The flow between a rotating and a stationary disc: application to near-wall hot-wire calibration

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Several experimental works in the literature have just assumed the validity of the power series solution provided by Stewartson in 1953 for the flow in the gap between a top rotating disc and a bottom stationary disc in an effort to devise a simple and compact calibration apparatus to calibrate the hot wire as a wall shear stress or velocity probe for near-wall measurements. This work seeks to verify the applicability of the series solution via the use of direct numerical simulation (DNS) of the flow field, and in doing so explicitly justify the underlying assumption of the previous experimental works. The simulated laminar flow indicates good agreement of the velocity profiles with the series solution provided the Reynolds number (, where is the angular velocity of the rotating disc and is the gap between the discs) is kept below 3.0, and the radial position is less than 0.9 disc radius away from the end-disc effect at the disc edge. Experiments carried out with a flush-mounted hot wire calibrated as a wall shear stress probe in the rotating disc apparatus (assuming the series solution) for measurement in a known laminar channel flow further attest to the applicability of the series solution in the disc gap.