© ram ramanan 8/27/2015 cfd 1 me 5337/7337 notes-2005-002 introduction to computational fluid...

© Ram Ramanan 04/19/23

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Introduction to Computational Fluid Dynamics

Lecture 2: CFD Introduction


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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)


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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


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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.


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Applications

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...



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CFD - How It Works

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.

Filling Nozzle

Bottle



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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.



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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.



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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



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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.



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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.



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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



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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.



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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 mesh refinement is one way to deal with truncation error.



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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.

poor better

Fully Developed Inlet Profile

Computational Domain

Computational Domain

Uniform Inlet Profile



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Summary

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.



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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)


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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

© ram ramanan 8/27/2015 cfd 1 me 5337/7337 notes-2005-002 introduction to computational fluid...

Documents

cfd introduction slide

ram ramanan

result of cfd analyses

fluid region

fluid properties

heat exchangers

mass transfer

structures codes