Shock Wave Detachment Research Articles

Unsteady measurement in a transonic axial compressor with optimized axial slot casing treatment

Casing treatment has been widely adopted to enhance the operating range of compressors by extending the stall margin. In this article, a high-precision experimental investigation was conducted in a transonic compressor. Unsteady pressure is measured in the casing wall using a cluster of time-resolved transducers with axial and circumferential spatial resolution. The experimental data show that the optimized axial slot casing treatment improves the stall margin without peak efficiency penalty for all measured speedlines. A comprehensive flow field analysis indicates that the surge boundary of transonic compressor is sensitive to the position of shock wave and tip leakage flow. After the application of optimized axial slot casing treatment, the flow structure can be significantly modified, which specifically manifests as both the mitigation in shock wave detachment and redistribution of tip leakage flow trajectory toward the trailing edge of the blade. Furthermore, power spectral density analysis is conducted to examine the unsteady effect. The amplitude of characteristic frequency band induced by the unsteady fluctuation of tip leakage flow and shock wave is considerably suppressed, which can also be regard as the stability enhancement mechanism of casing treatment.

Interferometric measurements of laser-induced shockwaves in air: Variable laser energy

When focused to a small spot size in air, a sufficiently energetic laser pulse initiates a rapidly expanding plasma. After a delay, a shockwave detaches from the plasma boundary and propagates. General features of the shockwaves can be deduced from condenser microphone measurements. However, the minimum range is limited by damage thresholds, and the presence of the microphone introduces a number of measurement artifacts. Distortion of the signal is caused by diffraction around the sensor, and the limited bandwidth does not allow rise times to be correctly quantified. In contrast, optical interferometry is a nonintrusive diagnostic for quantifying shockwave characteristics. In this study, a Nd:YAG laser is focused through a converging lens in order to generate laser-induced shockwaves. By using a variable attenuator, four laser energy outputs are examined: 25, 50, 75, and 100% of the maximum energy transmission. Heterodyne Mach–Zehnder interferometer measurements are made from 10 mm to 200 mm from the focal point of the lens. Virtual velocity signals, proportional to the time derivative of optical phase differences, are used to estimate density and pressure time histories, along with peak pressure as a function of distance.

A quasi-one-dimensional study on global characteristics of tube train flows

The global characteristics of tube train flows under wide ranges of blockage ratios and train speeds are comprehensively investigated by quasi-one-dimensional numerical simulation and theoretical analysis. The established quasi-one-dimensional model for the tube train flow and the numerical method are both proven to be reliable and efficient. Investigation reveals the typical patterns of both inviscid and viscous flows. The transition limits for these flow patterns are determined. The flows tend to be unstarted when the train moves at a high subsonic speed or a low supersonic speed and tend to be started otherwise. The transition limits between started and unstarted modes do not vary much between inviscid and viscous flows, which allows the use of analytical inviscid criteria in approximate estimation of the start/unstart state of the viscous flow. Between the supersonic isentropic limit and the Kantrowitz limit lies a dual-solution area. Which solution the flow follows depends on how the attempted cruise speed of the train is reached; a large acceleration tends to induce a started flow. The unstarted inviscid tube train flow appears to be self-similar as the train suddenly moves at a constant speed. This flow involves a precursor shock wave in front of the train and a secondary shock wave on or behind the train at the same time. By contrast, the unstarted viscous flow eventually remains a steady laminar structure that moves with the train after a sufficiently long process of development. In the stabilized flow, the precursor shock wave only occurs in the supersonic case, and the secondary shock wave only occurs in the subsonic case. For both inviscid and viscous flows, the unstarted flow can be divided into two submodes according to whether the secondary shock wave detaches from the train. Aerodynamic drag on the train is strongly correlated with the flow modes. The drag in unstarted flow increases with train speed, while the drag coefficient peaks at the secondary shock attach–detach limit. The wall transport effects cause larger drag but do not change its overall features.

Nonlinearity Analysis of Increase in Lift of Double Swept Waverider

The double swept waverider is a classic example of the planform-customized osculating-cone waveriders, delivering satisfactory performances over a wide range of velocities. The nonlinear increase in the lift of double swept waveriders at high angles of attack is of vital interest. In this paper, the aerodynamic performance of the double swept waverider is calculated and compared with single swept waveriders. The results suggest that the nonlinear increase in the lift of the double swept waverider is stronger than that of the equal-planform-area single swept waverider, and it increases with the Mach number. Some scholars have proposed the “vortex lift” to explain the nonlinear increase in lift, but it is controversial because the main lift of the waverider comes from the lower rather than the upper surface. This paper proposes that this nonlinear increase is related to the attachment of the shock wave influenced by the leading-edge sweep angle. The shock wave is more inclined to attach under the lower surface at a smaller sweep angle than a larger one as the angle of attack increases. When the shock wave attaches, the increase in pressure via the angle of attack is nonlinear, leading to a nonlinear increase in lift. When the shock wave detaches, the increase in lift is approximately linear.

