Uncertainty Quantification Integrated to CFD Modeling of Synthetic Jet Actuators

Abstract

The Point Collocation Non-Intrusive Polynomial Chaos (NIPC) method has been applied to two stochastic synthetic jet actuator problems used as test cases in the CFDVAL2004 workshop to demonstrate the integration of computationally efficient uncertainty quantification to the high-fidelity CFD modeling of synthetic jet actuators. In Case1 where the synthetic jet is issued into quiescent air, the NIPC method is used to quantify the uncertainty in the long-time averaged u and v-velocities at several locations in the flow field, due to the uniformly distributed uncertainty introduced in the amplitude and frequency of the oscillation of the piezo-electric membrane. Fifth order NIPC expansions were used to obtain the uncertainty information, which showed that the variation in the v-velocity is high in the region directly above the jet slot and the variation in the u-velocity is maximum in the region immediately adjacent to the slot. Even with a ten percent variation in the amplitude and frequency, the long-time averaged u and v velocity profiles could not match the experimental measurements at y=0.1mm above the slot indicating that the discrepancy may be due to other uncertainty sources in CFD or measurement errors. In Case 2 which includes a cross flow, the free stream velocity is treated as an uncertain input variable. Fifth degree NIPC expansions were employed to quantify the uncertainty in phase averaged velocity profiles as well as long-time averaged wall pressure and skin friction coefficient distributions. The results of Case 2 show that the uncertainty in phase averaged velocity profiles gets larger when approaching the main stream. The size of a separation bubble observed in this case remains relatively insensitive to the uncertain free stream velocity within the tolerance range considered.