Supersonic Stage Research Articles

Acoustic approximation in the slamming problem

The plane unsteady problem of the deflection of a solid, slightly curved plate in collision with an ideal weakly compressible liquid is considered. In order to describe the impact process, the acoustic approximation and the method of normal modes are used. The analysis is focused on the supersonic stage of the impact when the liquid surface remains undisturbed outside the contact spot between the solid plate and the liquid. However, the positions of the contact points are unknown in advance, in contrast to the case of undeformable body impact, and have to be found together with the liquid flow, the pressure distribution, and the bottom deformations. It was shown that the duration of the supersonic stage depends on the entering body elasticity. A spray jet is formed earlier and the stage at which the liquid compressibility is a governing factor is shorter than under rigid-body impact. It is revealed that the elastic plate deflection is quite small and can be satisfactorily approximated by a few modes. On the other hand, the calculation of the bending stress distribution needs a much greater number of normal modes. The pressure distribution over the contact region is quite difficult to find by the mode method ; an alternative approach is suggested.

Integral properties of solutions to some boundary initial-value problems in linear anisotropic elastodynamics

We study some integral properties of weak solutions to some boundary initial-value problems in the linearized dynamical theory of elasticity. These problems arise during the indentation of an anisotropic half-space by a convex punch having an arbitrary indenting velocity and shape. In contrast to previous studies of the problem, we consider various boundary conditions, e. g., adhesive or frictional, in the case when this non-frictionless boundary initial-contact problem has two orthogonal planes of symmetry, which are both orthogonal to the boundary of half-space. We show that if the non-frictionless boundary initial-contact problem has such a symmetry, then the problem for integral characteristics of the solutions is equivalent to a problem of plane-wave propagation in the same medium. A proof is given that the instantaneous value of the force required to indent the punch during the first supersonic stage of contact is directly proportional to the product of the velocity of indentation and the area of contact at that instant, and is independent of the boundary conditions in the contact region.

Wave front in the blunt body immersion problem

The immersion of a three-dimensional blunt convex body in a compressible fluid with nonpositive acceleration is considered in the linear formulation. It is shown that at every instant the perturbation zone will be convex. The fluid particle velocity and pressure are calculated at each point on the wave front. At every instant the wave front is wholly determined by the initial supersonic stage of propagation of the boundary of the body-fluid interaction zone.

Off-Design Performance of Supersonic Compressors With Fixed and Variable Geometry

Regarding the extremely high pressure ratios of jet-engine compressors for the next decade, increasing interest belongs to the further development of supersonic compressors with supersonic relative flow at rotor inlet and supersonic absolute flow at stator inlet. In the past, different suitable design procedures for these components have been developed and tested successfully. However, there is a lack of information concerning the off-design performance of supersonic compressors. The present paper first systematically shows blading and flow path geometry of different experimentally investigated supersonic axial flow compressors. These investigations refer to combinations of characteristic rotors and stators with fixed and variable geometry. A comparison of these geometric data with the main characteristics of the flow pattern shows that, for the investigated stages, the three-dimensional passage geometry has an essential influence on the off-design performance. On the basis of this information semi-empirical models are established for a numerical description of the flow phenomena with predominant influence, as for example shock-, profile-, and endwall boundary layer losses and rotor-stator interactions. For the determination of the off-design performance, these models are incorporated into a streamline curvature calculation method. The computer model established is able to describe the off-design characteristics of the different investigated supersonic compressor stages in the most important operating range.

