ShockWaves manuscript No. (will be inserted by the editor) Two-Dimensional Numerical Study of Planar Shock- Wave/Moving-Body Interactions Part I: Plane Shock-on-shock interactions ? C Law, LT Felthun a , and BW Skews School of Mechanical Engineering, University of the Witwatersrand, PO Wits 2050, South Africa Received: date / Revised version: date Abstract. The interaction of a planar shock wave with a body moving at supersonic speed has been considered with particular focus on shock-on-shock interactions. Three interaction types were previously identified by Smyrl (1964). This work adds a fourth type to these interactions and restates the interaction type classification and the transitions between the various interaction types. A pseudo-steady analysis of key interaction points and flow features is used to predict the various transitions. The criteria presented here are compared to results from a numerical Euler model of the interactions. A comparison of results from the numerical model with experimental results shows good agreement and thus the existence of the various interaction types and transition criteria have been confirmed using the numerical model. Key words: shock-on-shock, shock-wave/moving-body interactions, CFD 1 Introduction The interaction of shock waves with other shocks or a va- riety of boundaries such as contact surfaces and wedge faces, has been a field of intense interest for many years. In the 1960’s and 70’s the interaction of a shock with a supersonic body was given a great deal of attention where work done by Merrit and Aronson (1967) and by Kutler et al. (1975) are examples of experimental and numerical work done on shock-on-shock (s-o-s) interactions. Shock- on-shock interactions are defined here as the interaction of a supersonic bow wave with an impinging shock. The impinging shock can be a supersonic bow wave generated by a wedge passing close by a second wedge, as is illus- trated in Fig. 1. The impinging shock can be considered as a normal shock of strength M s = M w2 sin β 2 , at an angle of incidence λ, interacting with a wedge at M w = M w1 with a half angle θ w = θ w1 , in still air. A linearised analytical model of the head-on s-o-s in- teraction was presented by Smyrl (1964), in which three types of shock interaction were proposed. The three con- figurations are defined by the manner in which the post interaction bow shock interacts with a sonic circle gener- ated by the passage of the impinging wave. More recently, ? Aspects of this work were presented at the 23 rd ISSW by Law et al. (2001) a Present address: Computational Dynamics, 3 Schoolhouse Lane, Etna, NH 03750, USA Correspondence to : C Law (e-mail: claw@mech.wits.ac.za) q w2 q w1 M w2 M w1 b 2 l b 1 Fig. 1. Two supersonic wedges in close proximity Li and Ben-Dor (1997) presented a more general analytical model of the s-o-s interaction which included the oblique interaction. Their model also redefined the original inter- action types of Smyrl (1964) as either regular, or irregular s-o-s interactions. Any classification of shock interactions is, by its nature somewhat arbitrary as various factors could be used to dis- tinguish interaction configuration features. Smyrl’s clas- sifications are based on linearising assumptions and the classification of Ben-Dor applies only to s-o-s interactions and does not distinguish between interaction subtypes. An investigation of shock-wave/moving-body (s-w/m-b) interactions conducted by Law (2002) showed that a clas- sification of s-o-s interactions should tie in with a general classification of s-w/m-b interactions as s-o-s interactions form a class of s-w/m-b interactions. Law (2002) chose to classify the interactions according to the geometry of