Numerical study of unsteady rarefied diatomic gas flows in a plane microchannel

The numerical solution of a kinetic equation for a diatomic gas (nitrogen) is used to study two-dimensional unsteady gas flows in a plane microchannel caused by discontinuous in the initial distributions of macroscopic gas parameters. The plane discontinuity fronts are perpendicular to the walls of the channel. The arising flows are model ones for gas flows in a shock tube and a microchannel. The reflection of an incident shock wave from a flat end face is studied. It is found that the gas piles up at the cold wall, which slows down the shock wave detachment. The numerical results are in qualitative agreement with experimental data.

Speed of sound from shock fronts in granular flows

We show, in two different experiments on stationary flow past an obstacle, that several features such as Mach cones and shock wave detachment usually observed in supersonic molecular fluids under extreme conditions are also observed for granular fluids. By pursuing this analogy, we measure the speed of sound in these experiments and find it in agreement with predictions from granular kinetic theories. Surprisingly, and in spite of this agreement, measured velocity distributions are far from being Gaussian and display algebraic tails.

An experimental research on the flow field of water entry by pressure measurements

The underwater acoustic field in water entry of a 352 m/s blunt body has been investigated by pressure measurements. The experimental results show that from the initial stage to the later stage of water entry, there are: (1) a high peak pressure caused by the compressible behavior in high speed solid/liquid impact; (2) a negative pressure region caused by the expansion waves which are generated when the initial primary shock wave detaches from the solid body and the high pressure region is released; and (3) a significant motion of the fluid particles driven by the shock wave. It is found that at the entry velocity of this experiment, the shock wave behaves like an acoustic wave in water. The wave has a stronger energy distribution on the forward direction and a weaker energy distribution on the lateral direction.

Cherenkov-like shock waves associated with surpassing the light velocity barrier

The effects arising from the accelerated and decelerated motion of a point charge inside a medium are studied. The motion is manifestly relativistic and may be produced by a constant uniform electric field. It is shown that in addition to the bremsstrahlung and Cherenkov shockwaves, the electromagnetic shock wave arises when the charged-particle velocity coincides with the light velocity in the medium. For the accelerated motion, this shock wave, forming an indivisible entity with the Cherenkov shock wave, arrives after the arrival of the bremsstrahlung shock wave. For the decelerated motion the above shock wave detaches from the charge at the moment when its velocity coincides with the light velocity in the medium. This wave, existing even aftertermination of the charge motion, propagates with the velocity of light in the medium. It has the same singularity as the Cherenkov shock wave andis more singular than the bremsstrahlung shock wave.The space-time regions, where these shock waves exist, and conditions under which they can be observed are determined.PACS No.: 41.60

Cherenkov-like shock waves associated with surpassing the light velocity barrier

The effects arising from accelerated and decelerated motion of a point charge inside a medium are studied. The motion is manifestly relativistic and may be produced by a constant uniform electric field. It is shown that in addition to the bremsstrahlung and Cherenkov shock waves, the electromagnetic shock wave arises when the charge particle velocity coincides with the light velocity in the medium. For the accelerated motion this shock wave forming an indivisible entity with the Cherenkov shock wave arrives after the arrival of the bremsstrahlung shock wave. For the decelerated motion the above shock wave detaches from the charge at the moment when its velocity coincides with the light velocity in the medium. This wave existing even after termination of the charge motion of the charge propagates with the light velocity in the medium. It has the same singularity as the Cherenkov shock and is more singular than the bremsstrahlung shock wave. The space-time regions, where these shock waves exist, and conditions under which they can be observed are determined.

Viscous hypersonic flows for various aerophysical models

The results of mathematical simulation of hypersonic air flow past a sphere with allowance for chemical nonequilibrium and ionization are presented. The calculated data are obtained on the basis of a numerical solution of the Navier-Stokes equations and the hypersonic viscous shock layer equations. The equilibrium radiation temperature of the body surface, the pressure, and the shock wave detachment are compared for these models. The combined effect of molecular transport and the catalytic properties of the body surface on the aerodynamic heating is analyzed. The results of the effect of certain models of the thermochemical disequilibrium of the gas on the temperature of the body surface are also analyzed along a heat-stressed interval of the reentry trajectory of an aerospace vehicle.

