Unsteady Transonic Flows in Two-Dimensional Channels with Oscillating Boundaries


Book Description

Unsteady transonic flow in two-dimensional duct with a shock wave is considered. The flow entering the duct is uniform and steady; unsteadiness is caused by any mixture of impressed oscillations in wall shape and back pressure. Asymptotic methods are employed to give solutions for flow properties and for position and velocity of the shock wave in several different problems, characterized by the relative orders of the nondimensional amplitude and frequency of the oscillations. Illustrative example flows are considered, with a numerical solutions used for complex wall shapes. (Author).




Unsteady Transonic Flows in Two Dimensional Channels


Book Description

A two dimensional unsteady transonic irrotational inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonic regime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady channel flows with either stationary or time varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow). (Author).




Unsteady Transonic Flow in Two-Dimensional Channels


Book Description

Unsteady transonic flow with a shock wave in a two-dimensional channel is considered. Solutions valid in a thin inner region enclosing the nozzle throat, where previous solutions showed singular behavior, are presented. A brief description of a computer movie is given; this movie shows solutions for unsteady transonic channel flow for two different cases in which the shock wave, as a result of pressure oscillations impressed downstream of the nozzle throat, moves to and upstream of the throat, disappears, and reforms at the throat. An analysis showing how results derived for the interaction between a shock wave and a turbulent boundary layer in steady flow may be used in the corresponding quasi-steady flow problem, is presented; a discussion of how these results may be used to deduce the order of the distance from the shock wave to the separation point and the time characteristic of the life of a shock induced separation bubble in unsteady flow is given. (Author).




A Study of Unsteady Transonic Flows with Shock Waves in Two Dimensional Channels


Book Description

A two dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, with solutions found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are included so that shock waves can be considered. The case where the characteristic time of a temporal flow disturbance is large compared to the time taken by a sonic disturbance to cross the transonic regime is considered. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady channel flows with shock waves, for the case where the walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves in unsteady flows, both for decelerating and accelerating channel flows. For the thin shock case, both numerical and asymptotic solutions are given. (Author).




Unsteady Motion of Shock Waves in Two Dimensional Transonic Channel Flows


Book Description

Two dimensional unsteady transonic channel flow with a shock wave is considered for the so-called slowly varying time regime. Solutions are studied for two specific cases within this general time regime, the cases corresponding to small and large amplitude shock wave motions. For the large amplitude case, conditions are considered under which the shock wave travels upstream of the throat, disappears, and then reforms at the throat. A unified solution which covers both cases is developed. Numerical results are presented. A short discussion of shock induced separation in unsteady flows is given. (Author).




UNSTEADY TRANSONIC FLOWS WITH SHOCK WAVES IN AN ASYMMETRIC CHANNEL..


Book Description

Two-dimensional inviscid, unsteady transonic flows with shock waves in asymmetric channels with arbitrary wall shapes are investigated, using the method of matched asymptotic expansions. With the exception of thin regions in the neighborhood of the channel throat and the neighborhood of the shock wave, solutions found using linearized governing equations are valid. In the regions enclosing the shock wave, an inner solution which satisfies the shock jump conditions and matches with the outer solutions, is presented. The shock shape is found as part of the solution, which is obtained numerically using the method of integral relations. A composite solution, uniformly valid throughout the channel, and the relation between the instantaneous shock wave position and back pressure far downstream are presented. (Author).




ANALYSIS OF UNSTEADY TRANSONIC CHANNEL FLOW WITH SHOCK WAVES..


Book Description

Inviscid unsteady transonic flow in a two-dimensional channel is analyzed using asymptotic techniques. The analysis includes the case where a shock wave is present in a channel having arbitrary wall shape, with artibrary small disturbances imposed at a given downstream location. Second-order solutions are not uniformly valid near the shock wave, since they do not satisfy the shock jump conditions. It is therefore necessary to obtain inner solutions which are matched asymptotically to those in the outer channel-flow region.




Scientific and Technical Aerospace Reports


Book Description

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.