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Showing papers on "Oblique shock published in 1970"


Journal ArticleDOI
TL;DR: In this article, the fluid mechanics of the interaction between a shock wave and a turbulent boundary layer at speeds ranging from transonic to high supersonic are discussed, and some possibly fruitful avenues for further research are indicated.

289 citations


Journal ArticleDOI
TL;DR: In this article, the self-similar one-dimensional flow behind a plane shock propagating upward into an exponentially decreasing atmosphere is considered, and the flow is taken to be isothermal in view of the large radiation mean free paths associated with high altitudes and the intense radiation heat transfer accompanying the high temperatures characteristic of an accelerating shock wave.
Abstract: The self‐similar one‐dimensional flow behind a plane shock propagating upward into an exponentially decreasing atmosphere is considered. The flow is taken to be isothermal in view of the large radiation mean free paths associated with high altitudes and the intense radiation heat transfer accompanying the high temperatures characteristic of an accelerating shock wave. The equations of motion are formulated in Lagrangian coordinates and are integrated exactly for all values of the shock density ratio. Solutions are presented for the cases where the boundary conditions at the shock correspond to a Hugoniot shock and to a Chapman‐Jouguet shock. A significant result of the analysis is that in both of these cases the shock propagates much faster than for the case of adiabatic flow.

92 citations


Journal ArticleDOI
TL;DR: In this article, high-resolution plasma measurements were made on the upstream edge of the earth's bow shock by the combination of a Faraday cup with modulation grid and a curved-plate analyzer on the satellite OGO 5.
Abstract: High time resolution (Δt = 0.288 to 9.5 seconds) plasma measurements have been made on the upstream edge of the earth's bow shock by the combination of a Faraday cup with modulation grid and a curved-plate analyzer on the satellite OGO 5. These observations show that the solar wind positive ions often undergo a substantial deceleration just upstream of the shock's steep gradient of magnetic-field strength. This deceleration, which is not necessarily accompanied by a temperature increase, may be caused by a charge-separation electric field on the upstream side of the bow shock.

69 citations


Journal ArticleDOI
TL;DR: In this article, two theories for periodic permanent roll waves are presented which are based on the shallow-water wave equations for the gradually varied portion of the wave profile, and the shock conditions for the rapidly varied portion.
Abstract: Two theories for periodic permanent roll waves are presented which are based on the shallow-water wave equations for the gradually varied portion of the wave profile, and the shock conditions for the rapidly varied portion. In the first theory the channel slope, S 0 , is assumed to be sufficiently small that the weight of the shock can be neglected in the shock condition. Comparison of results from this theory for small S 0 with experimental results reveals good agreement for S 0 = 0.019, but rather large discrepancies for S 0 = 0.050, 0.084, and 0.12. In the second theory the shock weight is included in the shock condition. Using the measured shock profiles to evaluate the weight of the shock yields theoretical predictions which are in substantial agreement with the experimental results.

60 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the structure of shock waves in liquids containing gas bubbles and showed that the overall thickness of the shock appears to be determined by the dispersion effect.
Abstract: The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave.

52 citations


Journal ArticleDOI
TL;DR: In this paper, the reflected wave field produced by a plane oblique shock wave impinging on a turbulent boundary layer at an initial Mach number of 2·5 was measured and the observed wave systems broadly agree with the suggestions of previous workers, but not with a recent theoretical treatment.
Abstract: Measurements are presented of the reflected wave field produced by a plane oblique shock wave impinging on a turbulent boundary layer at an initial Mach number of 2·5. The outgoing waves are either a single shock, with the same deflexion as the incident shock, or a shock of approximately 10° deflexion followed by a region of compression in which is embedded an expansion fan having the same turning as the incident shock. The transition between these two types of wave field was not studied, but it is fairly abrupt and appears to be closely linked to the onset of boundary-layer separation. The observed wave systems broadly agree with the suggestions of a number of previous workers, but not with a recent theoretical treatment. Surface-pressure measurements and oil flow photographs are used to determine the onset of separation, and from these it is found that the overall pressure rise associated with incipient separation is rather smaller than previous work would suggest.

