Turbulence models for CFD in the 21st century

Brian Spalding, of CHAM Ltd

Invited lecture presented at ACFD 2000, Beijing

Example 1. The LVEL turbulence model used in a simultaneous solid-stress, fluid-flow and heat-transfer example

• Heat is supplied to a fluid in which a horseshoe-shaped object is suspended.

• The outer cylindrical container is cooled.

• The task is to compute the stresses in the solid.

• The following images are shown:

1. The thermally-induced volumetric expansion of the solid

2. The temperature distribution in the solid and fluid, when heat is supplied along the axis, and gravity acts vertically

3. The associated velocity vectors (in the fluid) and displacement vectors (in the solid)

4. The thermally-induced radial stresses in the solid

5. The thermally-induced circumferential stresses in the solid

6. The computed distance from the walls, needed by the underlying LVEL model, of:
   1. the horseshoe-shaped solid, and
   2. an outer cylinder

7. The effective viscosity determined by the LVEL model

The effective viscosity is evidently greatest where the buoyancy-driven velocity is greatest, and the distance from the wall not too small.

The equations for the wall-distance, effective viscosity, velocities, temperatures and displacements, are all solved simultaneously by means of a single computer code (PHOENICS).

The computer time is not significantly greater than would be taken for the velocities and temperatures alone.