1. Computational Fluid Dynamics 5Final Thoughts 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) • Estimate simulation results through extrapolation

4. Stuff Sources: Starccm+ Help pages Versteeg/Anderson/colleagues

5. Convergence • My simulation won’t converge • are my units correct? • am I using the correct category of models for the flow? • is my grid too heavily skewed or too fine/coarse ? • My simulation partially converges • am I using the best sub-class of models? • is my solution time-dependent? • My simulation still won’t converge • is the domain dominated by elliptical solutions? • can I use a time-dependent flow to reach steady-state solution?

6. Relaxation • The relaxation governs the rate at which the solution is approached. Too fast can lead to over-shoot and instability. • Finite-difference schemes - over-relaxation • calculate the difference to the next value and multiply by a factor >1, typically up to 1.9 for well-behaved solutions • this speeds up convergence • Finite-volume schemes - under-relaxation • multiply predicted difference by a factor <1, actual value depends on variable • lower value can stabilise convergence, especially in the early stages

7. solver formulation • segregated solver • equations solved sequentially • roots in incompressible flows • coupled solver • momentum, continuity (& energy) equations solved simultaneously • roots in compressible flows

8. Turbulence modelling • The turbulence models in STAR-CCM+are responsible for providing closure of the governing equations in turbulent flows. • This section first provides general overviews of: • Selecting a turbulence modeling approach • Using Reynolds-Averaged Navier-Stokes (RANS) turbulence models • Using large eddy simulation (LES) • Using detached eddy simulation (DES) • Using wall treatment models

11. Abe-Kondoh-Nagano, better for complex low Re Satisfies the Physics of turbulence Original and still used often What it says on the tin! Allows low y+ values Better for near-wall turbulence with separation

12. Steps • What do I think will be the outcome? • Order of magnitude calculation • What can be expected of CFD? • What are the appropriate models? • Do a literature search • Now model