49 citations


Journal ArticleDOI
TL;DR: In this paper, the de Hoffmann-Teller relations across the shock have been applied graphically by making use of the geometry of the hydromagnetic wave normal surfaces in a moving medium, and it has been shown that the turbulent character of the region between the bow shock of the earth and the magnetopause may be due in part to the amplification of turbulent waves in the solar wind on passing through a bow shock.
Abstract: The problem of the interaction of small‐amplitude plane hydromagnetic waves with plane, oblique hydromagnetic shocks is treated. When the perturbations of the flow field on either side of the shock are expanded in terms of incident and diverging eigenwaves, the linearized de Hoffmann‐Teller relations across the shock yield a system of equations for the amplitudes of the diverging waves and the motion of the perturbed shock. The shock motion and the amplitudes of the diverging waves as a function of the amplitude and direction of any given incident wave are found using this system of seven linear, inhomogeneous equations, along with Snell's laws. Snell's laws are interpreted graphically by making use of the geometry of the hydromagnetic wave normal surfaces in a moving medium. By considering some special cases it is shown that hydromagnetic waves are amplified on passage through a fast shock. The turbulent character of the region between the bow shock of the earth and the magnetopause may be due in part to the amplification of turbulent waves in the solar wind on passing through the bow shock.

48 citations


Journal ArticleDOI
TL;DR: Heat transfer from turbulent boundary layer interacting with shock and expansion waves in supersonic flow was studied in this article. But the results were limited to the case of a single wave.
Abstract: Heat transfer from turbulent boundary layer interacting with shock and expansion waves in supersonic flow

43 citations


Journal ArticleDOI
TL;DR: In this article, a coaxial supersonic jet flows noise reduction based on noise distribution characteristics measurement in anechoic chamber is presented. But the authors do not consider the effects of noise distribution on the flight dynamics of the jet flows.
Abstract: Interacting coaxial supersonic jet flows noise reduction based on noise distribution characteristics measurement in anechoic chamber

41 citations


Journal ArticleDOI
TL;DR: The X-type pseudo-shock was investigated in this article, which appeared at comparatively high Mach number, and was compared with the λ-type Pseudo-Shaking reported in the previous paper.
Abstract: The X-type pseudo-shock was investigated, which appeared at comparatively high Mach number, and was compared with the λ-type pseudo-shock reported in the previous paper. The similarity and difference between them were discussed. At the duct center, the shock loss by the leading shock wave is smaller for the X-type pseudo-shock than for the λ-type one, but near the wall and in the subsonic region, the flow conditions are similar. The over-all total pressure loss is affected by the mixing of the flow near the wall with the main stream and the so-called shock loss is rather small. the effect of the boundary layer and the wall friction force on the static pressure rise of the pseudo-shock is also made clear. The simple model for the mechanism of the pseudo-shock is presented in the appendix.

38 citations


Journal ArticleDOI
TL;DR: A supersonic two-phase tunnel was designed and built with such versatility and precision that normal and oblique shock structures can be photographed and analyzed in the absence of boundary-layer interference as mentioned in this paper.
Abstract: Homogeneous two-phase flows of dispersed liquid and gas having gas-to-liquid volume ratios around 1:1 exhibit the characteristics of a continuum flow with a greatly reduced sound propagational velocity that approaches 66 ft/sec at atmospheric pressure, and that is reduced further in value as the square root of the pressure. Flows of such mixtures at velocities in excess of the local velocity of sound can produce shock phenomena similar to that experienced in supersonic gaseous media. A supersonic two-phase tunnel was designed and built with such versatility and precision that normal and oblique shock structures can be photographed and analyzed in the absence of boundary-layer interference. The applicability of the isothermal continuum theory to such flows is confirmed empirically for volume ratios near 1:1, and the theory is mathematically extended for both normal and oblique shocks over a wide range of volume ratios centered about the 1:1 value. Auxiliary flow devices were constructed for the measurement of such difficult flow parameters as the relative phase velocity, local void ratio, coefficient of friction, and stagnation pressure. A general change in the flow model matrix was found at volume ratios approaching 1:1. Pressure gradients and relative phase velocities were correlated with the proposed flow models with generally good agreement. The coefficient of friction measured for supersonic flow was found to be a simple function of the local void ratio. Stagnation pressures measured for a wide range of flow conditions approximate an isentropic relation for a substantial part of the lower velocity spectrum. At higher velocities, the stagnation pressure closely approaches the normal shock plus isentropic slowdown theory. Considerable photographic information pertaining to shock structure and phase movement is obtained over the spectrum of flow conditions with Mach numbers ranging from 2 to 20.

Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of the interaction between normal shock waves and deformable solid materials, with particular reference to the characteristics of the reflected shock wave, is presented, which is of importance in all those cases in which a shock wave impings on solid walls.
Abstract: A theoretical-experimental study has been performed on the interaction between normal shock waves and deformable solid materials, with particular reference to the characteristics of the reflected shock wave. The present study is of importance in all those cases in which a shock wave impings on solid walls (i. e. explosions, sonic booms etc.). The first part presents a theoretical analysis which gives the solution for the shock wave intensity reflected into the gas and for the transmitted shock wave propagating into the elastic solid material for both the cases of linear (Hooke type) and non linear solids. For the first kind of materials a closed form solution is found. For the non-linear materials the problem is solved through a numerical analysis. The experiments concern with two kinds of expanded foams (closed cell and open cell foams). These materials have been selected because of the good deformation and density characteristics which both are necessary to evidentiate the shock wave interaction phenomena. The tests have been performed putting a cylindrical model of the material under study at the closed end of a shock tube and creating shock waves of variable strength which impinge on the material. Slightly upstream of the free end wall of the model, the pressures history is recorded by means of a pressure pick up and of an oscilloscope. The range of the shock wave Mach number has been1,2⩽Ms⩽2,2 with initial pressures ranging between50⩽p 1 ⩽760 mmHg. The theoretical analysis seems to be in a very good agreement with the experiments performed, especially when due account is given to the gap existing between shock tube and model walls.

Journal ArticleDOI
TL;DR: In this paper, the authors obtained a set of boundary layer interaction data for adiabatic wall conditions at supersonic free stream Mach numbers, including suction effects, including shock wave-turbulent boundary layer interactions.
Abstract: Conical shock wave-turbulent boundary layer interaction data obtained for adiabatic wall conditions at supersonic free stream Mach numbers, including suction effects

Journal ArticleDOI
TL;DR: In this paper, the amplitude and polarization of cyclotron waves produced by a steady thin current sheet in the plane of the bow shock have been calculated by using cold plasma dispersion relations.
Abstract: Cyclotron waves should be produced upstream and downstream from the bow shock by current in the shock. Amplitudes and polarizations of waves produced by a steady thin current sheet in the plane of the shock have been calculated by using cold plasma dispersion relations. The steady current leads to waves that are stationary in the shock frame. Waves upstream from the shock are circularly polarized electron waves, the polarization is in the sense of a right-hand screw when the interplanetary field is directed generally toward the shock and of a left-hand screw when the field is directed away. The downstream magnetic wave field has two components, one from the electron cyclotron branch and one from the ion cyclotron branch of the dispersion relation. The second component has a longer wavelength and a larger amplitude (by the ion/electron mass ratio) than the electron wave. It is elliptically rather than circularly polarized and is always polarized in the opposite sense to the upstream electron wave. Therefore, the sense of polarization would be seen to reverse as the shock is traversed in either direction. When the ambient magnetic field is not perpendicular to the shock, there is also a stationary electrostatic wave with its electric field normal to the shock. Both upstream and downstream the ratio of the electrostatic wave to the magnetic wave amplitudes is of the order u/c tan θ, where θ is the angle between the normal to the shock and the magnetic field, and u is the plasma flow velocity.

Journal ArticleDOI
TL;DR: In this article, the unsteady numerical method of Godunov has been applied to compute high Mach number axisymmetric flow past bell-shaped bodies of varying bluntness.


