Introduction to Computational Introduction to Computational Fluid DynamicsFluid Dynamics

Adapted from notes by:

Tao Xing and Fred Stern

The University of Iowa

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OutlineOutline

What is CFD?Why use CFD?Where is CFD used? PhysicsModelingNumericsCFD processResources

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What is CFD?What is CFD?

What is CFD and its objective?

– Computational Fluid Dynamics– Historically Analytical Fluid Dynamics (AFD) and EFD

(Experimental Fluid Dynamics) was used. CFD has become feasible due to the advent of high speed digital computers.

– Computer simulation for prediction of fluid-flow phenomena. – The objective of CFD is to model the continuous fluids with

Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem (Taylor series), solve it, validate it and achieve simulation based design.

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Why use CFD?Why use CFD?

Why use CFD?– Analysis and Design

Simulation-based design instead of “build & test”– More cost effectively and more rapidly than with experiments– CFD solution provides high-fidelity database for interrogation of

flow field Simulation of physical fluid phenomena that are difficult to be

measured by experiments– Scale simulations (e.g., full-scale ships, airplanes)– Hazards (e.g., explosions, radiation, pollution)– Physics (e.g., weather prediction, planetary boundary layer,

stellar evolution)

– Knowledge and exploration of flow physics

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Where is CFD used? (Aerospace)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

F18 Store Separation

Wing-Body Interaction Hypersonic Launch Vehicle

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Where is CFD used? (Appliances)

• Where is CFD used?– Aerospace

– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

Surface-heat-flux plots of the No-Frost refrigerator and freezer compartments helped BOSCH-SIEMENS engineers to optimize the location of air inlets.

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Where is CFD used? (Automotive)

• Where is CFD used?– Aerospace– Appliances

– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

External Aerodynamics Undercarriage Aerodynamics

Interior Ventilation Engine Cooling

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Where is CFD used? (Biomedical)

• Where is CFD used?– Aerospace– Appliances– Automotive

– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

Temperature and natural convection currents in the eye following laser heating.

Spinal Catheter

Medtronic Blood Pump

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Where is CFD used? (Chemical Processing)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical

– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

Polymerization reactor vessel - prediction of flow separation and residence time effects.

Shear rate distribution in twin-screw extruder simulation

Twin-screw extruder modeling

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Where is CFD used? (HVAC&R)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing

– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

Particle traces of copier VOC emissions colored by concentration level fall behind the copier and then circulate through the room before exiting the exhaust.

Mean age of air contours indicate location of fresh supply air

Streamlines for workstation ventilation

Flow pathlines colored by pressure quantify head loss in ductwork

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Where is CFD used? (Hydraulics)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R

– Hydraulics– Marine– Oil & Gas– Power Generation– Sports

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Where is CFD used? (Marine)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics

– Marine– Oil & Gas– Power Generation– Sports

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Where is CFD used? (Oil & Gas)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine

– Oil & Gas– Power Generation– Sports

Flow vectors and pressure distribution on an offshore oil rig

Flow of lubricating mud over drill bit

Volume fraction of water

Volume fraction of oil

Volume fraction of gas

Analysis of multiphase separator

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Where is CFD used? (Power Generation)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas

– Power Generation– Sports

Flow pattern through a water turbine.

Flow in a burner

Flow around cooling towers

Pathlines from the inlet colored by temperature during standard operating conditions

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Where is CFD used? (Sports)

• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation

– Sports

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PhysicsPhysics

CFD codes typically designed for representation of specific flow phenomenon– Viscous vs. inviscid (no viscous forces) (Re)– Turbulent vs. laminar (Re)– Incompressible vs. compressible (Ma)– Single- vs. multi-phase (Ca)– Thermal/density effects and energy equation (Pr, , Gr, Ec)– Free-surface flow and surface tension (Fr, We)– Chemical reactions, mass transfer– etc…

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PhysicsPhysics

Fluid Mechanics

Inviscid Viscous

Laminar Turbulence

Internal(pipe,valve)

External(airfoil, ship)Compressibl

e(air, acoustic)

Incompressible(water)

Components of Fluid Mechanics

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Governing EquationsGoverning Equations

Continuity

Equation of motion

(Equations based on “average” velocity)(Equations based on “average” velocity)

xzxyxxxx

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yx

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Claude-Louis Navier George Gabriel Stokes

Navier-Stokes EquationsNavier-Stokes Equations

C.L. M. H. Navier, Memoire sur les Lois du Mouvements des Fluides, Mem. de l’Acad. d. Sci.,6, 398 (1822)C.G. Stokes, On the Theories of the Internal Friction of Fluids in Motion, Trans. Cambridge Phys. Soc., 8, (1845)

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Navier-Stokes EquationsNavier-Stokes Equations(constant (constant and and ))

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D 2

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Navier–Stokes ExampleNavier–Stokes Example

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Fluid

L

x

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)x-Lx(2

1 Expression Final

0 2

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Lat x 0 0,at x 0 B.C.

