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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### 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
• 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.

• 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