Showing papers on "Oblique shock published in 1980"

Conditions for acceleration of energetic ions ≳30 keV associated with the Earth's bow shock

Abstract: A statistical analysis of particles (greater than 30 keV/charge) upstream of the earth's bow shock is conducted and shows that the rate of occurrence of upstream particle events is relative to the angle between the magnetic field and the shock normal at the shock intersection point as well as relative to the angle between the magnetic field and the radial direction (i.e., the sun-earth line). In addition, the occurrence rate of upstream particle events relative to the bow shock connection time of a field line convected with the solar wind is presented for a model bow shock. A linear dependence of the diffusion coefficient on energy per charge is apparent with the value of the mean free path of a 30-keV proton found to be about 4 earth radii, and the free escape boundary to be at about 30 earth radii in front of the bow shock.

Upstream particle events close to the bow shock and 200 RE upstream: ISEE-1 and ISEE-3 observations

Abstract: Two energetic particle events (28 keV - 145 keV) upstream of the earth's bow shock have been investigated with two identical experiments of the Max-Planck-Institut/University of Maryland on ISEE-1 and ISEE-3. Close to the bow shock the particle distribution is more or less isotropic and indicates strong scattering of these particles in the upstream wave field. At ISEE-3 the particles move essentially scatter-free from the general bow shock direction. The temporal evolution of the particle bursts is discussed in terms of the interplanetary magnetic field topology and the scattering conditions.

Interaction between a discontinuity wave and a shock wave: critical time for the fastest transmitted wave, example of the polytropic fluid

Abstract: In this paper we consider a homogeneous quasi-linear hyperbolic system in two independent variables, we evaluate the critical time for the fastest transmitted wave generated by the interaction between a discontinuity wave and a shock wave; We prove that in the case of propagation in a constant state the critical time is greater (smaller) than it would be in absence of interaction if the weak discontinuity of the incident wave velocity decreases (increases) through the shock. An application is made to a polytropic fluid in case of interaction with a contact shock; we prove that the critical time is smaller than it would be in absence of the shock

Three-Dimensional Shock Structures for Transonic/Supersonic Compressor Rotors

Abstract: This paper reviews experience at evaluating three-dimensional shock structures for transonic/supersonic compressor rotors, including experimental results obtained by holography, laser velocimetry, and highfrequency pressure transducers. Typical shock wave angles are oblique to the relative flow with angles in the range 60-65 deg range for maximum deflection, rather than the 40-50 deg range predicted by conventional cascade analyses. Results are partially explained by obliquity of the shocks in between-blade-streamsurfaces. Procedures for generating analytical flow patterns consistent with experiment, including supersonic/subsonic transition through oblique shocks, are demonstrated.

Oscillations of the Supersonic Flow Downstream of an Abrupt Increase in Duct Cross Section

Abstract: T HE flow in a duct following a sudden change in section is described herein. Sonic flow through a convergent nozzle expands into a larger cross section to produce a mixed supersonic flow, and a low base pressure in the upstream corners. Under certain pressure conditions, oscillations occur in the duct and excessive externally generated noise results. These self-excited oscillations are caused by a boundarylayer/shock-wave interaction, and can exist in both circular and rectangular ducts. Many types of oscillations have been observed in different test arrangements, and a complete description of the flow may be found in the full paper.] Contents Most of the tests were carried out in a duct through which atmospheric air was induced by means of a downstream vacuum. A schematic diagram, characteristic of all the ducts tested, is shown in Fig. 1. Figure 2 shows typical interferograms for the different flow regimes obtained with a Mach-Zehnder interferometer in a rectangular duct, as the downstream receiver pressure pe increased. The base pressure typically varies with the ratio of pe to input stagnation pressure pa, as shown in Fig. 3. The flow structure can either be dominated by a series of reflected oblique shock waves or, when the base pressure pw increases, a single normal shock wave (Mach disk) close to the nozzle exit. For very low values of pe/pa, the reflected oblique shock waves are repeated in the stable structure shown in Fig. 2a. With higher values of pe/pa, flow separation occurs in the presence of oblique shock waves, as is shown in Figs. 2b and 2c, where the flow separates in the region of the third and second oblique reflections, respectively. In both cases the separation points oscillate through a small distance. The oscillations represented by Figs. 2b and 2c may be called the downstream and midstream oscillations, respectively. A further oscillation type occurs with the higher pe lpa values when the main flow structure changes from an oblique to a normal shock during a cycle. Figure 2d shows an instant during the oscillations which are of large amplitude and have been called the shock-pattern oscillations.2 As the pressure ratio pe/pa increases further the flow becomes stable with a normal shock wave in the duct (e.g., Fig. 2e for a pressure ratio pe/pa of 0.314). After a pressure range of stable flow an instability occurs in which the normal

Axially symmetric explosion in magnetogasdynamics.

