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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)

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?

- 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

- 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

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.

Bottle

Domain for bottle filling problem.

Courtesy: Fluent, Inc.

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

- 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

- 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

- 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

- 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)

- 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

- 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.

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

poor

better

Courtesy: Fluent, Inc.

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.

Courtesy: Fluent, Inc.

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

- 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

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