What Is a General Methodology For an Explicitly Coupled Heat Transfer Analysis?

An explicitly coupled thermal analysis is one in which the non-isothermal flow problem is solved in one Simcenter STAR-CCM+ simulation, and the solid thermal problem is solved in a second simulation either using Simcenter STAR-CCM+ or another CAE code. This is typically done for analyses in which solid components exchange heat with a fluid whose properties vary in a cyclic manner, or cases in which the fluid and solid have disparate time scales.

An example for which this approach would be appropriate is an analysis of the heat transfer between the exhaust gases of an internal combustion engine (ICE) and its exhaust manifold. In such an analysis, the flow field leaving the engine will fluctuate in response to the exhaust valve dynamics. This means that the temperature of the fluid entering the exhaust manifold will experience rapid changes to the order of several hundred degrees. The solid body of the manifold will not respond so quickly to these temperature changes due to its greater thermal inertia relative to the fluid, so this results in a conjugate heat transfer problem where the time step that is appropriate for the fluid analysis is smaller than the time step that is appropriate for the solid thermal analysis -- hence the need to have two distinct simulations explicitly coupled by an exchange of thermal information on their common boundary. The solid thermal analysis will, in fact, tend towards a steady state solid conduction problem, as small fluctuations in solid temperatures during an engine cycle are not usually of interest.

A suggested methodology for conducting this analysis is illustrated in the figure below. Two separate simulations are set up, one for the fluid analysis and another for the solid thermal analysis.

In the first step, an assumed wall temperature is applied to the wall boundaries of the transient flow problem. This flow problem is solved for a total time equal to one engine cycle. It is important that this initial assumed wall temperature be reasonable in this step, as otherwise the solution may not converge. Following the simulation, a time-averaged, spatially varying, heat transfer coefficient and its corresponding reference temperature (both of which are calculated using field mean monitors and field functions) are calculated on the wall boundaries and then passed to the solid thermal simulation which is being run in steady state. To ensure that the time averaged heat transfer at the interface is conserved, the reference temperature (which is not the time averaged heat transfer reference temperature) that must be used is defined as:

Figure 1. EQUATION_DISPLAY

{\hat{T_{}}}_{r} = T_{w} - \frac{\bar{{\dot{q}}^{"}}}{\bar{h}}

(549)

where $\bar{{\dot{q}}^{"}}$ is the time averaged interface heat flux and $\bar{h}$ is the time averaged heat transfer coefficient. The solid thermal simulation is then run to convergence.

In the second step, the wall temperatures predicted by the solid thermal simulation are passed back to the transient flow simulation and applied to the wall boundaries. The flow simulation is solved for a second time to obtain a second set of heat transfer coefficients and reference temperatures. This new set of data is passed to the solid thermal simulation for a second time.

This iterative process continues until successive steps show little or no meaningful change in the values of the predicted heat transfer coefficients or temperatures. Some situations may require many co-simulation cycles until the overall converged state is achieved.

A key question in this approach is: what heat transfer coefficient and reference temperature should be exchanged between the simulations? Simcenter STAR-CCM+ provides several choices. For more information, see What Methods Are Available for Exchanging Heat Transfer Coefficients?