Abstract: A point explosion in a spheroid with axially symmetric exponential density distribution is investigated by generalizing the method of Laumbach and Probstein to include the effects of a magnetic field. It is shown that the shock velocity decreases and tends to zero. Also, the elongation of the shock envelope along the axis of symmetry is much reduced and the blowout of the shock wave is removed on account of the magnetic field.

Experimental Studies of the Production of Converging Cylindrical Shock Waves

Abstract: AN improved experimental technique for the production of cylindrical converging shock waves is presented. This is accomplished with an annular shock tube fitted with an axisymmetric area contraction which redirects an annular incident shock into a cylindrical implosion chamber. The contraction profile is designed in accordance with Whitham's ray-shock theory, and a three-element profile is found to provide the best overall performance on the basis of twodimensional tests. Experiments with a three-element conical contraction demonstrate that highly symmetrical cylindrical implosions may be achieved by this method, and that the cylindrical shock amplification is well predicted by the Chester-Chisnell-Whitham (CCW) area Mach No. rule.

Interaction Between a Normal Shock Wave and a Turbulent Boundary Layer at High Transonic Speeds. Part II: Wall Shear Stress

Abstract: Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.

Analytical solution of double-Mach reflection

Abstract: The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 x 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.

Transonic Axial Compressor Using Laser Anemometry and Unsteady Pressure Measurements

Abstract: A laser anemometer and high-response pressure probes were used to study in detail the complex flow in a transonic axial compressor rotor at 20,000 rpm. The investigation was aimed at providing complete data on the internal flowfield at the design speed for peak efficiency, near compressor surge, and choke. Useful information is presented on flow vectors, three-dimensional shock waves, oscillating total pressures, blade wakes, and losses downstream of the rotor.

Shock wave formation at a caustic

Abstract: The behavior of a weak acoustic compression near a caustic surface has been determined for a special class of specified incoming signals. This problem arises in various contexts, including the propagation of sonic booms generated by supersonic aircraft. The solution derives from a mapping of hodograph-like solutions to the physical plane. The maximum amplification for this class of signals of fixed amplitude depends on the width of the incoming signal. The solutions contain reflected shock waves that satisfy the appropriate shock jump conditions, provided the width of the incoming signal is greater than a certain critical value.

Interaction of a Shock Wave with a Turbulent Boundary Layer Disturbed by Injection

Abstract: An experimental investigation has been made to study the interaction between an incident oblique shock wave and a turbulent boundary layer on a solid surface downstream of a porous surface with air injection through the porous surface. The results are clearly of direct interest to the design of cooled turbine blades. However, the boundary-layer profiles in the absence of the shock are similar to those in a boundary layer subjected to an adverse pressure gradient so that the results at the interaction also give some indication of the effects of an isentropic compression upstream of a shock/boundary-layer interaction. The experiments show the surprising result that the shock strength to produce incipient Separation is virtually independent of the shape of the boundary-layer profile upstream of the interaction, although the scale of the interaction increases with increase in the injection rate.

Numerical investigation of shock starting of supersonic nozzles and comparison with experimental data

Abstract: A numerical investigation was made of the interaction of a shock wave with a contracting and expanding channel in the process of shock starting of planar and axisymmetric supersonic nozzles. The calculated results are compared with experimental data. The justification is given for the use of a method based on integration of the one-dimensional nonstationary equations of motion of an inviscid gas with allowance for a variable specific heat in the calculation of the propagation of wave structure in the nozzle starting process. The influence of the shape of the entrance opening of the reflecting channel during the nozzle starting is considered.

