Fluent Lecture Dr. Thomas J. Barber www.engr.uconn.edu/~barbertj

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Fluent LectureDr. Thomas J. Barberwww.engr.ucon
n.edu/barbertj
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Outline

• Background Issues
• Codes, Flow Modeling, and Reduced Equation Forms
• Numerical Methods Discretize, Griding, Accuracy,
  Error
• Data Structure, Grids
• Turbulence
• Fluent

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CFD Connection to Other Solution Approaches

• CFD (numerical) approach is most closely related
  to experimental approach, i.e.
• can arbitrarily select physical parameters
  (tunnel conditions)
• output is in form of discrete or point data
• results have to be interpreted (corrected) for
  errors in simulation.

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BackgroundLimiting Factors - I

• Computer size
• Moores law First postulated by Intel CEO George
  Moore. Observation that logic density of silicon
  integrated circuits has closely followed curve
  Bits per sq. in.(and MIPS) doubles power of
  computing (speed and reduced size), thereby
  quadrupling computing power every 24 months.

Calculations per second per year for 1000.
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Outline

• Background Issues
• Codes, Flow Modeling, and Reduced Equation Forms
• Numerical Methods Discretize, Griding, Accuracy,
  Error
• Data Structure, Grids
• Turbulence
• Fluent

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What is a CFD code?
Converts chosen physics into discretized forms
and solves over chosen physical domain
Geometry Definition
Computational Grid and Domain Definition
Boundary Conditions
Preprocessing
Discretization Approach
Solution Approach
Computer Usage Strategy
Processing
Performance Analysis
Solution Display
Solution Assessment
Postprocessing
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Problem FormulationEquations of Motion

• Conservation of mass (continuity) particle
  identity
• Conservation of linear momentum Newtons law
• Conservation of energy 1st law of thermo (E)
• 2nd law of thermo (S)
• Any others?????
• Most General Form Navier-Stokes Equations
• Written in differential or integral (control
  volume) form.
• Dependent variables typically averaged over some
  time scale, shorter than the mean flow
  unsteadiness (Reynolds-averaged Navier-Stokes -
  RANS equations).

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Reduced Forms of Governing Equations
Critical issue modeling viscous and
turbulent flow behavior
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Complex Aircraft Analysis, Circa 1968B747-100
with space shuttle Enterprise
What is different with these aircraft from normal
operation?
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Reduced Forms of Governing Equations
More Physics (More complex equations)
More Geometry (More complex grid
generation) (More grid points)
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Outline

• Background Issues
• Codes, Flow Modeling, and Reduced Equation Forms
• Numerical Methods Discretize, Griding, Accuracy,
  Error
• Data Structure, Grids
• Turbulence
• Fluent

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• Finite Difference
• Finite Volume
• Finite Element

All based on discretization approaches
P.D.E. Luf
Discretize
System of Linear Algebraic Eqns
Up
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Breakup Continuous Domain into a Finite Number of
Locations
Boundary Condition
B. C.
B. C.
Boundary Condition
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Discretization Order of Accuracy

• Taylor Series Expansion
• Polynomial Function Power Series
• Accuracy Dependent on Mesh Size and Variable
  Gradients

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Discretization Example

• Derivative approximation proportional to
  polynomial order
• Order of accuracy mesh spacing, derivative
  magnitude
• only reasonable if product is small

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Numerical Error Sources - I

• Truncation error
• Finite polynomial effect
• Diffusion acts like artificial viscosity damps
  out disturbances
• Dispersion introduces new frequencies to input
  disturbance
• Effect is pronounced near shocks

Exact Diffusion
Dispersion

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Numerical Error Sources - II
at t400
at t0
Traveling linear wave model problem
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Numerical Error Sources - III
at t400
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Numerical Error Sources - IV
at t400
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Time-Accurate vs. Time-Marching

• Time-marching steady-state solution from
  unsteady equations
• Intermediate solution has no meaning
• Time-accurate time-dependent, valid at any time
  step

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Numerical Properties of Method

• Stability
• Tendency of error in solution of algebraic
  equations to decay
• Implies numerical solution goes to exact solution
  of discretized equations
• Convergence
• Solution of approximate equations approaches
  exact set of algebraic eqns.
• Solutions of algebraic eqns. approaches exact
  solution of P.D.E.s as ?x ? t ? 0

Governing P.D.E.s L(U)
System of Algebraic Equations
Discretization
Consistency
Exact Solution U
Approximate Solution u
Convergence as ?x ? t ? 0
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How good are the results?

