Uncertainty Analysis and Robust Design of Low-Boom Concepts Using Atmospheric Adjoints

This paper seeks to quantify the uncertainty associated with atmospheric conditions when propagating shaped pressure disturbances from a vehicle flying at supersonic speeds. A discrete adjoint formulation is used to obtain sensitivities of boom metrics to atmospheric inputs such as temperature, wind, and relative humidity profiles in addition to deterministic inputs such as the near-field pressure distribution. This study uses a polynomial chaos theory approach to couple these adjoint-derived gradients with uncertainty quantification to enable robust design by using gradient-based optimization techniques. The effectiveness of this approach is demonstrated over an axisymmetric body of revolution and a low-boom concept. Results show that the mean and standard deviation of sonic-boom loudness are simultaneously reduced using robust optimization. Unlike the conventional optimization approaches, the robust optimization approach has the added benefit of generating probability distributions of the sonic-boom metrics under atmospheric uncertainty.