introduction to computational fluid dynamics lecture 2 cfd introduction
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Introduction to Computational Fluid Dynamics Lecture 2: CFD Introduction. Numerical Simulations. System-level CFD problems Includes all components in the product Component or detail-level problems Identifies the issues in a specific component or a sub-component

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numerical simulations
Numerical Simulations
  • System-level CFD problems
    • Includes all components in the product
  • Component or detail-level problems
    • Identifies the issues in a specific component or a sub-component
  • Different tools for the level of analysis
  • Coupled physics (fluid-structure interactions)
cfd codes
CFD Codes
  • Available commercial codes – fluent, star-cd, Exa, cfd-ace, cfx etc.
  • Other structures codes with fluids capability – ansys, algor, cosmos etc.
  • Supporting grid generation and post-processing codes
  • NASA and other government lab codes
  • Netlib, Linpack routines for new code development
  • Mathematica or Maple for difference equation generation
  • Use of spreadsheets (and vb-based macros) for simple solutions
what is computational fluid dynamics
What is Computational Fluid Dynamics?
  • Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena by solving the mathematical equations which govern these processes using a numerical process (that is, on a computer).
  • The result of CFD analyses is relevant engineering data used in:
    • conceptual studies of new designs
    • detailed product development
    • troubleshooting
    • redesign
  • CFD analysis complements testing and experimentation.
    • Reduces the total effort required in the laboratory.

Courtesy: Fluent, Inc.

  • Applications of CFD are numerous!
    • flow and heat transfer in industrial processes (boilers, heat exchangers, combustion equipment, pumps, blowers, piping, etc.)
    • aerodynamics of ground vehicles, aircraft, missiles
    • film coating, thermoforming in material processing applications
    • flow and heat transfer in propulsion and power generation systems
    • ventilation, heating, and cooling flows in buildings
    • chemical vapor deposition (CVD) for integrated circuit manufacturing
    • heat transfer for electronics packaging applications
    • and many, many more...

Courtesy: Fluent, Inc.

cfd how it works
CFD - How It Works

Filling Nozzle

  • Analysis begins with a mathematical model of a physical problem.
    • Conservation of matter, momentum, and energy must be satisfied throughout the region of interest.
      • Fluid properties are modeled empirically.
    • Simplifying assumptions are made in order to make the problem tractable (e.g., steady-state, incompressible, inviscid, two-dimensional).
    • Provide appropriate initial and/or boundary conditions for the problem.


Domain for bottle filling problem.

Courtesy: Fluent, Inc.

cfd how it works 2
CFD - How It Works (2)
  • CFD applies numerical methods (called discretization) to develop approximations of the governing equations of fluid mechanics and the fluid region to be studied.
    • Governing differential equations  algebraic
    • The collection of cells is called the grid or mesh.
  • The set of approximating equations are solved numerically (on a computer) for the flow field variables at each node or cell.
    • System of equations are solved simultaneously to provide solution.
  • The solution is post-processed to extract quantities of interest (e.g. lift, drag, heat transfer, separation points, pressure loss, etc.).

Mesh for bottle filling problem.

Courtesy: Fluent, Inc.

an example water flow over a tube bank
An Example: Water flow over a tube bank
  • Goal
    • compute average pressure drop, heat transfer per tube row
  • Assumptions
    • flow is two-dimensional, laminar, incompressible
    • flow approaching tube bank is steady with a known velocity
    • body forces due to gravity are negligible
    • flow is translationally periodic (i.e. geometry repeats itself)

Physical System can be modeled with repeating geometry.

Courtesy: Fluent, Inc.

mesh generation
Mesh Generation
  • Geometry created or imported into preprocessor for meshing.
  • Mesh is generated for the fluid region (and/or solid region for conduction).
    • A fine structured mesh is placed around cylinders to help resolve boundary layer flow.
    • Unstructured mesh is used for remaining fluid areas.
  • Identify interfaces to which boundary conditions will be applied.
    • cylindrical walls
    • inlet and outlets
    • symmetry and periodic faces

Section of mesh for tube bank problem

Courtesy: Fluent, Inc.

using the solver
Using the Solver
  • Import mesh.
  • Select solver methodology.
  • Define operating and boundary conditions.
    • e.g., no-slip, qw or Tw at walls.
  • Initialize field and iterate for solution.
  • Adjust solver parameters and/or mesh for convergence problems.

