Quasi-Steady Flow and Thrust in Accelerating Nozzles and Channels

Internal flows of compressible fluids in nozzles and constant-area channels subjected to constant axial acceleration or gravitation are examined in detail. It is found that the effect of nozzle acceleration or deceleration is analogous to that of perturbing the cross-section area of nonaccelerating nozzle. Acceleration enchances the effect of nozzle divergency and deceleration reduces it. Sonic speed is reached upstream of an accelerating nozzle throat and downstream of a decelerating nozzle. Integral relations of various flow properties are derived and methods for obtaining numerical solutions are developed. Using a power-series expansion in terms of a dimensionless number related to the rate of acceleration, a formula is derived for the estimation of impulse function increment due to acceleration. For constant-area channels, it is found that the flow Mach number always changes away for unity, whereas in a decelerating channel, the Mach number always changes toward unity. Continuous transitions between supersonic and subsonic flows are not possible.