Analytical and experimental investigation of flow between a smooth stationary disc and a grooved rotating disc

The radial outflow between a smooth or grooved rotating disc and a smooth stationary disc was examined both analytically and experimentally with the main interest on flow rate, drag moment and heat transfer. All investigations were conducted for a zero pressure differential across the disc.

The analysis was based on an integral method with an area-averaged boundary condition on the grooved rotor. A dimensional analysis is presented that shows the radial inertia terms must be included in the governing equations. These terms are usually considered negligible in this type of analysis. A finite difference scheme was employed in the radial direction and the zero pressure differential across the disc was satisfied by an iterative solution technique. This technique required iterating on separate initial flow rates to the gap region and grooves until compatible flow rates in the two regions were converged on.

Experimental data were not available in the existing literature for the range of parameters being investigated in this study so extensive data were generated. Two fluids, air and SAE l0 motor oil, were examined to determine the applicability of the non-dimensional variables used in the analysis. The drag moment was determined using strain gages for the oil test and a hot film surface probe for indirect measurement of the drag moment when air was utilized. Heat transfer data using only the SAE 10 motor oil were taken.

gap spacing, was found where flow transition from laminar to turbulent flow is believed to occur in the flow between the stator and rotor. Additionally a region was found near Re_w = 2000 Reynolds number is based on the groove width, where flow transition from laminar to turbulent flow is believed to occur in the grooves. Plausibility arguments supporting the idea of these transition regions are presented.

The agreement between theory and experiment was good for the flow rates in the region which was considered laminar flow. The drag moment predictions agreed well with the data at the larger disc spacings examined but the theory over-predicted the data for the smaller disc spacing examined.

The heat transfer analysis was based upon a Reynolds type of analogy and did not show good agreement with data. The theory predicted a much stronger dependence of the heat transfer coefficient on Reynolds number than the data showed.