Showing papers on "Oblique shock published in 1976"

The focusing of weak shock waves

Abstract: This paper reports an experimental investigation, using shadowgraphs and pressure measurements, of the detailed behaviour of converging weak shock waves near three different kinds of focus. Shocks are brought to a focus by reflecting initially plane fronts from concave end walls in a large shock tube. The reflectors are shaped to generate perfect foci, aretes and caustics. It is found that, near the focus of a shock discontinuity, a complex wave field develops, which always has the same basic character, and which is always essentially nonlinear. A diffracted wave field forms behind the non-uniform converging shock; its compressive portions steepen to form diffraction shocks, while diffracted expansion waves overtake and weaken the diffraction shocks. The diffraction shocks participate in a Mach reflexion process near the focus, whose development is determined by competition between the convergence of the sides of the focusing front and acceleration of its central portion. In fact, depending on the aperture of the convergence and the strength of the initial wave, the three-shock intersections of the Mach reflexions either cross on a surface of symmetry or remain uncrossed. In the former case, which is observed if the shock wave is relatively weak, the wavefronts emerge from focus crossed and folded, in accordance with the predictions of geometrical acoustics theory. In the latter, the strong-shock case, the fronts beyond focus are uncrossed, as predicted by the theory of shock dynamics. It is emphasized that in both cases the behaviour at the focus is nonlinear. The overtaking of the diffraction shocks by the diffracted expansions limits the amplitude of the converging wave near focus, and is the mechanism by which the maximum amplification factor observed at focus is determined. In all cases, maximum pressures are limited to rather low values.

Numerical Computation of Two-Dimensional Viscous Blunt Body Flows with an Impinging Shock

Abstract: Two-dimensional viscous blunt body flows with an impinging shock have been computed using a time-dependent finite-difference method which solves the complete set of Navier-Stokes equations for a compressible flow. For low Reynolds number flows, the entire flow field, including the bow shock and impinging shock, has been captured in the computation. For higher Reynolds number flows, the bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied, while the boundary layer and interaction regions are captured as before. Using this latter shock-fitting approach, a Type III shock interaction flow field has been computed with flow conditions corresponding to the space shuttle orbiter freestream conditions at 61 km (200,000 ft).

Bow Shock and magnetosheath waves at Mercury

Abstract: Mariner 10 measurements at the Mercury bow shock provide examples where the magnetic field is approximately parallel or perpendicular to the bow shock normal. Upstream of a broad irregular parallel shock, left hand circularly polarized waves are observed which cut off very sharply at approximately 4 Hz. Upstream of a perpendicular shock, right hand circularly polarized waves are observed which persist up to the Nyquist frequency of 12 Ha. Determination of the wave propagation vector as a function of frequency helps conclusively identify the waves as whistler mode waves propagating from the shock. The magnetosheath downstream of the parallel shock is disturbed more than that downstream of the perpendicular shock particularly below 1 Hz. In the latter case regular left hand polarized waves observed slightly above the proton gyrofrequency are identified as ion cyclotron waves with wavelength approximately 300 km which are Doppler shifted up to their observed frequency.

The stability of shock waves in ionizing and dissociating gases

Abstract: The stability of strong shock waves in argon and carbon dioxide has been studied in a free-piston shock tube using time-resolved interferometry. Unstable shock fronts have been found to occur close to velocities where (dP/dV)H (where P and V are the pressure and the specific volume behind the shock) on the Rankine-Hugoniot curve is positive due to completion of first ionization or dissociation. Such an instability has been described theoretically by D'iakov (1954). However, his stability limits have not been reached in this case, and this suggests that the linearized perturbation analysis is not accurate for the case of the real shock tube flow.

The interaction of a shock with a dust deposit

Abstract: The possibility is investigated that dust can be raised from a deposit over which a shock wave passes by the reflection of shock waves from the underlying surface. It is shown that dust is raised as a result of the rapid flow behind the shock rather than as a result of pressure waves passing through the layer. Dust-cloud profiles fit the ballistic trajectories of individual particles having an initial vertical velocity of about 4.5 m s-1.

A statistical study of the upstream wave boundary outside the Earth's bow shock

Abstract: The location of the forward boundary of the upstream wave region ahead of the earth's bow shock is investigated statistically using plasma and magnetic-field data obtained by Heos 1. The analysis is conducted on the assumption that the waves are produced by protons reflected from the bow shock and traveling upstream with an effective velocity equal to the product of a parameter, p, and the solar-wind bulk velocity. The data-reduction methods are summarized, and uncertainties in the determination of the value of p are discussed. It is found that the overall average boundary corresponds to a velocity of approximately twice the solar-wind velocity for protons reflected from the daytime sector of the bow shock. More refined analysis of the data shows that the value of p is approximately 1.6 near the subsolar point and greater than 2 along the daytime flanks of the bow shock.

