The Dispersion Relations of Kevin-Helmholtz Instability Wave of Supersonic Triple Jets
by
Joshua Z. Du and Liancheng Wang
Department of Mathematics, Kennesaw State University, Kennesaw, GA 30144, USA

Because of the need for large thrust and flexibility, high performance military aircraft are propelled by multiple jet engines housed close to each other. Since the complexity of the configuration of multiple jets and large tangential gradient of the velocity of the jets plumes, the Kelvin-Helmholtz instability wave and upstream propagated acoustic wave including the screech tone, would cause the instability of the jets and the damage of the engines vie metal fatigue. Advanced fundamental research is needed to explore and mathematically model supersonic multiple jets. Vortex sheet model has been used to investigate Kelvin-Helmoltz instability waves. The governing equations of triple jets flow are derived by using three physics laws, the Conservation of Mass, Momentum, and Energy. The general solution is obtained. The general solution is classified into 6 families by a self-invertible rotating matrix. By applying Kinematical and dynamical boundary conditions, we are able to derive 6 dispersion relations for Kelvin - Helmholtz Instability waves and acoustic waves. This work will give a frame work for general N jets with N > 3.

Date received: April 1, 2007