Journal ArticleDOI
TL;DR: Oblique shock initiated by 7 July 1966 proton flare in solar wind observed by satellite magnetometers outside magnetosphere as mentioned in this paper, which can be traced back to the events in the early 1970s.

Journal ArticleDOI
TL;DR: In this paper, a simple interaction analysis based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave was proposed to calculate the major features of the interaction between a laminar boundary layer and a supersonic corner expansion wave.
Abstract: There are three distinct effects involved in the interaction of a laminar boundary layer and a supersonic corner expansion wave. These are: the upstream influence effect causing some pressure decay ahead of the corner, transverse pressure gradients in the immediate neighborhood of the corner, and the interaction of the boundary layer downstream with the external flow. Arguments are presented to suggest that, when the flow is locally hypersonic and the wall is highly cooled, the dominant effect is the downstream interaction process. Hence the major features can be calculated by using a simple interaction analysis down stream of the corner based on the Prandtl boundary-layer equations and the equations of an inviscid noncentered simple wave. Numerical results are obtained by using the "cold wall" similarity solution to the boundary-layer equations. These show that pressure decay extends over a region which can be many times larger than the original plate length used to generate the boundary layer.

Journal ArticleDOI
TL;DR: In this article, an integrated double-oblique-shock scramjet model was developed to provide a test bed for supersonic combustion tests and for instrumentation development essential for analysis of combustion test results.
Abstract: : Some results of a continuing research program to develop a capability for testing integrated scramjets are reported. During this research program, an integrated double-oblique-shock scramjet model was developed to provide a test bed for supersonic combustion tests and for instrumentation development essential for analysis of combustion test results. Results are presented for tests in which hydrogen fuel was injected into the combustor. Injection of the fuel, from sonic orifices in the wall, normal to the flow did not lead to satisfactory combustion data, supposedly because of the cold boundary layer. Injection through sonic orifices in a series of diamond airfoil injectors led to combustion confirmed by all the following measurements: (1) an increase in static pressure within the combustor downstream of the injection station, (2) an increase in surface heat-transfer rate, (3) an increase in static temperature as measured by the sodium line reversal technique, (4) an increase in output of radiation sensor gages, and (5) a decrease in flow Mach number inferred from static to pitot pressure measurements. The measured increases were proportionate to increases in computed average equivalence ratio. The combustion results are compared with numerical solutions. In general, the measured temperatures and pressures in the combustor with heat addition were higher than the calculated values.

Journal ArticleDOI
TL;DR: In this paper, a study was made of airfoil optimization, using the equations of hypersonic gas dynamics to explore the 'Newtonian chine strip' theory that air-foil concavity enhances the lift-to-drag ratio for a fixed drag penalty.
Abstract: : A study was made of airfoil optimization, using the equations of hypersonic gas dynamics to explore the 'Newtonian chine strip' theory that airfoil concavity enhances the lift-to-drag ratio for a fixed drag penalty. The flow behind concave and convex exponential shock waves is investigated, and the corresponding airfoil surfaces are determined. The calculations show that the optimum lifting surface for fixed drag is only slightly more concave than a flat plate and that the improvement in performance is small. A limit line is shown to exist in the flow field behind convex exponential shock waves, so that is is not possible to construct a convex airfoil that supports an exponential shock wave over its entire length if the nose curvature is too large. (Author)

W. C. Rose1
01 Nov 1970
TL;DR: In this article, a method for predicting interaction produced by externally generated, oblique shock wave impinging on laminar or turbulent boundary layers is proposed, which is based on the prediction of the interaction between the two layers.
Abstract: Method for predicting interaction produced by externally generated, oblique shock wave impinging on laminar or turbulent boundary layers

