Method of Characteristics

Abstract

The governing equations of motion for two and three-dimensional inviscid irrotational supersonic flows are derived. Although these equations are nonlinear, there are unique curves in the physical space, known as characteristics that turn the governing partial differential equations into ordinary differential equations that may be integrated along the characteristics. Therefore, the method of characteristics (MOC) is an exact solution technique that is graphical in nature and since it is nonlinear, it applies to upper transonic flow when the local Mach number is sonic or supersonic. The theory of MOC is developed and applied to 2-D irrotational flows. Within MOC, two competing techniques known as wave-field method and lattice-point approach are presented. The first example that is detailed is the minimum-length supersonic nozzle design. The principle of wave cancellation at a solid boundary is used in supersonic nozzle design and it is well described. The next application is the wave pattern in supersonic exhaust plume. Here, wave reflection from a free boundary, i.e., the free shear layer, is introduced and analyzed. The cases of under- and over-expanded exhaust plumes are considered and MOC is applied to capture the spatial evolution of the jet. MOC is extended to axisymmetric irrotational flows. Family of supersonic nozzles, deflecting jets, non-uniform inlet condition, streamlines and ducts and curved shocks are the applications of MOC that are treated in this chapter. This chapter contains 9 MOC application examples and 21 practice problems at the end of the chapter.