SC08 Engineering Track: Introducing Modeling Skills

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SC08 Engineering Track Introducing Modeling
Skills CFD

• Jim Giuliani
• Client and Technology Support Manager
• jimg_at_osc.edu

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Agenda

• The CFD Process
• Solid Modeling
• Mesh Generation
• Physical Properties
• Initial and Boundary Conditions
• Numerical Solution
• Data Visualization

• Computational to Fluid Dynamics
• Partial Differential Equations
• Governing Equations
• Discretization
• Numerical Solutions

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Computational Fluid Dynamics (CFD)

• In CFD the equations that govern a process of
  interest are solved numerically
• Once we have classified our problem, we can
  derive equations that describe the fluid system
• Approximations can be made that allow the
  governing equations to be reduced incomplexity
• For complex flows or geometries we can
  approximate the governing equations in a form
  that can be solved numerically.
• CFD encompasses the entire process of
  solvingthe governing equations numerically

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The CFD Process
Solid Modeling Mesh Generation Physical
Properties Initial and Boundary
Conditions Numerical Solution Data Visualization
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The CFD Process

• Based on the classification of the problem to be
  analyzed, select the appropriate solver
• Based on flow classification, simplifications are
  made to the governing equations
• Simplified governing equations need to be solved
  using different numerical techniques
• Describe the physical problem
• Geometry
• Physical properties
• Set solution and solver settings
• Start the solution and monitor progress
• Solution parameters, residuals, Courant number,
  are monitored to determine if the solution is
  converging

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Solid Modeling

• The first step in creating a numerical model is
  to describe the geometry of the problem to be
  analyzed

• Most grid generation software have basic solid
  modeling capabilities
• Parts/geometries can be imported from CAD/CAM
  software packages

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Mesh Generation

• The physical domain defined by the solid model is
  discretized into small elemental surfaces/volumes
• A solution to the governing equations can now be
  approximated

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Grid/Mesh Limitations

• Overall flowfield model is on order of hundreds
  of feet
• Only 1.5 inch gap between belly and ground
• To properly represent flow through any gap,
  should have at least 5 cells between wall
  surfaces
• Turbulence modeling required first layer of cells
  on road and body to be 0.5
• This leaves only 0.5 for remaining 3 layers
  results in very high aspect ratio cells and
  misrepresented ground/vehicle boundary layer
  interaction

Boundary layer cells
0.5
1.5
Boundary layer cells
0.5
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Physical Properties

• Temperature
• Pressure
• Density
• Viscosity is a measure of the resistance of a
  fluid which is being deformed.
• Dynamic
• Kinematic (dynamic viscosity/density)

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Initial and Boundary Conditions

• For the solution to be well posed
• A solution must exist
• The solution must be unique
• The solution must depend on initial or boundary
  conditions
• There are 3 types of Boundary Conditions
• Dirchelt
• Neumann
• Robins or mixed

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Initial and Boundary Conditions

• Initial Conditions
• Specify properties at the beginning of the
  analysis
• Properties may change during simulation
• Choice of initial conditions can shorten solution
  time
• Boundary Conditions
• Describe how the simulation will behave at the
  edges of the computational domain
• Properties often are constant throughout
  simulation
• Common properties that are specified
• Velocity, Pressure and Temperature
• Special types of boundaries
• Symmetry, Extrapolated

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Boundary Conditions

• For the example of simulating the flow around the
  body of a car (U gt 200 m.p.h.), boundary
  conditions must be specified on all surfaces and
  edges of the computational domain

Symmetry on top and sides
Solution driven by fixed inlet velocities
Flow exits domain through pressure outlet
Zero velocity (no slip) at car surface
Solid, moving boundary for ground (speed equal to
free stream velocity)
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Numerical Solution

• Solution to the discretization equations are
  approximated numerically
• Choose solver settings (relaxation factor,
  tolerances)
• Set solution control parameters (start time, end
  time, time step)

• Residuals
• Errors of the discretized equations
• Monitored as a means to determine when solution
  has converged

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Data Visualization

• Grids that contain millions of elements can
  provide very high resolution information on flow
  field
• Colorized contour plots, particle traces and time
  lapse animations allow subtle flow patterns and
  overall flow characteristics to be examined
• User must specify at what interval data is
  written out
• More steps more data(gigabytes per
  simulation)(terabytes per design problem)
• Solutions can be run remotely, but visualizations
  perform best locally

