A Semi-empirical Model to Predict the Attached Axisymmetric Shock Shape

Abstract

In this work, a simple semi-empirical model is proposed, based on Response Surface Model, RSM, to determine the shape of an attached oblique shock wave emanating from a pointed axisymmetric nose at zero angle of attack. Extensive supersonic visualization images have been compiled from various nose shapes at different Mach numbers, along with some others performed by the author for the present paper. The method is based on the relationship between the body shape and the shock shape. The body shape and the free stream Mach number determine the shape of the oblique shock standing ahead. From the statistical data bank containing the visualization tests and employing the RSM, an analytic relationship has been established between the body and the shock shape. From this relationship, knowing the body shape and the Mach number, one can simply determine the shock shape. The visualization tests performed by the author for some other cases have approved the accuracy of the proposed relationship. However, the approach is restricted to attached shocks emanating from sharp noses at zero angle of attack. Despite the limitations, this relationship can effectively be used in model scale determination for wind tunnel tests to prevent shock reflection from the walls that could lead to erroneous results.