Showing papers on "Oblique shock published in 1968"

Interaction of Linear Waves with Oblique Shock Waves

Abstract: Linear wave interaction with oblique shock waves, noting dependence of transmission, reflection and generation coefficients on Mach number

The interaction of a shock wave with a laminar boundary layer

Abstract: A finite-difference solution to the problem of the interaction between an impinging shock wave and the laminar boundary layer on a flat plate is presented. The boundary-layer equations are used to calculate the flow with the Prandtl-Meyer formula being used to determine the pressure. Two different methods for calculating the region of separated flow are discussed. Comparisons between this theory and experimental results show good agreement. The effects of the viscosity and heat-conduction relationships on the calculated results are determined. Diagrams show the influence of the Mach number and the displacement thickness of the boundary layer at the start of the interaction on the pressure distribution. The insulated plate and the plate with given temperature are considered.

Effects of shock impingement on the heat transfer around blunt bodies.

Abstract: An extraneous shock impinging on a blunt body in hypersonic flow is observed to alter the flow around the body and increase the local heat-transfer rate near the impingement point. A novel, quasi-static technique is developed to study this phenomenon. A hemispherical, glass model, equipped with platinum thin-film thermometers, is injected into a hypersonic tunnel through a slot in a variable-incidence flat plate. Analog networks provide graphs of the heat-transfer rates at various points on the model as a function of the model's position relative to the extraneous shock. Peaks in local heat-transfer rates up to 10 times the local, unperturbed, freestream values are recorded as the model traverses the shock. The peak heating is severest on the side of the model nearest the plate and increases with increasing shock strength, occurring over a narrow region where a shear layer or jet, originating at the intersection of the bow shock and the impinging shock, meets the model surface. A physical model is set up which predicts variations in shock interference patterns, in surface pressure distributions, and in the intensity and extent of the peak heating in accordance with experiment. Nomenclature M = Mach number P = pressure normalized with respect to freestream pressure q = heat-transfer rate, cal-cm~2-sec~1 r = radius of hemisphere, mm t = time, sec T = temperature, °C U = velocity normalized with respect to freestream velocity V = injection speed, m-sec"1 x = distance along surface measured from stagnation point, mm

Experimental studies on the lip shock.

Abstract: Lip shock from separation edge of half angle wedge and resultant static pressure recovery distribution along wake

Detection of electric-field turbulence in the earth's bow shock.

Abstract: Detection of electric field turbulence in earth bow shock, noting wave amplitude correlation with magnetic field structure

On the Shock Wave Velocity and Impact Pressure in High-Speed Liquid-Solid Impact

Abstract: Shock wave velocity and pressure in high speed liquid-solid impact based on particle velocity

Shock wave from a lightning discharge

Abstract: A theoretical model of the shock wave from a lightning discharge ranging from the strong blast wave region out to the acoustic limit is given for the first time. The trajectory and overpressure of the strong shock wave are described by the well-known equations for cylindrical blast waves. In the intermediate shock strength region (1.1 < M < 3.3), the shock trajectory is given by the ‘correct limit’ equation of Vlases and Jones. We derive an additional ‘correct limit’ equation for overpressure that is valid out to the acoustic limit. The correct limit equations predict a much slower decay of the intermediate shock wave; thus, the shock wave is much stronger at large distances from the discharge than was previously believed. Consequently, the range of action of the lightning discharge via its shock wave, as it affects the shattering and freezing of supercooled hydrometeors, may be large.

Emission of plasma waves by the Earth's bow shock

Abstract: A general technique is given for calculating the spectrum of plasma waves emitted upstream and downstream by a turbulent shock transition for a plane shock of arbitrary structure. The problem of identifying the waves of frequency ∼1 cps that sometimes appear to emanate from the earth's bow shock is discussed.

Turbulent boundary-layer separation ahead of cylinders.

Abstract: A cylindrical protuberance mounted on a flat plate will cause the plate boundary layer to separate if the cylinder is long compared to the boundary-layer height. Tests made at M = 4.9 using an oil-flow technique are employed to determine the upstream extent of cylinder influence on a turbulent boundary layer. The results are found to be in reasonable agreement with data from other investigators for a wide range of flow conditions. A method is given for determining the angle of the oblique shock wave caused by separation. This permits calculation of the location of the triple point of the lambda shock pattern that characterizes the flow. An approximate method of calculating the peak value of the cylinder stagnation pressure and the location of the peak is also presented.

