Improved traceable measurement of the reflected step pressure in shock tube with the compensation of shock wave attenuation

Abstract Shock tube is an exceptional valuable facility that can produce approximately ideal step pressure from the reflected shock wave for the dynamic characterization of pressure sensors in aerospace industry. However, the traceable measurement accuracy of the reflected step pressure (RSP) is limited by the inevitable attenuation of the incident shock wave (ISW), leading to the dynamic characterization results with large error. This paper proposes an improved method for achieving high-accuracy traceable measurement of RSP in shock tube with the compensation of shock wave attenuation. The traceable measurement model of RSP relates to the ISW velocity is established firstly based on shock tube theory. To compensate the ISW velocity attenuation, a distributed measurement combined with a non-equidistant fractional-order grey (NFOG) method is implemented to establish ISW velocity model in consideration of the nonlinear, small-sample and non-equidistant features of the velocity sequence obtained by multiple sensors. Meantime, an ergodic optimization method based on a similarity index is adopted to estimate the optimal fractional-order in NFOG. With ISW velocity model, the velocity at the end-wall of shock tube is predicted and then more reliable RSP result is achieved with the traceable measurement model. Four experiments under different shock wave conditions are carried out to verify the proposed method. Results show that NFOG is able to establish the velocity model effectively, and the modeling error is less than that of the non-equidistant grey model and least square fitting methods. Furthermore, the traceable measurement accuracy of RSP by the proposed method is improved significantly than existing methods according to the investigation of pressure sensor sensitivity in both dynamic and static conditions.