Understanding heat transfer in 2D channel flows including recirculation

Abstract

Inviscid, irrotational two-dimensional flows can be modelled using the Schwarz–Christoffel integral. Although bounded flows including boundary layer separation and recirculation are not irrotational, a model is presented that uses the Schwarz–Christoffel integral to model these flows. The model separates the flow domain in the main flow area, where irrotational flow is assumed, and recirculation areas, which are modelled as monopolar vortices. The model has unknown parameters, which are geometric characteristics of the velocity field. The method is demonstrated on a channel with alternating baffles. Many variations of this system were modelled using CFD modelling, and the flow was a typical combination of main flow and recirculation. The CFD results were used as reference to calibrate the parameters of the Schwarz–Christoffel model. Many parameters appeared to be constant, and calibrating only three variable parameters yielded about 22% error for most velocity fields. After this, heat transfer was added to the CFD models, and the heat flux was analysed using the three variable parameters representing the velocity field. This way, a new model is found for the heat flux from a wall bounding a vortex, which has an error of 7%. Finally, we have calibrated the parameters using a limited number of given velocity vectors, demonstrating that the parameters can be calibrated against a real set of measurements.