Transonic flow

In this chapter we are going to study a special case of an external flow for which the free stream speed of the flow is close to the speed of sound, i. e. the Mach number is about unity. Under this condition the flow is called ‘transonic’. In transonic flows, the linearized version of the potential equation is not sufficient to model the flow; therefore, we resort to nonlinear but simplified version of the potential flow. The local linearization concept introduced by Dowell will be implemented for the series solution of the nonlinear transonic velocity potential. The local linearization technique enables us to study some simple steady and unsteady transonic aerodynamic problems analytically. Afterwards, we are going to study the examples for the numerical solution of the nonlinear potential equa­tion introduced by Murman and Cole (1971) in their work which handles the transonic flow region with a suitable numerical scheme. In the rest of the chapter, numerical solutions for transonic flow studies with three dimensional unsteady Euler Equation solutions and the effect of viscosity with thin shear layer approach will be considered. Further unsteady topics of transonic flow will be provided in the chapter for Modern Topics.