Courtesy: Fluent, Inc.

post processing
  • Extract relevant engineering data from solution in the form of:
    • x-y plots
    • contour plots
    • vector plots
    • surface/volume integration
    • forces
    • fluxes
    • particle trajectories

Temperature contours within the fluid region.

Courtesy: Fluent, Inc.

advantages of cfd
Advantages of CFD
  • Low Cost
    • Using physical experiments and tests to get essential engineering data for design can be expensive.
    • Computational simulations are relatively inexpensive, and costs are likely to decrease as computers become more powerful.
  • Speed
    • CFD simulations can be executed in a short period of time.
    • Quick turnaround means engineering data can be introduced early in the design process
  • Ability to Simulate Real Conditions
    • Many flow and heat transfer processes can not be (easily) tested - e.g. hypersonic flow at Mach 20
    • CFD provides the ability to theoretically simulate any physical condition

Courtesy: Fluent, Inc.

advantages of cfd 2
Advantages of CFD (2)
  • Ability to Simulate Ideal Conditions
    • CFD allows great control over the physical process, and provides the ability to isolate specific phenomena for study.
    • Example: a heat transfer process can be idealized with adiabatic, constant heat flux, or constant temperature boundaries.
  • Comprehensive Information
    • Experiments only permit data to be extracted at a limited number of locations in the system (e.g. pressure and temperature probes, heat flux gauges, LDV, etc.)
    • CFD allows the analyst to examine a large number of locations in the region of interest, and yields a comprehensive set of flow parameters for examination.

Courtesy: Fluent, Inc.

limitations of cfd
Limitations of CFD
  • Physical Models
    • CFD solutions rely upon physical models of real world processes (e.g. turbulence, compressibility, chemistry, multiphase flow, etc.).
    • The solutions that are obtained through CFD can only be as accurate as the physical models on which they are based.
  • Numerical Errors
    • Solving equations on a computer invariably introduces numerical errors
      • Round-off error - errors due to finite word size available on the computer
      • Truncation error - error due to approximations in the numerical models
    • Round-off errors will always exist (though they should be small in most cases)
    • Truncation errors will go to zero as the grid is refined - so meshrefinement is one way to deal with truncation error.

Courtesy: Fluent, Inc.

limitations of cfd 2
Computational Domain

Fully Developed Inlet Profile

Uniform Inlet Profile

Limitations of CFD (2)
  • Boundary Conditions
    • As with physical models, the accuracy of the CFD solution is only as good as the initial/boundary conditions provided to the numerical model.
    • Example: Flow in a duct with sudden expansion
      • If flow is supplied to domain by a pipe, you should use a fully-developed profile for velocity rather than assume uniform conditions.

Computational Domain



Courtesy: Fluent, Inc.

  • Computational Fluid Dynamics is a powerful way of modeling fluid flow, heat transfer, and related processes for a wide range of important scientific and engineering problems.
  • The cost of doing CFD has decreased dramatically in recent years, and will continue to do so as computers become more and more powerful.

Courtesy: Fluent, Inc.

numerical solution methods
Numerical solution methods
  • Consistency and truncation errors
    • As h-> 0, error -> 0 (hn, tn)
  • Stability
    • Converging methodology
  • Convergence
    • Gets close to exact solution
  • Conservation
    • Physical quantities are conserved
  • Boundedness (Lies within physical bounds)
    • Higher order schemes can have overshoots and undershoots
  • Realizability (Be able to model the physics)
  • Accuracy (Modeling, Discretization and Iterative solver errors)
cfd methodologies
CFD Methodologies
  • Finite difference method
    • Simple grids (rectangular)
    • Complex geometries -> Transform to simple geometry (coordinate transformation)
  • Finite volume method
    • Complex geometries (conserve across faces)
  • Finite element method
    • Complex geometries (element level transformation)
  • Spectral element method
    • Higher order interpolations in elements
  • Lattice-gas methods
    • Basic momentum principle-based