Numerical Simulation of Heat Transfer and Fluid Flow in Streamwise-Periodic Geometries: a Review

Streamwise-periodic variation of cross-sectional area causes the flow and the non-dimensional temperature fields to repeat periodically, after a certain developing length, in a variety of systems of practical interest. For these geometries, the numerical simulation of heat transfer and fluid flow can be conveniently confined to a single isolated module, thus to neglect the effect of the dynamic and thermal development and with a significant saving in computational resources. In this paper, a thorough review of the relevant literature is presented. While the solution of the periodic flow field is performed in a similar way in nearly all the studies that have been examined, different solution strategies for the temperature field have been published, for both cases of imposed wall heat flux and assigned wall temperature. The solution of the fully developed temperature field is more challenging than the solution of the periodic flow field, and for this reason both analytically accurate and approximate methods have been found in the relevant scientific literature. Solution techniques for both thermal boundary conditions have been implemented and successfully tested in ANSYS CFX. Although the implementation of a complete, non-iterative analytical model for a prescribed wall temperature boundary condition proved to be almost impossible, because of the difficulties associated to the lack of access to the detailed data structure within the code, an original improvement of a simpler and only slightly less accurate method found in the literature has been developed, and will be presented.