Shock wave/turbulent boundary-layer interactions with and without surface cooling

Abstract: An experimental investigation was conducted to delineate the structure of the flowfield and temperature distributions in a shock wave/turbulent boundary-layer interaction with and without surface cooling. The Mach number upstream was about 3.5, and the wave angle was 23 deg. The wall to stagnation temperature ratio was 0.44 with cooling and 1.1 with heating. A detailed map of the interaction flowfields deduced from numerous boundary-layer traversing stations revealed the influence of wall cooling on the flowfield, wave structure, and size of the flow separation region. With surface cooling, the size of the separation region was much smaller, and the separation and reflected shock waves merged together near the edge of the velocity boundary layer, extending into the freestream as one wave.

Influence of particle drag coefficient on particle motion in high-speed flow with typical laser velocimeter applications

Abstract: The effect of using different particle drag coefficient C sub D equations for computing the velocity of seeded particles in high-speed gas flows was investigated. The C sub D equations investigated included the Stokes equation, a second incompressible equation valid for higher relative Reynolds numbers, and six equations that account for the effects of compressibility together with the effects of relative Reynolds numbers greater than one. The flows investigated were center-line nozzle flows, normal shocks, and oblique shocks for free-stream Mach numbers of 1.6 to 6 and stagnation pressures of 1 and 3.4 atmospheres. The net result was empirical C sub D equation based on the latest sphere C sub D data for the low relative Mach number and Reynolds number conditions that are encountered in supersonic flows.

Analytical Theory of Transonic Normal Shock-Turbulent Boundary-Layer Interaction

Abstract: This paper describes an approximate analytical theory of the nonseparating transonic interaction of a weak normal shock with an isobaric laminar or turbulent boundary layer The complicated multisubregion disturbance field structure is simplified by appropriate approximations (including neglect of the small scale details within the shock structure regions) which reduce the problem to an analytical form, provided the incoming Mach number is not very near unity The resulting mixed transonic flow boundary value problem is solved by Fourier transformation methods Lateral pressure gradient effects are included Results are presented for turbulent boundary-layer pressure distributions, flow geometry, and skin friction Following a small post-shock subsonic expansion region, the approach of the downstream interaction pressure to the final subsonic value is found to be a slow algebraic (l/;c)-type decay in agreement with experimental observations

Non-equilibrium ideal-gas dissociation after a curved shock wave

Abstract: Analytic solutions are obtained for non-equilibrium dissociating flow of an inviscid Lighthill-Freeman gas after a curved shock, by dividing the flow into a thin reacting layer near the shock and a frozen region further downstream. The method of matched asymptotic expansions is used, with the product of shock curvature and reaction length as the small parameter. In particular, the solution gives expressions for the reacting-layer thickness, the frozen dissociation level, effective shock values of the frozen flow and the maximum density on a stream-line as functions of free-stream, gas and shock parameters. Numerical examples are presented and the results are compared with experiments.

Supersonic Shock Wave Turbulent Boundary-Layer Interactions

Abstract: Results are presented of an experimental investigation of shock wave turbulent boundary-layer interactions in supersonic flow. The experiments were conducted at a freestream Mach number of 2.96 and over a boundarylayer Reynolds number range of 10 5 to 10 6. Surface static pressure measurements, oil flow photographs, and interferograms were obtained to define the length of separation and the incipient separation angles for 1) twodimensional compression corner and 2) planar shock wave interactions with a turbulent boundary layer. The tests were conducted in a high unit Reynolds number freestream on a long flat plate with a turbulent boundarylayer thickness in the interaction region of from 0.12 to 0.18 in. Direct comparisons were made between the compression corner and incident shock wave interactions to determine the effects of configuration on turbulent boundary-layer separation. For both configurations the length of the separated region was found to decrease and the incipient separation angle to increase with increasing Reynolds number. For constant Reynolds number, the overall pressure rise for incipient separation was approximately the same for the compression corner interaction and the incident shock wave interaction. Turbulent boundary-layer separation was found to be of the "free interaction" type whereby the separation angle and pressure distribution through separation were independent of Reynolds number, overall pressure rise, and configuration. fo Nomenclature skin friction coefficient at beginning of interaction freestream Mach number pressurepressure freestream pressure Reynolds number based on freestream condition and boundary-layer thickness at beginning of interaction . span °f shock generator stagnation temperature wall temperature axial distance from flat plate leading edge axial location of center of interaction axial distance from flat plate/ramp hinge line to shock generator leading edge axial location of separation point axial offset distance vertical distance between flat plate and shock generator leading edge effective incipient separation corner angle compression ramp angle shock generator angle boundary-layer thickness at beginning of interaction

Analysis of unsteady transonic channel flow with shock waves

Abstract: : 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.

