Numerical investigation of the axial impulse load during the startup in the shock tunnel

A shock tunnel is a representative type of ground-based equipment in the hypersonic field, which has the advantage of free stream of excellent quality. Accurate measurements of aerodynamic forces in the shock tunnel are great challenges. The impulse loads during the start-up process induce the vibration of the model and its support. Aerodynamic signals are disturbed by vibrational signals. The identification of the starting time of the steady periodic vibration and excited natural frequencies of the whole structure would contribute to improve the accuracy of measurement. These two factors are closely related to the properties of the impulse forces. However, there is currently no published research on the impulse forces. In this paper, the type of impulse forces (drag history) acting on the sharp cone during the start-up process was investigated by numerical simulation. The distribution of the static pressure of the typical wave structures was found to have a significant influence on the types of the drag history. A formula, based on the physical analysis of start-up process, was put forward to estimate the starting time of the steady stage. Additionally, the subsequent analysis and design optimization such as vibration of structure and disturbing frequencies needed an analytical and simple formation of drag history. Thus, the drag history was approximated by numbers of sine functions. Different phases exhibited notable difference in composition. Also, a metric denoted as the energy coefficient was derived to identify the critical frequencies and simplify the analytical expression of the impulse force.