Method of Characteristics for designing diverging section of supersonic nozzles.

The code utilizes method of characterisitics to solve the velocity potential equation (which is a hyperbolic partial differential equation) used for modelling compressible, inviscid and irrotational fluid flow.

Figure: PDE modelling the flow (J.D Anderson, Fundamentals of Aerodynamics)

Results

Figures attached below demonstrate the progression of the nozzle contour for required exit Mach number of '2' with adiabatic gas constant of 1.4. As the number of characteristic curves are increased, the contour becomes smoother and more accurate.

Figure 1: Contour for considering 2 characteristic curves

Figure 2: Contour for considering 5 characteristic curves

Figure 3: Contour for considering 50 characteristic curves

Figure 4: Contour for considering 90 characteristic curves

Note: Contours shown above only represent the nozzle boundary above the centre line, as due to symmetry, a similar profile will be obtained below the centreline as well.