Thermo-Mechanical Calculation of Printed Circuit Heat Exchanger Using Homogenization

The Finite-Element Method(FEM) is mainly used to design Compact Heat Exchanger structures. However, the narrow channel structures require fine mesh to accurately compute stress and strain. Combined with the dimensions of the overall component, this leads to an excessively large numerical model and therefore long computing time. This is especially true for transient thermal analyses, which require taking into account the full geometry. It is therefore interesting to reduce the size of the mesh. Periodic homogenization is an efficient method for achieving this goal. It can be applied to the core of the structure when periodic patterns(identified on basis of the arrangement of the channels) exist. A method based on this technique, with some improvements, is proposed in this paper for thermal loading without internal pressure. In addition to the Equivalent Homogenous Medium(EHM) replacing the periodic patterns, some explicit channels are interposed between the EHM and the cover plates. This has two advantages. The first is to smooth the transition of stiffness between the cover plates and the homogenized medium. The second one is to be able to directly compute stress and strain on the most critical channels located in this area. This paper assesses the method’s effectiveness for thermal loadings in order to conduct thermal stress analyses. First, the equivalent elastic constants of the EHM are obtained with a numerical Finite Elements Method. Then, two 2D cases using EHM are compared against a 2D explicit model(i.e. explicit geometry for the core channels). These cases are chosen to validate the EHM itself and its effectiveness for a real section of the heat exchanger. Results show very good agreement with a relative difference lower than 1%. In addition, the sensitivity to the number of layers added between the EHM and the cover plates is analysed. It is recommended interposing at least two layers of patterns to obtain converged results for the considered configuration. Finally, a triangular mesh is considered to reduce the size of the model. No difference with a regular quadrangular mesh can be observed whereas the computing time is reduced. This method can be used to perform the design of any CHE under thermal loading as long as the channel arrangement shows periodicity.