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This study concerns an underexpanded jet, issuing from a convergent slot into quiescent air, as it is deflected by a convex surface of constant radius. Emphasis Is placed on the mechanism of breakaway, a phenomenon whereby the jet leaves the surface tangentially. An optical system based on the standard Z-type Schlieren configuration and capable of interferometric, Schlieren and shadowgraph techniques has been designed. The techniques are interchanged simply, a laser source being employed for Interferometry and a Xenon spark source for Schlieren and shadowgraph. Vibrations limit the interferometry and improvements are discussed. Shadowgraph and both spark and continuous Schlieren techniques gave good results. Total pressure traverses and surface oil flow visualization show that the influence of secondary flows on breakaway is small. Measurements of the coefficient of discharge show an increase both as the stagnation pressure Is Increased and as the slot width is reduced. The existence of a separation bubble has been established from surface static pressure measurements and shadowgraph and Schlieren photographs. Surface oil flow visualization shows a region of reversed flow withhin the bubble. The bubble grows as the stagnation pressure Is increased and eventually causes breakaway. A potential flow calculation method using the method of characteristics has been developed. Calculation of a fully attached Jet is inaccurate because the separation bubble is ignored. A calculation using the measured surface static pressures accurately predicts the main features of the first shock cell. Reattachment occurs further downstream of the jet and its breakaway should involve a coupling of the solutions of the outer shear layer, potential core and separated boundary layer, the latter including reversed flow.

Unsteady flow analysis has been gradually introduced in turbomachinery design systems to improve machine performance and structural integrity. A project on computation of unsteady flows in turbomachinery has been carried out. A quasi 3-D time-linearized Euler/Navier-Stokes method has been developed for unsteady flows induced by the blade oscillation and unsteady incoming wakes, hi this method, the unsteady flow is decomposed into a steady flow plus a harmonically varying unsteady perturbation. The coefficients of the linear perturbation equation are formed from steady flow solutions. A pseudo-time is introduced to make both the steady flow equation and the linear unsteady perturbation equation time-independent. The 4-stage Runge-Kutta time-marching scheme is implemented for the temporal integration and a cell-vertex scheme is used for the spatial discretization. A 1-D/2-D nonreflecting boundary condition is applied to prevent spurious reflections of outgoing waves when solving the perturbation equations. The viscosity in the unsteady Navier- Stokes perturbation equation is frozen to its steady value. The present time-linearized Euler/Navier-Stokes method has been extensively validated against other well- developed linear methods, nonlinear time-marching methods and experimental data. Based upon the time-linearized method, a novel quasi 3-D nonlinear harmonic Euler/Navier-Stokes method has been developed. In this method, the unsteady flow is divided into a time-averaged flow plus an unsteady perturbation. Time-averaging produces extra nonlinear "unsteady stress" terras in the time-averaged equations and these extra terras are evaluated from unsteady perturbations. Unsteady perturbations are obtained by solving a first order harraonic perturbation equation, while the coefficients of the perturbation equation are forraed from time-averaged solutions. A strong coupling procedure is applied to solve the time-averaged equation and the unsteady perturbation equation simultaneously in a pseudo-time domain. An approximate approach is used to linearize the pressure sensors in artificial smoothing

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