Computation of Steady Nozzle Flow by a Time-Dependent Method

Theme T HE equations of motion governing steady, inviscid flow are of a mixed type, that is, hyperbolic in the supersonic region and elliptic in the subsonic region. These mathematical difficulties may be removed by using the so called time-dependent method, where the governing equations become hyperbolic everywhere. The steady-state solution may be obtained as the asymptotic solution for large time. This technique has been used to compute converging-diverging nozzle flows by Prozan (as reported by Saunders 1 and Cuffel et al. 2), Migdal et al., 3 Wehofer and Moger,4 Laval,5 and Serra.6 This technique has also been used to compute converging nozzle flows by Wehofer and Moger4 and Brown and Ozcan.7 While the results of the preceding calculations are for the most part good, the computational times are rather large. In addition, although the computer program of Ref. 6 included a centerbody and those of Refs. 4 and 7 included the exhaust jet, none of the preceding codes is able to calculate both, that is, plug nozzles. Therefore, the object of this research was to develop a production type computer program capable of solving converging, convergingdiverging, and plug two-dimensional nozzle flows in computational times of 1 min or less on a CDC 6600 computer. Contents The nonconservation form of the Euler equations for twodimensional, inviscid, isentropic, rotational flow of a perfect gas are solved. The physical plane is mapped into a rectangular computational plane. The interior mesh points are computed using the MacCormack8 scheme. The inlet, wall and centerbody, and exhaust jet boundary mesh points are calculated using a reference-plan e characteristic scheme. The exit mesh points are computed using linear extrapolation for supersonic flow and a characteristic scheme for the subsonic case. The results in the present study were obtained using a CDC 6600 computer. The computational times given are the central processor time not including compilation. In order to compare these results with those of other investigators, Table 1 is given (see backup paper for references). The initial data in each case were computed internally by the program assuming one-dimensional, steady, isentropic flow with area change. When the relative change in axial velocity in the throat and downstream regions was less than a prescribed convergence tolerance, the flow was assumed to have reached Table 1 Relative machine speeds