run in the steady mode for a few iterations for getting a better initial conditions 13 Modeling boundary conditions Boundary conditions No slip or slip free on walls periodic inlet velocity inlet mass flow rate constant pressure etc outlet constant pressure velocity convective numerical beach zerogradient and non reflecting for compressible flows such as acoustics etc No slip walls u 0 v 0 Outlet p c Inlet u c v 0 r o x v 0 dp dr 0 du dr 0 Periodic boundary condition in spanwise direction of an airfoil Axisymmetric 14 Modeling selection of models CFD codes typically designed for solving certain fluid phenomenon by applying different models Viscous vs inviscid Re Turbulent vs laminar Re Turbulent models Incompressible vs compressible Ma equation of state Single vs multi phase Ca cavitation model twofluid model Thermal density effects and energy equation Pr Gr Ec conservation of energy Free surface flow Fr level set surface tracking model and surface tension We bubble dynamic model Chemical reactions and combustion Chemical 15 Modeling Turbulence and free surface models Turbulent flows at high Re usually involve both large and small scale vortical structures and very thin turbulent boundary layer BL near models theTurbulent wall DNS most accurately solve NS equations but too expensive for turbulent flows RANS predict mean flow structures efficient inside BL but excessive diffusion in the separated region LES accurate in separation region and unaffordable for resolving BL Free surface models DES RANS inside BL LES in separated regions Surface tracking method mesh moving to capture free surface limited to small and medium wave slopes Single two phase level set method mesh fixed and levelset function used to capture the gas liquid interface capable of 16 Examples of modeling Turbulence and free surface models URANS Re 105 contour of vorticity for turbulent flow around NACA12 with
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