© Ram Ramanan 8/27/2015 CFD 1 ME 5337/7337 Notes Introduction to Computational Fluid Dynamics Lecture 2: CFD Introduction

© Ram Ramanan 8/27/2015 CFD 2 ME 5337/7337 Notes 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)

© Ram Ramanan 8/27/2015 CFD 3 ME 5337/7337 Notes 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

© Ram Ramanan 8/27/2015 CFD 4 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 5 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 6 ME 5337/7337 Notes 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 Courtesy: Fluent, Inc.

© Ram Ramanan 8/27/2015 CFD 7 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 8 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 9 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 10 ME 5337/7337 Notes Using the Solver  Import mesh.  Select solver methodology.  Define operating and boundary conditions. e.g., no-slip, q w or T w at walls.  Initialize field and iterate for solution.  Adjust solver parameters and/or mesh for convergence problems. Courtesy: Fluent, Inc.

© Ram Ramanan 8/27/2015 CFD 11 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 12 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 13 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 14 ME 5337/7337 Notes 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. Courtesy: Fluent, Inc.

© Ram Ramanan 8/27/2015 CFD 15 ME 5337/7337 Notes 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. poorbetter Fully Developed Inlet Profile Computational Domain Uniform Inlet Profile Courtesy: Fluent, Inc.

© Ram Ramanan 8/27/2015 CFD 16 ME 5337/7337 Notes 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.

© Ram Ramanan 8/27/2015 CFD 17 ME 5337/7337 Notes Numerical solution methods  Consistency and truncation errors As h-> 0, error -> 0 (h n, t n )  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)

© Ram Ramanan 8/27/2015 CFD 18 ME 5337/7337 Notes 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