Chapter 8 Sample Problems

“I know there’s an answer, I know now but I have to find it by myself.”

The Beach Boys, I Know There’s An Answer (1966).

The preceding chapters establish some general principles of CFD, covering topics in fluid dynamics, numerical methods, boundary conditions, algorithms, solvers and turbulence and its modelling.

This chapter aims to bring together some of these principles using four sample CFD problems, some of which are mentioned in the earlier chapters. The four examples demonstrate a variety of flow types, including:

  • two internal flows, inside a room and a Venturi tube, in which, beyond regions of significant inflow and outflow, the fluid is contained by solid boundaries;
  • two external flows, around a vehicle and a cylinder, in which a considerable part of the domain is unbounded.

The flow in the room and around the vehicle are turbulent, so demonstrate turbulence modelling and wall functions from Chapter 7 . The flow is laminar in the other examples.

The vehicle and Venturi tube cases are simulated using the steady-state algorithm in Sec. 5.12 , whereas the room and cylinder cases use the transient algorithm in in Sec. 5.19 .

Mesh generation

The sample problems are supported by additional information on mesh generation. Strategies for meshing between the far-field and a body of interest in external flows are discussed in Sec. 8.1 .

Meshes may include cells with high aspect ratio to increase the solution efficiency, particularly with external flows. Including these cells, however, increases the range of magnitudes of the matrix coefficients, which adversely affects solution convergence, as discussed in Sec. 8.2 .

The generation of block-structured and unstructured meshes are discussed in Sec. 8.3 and Sec. 8.5 respectively. The block-structured approach is suited to problems whose boundaries are described by relatively simple geometric forms, e.g. cylinders, cuboids, etc.

The unstructured approach is designed to accommodate more complex boundary geometries, e.g. the vehicle in the external aerodynamics example. The geometries are typically defined by a computer-aided design (CAD) model.

Boundary Conditions

The examples demonstrate a variety of specialised boundary conditions. The cylinder and vehicle both use the freestream condition, described in Sec. 4.16 at the far-field boundary. The Venturi example uses a nonuniform inlet condition for eqn, described in Sec. 8.7 . Finally, the flow in a room uses a condition for eqn to ensure correct boundary fluxes, as described in Sec. 5.11 and the external heat flux condition for eqn from Sec. 4.17 .
Notes on CFD: General Principles - Chapter 8 Sample Problems