2

x Integrate

x Integrate

0

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21

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Laminar Flow Static Parallel Plates

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ModelingModeling Mathematical representation of the physical problem

– Some problems are exact (e.g., laminar pipe flow)– Exact solutions only exist for some simple cases. In these cases nonlinear

terms can be dropped from the N-S equations which allow analytical solution.– Most cases require models for flow behavior [e.g., K-, K-, Reynolds

Averaged Navier Stokes equations (RANS) or Large Eddy Simulation (LES) for turbulent flow]

Initial —Boundary Value Problem (IBVP), include: governing Partial Differential Equations (PDEs), Initial Conditions (ICs) and Boundary Conditions (BCs)

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Turbulent Flow RepresentationTurbulent Flow Representation

(K- (K- as an example) as an example)

velocityousinstantaneu and flow, ofdirection in the

ty net velociconstant uvelocity,deviatingu': Whereu'uu

i

i

Turbulent Boundary LayerTurbulent Boundary Layer

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Wall

y

x

U0

Bulk Stream

Outer layer

Fully turbulent layer

Sublayer + buffer layer

Edge of boundary layer

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yuyy

uu

dy

Udw

y

w

ScaleLength Viscous Velocity Friction StressShear Wall

0

y+ is similar to a local Reynolds number. Small y+ - Viscous effects dominateLarge y+ - Turbulence dominates

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COMSOL has many turbulent models available

Low-Re models require a y+ resolution of < 1 to guarantee accuracy

Low-Re models are necessary to accurately estimate skin friction and flow separation

High-Re models use wall functions to approximate averaged turbulent flow properties

Less accurate, but more computationally efficientIn COMSOL, a minimum y+ of 11.06 is enforced. To maintain accuracy, ensure cells meet this requirement

yy++ and Turbulence Models and Turbulence Models

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Numerics / DiscretizationNumerics / Discretization

Computational solution of the IBVPMethod dependent upon the model equations and

physicsSeveral components to formulation

– Discretization and linearization– Assembly of system of algebraic equations– Solve the system and get approximate solutions

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Finite DifferencesFinite Differences

Methods of Solution

Direct methods Iterative methods

Cramer’s Rule, Gauss eliminationLU decomposition

Jacobi method, Gauss-SeidelMethod, SOR method

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Finite differencerepresentation

Truncation error

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Numeric SolutionNumeric Solution (Finite Differences) (Finite Differences)

o xi i+1i-1

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3

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32

,

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,,,1

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Taylor’s Series Expansion u i,j = velocity of fluid

Discrete Grid Points

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Finite Difference Truncation ErrorFinite Difference Truncation Error

percentErrorfforsolutionExact

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CFD processCFD process

Geometry descriptionSpecification of flow conditions and propertiesSelection of modelsSpecification of initial and boundary conditionsGrid generation and transformationSpecification of numerical parametersFlow solutionPost processing: Analysis, and visualizationUncertainty assessment

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Geometry descriptionGeometry description

Typical approaches

– Make assumptions and simplifications

– CAD/CAE integration– Engineering drawings– Coordinates include Cartesian

system (x,y,z), cylindrical system (r, θ, z), and spherical system(r, θ, Φ)

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Flow conditions and propertiesFlow conditions and properties

Flow conditions and properties required are unique for each flow code and application– FlowLab requires all variables in dimensional

form– Because of focused application, research codes

often use non-dimensional variables.

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Selection of models for flow fieldSelection of models for flow field Direct Numerical Simulations (DNS) is to solve the N-S equations

directly without any modeling. Grid must be fine enough to resolve all flow scales. Applied for laminar flow and rare be used in turbulent flow.

Reynolds Averaged Navier-Stokes (NS) equations (RANS) is to perform averaging of NS equations and establishing turbulent models for the eddy viscosity. Too many averaging might damping vortical structures in turbulent flows

Large Eddy Simulation (LES), Smagorinsky’ constant model and dynamic model. Provide more instantaneous information than RANS did. Instability in complex geometries

Detached Eddy Simulation (DES) is to use one single formulation to combine the advantages of RANS and LES.

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Initial and boundary conditionsInitial and boundary conditionsFor steady/unsteady flow

IC should not affect final solution, only convergence path, i.e. iteration numbers needed to get the converged solution.

Robust codes should start most problems from very crude IC, . But more reasonable guess can speed up the convergence.

