Efficient Uncertainty Quantification for the Design of a Supersonic Pressure Probe

The Point-Collocation Non-Intrusive Polynomial Chaos (NIPC) method utilizing Euler CFD simulations has been applied to the stochastic analysis of a pressure probe designed for Mach number measurements in three-dimensional supersonic flows with moderate swirl. The probe is in the shape of a truncated cone with a flat nose opening for total pressure measurement and includes four holes on the cone surface for static pressure measurements. The present stochastic CFD study is performed to provide information for further refinement of the supersonic pressure probe design in the presence of geometric uncertainties and to quantify the variation in the pressure measurements and the Mach number due to the uncertainty in the cone angle, the nose diameter, and the location of the static pressure port on the cone surface. Each uncertain parameter was modeled as a uniform random variable with a specified range and mean value based on the tolerances supplied by the manufacturer. The uncertainty information for various output variables obtained with a second order polynomial chaos expansion fell within the confidence interval of the Latin Hypercube Monte Carlo statistics. The second order NIPC required only 20 CFD solutions to obtain the uncertainty information, whereas the Monte Carlo simulations were performed with 1000 samples (CFD solutions), indicating the computational efficiency of the polynomial chaos approach. The relative variation in the Mach number due to the specified geometric uncertainty was found to be less than 1%. The sensitivity analysis obtained from the polynomial chaos expansions revealed that the Mach number is an order of magnitude more sensitive to the variation in the cone angle than the uncertainty in the other geometric variables. The stochastic results also showed that the uncertainty in the cone pressure measurement remains constant and minimum as long as the static pressure holes are located beyond 20% of the truncated cone surface length indicating the possibility for a smaller-size probe design by moving the static pressure ports further upstream on the cone surface