The structure of normal shock waves in a binary gas mixture

Abstract: A previous study of normal shock waves through numerical experiments with a simulated gas on a digital computer is extended to binary gas mixtures. The mixture is simulated by two sets of rigid elastic sphere molecules with the appropriate mass and diameter ratios. Velocity profile results for medium strength waves in a mixture of equal parts argon and helium are in qualitative agreement with the continuum calculations of Sherman (1960), but there is no initial acceleration of the argon in mixtures containing a very small initial mole fraction of this gas. The temperature profiles are similar to those for the velocity in that the argon profile lags behind the helium profile. However, when there is a small proportion of heavy gas, the profiles cross-over and the temperature of the heavy gas overshoots the Rankine-Hugoniot downstream value. For very strong shock waves, the overall shock thickness expressed in upstream mean free paths becomes larger, but the profiles are generally similar to those for the medium strength waves.

An interaction model of a supersonic laminar boundary layer on sharpand rounded backward facing steps.

Abstract: An implicit finite-difference method is used to study the interaction of a laminar boundary layer with a supersonic, external, inviscid flow on a flat plate with a sharp or rounded backward facing step. The boundary-layer equations are used to describe the subsonic portion of the flow with the effect of transverse pressure gradients in the supersonic viscous region included through the use of an inviscid transverse momentum equation. Initial profiles are assumed to be similar (Blasius) in shape, but with the boundary-layer edge flow inclination not specified. The qualitative nature of the downstream flow is determined by the particular value of initial edge flow inclination chosen, with two families of solutions bounded by a particular solution which continues downstream on the body without separation. A perturbation in the initial edge flow inclination from this particular value results in a flowfield such as one would expect approaching a sharp backward facing step. A perturbation in the opposite direction results in a flowfield such as one would expect for a boundary layer separating from a smooth wall in an adverse pressure gradient. Computed wall pressure distributions agree well with experiments for both sharp and rounded corners and the computed flowfield for a rounded corner contains a separation shock whose location also agrees with experiment.

An investigation of the reflected shock interaction process in a shock tube.

Abstract: Following the first interaction between the reflected shock from the end wall and the advancing contact surface in a shock tube, cold gas has been observed at the end plate at a time much earlier than that predicted on the basis of simple shock tube theory. Investigation of the nature of this cold gas has been made by an infra-red absorption technique. The driver gas hydrogen is "tagged" with a small quantity of infrared active gas, and shocks are driven with this gas mixture into an infrared inactive test gas. The time of arrival of driver gas at the end plate is measured from the absorption records and calculations based on a modification of the shock bifurcation model agree substantially with these experimental results. Use is also made of an infrared absorption/emission technique to determine the temperature of the infrared source.

Experimental and theoretical study of the stability of plane shock waves reflected normally from perturbed flat walls

Abstract: The rate of damping of perturbations on a shock wave reflected from a perturbed flat wall was measured in a shock tube. Incident shock wave Mach numbers of 1·45 and 1·09 in air together with sinusoidal and Gaussian wall perturbations were employed. These measurements were compared with a modified form of a linearized theory due to Zaidel (1960). The linearization was performed about the basic solution of a plane shock wave reflected normally from a flat wall.The rate of decay and the frequency and phase of oscillations agreed very well with the theoretical predictions; the amplitudes of the oscillations were some-what larger than predicted. The reflected shock shape was initially in good agreement with theory, but higher frequency perturbations on the reflected shock front caused deviations from the predicted shape after the shock front had travelled about one wall-wavelength away from the wall.The generally satisfactory agreement between theory and experiment supports the use of linearized analysis in predicting shock wave stability.

Calculation of transonic flow over thick airfoils by integral methods.

Abstract: Starting with the exact two-dimensional inviscid flow equations (with entropy gradients) and for shock waves that are locally normal to the surface, an exact integral representation for transonic flow about thick airfoils has been obtained. This integral representation is the analog of that obtained by Oswatitsch for thin airfoils. Some of the integrals may be neglected while still retaining the thick-airfoil character of the representation. Various forms of the transonic integral relation are presented. Solutions are obtained by iteration, and it is shown that a particular (simple) form does not lead to convergent iterations but that an alternate form does lead to convergence. Careful consideration has been given to the numerical evaluation of the integrals involved. The transonic flow about a circular arc airfoil is computed allowing for various approximations of the integrals and the results compared with each other.

The structure of a weak shock wave undergoing reflexion from a wall.