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Exercise 2D Heat Conduction

• Cooling_channel_descripton.doc contains a
  detailed description of the problem
• We have used Java applet to solve for a solution,
  but adiabatic boundary condition was not able to
  be modeled accurately
• Open Heat_transfer_CFD_portal.doc for
  instructions on how to solve this problem with
  the OpenFOAM CFD solver
• Compare results to solution obtained with Java
  Applet

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Steady / Unsteady Flow

• Steady flow denotes a system where the flow does
  not change with time
• When the fundamental equations are discussed, we
  will see that steady flow denotes that all time
  derivatives are zero
• When the stability of a numerical solution is
  discussed, we will see that selection of B.C. for
  unstable flow strongly impacts stability

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Fluid Flow Streamlines

• Streamlines
• A moving fluid element is seen to trace out a
  fixed path in space
• A streamline is this fixed path

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Classification of Fluid Mechanics

• Continuum Fluid Mechanics
• Inviscid
• Viscous
• Laminar
• Turbulent
• Compressible/Incompressible

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Classification of Flows

• Compressible/Incompressible
• Inviscid
• Viscous
• Laminar
• Flow where the streamlines are smooth and regular
  and a fluid element moves smoothly along a
  streamline
• Turbulent
• Flow where the streamlines break up and a fluid
  element moves in a random, irregular, and
  tortuous fashion

Turbulent Flow
Laminar Flow
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Exercise Flow Past a Circular Cylinder

• Model low speed flow around a cylinder

• Assumptions/Simplifications
• Incompressible all density derivatives are zero
• Inviscid neglect viscous forces
• Possible Objectives
• Practical application of the fundamental flow
  equations
• Examine assumptions and simplifications that can
  reduce complex partial differential equations to
  simple analytic equations

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Exercise Flow Past a Circular Cylinder

• Possible Objectives (cont)
• Understand when higherfidelity tools are needed
  to examine complex flow phenomena
• Top image - ideal flowsolution
• Bottom imageLandsat 7 imageof Juan
  Fernandezislands off of thecoast of Chili

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Exercise Flow Past a Circular Cylinder

• Model low speed flow around a cylinder

• To study the ideal flow model, open
  Cylinder_ideal_flow.doc to see the assignment
• Open Cylinder_CFD_portal.doc to see the
  assignment for the viscous, CFD solution
• For the CFD assignment, follow steps through page
  6 and stop after SUBMIT button has been pressed
  and job is submitted
• Simulation takes about 45 minutes and results
  should be available towards the end of the
  workshop

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Computational Fluid Dynamics

• Partial Differential Equations
• Physical Classification
• Numerical Classification
• Governing Equations
• Continuity
• Momentum
• Turbulence
• Discretization
• Finite Difference
• Laplaces Equation
• Finite Volume
• Numerical Solutions

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Partial Differential Equations

• Partial Differential Equations (PDEs)
• Many important physical processes are governed by
  PDEs
• We will look at some PDEs commonly encountered in
  fluid dynamics
• Physical Classification
• Equilibrium Problems
• Marching Problems
• Numerical Classification
• Elliptic
• Parabolic
• Hyperbolic

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PDEs Physical Classification

• Equilibrium Problems
• Solution desired in a closed domain
• Boundary value problem
• Governed by elliptic PDEs
• Examples
• Steady state temperature distribution
• Incompressible, inviscid flow

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PDEs Physical Classification

• Marching Problems
• Transient
• Prescribed set of initial conditions in addition
  to boundary conditions
• Solution computed by marching from the initial
  conditions, constrained by boundary conditions
• Governed by parabolic or hyperbolic PDEs
• Examples
• Unsteady, inviscid flow
• Steady supersonic inviscid flow
• Boundary layer flow

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PDEs Numerical Classification

• Hyperbolic
• Fundamental propertyis the limited domain of
  dependence
• Solution at point P dependsonly on information
  in thedomain of dependence
• Any disturbance that occurs outside this
  interval can never influence the solution at
  point P
• Example Wave Equation

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PDEs Numerical Classification

• Parabolic
• Unlike hyperbolic equations,solution at some
  time tndepends upon the entirephysical domain
  at earliertimes, including side boundary
  conditions
• Start at some initial data plane and march
  forward
• Diffusion processes
• Example 1D heat transfer equation

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PDEs Numerical Classification

