Extended Conical Flow Theory for Design of Pressure Probes in Supersonic Flows with Moderate Flow Angularity and Swirl

Abstract

Total and static pressures are vital measurements in any supersonic experiment. By measuring these two pressures, the Mach number can be inferred. Most ows of interests are highly three dimensional, but with moderate swirl. Because of this threedimensionality, the total and static pressures must be measured ideally at the same location. A miniature probe of 10deg: half-angle was designed and experimentally calibrated to asses the eectiveness of the Krasnov similarity laws to scale the inuence of the truncated tip on the downstream cone surface pressure distribution. A recently developed uncertainty quantication approach based on polynomial chaos has been used to quantify the eect of geometric uncertainty coming from probe manufacturing tolerances on the measured Mach number utilizing computational uid dynamics. The relative variation in the Mach number due to geometric uncertainty was found to be less than 1.0%. The cone angle was determined to be the most dominant uncertain geometric parameter on the results as a result of a sensitivity analysis. The applicability of the Krasnov similarity laws is proposed as a mean to circumvent or guide the traditional and expensive experimental approach used for the calibration of a multi-hole conical probe at zero angle of attack.