Shock waves ahead of a fan with nonuniform blades

When a fan operates at supersonic tip speeds, shock waves are generated ahead of the blades. If these blades . are nonuniform, then the shock waves are also nonuniform, and tones at harmonics of the fan rotational frequency are generated. This paper presents a simple theory for the relation between the strengths of the individual shock waves, the blade stagger angles and the blade thicknesses, when the shock wave is detached from the blade leading edge. The analysis is in two parts: first a relation is found between the shock wave detachment and the blading nonuniformity. Then, weak shock wave theory is used to relate the detachment to the shock strength ahead of the fan. The results of the theory are in good agreement with experiments and so provide a theoretical basis for the blade shuffling procedures used to minimize blade-to-blade variations and to control shaft order tone generation by these variations.

Experimental investigation of shock wave detachment in real gases

A method is proposed for measuring the detachment distance of the forward shock wave from the surface of a free-flying blunt body. The effect of excitation of vibrational degrees of freedom of the gas on the position of the detached shock wave is investigated for air and carbon dioxide.

鈍頭物体の先端付近における非平衡流

Analyses have been made of the effects of coupled chemical and vibrational rate processes in external hypersonic flows at high enthalpy levels. Exact (numerical) solutions have been obtained by the inverse method for inviscid nitrogen gas flows over a circular cylinder under the conditions where nonequilibrium prevails through the nose region. The results illustrate the general importance of the coupling among the chemical and vibrational rate processes. In order to sustain a prominent effect of pre-shocknonequilibrium, values of shock wave detachment distance have been compared under the condition of the same total enthalpy.

Hugoniot Curve Determined by Shock Wave Detachment from an Infinite Wedge

A method is presented for the determination of the Hugoniot curve of an arbitrary inviscid compressible fluid flowing at supersonic speed past an infinite wedge. A shock wave is attached to the apex of the wedge provided the wedge angle is less than a certain critical value. The shock wave detaches from the wedge if the wedge angle becomes greater than this critical value. If the Hugoniot curve of the fluid is known, the critical wedge angle can be calculated for a given initial fluid flow velocity. The critical angle also can be determined by an experimental method. This paper treats the theoretical problem of utilizing the discrepancy between theoretical predictions and experimental results to obtain an improved Hugoniot curve of the fluid. A perturbation method is applied to the case of solid copper for which both theoretical and experimental information exists. The actual experimental Hugoniot curve for copper does not differ sufficiently from its theoretical value to yield a fair test of the method; therefore, synthetic experimental data are used to solve a typical numerical example. In the example treated, a 10% discrepancy between theory and experiment was reduced to about 1% by one application of perturbation theory.

Blunt Body Viscous Layer with and without a Magnetic Field

The present paper is mainly concerned with the solution for the viscous flow in the shock layer about the stagnation region of a sphere in hypersonic flow. The Reynolds numbers considered are in a range too low to apply usual boundary layer theory within the shock layer, but are large enough that the shock wave may be regarded as a discontinuous surface. This viscous layer problem has been studied previously by Probstein. With the assumption of constant density in the shock layer an analytic solution is applied to this problem both with and without an applied magnetic field. This solution makes use of the fact that the ratio of the density ahead of the shock to that behind the shock (ε) is small. The solution has been found in analytic form to first order in ε. In the nonmagnetic case numerical results for both the shock wave detachment distance and skin friction are presented for a value of ε = 0.1 and they are shown to be in good agreement with the exact numerical calculations of Probstein and Kemp. Numerical results are also presented on the effect of an applied magnetic field on both the shock wave detachment distance and skin friction. It is found that for a fixed value of ε and Reynolds number the skin friction decreases and the detachment distance increases for increasing values of the magnetic field parameter S which is proportional to the magnetic pressure divided by the total pressure.

Two-Dimensional Bow Shock Wave Detachment Distances

In the recent paper by Warren a summary was made of current data on two-dimensional bow shock wave detachment distances. It was shown that the experimental results of Griffith and Alperin, as well as the detachment distances computed by Vincenti and Wagoner, could be collapsed into a single curve by using Spreiter's Transonic Similarity Parameter. This has been confirmed by the present authors who have found that the experimental results for wedges obtained by Bryson also correlate favourably with the curve given by Warren (Fig. 3 of Ref. 4).The results of the foregoing workers have been for steady flow conditions. However, it has been noted by Lilleyet aliathat a steady shock wave pattern can be established in free flight only after steady motion has been maintained for a considerable (infinite) time. In general, the locus of detached bow shock waves depends on the time history of the motion whenever a body is accelerated from subsonic speed.