• Elliptic
• Boundary value problem
• Subject to a prescribed setof boundary
  conditions ona closed domain
• Solution at any point depends upon the specified
  conditions at all points on the boundary
• Example Laplaces Equation

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Conservation Laws

• Mass conservation
• Matter may neither be created or destroyed
• Conservation of momentum
• Newtons 2nd law of motion
• Conservation of energy
• First law of thermodynamics

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Continuity Equation
For a given control volumn The rate increase of
mass within the control volume is equal to the
net rate at which mass enters the control volume
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Continuity Equation
The partial differential form of the continuity
equation in cartesian coordinates is
where
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Conservation of Momentum
Newtons 2nd law
(in 2 dimensions)

• Body forces
• Gravity
• Centrifugal
• Corolis
• Electromagnetic
• Surface forces
• Normal stress
• Tangential stress

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Conservation of Momentum

• Combining forces yields

Body forces
Surface forces
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Navier-Stokes Equations
Replacing stress terms with stress-strain
relationship Assumptions/simplifications
can reduce complexity
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Navier-Stokes for Incompressible Flow

• For an incompressible, constant viscosity flow,
  the viscous terms simplify significantly (more
  applicable to gasses than fluids)

Pressuregradient
advection
acceleration
diffusion
How much detail was skipped? 1st year graduate
course in continuum mechanics in 5 slides
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Turbulence Models

• Turbulence depends on the ratio of the inertia
  force to viscous force
• Laminar flows can be described by the continuity
  and momentum equations
• Rotational flow structure have a wide range of
  length and velocity scales, called turbulent
  scales
• Several popular techniques for accounting for
  turbulence are
• Direct Numerical Simulation (DNS)
• Large Eddie Simulation (LES)
• K-epsilon

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Large Eddy Simulation (LES)

• Large scale motions are generally much more
  energetic and transport most of the conserved
  properties
• Large eddies are modeled exactly
• Small eddies are approximated
• Smaller universal scales, called sub-grid scales,
  are modeled using a sub-grid scale (SGS) model

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K-epsilon Model

• Time averaged governing equations yield the
  Reynolds-averaged Navier-Stokes equations (RANS)
• Point velocities are considered to be comprised
  of two components
• Steady mean value
• Fluctuating component
• Additional unknowns due to turbulent fluctuations
  can be handled with transport equations
• Two important turbulent quantities in these
  transport equations
• k turbulent kinetic energy
• epsilon dissipation of turbulent kinetic energy

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Discretization

• Conversion of the governing equations into a
  system of algebraic equations
• Two popular discretization techniques in CFD are
• Finite difference method
• Finite volume method

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Finite Difference Method

• First order derivatives
• Fordward difference
• Backward difference
• Central difference

ui,j1
Ui-1,j
Ui1,j
ui,j
ui,j-1
y(j)
x(i)
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Finite Difference Approximations

• Second order derivative
• Central difference
• For time derivatives

ui,j1
Ui-1,j
Ui1,j
ui,j
ui,j-1
y(j)
x(i)
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Finite Volume Method

• Unstructured mesh offers more flexibility
• Control volumes are defined by the surfaces of
  the elements
• Control volume integrals can be converted to
  discretized equations base on face area and flow
  across boundaries

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Numerical Solution

• Discretization results in a system of linear or
  non-linear equations
• Numerical methods are applied to solve these
  equations
• Direct methods
• Iterative methods

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Convergence

• With iterative methods, as progress proceeds
  towards a solution, the equations are determined
  to have converged to a solution when certain
  values do not change between iterations by a
  specified tolerance
• Additional characteristics
• Numerical solution does not change with
  additional iterations
• Mass, momentum and energy balances are obtained

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Residuals

• Residuals are the errors of the discretized
  equations
• Residuals are calculated for each equation (Ux,
  Uy, P, )
• Residuals should diminish as the numerical
  process progresses
• They are often used to monitor the behavior of
  the numerical process

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Exercise Flow Past a Circular Cylinder

• Open Cylinder_CFD_portal.doc
• Continue where you left off (page 6 after
  initial simulation submitted)

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Exercise Turbulent Flow over a Backward Facing
Step

• Open Backward_step.doc for instructions on how to
  solve this problem with the OpenFOAM CFD solver
• Examine the model assumptions and setup
• Run the model in its current form
• Includes turbulence modeling