Boundary conditions– No-slip or slip-free on the wall, periodic, inlet (velocity

inlet, mass flow rate, constant pressure, etc.), outlet (constant pressure, velocity convective, buffer zone, zero-gradient), and non-reflecting (compressible flows, such as acoustics), etc.

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Grid generationGrid generation Grids can either be structured (hexahedral) or

unstructured (tetrahedral). Depends upon type of discretization scheme and application

– Scheme Finite differences: structured Finite volume or finite element:

structured or unstructured– Application

Thin boundary layers best resolved with highly-stretched structured grids

Unstructured grids useful for complex geometries

Unstructured grids permit automatic adaptive refinement based on the pressure gradient, or regions of interest (FLUENT)

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Grid ResolutionGrid Resolution

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Grid generation and transformationGrid generation and transformation

Grids designed to resolve important flow features which are dependent upon flow parameters (e.g., Re)

Commercial codes such as Gridgen, Gambit

For research code, grid generated by one of several methods (algebraic vs. PDE based, conformal mapping)

For complex geometries, body-fitted coordinate system will have to be applied (next slide). Grid transformation from the physical domain to the computational domain will be necessary

Sample grid established by Gambit of FLUENT

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Grid transformationGrid transformationy

xo o

Physical domain Computational domain

x x

f f f f f

x x x

y y

f f f f f

y y y

Transformation between physical (x,y,z) and computational () domains, important for body-fitted grids. The partial derivatives at these two domains have the relationship (2D as an example)

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Numerical parameters & flow Numerical parameters & flow solutionsolution

Numerical parameters are used to control flow solution. – Under relaxation factor, tridiagonal or pentadiagonal solvers – CFD Labs using FlowLab

Monitor residuals (change of results between iterations) Number of iterations for steady flow or number of time steps for unsteady flow

Flow solution– Solve the momentum, pressure Poisson equations and get flow field quantities, such as velocity, turbulence intensity,

pressure and integral quantities (drag forces)

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Numerical parameters & flow Numerical parameters & flow solution solution

Typical time history of residuals

The closer the flow field to the converged solution, the smaller the speed of the residuals decreasing.

Solution converged, residuals do not change after more iterations

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Post-processingPost-processing Analysis, and visualization

– Calculation of derived variables Vorticity Wall shear stress

– Calculation of integral parameters: forces, moments– Visualization (usually with commercial software)

Simple X-Y plots Simple 2D contours 3D contour carpet plots Vector plots and streamlines (streamlines are the lines

whose tangent direction is the same as the velocity vectors)

Animations (dozens of sample pictures in a series of time were shown continuously)

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Post-processing (Parallel Plates)Post-processing (Parallel Plates)

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Post-Processing (example)Post-Processing (example)

Pressure contour and velocity vectors .

Note the locations of the highest and lowest pressure regions.

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Uncertainty assessmentUncertainty assessment Rigorous methodology for uncertainty assessment using

statistical and engineering concepts– Verification: process for assessing simulation numerical uncertainty

Iterative convergence: monitoring point & integral quantities should change within the convergence criterions

Grid independent studies: 3-grids and Richardson Extrapolation– Validation: process for assessing simulation modeling uncertainty by

using benchmark experimental data Certification: full Verification and Validation done for a

certain range of geometries & parameters which are well known and then extrapolated, qualitatively as well as quantitative

– Simulating flows for which experiments are difficult (e.g., full-scale Reynolds numbers, hypersonic flows, off-design conditions)

– Objective: Simulation-based design

CFD ExampleCFD Example

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Sulzer Chemtech250 Y Plastic Structured Packing

GeometryGeometry

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• CT > STL > CFD

• CT = 0.322 mm Min Resolution

• Copy/Pasted 2x

• Surface Wrapping

• Adaptive Meshing

• Tetrahedral Mesh

• Polyhedral Mesh

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Mess DimensionsMess Dimensions

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Experiment vs. SimulationExperiment vs. Simulation

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Velocity MapVelocity Map

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Software and resourcesSoftware and resources CFD software was built upon physics, modeling, numerics. Two types of available software

– Commercial (e.g., FLUENT, CFX, Star-CCM, COMSOL)– Research (e.g., CFDSHIP-IOWA, U2RANS)

More information on CFD can be got on the following website:– CFD Online: http://www.cfd-online.com/– CFD software

FLUENT: http://www.fluent.com/ COMSOL http://www.comsol.com/ CD-adapco: http://www.cd-adapco.com/

– Grid generation software Gridgen: http://www.pointwise.com GridPro: http://www.gridpro.com/

– Visualization software Tecplot: http://www.amtec.com/ Fieldview: http://www.ilight.com/