But more reasonable guess can speed up the convergence. Boundary conditions – No-slip or slip-free on the wall, periodic, inlet (velocity inlet, mass flow rate, constant pressure, etc.), outlet (constant pressure, velocity convective, buffer zone, zero-gradient), and non-reflecting (compressible flows, such as acoustics), etc.
36 Grid generation Grid generation Grids can either be structured (hexahedral) or unstructured (tetrahedral). Depends upon type of discretization scheme and application – Scheme Finite differences: structured Finite volume or finite element: structured or unstructured – Application Thin boundary layers best resolved with highly-stretched structured grids Unstructured grids useful for complex geometries Unstructured grids permit automatic adaptive refinement based on the pressure gradient, or regions of interest (FLUENT)
37 Grid Resolution Grid Resolution
38 Grid generation and transformation Grid generation and transformation Grids designed to resolve important flow features which are dependent upon flow parameters (e.g., Re) Commercial codes such as Gridgen, Gambit For research code, grid generated by one of several methods (algebraic vs. PDE based, conformal mapping) For complex geometries, body-fitted coordinate system will have to be applied (next slide). Grid transformation from the physical domain to the computational domain will be necessary Sample grid established by Gambit of FLUENT
39 Grid transformation Grid transformation y x o o Physical domain Computational domain x x f f f f f x x x y y f f f f f y y y Transformation between physical (x,y,z) and computational ( ) domains, important for body-fitted grids. The partial derivatives at these two domains have the relationship (2D as an example)
40 Numerical parameters & flow Numerical parameters & flow solution solution Numerical parameters are used to control flow solution. – Under relaxation factor, tridiagonal or pentadiagonal solvers – CFD Labs using FlowLab Monitor residuals (change of results between iterations) Number of iterations for steady flow or number of time steps for unsteady flow Flow solution – Solve the momentum, pressure Poisson equations and get flow field quantities, such as velocity, turbulence intensity, pressure and integral quantities (drag forces)
41 Numerical parameters & flow Numerical parameters & flow solution solution Typical time history of residuals The closer the flow field to the converged solution, the smaller the speed of the residuals decreasing. Solution converged, residuals do not change after more iterations
42 Post-processing Post-processing Analysis, and visualization – Calculation of derived variables Vorticity Wall shear stress – Calculation of integral parameters: forces, moments – Visualization (usually with commercial software) Simple X-Y plots Simple 2D contours 3D contour carpet plots Vector plots and streamlines (streamlines are the lines whose tangent direction is the same as the velocity vectors) Animations (dozens of sample pictures in a series of time were shown continuously)
43 Post-processing (Parallel Plates) Post-processing (Parallel Plates)
44 Post-Processing (example) Post-Processing (example) Pressure contour and velocity vectors .
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- Fall '19