2D Transonic Internal Flow

Ramki

Hi, I have recently developed a 2D Euler solver based on Jameson's Finite volume formulation with 2nd and 4th order aritificial dissipation.

To benchmark the accuracy of the code, I am trying to apply it to a transonic flow through a 2D converging-diverging nozzle. With this I can compare the results along the plane of symmetry with the quasi-1D analytical results from Shapiro, or any other place.

However, the results I obtain depend on the boundary conditions I use as follows:

1. I explictly set the exit boundary condition to a constant pressure - 1 BC specified, and remaining extrapolated. At the inlet I specify the total pressure and temperature, and calculate the inlet Mach number from isentropic relations - 3 BC specified, 1 extrapolated. In this case, the results I obtain are the closest to the analytical case - I get a Mach number of 1 at the throat.

2. I retain the constant pressure boundary condition at the exit. However, at the inlet I use the Reimann invariant boundary conditions, calculating R+ from pinf = p0, Tinf = T0 & uinf = 0. In this case I get a completely subsonic flow, with the throat Mach number nowhere near zero. In fact, the inlet pressure is much lower than that obtained in case 1.

3. Used the boundary conditions from Jameson's paper: a) inlet conditions based on non-reflecting BCs based on linear characteristics and, b) exit conditions specified using a mixed formulation of non-reflecting+fixed pressure (ref:Rudy & Strikwerda). The results I obtain are similar to 2 above.

Since 2 & 3 were based on non-reflecting BCs, I did see a marked acceleration of convergence. However, the converged values were markedly different from 1) above or the analytical solutions.

Any insights, experiences ?

Thanks. - Ramki