Turbulence models for CFD in the 21st century
by
Brian Spalding, of CHAM Ltd
October, 2000
Invited lecture presented at ACFD 2000, Beijing
Example 1. The LVEL turbulence model used in a simultaneous solidstress,
fluidflow and heattransfer example
 Heat is supplied to a fluid in which a horseshoeshaped object is
suspended.
 The outer cylindrical container is cooled.
 The task is to compute the stresses in the solid.
 The following images are shown:

The thermallyinduced volumetric expansion of the solid

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

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

The thermallyinduced radial stresses in the solid

The thermallyinduced circumferential stresses in the solid

The computed distance from the walls, needed by the underlying LVEL model,
of:
 the horseshoeshaped solid, and
 an outer cylinder

The effective viscosity determined by the LVEL model
The effective viscosity is evidently greatest where the buoyancydriven
velocity is greatest, and the distance from the wall not too small.
The equations for the walldistance, 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.