Compressible flows in micro-channels: an enhanced quasi-2D Fanno-based numerical model

Fanno theory provides an analytical model for the prediction of confined viscous compressible flows under the hypotheses of constant cross-section channel and adiabatic flow. From theory, differentials of flow characteristic quantities can be expressed in function of Mach number and friction factor. Yet, the theory does not assess how to evaluate friction, whereas classical formulas for friction prediction in channels are derived under the hypothesis of incompressible flow and are no longer valid in case of compressible flows. Compressibility deforms the velocity profiles in the channel by making them more flat. As a consequence friction is increased compared to the incompressible case. At the same time, the change in the velocity profiles affects the average dynamic pressure and the bulk temperature along the channel. Correlations, function of Mach and Reynolds numbers, are required for quantifying these changes and improve the prediction of the Fanno model. In the present paper, the impact of compressibility on laminar and turbulent flows in micro-channels is assessed on the basis of a series of CFD simulations, and correlations are presented for friction, average dynamic pressure, and bulk temperature. The correlations are proven to enhance the accuracy of the Fanno model predictions.