Shock formation distance in a pressure driven shock tube

Abstract: Measurements of the shock formation distance in a conventional pressure driven shock tube of 5.2 cm i.d. using two different diaphragm types and three different driver gases with a driven gas of air are presented. The shock formation distance is found to be approximately proportional to the effective opening time of the diaphragm and inversely proportional to the average speeds of sound of the driver and driven gases.

Three-dimensional swept shock/turbulent boundary-layer separations with control by air injection

Abstract: Experimentally determined wall pressure distributions, local surface shear stresses and their directions, and detailed turbulent boundary-layer traverses in near zero heat transfer conditions, are presented through skewed shock/boundary-Iayer interaction regions generated by a wedge standing normal to a test wall. The mainstreamMach numbers were 2 and 4, while the Reynolds number based on the undisturbed test boundary-layer thickness of 0.2-in., growing along the nozzle sidewall of the NAE 5 X 5-in. blowdown wind tunnel, was -2 X 105. Tangential air injection at a jet exit Mach number of 3 was then introduced into the 3D shock separated Mach 2 boundary layer, to control the separation. The optimum direction of blowing was found to be along a line somewhere between the deflected surface of the wedge and the line of the oblique shock wave

Structure of shock waves in a liquid containing gas bubbles

Abstract: The structure of a stationary shock wave in a liquid containing gas bubbles is investigated theoretically. For the description of such a two-phase mixture the two-velocity two-temperature model with two pressures is used [1], taking into consideration the small-scale frictions, the noncoincidence of the velocities, temperatures, and pressures of the phases, and the oscillations of the bubbles. The existence of shock waves having a discontinuity surface in front as well as of shock waves with continuous structure is shown. It is shown that unlike the two-phase mixtures of gas with drops or particles where the structure of the wave depends mainly on the interphase friction, in two-phase mixtures of a liquid with bubbles the behavior of the wave and its structure depends essentially on the interphase heat transfer. Wave characteristics, such as the wavelength of the pulsations, their damping decrement, do not have a monotonic dependence on the parameters governing the intensity of heat transfer and do not lie between the corresponding values for isothermic and adiabatic regimes of behavior of the bubbles. Shock waves in liquids with gas bubbles were investigated theoretically and experimentally in [3–7]. A detailed review of the work up to 1971 is given in [8].

Diffraction of a shock wave by a compression corner. I - Regular reflection

Abstract: The unsteady, two-dimensional flowfield resulting from the interaction of a moving planar shock wave with a compression corner is determined using a second-order, discontinuity-fitting, finite-difference approach. The time-dependent Euler equations are transformed to normalize the distance between the body and peripheral shock and to include the existing self-similar property of the flow. The resulting set of partial differential equations in conservation-law form is then solved in a time-dependent fashion using MacCormack's scheme. The vortical singularity, which lies on the body surface, and the single reflected shock are both treated as discontinuities in the numerical procedure. The results of the numerical simulation compare quite favorably with existing experimental interferograms and yield better flowfield resolution than previous first-order, shock-capturing, numerical solutions.

On the motion of shock waves on an airfoil with oscillating flap

Abstract: Results are presented of measurements of the periodical motion of the shock waves on a NACA 64A006 airfoil with harmonically oscillating flap in two-dimensional attached transonic flow. It is shown that three different types of shock wave motion can be distinguished. An analytical model is developed, with which a satisfactory explanation can be given of the observed types of shock wave motion.

Shock Waves Generated by an Oscillating Electric Field in an Expanding Plasma

Abstract: A strong radio-frequency field applied to an expanding plasma is found to produce a shock at the surface where the local plasma frequency matches the applied frequency. The shock propagates towards the upstream overdense region with the ion-acoustic speed relative to the plasma flow. The density jump at the shock front is found to be proportional to the field amplitude.

Propagation of magnetogasdynamic plane shock waves in an exponential medium

Abstract: An analytic solution for propagation of strong plane magnetogasdynamic shock waves in a medium with density increasing exponentially under low pressure is obtained in this paper. The shock wave moves with variable velocity and the total energy of the wave is variable.

