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Computational Fluid Dynamics 5 Errors

Computational Fluid Dynamics 5 Errors. Professor William J Easson School of Engineering and Electronics The University of Edinburgh. Things you can do. Create simple geometries in Star-Design

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Computational Fluid Dynamics 5 Errors

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  1. Computational Fluid Dynamics 5Errors Professor William J Easson School of Engineering and Electronics The University of Edinburgh

  2. Things you can do • Create simple geometries in Star-Design • Produce meshes of different densities and of varying density (by changing the parameters before meshing) • Solve for laminar flow in a 2D channel • Present the output in a variety of formats • Solve for 2D laminar jets • Solve for 2D flows with wall attachment • Solve to 1st & 2nd order simulations (check this) • Test the appropriateness of your mesh density (check) • Test the appropriateness of the extent of your domain

  3. Things you can do • Simulate steady, turbulent flow • Simulate flow past objects in a domain • Calculate the drag coefficient using the sum of forces on an object in a flow • Determine whether flow solution is dominated by hyperbolic, parabolic or elliptic behaviour • Utilise time-dependant equations to enhance convergence for elliptically-dominated solutions • Adapt grids to improve local resolution of flow • Simulate time-dependant laminar flow past a cylinder (vortex shedding)

  4. Errors Anderson and Versteek & Malalasekera weak on errors

  5. Main sources of error • Grid • Is it sufficiently fine? • Physics • Are you modelling the physical situation with the correct equations? • Discretisation of Partial Differential Equations • Is your solution heavily dependant on the order of the solution? • Numerical errors arising from the limitations of your software/hardware

  6. Grid • Test the grid resolution accuracy by refining the grid • By doubling • By gradients in the flow (if doubling not possible) • Plot your solutions and extrapolate to grid spacing of zero • Richardson extrapolation

  7. Extrapolation Final value • As the grid size is reduced, the values of the solution should get closer to the value obtained under conditions of minimum grid spacing. • Note that the first couple of points on the right would not give a good estimate for the final value Δx

  8. Grid over-refinement • Not possible to over-refine for laminar flow • In turbulent flow the grid can become too fine if it enters the laminar sub-layer • Turbulent flow assumes that the law of the wall applies – which it does not in the laminar sub-layer • Solution: check that the y*/y+ values are not too small

  9. Physics • Default in Fluent is laminar solution • Is the flow turbulent? (S-A, k-e, RSM) • Is the flow compressible? • Do you have temperature fluctuations? • Is there more than one phase? • Is the second phase significant?

  10. Discretisation of the equations • Order of solution is that of the first missing term in the expansion (discretisation) of the pde • 1st order can give sufficiently good results in some cases • 2nd order is required for most cases • If solutions with high degree of accuracy are required 4th order can be used • Solution order and grid refinement can be balanced

  11. Numerical errors • Not the problem they once were (16 bit) • Arise due to truncation of the numbers • Can go to ‘double-precision’ if necessary • Watch for unusual limitations • Fluent uses real reals – does not scale the problem to fit the arithmetic to the processor • For very small or very large dimensions the onus may be on you to do the scaling

  12. Silly Errors • We are all guilty of these. Even Professors of Fluid Dynamics • or should that read especially Professors of Fluid Dynamics • A sample: • Solution not actually converged • Modelling the wrong fluid • Not having calculated the Re/Ma/etc before starting • Boundary conditions not set properly (or at all!)

  13. Verification & Validationhttp://www.grc.nasa.gov/WWW/wind • Verification • The process of determining that a model implementation accurately represents the developer’s conceptual description of the model and the solution to the model • Validation – solving the right equations • The process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended use of the model • Compare with experimental data

  14. This week’s exercise • Create a number of grids in gambit for 2D flow past a flat plate perpendicular to the flow • Create a graph of solution values for the drag force and hence estimate the ‘real’ value

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