Ionization and nonequilibrium radiation of air behind strong shock waves

Abstract: It is shown that at high velocities of shock waves (V ≳ 9.5 km/sec) an important factor influencing the rate of ionization is the depletion of the number of excited states of the atoms through de-excitation. In the case of low pressures (p∞ ≲ 1 torr) and for a bounded and optically transparent region of gas heated by the shock wave (for example, for the motion of gas in a shock tube or in a shock layer near a blunt body), the effective ionization rate kf depends on the pressure [1], which leads to violation of the law of binary similarity which holds under these conditions without allowance for de-excitation. On leaving the relaxation zone, the gas arrives at a stationary state with constant parameters differing from those in thermodynamic equilibrium. The electron concentration and also the radiation intensity in the continuum and the lines are lower than the values for thermodynamic equilibrium. These considerations explain the results of known experiments and some new experiments on ionization and radiation of air behind a travelling shock wave.

Characteristics of Free Surface Shock Waves around Wedge Models

Abstract: Characteristics of free surface shock waves are experimentally investigated with wedge models, which clarify the ways how the occurrence of free surface shock waves at the bow is ruled by velocity of advance, draft and entrance angle. The variation of shock angle is very similar to that of shock waves in shallow water. Application of nonlinear shallow water theory is attempted by introducing equivalent shallow water depth that connects shock waves in deep water with those in shallow water. The estimations of shock angle and resistance due to free surface shock waves turn out successful for the improvement of hull forms.

Evolution of the initial ionizing discontinuity in a transverse magnetic field

Abstract: The problem of the non-stationary evolution of the magnetic structure of transverse ionizing shock wave, arising from a gas-dynamic shock wave ahead of a piston moving into an initially neutral gas, is solved. Photo-ionization of the cold gas ahead of the shock front by the radiation of the shock-heated gas is taken into account. When the stationary regime is achieved, the structure and boundary conditions are those obtained previously for stationary ionizing shock wave (Liberman and Velikovich, 1978). The time of achieving the stationary regime depends on the magnitude of the electric field ahead of the initial gas-dynamic discontinuity and the intensity of the precursor photo-ionization. The results of computation for shock waves in hydrogen are in good agreement with the measurements of Stebbins and Vlases (1968).

Transonic Shock Wave - Boundary Layer Interactions.

Abstract: : A series of 2D experiments was performed in a large-scale Ludwieg tube to investigate the interactions of a normal shock with a turbulent boundary layer at unit Reynolds numbers 14.8 million and 29.5 million/m and Mach numbers 1.43 and 1.60. In addition, the effects of a diverging flow field downstream of the shock, such as that which might be encountered on an airfoil, were explored by testing with a shock holder having a perforated top wall. The latter experiments were performed at the two Reynolds number values of 9 million and 35 million. Results show that unit Re variations affected the interacting flow only by changing the boundary layer entering the interaction. The surface pressure distribution normalized by the thickness of the incoming boundary layer, which was measured in each experiment, describes an interaction independent of unit Re. In contrast, the interaction flow field was found to be very dependent on Mach number and on constrainment of the subsonic region. In fact, shock configuration, surface pressure, skin friction and velocity profiles were found much more sensitive to these parameters than to the Reynolds number, which was investigated in earlier studies. the bifurcation height and the length of separated flow increased with increasing M. Both quantities responded dramatically to the moderate but sustained flow deflections imposed by the perforated shock holders. The initial rise in surface pressure was found to correlate directly with the height of the bifurcated shock structure.

Strong cylindrical shock in a rotating gas

Abstract: A characteristic method has been used to study the propagation of a strong diverging cylindrical shock wave through a rotating gas. An analytical expression for shock velocity has been obtained. It is shown that, for smaller values of the propagation distancer, the shock velocity must decrease with shock propagation; for larger values ofr, however, it must increase with further advancement of the shock. The shock propagation distance corresponding to the minimum value of the shock velocity has also been obtained.

Shock waves in relativistic nuclear matter. I

Abstract: We develop the relativistic Rankine-Hugoniot relations for a three-dimensional plane shock and a three-dimensional oblique shock. Using these discontinuity relations together with various equations of state for nuclear matter, we calculate the temperatures and the compressibilities attainable by shock compression for a wide range of laboratory kinetic energy of the projectile.