Abstract: Weak shock wave unsteady structure under reflection from plane wall analyzed by Navier- Stokes equations, noting analogy to Burger equation

Hypersonic viscous interaction on sharp and blunt inclined plates.

Abstract: Mach 42 test measuring surface pressures, surface heat transfer rates and shock wave shapes in strong interaction regime for sharp and blunt plates

On the irregular refraction of a plane shock wave at a Mach number interface

Abstract: The paper considers the refraction of a plane shock wave at an interface between two streams of different Mach number. Particular attention is paid to the irregular wave systems. It is found that when the interface is slow-fast, that is when the speed of sound a0 in the first or incident wave medium is less than the speed of sound aB in the second or transmitted wave medium, then there are two irregular systems, one being a double Mach reflexion type and the other being a four-wave confluence type. There are also two irregular systems when the refraction is fast-slow; these are a single Mach reflexion type and an expansion wave type. This last system has a central expansion wave when the flow is steady and a continuous band expansion wave when the flow is self-similar. Only two of the irregular wave systems have been observed experimentally in the fully developed state. Possible degeneracies are discussed.

A method for predicting shock shapes and pressure distributions for a wide variety of blunt bodies at zero angle of attack

Abstract: Relationship of shock standoff distance, at sonic and stagnation points, to body geometry of blunt bodies at zero angle of attack

Experimental Investigations of Normal Ionizing Shock Waves

Abstract: Experiments have been conducted on normal ionizing shock waves produced in a coaxial electromagnetic shock tube. Steady shock velocities were measured as a function of initial gas pressure, drive current, and applied axial magnetic field. The speeds agreed well with theoretical values. Measurements were made of the switch‐on magnetic field, the upstream transverse electric field, and the density ratio across the front. The data all show that trans‐Alfvenic shocks (uA l f1 < us ≲ 3uA l f1) exhibit Chapman‐Jouguet behavior, with current flow in the shock front, and no separation of shock and drive currents. In contrast, super‐Alfvenic shocks (us ≳ 3uA l f1) appear to be gas dynamic in nature. Spectroscopic measurements and shock‐reflection studies demonstrated the presence of a nonluminous front and shock‐heated gas preceding the luminous drive current.

Comparison of experimental and theoretical shock shapes and pressure distributions on flat-faced cylinders at Mach 10.5

Abstract: Integer relations method of determining inviscid shock layer flow and pressure distributions over blunt bodies

Shock-wave reflection from a turbulent boundary layer with mass bleed.

Abstract: Methods for calculating the changes in turbulent boundary-layer characteristics across an oblique shock reflection based on integral flow models are developed for two-dimensional and axially symmetric flows with solid boundaries and mass bleed through porous walls, slots, or scoops. For each model, a control surface is assumed about the region of interaction; the velocity profiles upstream and downstream of the interaction are assumed to be power laws, and the integral continuity and momentum equations are written for the control volume. For a given mass-bleed configuration, specification of the upstream conditions and the bleed rate permits solution for the downstream boundary-layer thickness and velocity-profile exponent. Numerical results are presented for a range of upstream Mach numbers, mass-bleed rates, and incident-shock strengths. Comparison with data for two-dimensional shock reflections with zero bleed indicates that the analysis yields the correct trends.

The influence of boundary layer growth on shock tube test times

Abstract: A theoretical and experimental investigation of the limitation on shock tube test times which is caused by the development of laminar and turbulent boundary layers behind the incident shock is presented. Two theoretical methods of predicting the test time have been developed. In the first a linearised solution of the unsteady one-dimensional conservation equations is obtained which describes the variations in the average flow properties external to the boundary layer. The boundary layer growth behind the shock is related to the actual extent of the hot flow and not, as in previous unsteady analyses, to its ideal extent. This new unsteady analysis is consequently not restricted to regions close to the diaphragm. Shock tube test times are determined from calculations of the perturbed shock and interface trajectories. In the second method a constant velocity shock is assumed and test times are determined by approximately satisfying only the condition of mass continuity between the shock and the interface. A critical comparison is made between this and previous theories which assume a constant velocity shock. Test times predicted by the constant shock speed theory are generally in agreement with those predicted by the unsteady theory, although the latter predicts a transient maximum test time in excess of the final asymptotic value. Shock tube test times have also been measured over a wide range of operating conditions and these measurements, supplemented by those reported elsewhere, are compared with the predictions of the theories; good agreement is generally obtained. Finally, a simple method of estimating shock tube test times is outlined, based on self similar solutions of the constant shock speed analysis.