Calculation of the Laminar Viscous Shock Layer on a Blunt Biconic Body at Incidence to Supersonic and Hypersonic Flow

Abstract: : A fully viscous shock layer computation method developed by others to treat laminar flow over a sharp cone at incidence to a supersonic or hypersonic free stream has been extended to consider the case of flow over a blunt biconic configuration at angle of attack. The basic method treats the flow between the body surface and the bow shock wave by one set of equations which are valid in both the viscous and inviscid flow regions. A description is given of the computational methods used, particularly the method developed to treat the viscous shock layer over the spherical nose and the method used to take data from the end of the forecone solution to provide initial data for starting the aft-cone solution. Results from calculations which have been performed using the method developed in this investigation are compared with results from boundary- layer and inviscid flow calculations and with experimental data. The present technique is validated by the good agreement between the computed data and experimental data. (Author)

Modified thin shock layer method for supersonic flow past an oscillating cone

Abstract: The problem of supersonic flow past a circular cone oscillating about its vertex is considered. The amplitude and the frequency parameter of the oscillation are assumed to be small, and a perturbation solution in the amplitude and frequency is sought. Furthermore, thin shock layer expansion is used to derive the flowfield solution in the form of a series. The first three terms in the series are obtained, showing that the series solution tends to converge when the shock layer is very thin and otherwise it tends to diverge. The technique of parameter straining then is applied which greatly improves the accuracy and extends the range of applicability of the thin shock layer solution. In particular, simple explicit formulas for the stability derivatives are valid for moderate as well as high freestream Mach numbers and for thick as well as slender cones. Variations of the stability derivatives with the freestream Mach number, specific heat ratio, and the cone semiangle are investigated and comparisons with existing theories are included. The relation of limiting gasdynamic theory with unsteady Newtonian flow theory also is discussed. k £ MOO m n p r t t utv,w

Experimental investigation of shock waves in liquid helium I and II

Abstract: The flow field produced by a shock wave reflecting from a helium gas-liquid interface was investigated using a cryogenic shock tube. Incident and reflected shock waves were observed in the gas; transmitted first- and second-sound shocks were observed in the liquid. Wave diagrams are constructed to compare the data with theoretical wave trajectories. Qualitative agreement between data and theory is shown. Quantitative differences between data and theory indicate a need for further analysis of both the gas-liquid interface and the propagation of nonlinear waves in liquid helium. This work was a first step in the experimental investigation of a complex non-equilibrium state. The results demonstrate clearly the usefulness of the cryogenic shock tube as a research tool. The well-controlled jump in temperature and pressure across the incident shock wave provides unique initial conditions for the study of dynamic phenomena in superfluid helium.

Increase of initial velocity and pressure upon impact on an inhomogeneous target

Abstract: It is proved on the basis of an analysis conducted by means of the method of (p, u)-diagrams in an acoustic approximation that the mass velocity of the material of a target increases when a shock wave propagates along a target in which the acoustic resistance of the layers decreases in the direction of propagation, and it can even exceed the initial velocity of the striker. An increase in pressure behind the wave front similar to the example of unbounded accumulation in a plane shock wave considered in [2] is observed when a striker impacts on a target in which the acoustic impedance of the layers increases in the direction of propagation of the shock wave. The increase in velocity is experimentially verified.

Perpendicular explosive drive and oblique shocks

Abstract: Oblique shocks in various materials driven by Composition B-3, 9404, and TNT with the detonation wave perpendicular to the interface are investigated with flash radiographic techniques. The detonation products in the rarefaction behind the detonation front expand laterally as the explosive-sample interface bends under shock compression of the sample. With the products described by a polytropic gas equation of state, this expansion is shown to be adequately described in the vicinity of the detonation front by Prandtl-Meyer flow. Some new Hugoniot data for antimony are obtained in the course of the investigation. In some instances of perpendicular drive the compression of the sample is not accomplished strictly by strong shocks. This circumstance is exemplified by baratol driving aluminum, a case where the bulk sound speed exceeds the detonation velocity, and by 9404 driving beryllium, a case where it does not. Some experimental results are presented for both these systems.

A nonasymptotic triple deck model for supersonic boundary-layer interaction

Abstract: This investigation presents an approximate nonasymptotic theory for the Lighthill-Stewartson triple-deck model of supersonic laminar boundary-layer interaction. The emphasis of the present study is on supersonic flows in the Reynolds number range 10 4

Characteristics procedure for supersonic flows including consideration of viscous contributions to flow rotationality

Abstract: A characteristics procedure has been developed which includes viscous and conductive transport terms normal to streamlines. By introducing the transport terms as corrections, the equations retain their hyperbolic character. The solutions have been developed using an inverse grid scheme in a streamline-normal network. Inclusion of the transport terms enables tracing of shock waves through the supersonic portion of the boundary layer so that shock reflections are well-located. Excellent agreement is obtained with the results of other characteristics procedures and with the experimental pressure distributions for the waisted body of Winter, Smith and Rotta.