Problems of the interaction of a blunt body with an acoustic medium

The initial (supersonic) stage of the interaction of a blunt body (penetration and impact) with an acoustic medium (a compressible fluid) is examined in a laminar formulation. It is assumed that the boundary of the domain of interaction of the body with a medium moves at a velocity exceeding the velocity of sound in the medium. Explicit formulas are derived for the velocity of the particles of the medium and the pressure at each point of the interaction domain boundary. It is shown that the general solution of the linearized problem for the supersonic stage of blunt body penetration, given by an explicit formula /1–3/ in the form of a double integral, can be converted in such a manner as to reduce the formula to a single integral for an arbitrary body penetrating the fluid at an arbitrary velocity. Earlier only problems of the penetration of bodies of revolution bounded by second-order surfaces (cone /3, 4/, paraboloid /4, 5/, ellipsoid and hyperboloid /4/) at a constant velocity were investigated analytically using such a reduction. An exact expression is obtained for the law of motion on the inertia of a body of arbitrary shape after its contact with the fluid.

Aerodynamic Design and Verification of a Two-Stage Turbine With a Supersonic First Stage

The detailed aerodynamic design and test verification of a 6000-hp (4474-kW) turbine with a supersonic first stage for an airborne application is described. The 12.3-in. (312.4-mm) pitch diameter turbine is driven by products of hydrazine decomposition at 700 psia (4.826 MPa) and 2110 R (1172 K) with an overall pressure ratio of 41.2. The design of the supersonic nozzles and rotor incorporated improved concepts compared to previously reported designs. Test results show that the predicted performance was verified. The supersonic design concepts described are applicable to other high-pressure ratio designs where maximum efficiency is required.

Measurements of Quasi-Steady and Unsteady Flow Effects in a Supersonic Compressor Stage

In the present paper results of measurements are discussed that give a survey of the flow through rotor and stator of a supersonic compressor stage. In order to analyze the flow, piezoelectric and semiconductor transducers are used for measuring the unsteady pressure distributions along the casing on the one hand and schlieren photography procedure and stroboscopic technique for flow visualization on the other. The pressure transducers are mounted at the casing and shifted along the test region by different series of measurements. The effects of the unsteady flow to the stator produced by the rotor, on the behavior of the flow in the stator channels were analyzed. The oscillation of the pressure at the entrance region of the stator is reduced in axial direction by the cascades, so that the amplitudes diminish at the exit region of the stator. Nevertheless the frequency, induced by the rotor, can be well recognized in the unsteady pressure distribution downstream of the stator. These measurements were completed by the visualization of the flow through the stator. The optical system is working by a modified coincidence method. The starting procedure of the stage up to design speed was observed using shadow and schlieren method at continuous and stroboscopic illumination. The development of the shock waves, the shock-boundary-layer-interaction, and the influence of the rotor-wakes to the stator-flow are discussed.

Time-evolution of the optical radiation emitted after the laser-induced breakdown

The light emitted after the breakdown produced by laser pulses shows an interesting behavior: its intensity reaches several maxima. Tests were performed both in gases and on solid surfaces. We suppose the shock wave produced in the breakdown screens the light emitted from the plasma, for some time. This hypothesis seems to be confirmed by our tests. The screening effect acts for a time depending on the experimental conditions as energy density, sample and so on; the effect involves the shock wave in its supersonic stage.

A Method for Predicting Compressor Cascade Total Pressure Losses When the Inlet Relative Mach Number Is Greater Than Unity

During the last few years, considerable progress has been made in predicting the total pressure losses from viscous effects for axial-flow compressor cascades. With the advent of the transonic and the supersonic stage, another pressure loss generating mechanism was introduced—the shock wave. Various methods have been published over the past few years accounting for the pressure losses associated with the shock formation, but of those reviewed by this author, none of them has been consistently successful for predicting the losses at other than design conditions. This paper develops a method which has given consistent success at all flow conditions for compressors with subsonic axial and supersonic relative velocities.

Performance Prediction for High Turning Low Aspect Ratio Stator Cascades in the Transonic Regime

This paper describes a method for the prediction of the transonic flow field in a high solidity, high turning cascade, suitable for use as stator of a shock-in-rotor supersonic compressor stage. Effects of shock boundary layer interaction is taken into account by empirical correlation, valid for blade aspect ratios below unity. Use of partial slots for reduction of the secondary flows is briefly discussed and a correlation on slot efficiency is presented.