Experimentally Determined Structure of the Shock Reflection Process in Ionizing Xenon

Abstract: The results of an experimental investigation of the reflection of strong shocks in xenon from the end wall of a shock tube are presented. The reflection of the incident shock structure, consisting of a frozen shock front, a region of relatively uniform frozen flow, and an ionization front, was observed with a fast‐rise (0.3 μsec) pressure gauge mounted in the shock‐tube end wall. The incident shock Mach number was varied from 11‐20, and the initial pressure was varied from 0.1‐1.5 mm Hg. The interaction between the reflecting shock and the ionizing gas in the incident shock structure produces a complicated series of shock and rarefaction waves; those waves that propagate back to the end wall were observed with the pressure gauge. A simple model which includes the gross features of the shock reflection process is used to calculate end wall pressures. The calculated pressures agree well with the experimental observations. In addition, ionization relaxation times for xenon behind the incident and reflected s...

Interaction of an oblique shock wave with a turbulent boundary layer.

Abstract: C success has been achieved in developing analytical models for an oblique shock wave impinging on a boundary layer that is initially laminar and remains laminar throughout the interaction.' It is generally recognized that a more important type of interaction is one in which the boundary layer entering the interaction is turbulent. Understanding the interactions between turbulent boundary layers arid shock waves is particularly important in the design of hypersonic inlets for airbreathing propulsion systems. For this application, the interaction details of interest include the boundary-layer profiles entering and leaving an interaction, and the description of the shock-wave structure through the interaction. Neither the profiles nor the shockwave structure in the immediate vicinity of the interaction is obtainable from standard boundary-layer theory. This condition led to the development of the analytical model described herein.

Radiation induced precursor flow field ahead of a reentering body.

Abstract: Three dimensional flow field induced ahead of shock wave by radiation from shock layer over blunt body, determining perturbation velocity potential

Calculations of expanding shock waves and late-stage equivalence

Abstract: : A numerical scheme based on the method of characteristics is developed and applied to the flow field of the expansion of a high pressure sphere into atmosphere. It is shown that this method is very accurate, involving errors of less than 1%. In calculating the expanding sphere, two rather challenging problems, namely, the initial singularity and the formation of a second shock, are successfully solved through special techniques. The formation of an inward traveling shock, in addition to the main shock, is found to exist at the tail of the left traveling rarefaction wave. The strength of the second shock remains rather weak at the early stage of its development, it becomes very strong just before reaching the center of the sphere. It is shown that 'late-stage equivalence' exists in the expansion of high pressure spheres into atmosphere, provided the initial total energy in each of the spheres is held constant. Late-stage equivalence is assumed to exist if the peak pressure distribution for different expanding spheres are the same for long times.

Heat-transfer measurements in the shock-induced flow separation region in a supersonic nozzle.

Abstract: Pressure and semilocal wall heat flux measurements in shock induced flow separation region in supersonic nozzle, noting shock waves-flow interaction

Regularization in optimal trajectory problems.

Abstract: Fig. 3b Oscilloscope trace from the pressure gage in the surface of the 9° cone model. 20^5 Mach reflection theory. There is a kink in the reflected shock wave, downstream from the Mach stem. The kink suggests some further shock reflections in the flow behind the Mach stem. The pressure gage trace corresponding to the 41° indicident angle adds evidence that something more than classical Mach reflection is occurring. The trace, Fig. 2b, shows a step in the gage's initial response as if the gage had been struck by two successive shock waves, one close behind the other. The pressure rise associated with the first step is exactly what we would expect to get from the Mach stem alone. The additional pressure rise from the step to the peak brings the pressure up to a level very close to that attained by regular reflection at 39°. So the large drop in pressure from regular to Mach reflection predicted by simple theory does not really exist. The additional compression that we expected to follow the Mach stem does take place, and it appears as though the mechanism for this additional compression is a second reflected shock wave. Further proof of the existence of a second shock wave behind the Mach stem was found by looking at incident angles much larger than the limiting angle. Figure 3a shows a case where the incident angle is 54°. The second reflected shock wave is now clearly visible. The pressure gage trace, Fig. 3b, shows a well-defined "step." The time between the two shock waves, as measured from the pressure gage trace, corresponds exactly to the separation distance between the Mach stem and the second shock wave. Again, the second shock wave compressed the gas behind the Mach stem to a level well above that predicted by simple Mach reflection theory. Conclusions