Journal ArticleDOI
TL;DR: In this paper, it was shown that there exist unstable waves of mixed polarization which can be described as coupled ion beam and whistler modes with frequencies given by ω≈k·u where u is the streaming velocity of the ions relative to the electrons.
Abstract: Instabilities produced by a current across a magnetic field and propagating obliquely to the field are studied in connection with the description of hydromagnetic shock waves. It is shown that there exist unstable waves of mixed polarization which can be described as coupled ion beam and whistler modes with frequencies given by ω≈k·u where u is the streaming velocity of the ions relative to the electrons. These waves are investigated in the small electron Larmor radius approximation and in the frequency range Ωi ≪ ω ≪ Ωe where Ωi and Ωe are the cyclotron frequencies of the ions and electrons, respectively. The maximum growth rate is limited by γ < 123 (meu/2miυ¯e)1/3Ωe where υ¯e is the electron thermal velocity. The effect of collisions is considered, and the possibility of observing the instability in oblique shock wave experiments is discussed.

Journal ArticleDOI
TL;DR: In this paper, the structure of shock wave and solitons propagating oblique to a magnetic field in a warm plasma is analyzed based on two-fluid equations including resistive dissipation.
Abstract: The structure of shock waves and solitons propagating oblique to a magnetic field in a warm plasma is analyzed. The calculations are based on two‐fluid equations including resistive dissipation. A classification scheme for the various structures obtained as the shock speed and plasma parameters vary is given. The problem of high Mach number shock structure is also discussed.

Journal ArticleDOI
TL;DR: In this paper, a higher order theory is developed to treat the refraction of the incident oblique shock wave by irrotational or rotational disturbances of arbitrary amplitude provided the flow is supersonic behind the shock.
Abstract: : The general problem studied is the propagation of an oblique shock wave through a two-dimensional, steady, non-uniform oncoming flow. A higher order theory is developed to treat the refraction of the incident oblique shock wave by irrotational or rotational disturbances of arbitrary amplitude provided the flow is supersonic behind the shock. A unique feature of the analysis is the formulation of the flow equations on the downstream side of the shock wave. Analytical and numerical solutions to the basic shock refraction relation are presented for a broad range of flows in which the principal interaction occurs with disturbances generated upstream of the shock. These solutions include the passage of a weak oblique shock wave through: a supersonic shear layer, a converging or diverging flow, a pure pressure disturbance, Prandtl-Meyer expansions of the same and opposite family, an isentropic non-simple wave region, and a constant pressure rotational flow. The comparison between analytic and numerical results is very satisfactory. (Author)

01 Nov 1970
TL;DR: In this article, a time-dependant method for calculating supersonic blunt body flow fields with sharp corners and embedded shock waves is proposed, which is based on the time-dependent estimation of body motions.
Abstract: Time-dependant method for calculating supersonic blunt body flow fields with sharp corners and embedded shock waves


Journal ArticleDOI
TL;DR: In this paper, the problem of propagation of an initially plane shock wave along a fluid interface is solved numerically, using the method of characteristics in conjunction with Whitham's technique.


Journal ArticleDOI
TL;DR: In a high-β plasma ion cyclotron radius, dispersion forms a trailing wave train for a perpendicular fast shock and collisionless dissipation is provided by the three-wave decay of the wave train into very oblique fast and parallel Alfven waves as discussed by the authors.
Abstract: In a high-β plasma ion cyclotron radius, dispersion forms a trailing wave train for a perpendicular fast shock. Collisionless dissipation is provided by the three-wave decay of the wave train into very oblique fast and parallel Alfven waves. Particle thermalization results from Landau damping of oblique fast wave turbulence. The shock damping length to three-wave decay is many ion cyclotron radii. Undamped Alfven turbulence should persist far downstream from the shock.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the three-dimensional flow in the plane of symmetry in the region of interaction of a boundary layer with a shock wave which arises ahead of an obstacle mounted on a plate.
Abstract: In a supersonic stream we consider the three-dimensional flow in the plane of symmetry in the region of interaction of a boundary layer with a shock wave which arises ahead of an obstacle mounted on a plate. The principal characteristic of this flow is the penetration of a filament of the ideal fluid within the separation zone and the formation on the surface of the plate and obstacle of narrow segments with high pressures, high velocity gradients, and large heat transfer coefficients.