An integral perturbation model of flow and momentum transport in rotating microchannels with smooth or microstructured wall surfaces

Abstract

This paper summarizes the development of an integral perturbation solution of the equations governing flow momentum transport and energy conversion in microchannels between disks of multiple-disk drag turbines such as Tesla turbines. Analysis of this type of flow problem is a key element in optimal design of Tesla drag-type turbines for geothermal or solar alternative energy technologies. In multiple-disk turbines, high speed flow enters tangentially at the outer radius of cylindrical microchannels formed by closely spaced parallel disks, spiraling through the channel to an exhaust at a small radius, or at the center of the disk. Previous investigations have generally developed models based on simplifying idealizations of the flow in these circumstances. Here, beginning with the momentum and continuity equations for incompressible and steady flow in cylindrical coordinates, an integral solution scheme is developed that leads to a dimensionless perturbation series solution that retains the full complement of momentum and viscous effects to consistent levels of approximation in the series solution. This more rigorous approach indicates all dimensionless parameters that affect flow and transport and allows a direct assessment of the relative importance of viscous, pressure, and momentum effects in different directions in the flow. The resulting lowest-order equations are solved explicitly and higher order terms in the series solutions are determined numerically. Enhancement of rotor drag in this type of turbine enhances energy conversion efficiency. We also developed a modified version of the integral perturbation analysis that incorporates the effects of enhanced drag due to surface microstructuring. Results of the model analysis for smooth disk walls are shown to agree well with experimental performance data for a prototype Tesla turbine and predictions of performance models developed in earlier investigations. Model predictions indicate that enhancement of disk drag by strategic microstructuring of the disk surfaces can significantly increase turbine efficiency. Exploratory calculations with the model indicate that turbine efficiencies exceeding 75% can be achieved by designing for optimal ranges of the governing dimensionless parameters.