• Assess the calculation for
• Grid independence
• Convergence (mathematical) residuals as measure
  of how well the finite difference equation is
  satisfied.
• Look for location of maximum errors
• Look for non-monotonicity

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How good are the results?

• Convergence (physical) Check conserved
  properties mass (for internal flows), atom
  balance (for chemistry), total enthalpy, e.g.

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Outline

• Background Issues
• Codes, Flow Modeling, and Reduced Equation Forms
• Numerical Methods Discretize, Griding, Accuracy,
  Error
• Data Structure, Grids
• Turbulence
• Fluent

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2-D Problem Setup

• Structured Grid / Data
• Unstructured Data / Structured Grid

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2-D Problem Setup

• Semi -Structured Grid / Unstructured Data
• Unstructured Data / Unstructured Grid

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Grid Generation
Transformation to a stretched grid
Transformation to a new coordinate system
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Grid Generation - Generic Topologies

• More complicated grids can be constructed by
  combining the basic grid
• topologies - cylinder in a duct

Block-structured O H
Overset or Chimera Cartesian Polar
Both take advantage of natural symmetries of the
geometry
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Grid Generation - Generic Topologies

• More complicated grids can be constructed
  taking advantage of simple elements

Cartesian-stepwise
Unstructured-hybrid
Dimension Unstructured Structured
2D triangular quadrilateral
3D tetrahedra hexahedra
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Outline

• Background Issues
• Codes, Flow Modeling, and Reduced Equation Forms
• Numerical Methods Discretize, Griding, Accuracy,
  Error
• Data Structure, Grids
• Turbulence
• Fluent

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Viscosity and Turbulence
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Viscosity and Turbulence
Laminar
Steady Unsteady
Turbulent
Steady Unsteady
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Viscosity and TurbulenceProperties Averaged Over
Time Scale Much Smaller Than Global Unsteadiness
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Viscosity and Turbulence

• Laminar viscosity modeled by algebraic law
  Sutherland
• Turbulent viscosity modeled by 1 or 2 Eqn. Models
• Realizable k-? model is most reliable
• kturbulence kinetic energy
• ? turbulence dissipation
• Model near wall behavior by
• Wall integration more mesh near wall, y ? 1-2
• Wall functions less mesh, algebraic wall model,
  y ? 30-50

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Outline

• Background Issues
• Codes, Flow Modeling, and Reduced Equation Forms
• Numerical Methods Discretize, Griding, Accuracy,
  Error
• Data Structure, Grids
• Turbulence
• Fluent

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Finite Volume

• Basic conservation laws of fluid dynamics are
  expressed in terms of mass, momentum and energy
  in control volume form.
• F.V. method on each cell, conservation laws are
  applied at a discrete point of the cell node.
• Cell centered
• Corner centered

Piecewise constant interpolation
Piecewise linear Interpolation
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2D Steady Flux Equation
Finite-difference centered in space scheme
i,j1
i-1,j
i,j-1
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Steady Governing Equations
? transport coeff. ? / ? diffusivity
Start with generalized RANS equations
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Fluent Solution MethodSimple Scheme
SIMPLE Semi-Implicit Method for Pressure Linked
Equations
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Fluent Solution MethodSimple Scheme

• Solution algorithm
• Staggered grid convected on different grid from
  pressure.
• Avoids wavy velocity solutions

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Fluent Solution MethodSimple Scheme
CV for u-eqn.
Two sets of indices or one and one staggered at
half-cell
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Fluent Solution MethodSimple Scheme
CV for v-eqn.
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Fluent Solution MethodSimple Scheme
CV for p-eqn.
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Fluent Solution MethodSimple Scheme
5-point computational molecules for linearized
system using geographical not index notation
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Fluent Solution MethodSimple Scheme
Multidimensional Model
2-D and 3-D computational molecules using
geographical not index notation
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Fluent Operational Procedures

• Generate Geometry
• Generate Computational Grid
• Set Boundary Conditions
• Set Flow Models Equation of State, Laminar or
  Turbulent, etc.
• Set Convergence Criteria or Number of Iterations
• Set Solver Method and Solve
• Check Solution Quality Parameters Residuals,
  etc.
• Post-process Line Plots, Contour Plots
• Export Data for Further Post-processing

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Suggested Fluent Development Path

• Read FlowLab FAQ notes Barber Web site
• Run FlowLab to familiarize yourself with GUI,
  solution process and post-processing
• Read Cornell University training notes Handout
• Develop a relevant validation-qualification
  process, i.e. compare with known analyses or data
• Developing laminar flow in straight pipe
• Developing turbulent flow in a straight pipe if
  appropriate
• Convection process
• Convergent-divergent nozzle flow
• .