Due to a large disparity in time scales between fluid convection and solid diffusion, the transient modeling of a CHT (Conjugate Heat Transfer) problem is impractical, without special numerical treatment, because it can take many time steps for the temperature distribution in the solid to reach a steady state. For example, in a hot streak migration simulation, thousands of blade passing periods may have to be computed before the solution in the solid converges and reaches a steady-state temperature.

A good engineering approximation is to advance the simulation in time while altering the thermal response of the solid to effectively accelerate the solid thermal diffusion convergence. The thermal response in the solid can be altered by Timescale Control settings. Using the Domain Solver Control > Timescale Control settings, you can specify a value for Timescale Factor.

You must enter the solid Timescale Factor, which is defined as:

where is the simulation time-step size necessary to resolve flow features of interest.

The solid time scale can be determined by the following formula:

where is the characteristic length of the solid (in the case of a turbine blade, can be the blade chord) and is the solid material thermal diffusivity. You can alter the rate of the solid response by a slight modification of the Timescale Factor.

This modeling approximation increases the thermal response of the solid to the temperature variation in the fluid. As a result, the temperature at any given point in the solid will, during convergence, fluctuate slightly about an average value. It should be noted that the fluctuations in solid temperature are nonphysical. The time-averaged temperature (after convergence) is very close to the real physical temperature.