Dimensional analysis and surrogate models for the thermal modeling of Multiphysics systems

This paper presents an original form of surrogate models and the associated construction procedure adapted to the thermal modeling of Multiphysics systems. This method of meta-modeling, which uses dimensional analysis, extracts compact models suitable for preliminary design from finite element simulations. The mathematical expression used for the model is a product of variable power laws of dimensionless numbers. Compared to traditional surrogate models (polynomial response surfaces, kriging and radial basis functions), it has the advantage of giving light, compact forms with good predictive accuracy over a wide range of the design variables (several orders of magnitude). The general regression process is first explained and illustrated with a study of the Marangoni effect. Then the methodology is used to build thermal models of an electromechanical actuator (EMA) which are used to size an aileron EMA for two different cooling strategies. Finally the models are also used to discuss the effect of confinement on the actuator's overall thermal resistance.