Position Of Shock Wave Research Articles

Unsteady wave structure near separation in a Mach 5 compression rampinteraction

Fluctuating wall-pressure measurements have been made under the unsteady separation shock and the separated shear layer in a Mach 5 compression ramp-induced turbulent interaction. The freestream unit Reynolds number was 49.6x10 6 m -1 and the turbulent boundary layer developed on the tunnel floor under approximately adiabatic wall-temperature conditions. Conditional sampling and «variable-window» ensemble-averaging techniques have been used to determine ensemble-averaged pressure distributions for different separation shock-wave positions.

Sideslip effects on fin-fin interference in supersonic missile aerodynamics

The supersonic missile fin-fin interference factor K0 is a measure of the normal force change on a fin, in the presence of a body and other fins, caused by changes in sideslip angle. A finite-difference Euler code, SWINT, is used to numerically determine the fin forces for different sideslip angles for two-, three-, four-, and six-fin missile configurations at small angles of attack. The fin forces are used to evaluate K^ at Mach numbers from 2.5-3.5, positive arid negative sideslip angles, and various fin aspect ratios. The K+ values from SWINT for two-fin configurations have similar magnitudes to those from previously published slender body theory analytical solutions; however, the SWINT predictions for four-fin configurations show that K+ breaks away sharply from the slender body theory values as the fin span increases. The fin span at which the breakaway occurs is shown to be directly related to the position of shock waves and expansion fans originating from neighboring fins. The breakaway fin span is also shown to be a strong function of the number of fins, Mach number, and sideslip angle. Values of K^ for use in preliminary design are presented.

Studies of Condensation Shock Waves : 2nd Report, Relation between Condensation Shock Wave and Condensation Zone

A rapid expansion of moist air or steam in a supersonic nozzle gives rise to condensation phenomena and a condensation shock wave appears in the supersonic section of the nozzle. In the first paper, the mechanism of the formation of a condensation shock wave was studied. In the condensing process, nonequilibrium process of condensation by homogeneous nucleation is followed by equilibrium process of condensation where saturated expansion takes place. In the present study, the nonequilibrium condensation region has been experimentally investigated, and the relation between the position of the condensation shock wave and the nonequilibrium condensation region has been clarified. Furthermore, the flow field of condensation zone with and without a condensation shock wave has been well explained by the results of optical observations and pressure measurements.

Point explosion simulation by fast spark discharges

It is shown here that the late hydrodynamic effects of fast spark discharges (dI/dt‖t=0≥1010 A/sec), i.e., after the discharge period, can be described by a point explosion simulation. The solution is not self-similar since counterpressure has to be taken into consideration. This non-self-similar model is confirmed experimentally by shock wave position and velocity measurements.

Studies of condensation shocks (2nd report, Relation between condensation shock and condensation zone)

A rapid expansion of moist air or steam in a supersonic nozzle gives rise to condensation phenomena and a condensation shock wave appears in the supersonic section of the nozzle. In the first paper, the mechanism of the formation of a condensation shock wave was studied. In the condensing process, nonequilibrium process of condensation by homogeneous nucleation is followed by equilibrium process of condensation where saturated expansion takes place. In the present study, the nonequilibrium condensation zone has been experimentally investigated, and the relation between the position of the condensation shock wave and the nonequilibrium condensation zone has been clarified. Furthermore, the Flow of condensation zone with and without a condensation shock wave have been wall explained by the results of optical observations and pressure measurements.

Turbulence Modeling for Unsteady Transonic Flows

Conditionally sampled, ensemble-averaged velocity measurements, made with a laser velocimeter, were taken in the flowfield over the rear half of an 18% thick circular arc airfoil at zero incidence tested at M = 0.76 and at a Reynolds number based on chord of 11 x 10(exp 6). Data for one cycle of periodic unsteady flow having a reduced frequency f of 0.49 are analyzed. A series of compression waves, which develop in the early stages of the cycle, strengthen and coalesce into a strong shock wave that moves toward the airfoil leading edge. A thick shear layer forms downstream of the shock wave. The kinetic energy and shear stresses increase dramatically, reach a maximum when dissipation and diffusion of the turbulence exceed production, and then decrease substantially. The response lime of the turbulence to the changes brought about by the shock-wave passage upstream depends on the shock-wave strength and position in the boundary layer. The cycle completes itself when the shock wave passes the midchord, weakens, and the shear layer collapses. Remarkably good comparisons are found with computations that employ the time-dependent Reynolds averaged form of the Navier-Stokes equations using an algebraic eddy viscosity model, developed for steady flows.

渦後流内の衝撃波

The density gradient is, in some cases, observed near the body surface when a pair of vortices in vortex wake, which develops behind vehicle flying in supersonic speed with incidences, is still stable and their strength is enough strong. The purpose of this paper is to examine the mechanism responsible for the generation of this density gradient and to find out it's characteristics. The systematic experiments including pitot tube traverse and schlieren photographing are conducted and further the computational simulation of the flow field are carried out, the flow model of which is two dimensional jet impingement. Their results are readjusted as follows.1. There is an entropy jump across this density gradient.2. The flow field caused by interaction between the boundary layer and this density gradient turning down by other shock wave is similar to that of shock-boundary layer interaction.3. The position of shock wave obtained by computational simulation is almost coincident with that of this density gradient observed on the schlieren photographs.On the base of the reasons above mentioned, it is confirmed that this density gradient is shock wave, which is produced by blowdown of a pair of vortices. And if there are stable vortices being enough strong and their space is favorable, it is concluded that this shock wave is surely observed near the body surface in vortex wake even in the cases of wider range of Mach number and more complicated body shapes.

Unsteady transonic flows with shock waves in an asymmetric channel

Abstract : Two-dimensional inviscid, unsteady transonic flows with shock waves in asymmetric channels with arbitrary wall shapes are investigated, using the method of matched asymptotic expansions. With the exception of thin regions in the neighborhood of the channel throat and the neighborhood of the shock wave, solutions found using linearized governing equations are valid. In the regions enclosing the shock wave, an inner solution which satisfies the shock jump conditions and matches with the outer solutions, is presented. The shock shape is found as part of the solution, which is obtained numerically using the method of integral relations. A composite solution, uniformly valid throughout the channel, and the relation between the instantaneous shock wave position and back pressure far downstream are presented. (Author)

Shock loading on a submerged structure

The problem of propagation of a two-dimensional shock wave in water over a submerged rigid structure (semicylinder) due to a nearby underwater explosion has been solved numerically using a method of characteristics based upon a curvilinear co-ordinate system fixed in successive shock wave positions. Maximum surface pressures occur at the transition from regular to irregular reflection, and nonlinear theory appears essential there, even for shocks of Mach number close to unity. Results are given for a range of explosive strengths, distances from the structure, and structural dimensions.

Investigation of the expansion side of a delta wing at supersonic speed.

An experimental investigation has been made of the flowfield on the expansion side of a flat delta wing with a semiapex angle of 45.3° and an angle of incidence of 12°. The measurements were performed at a Mach number of 2.94 in a 15 cm x 15 cm blow-down wind tunnel at a Reynolds number of 5 x 105 per cm. A five-hole conical-head probe, measuring pitot pressure and flow angularity, was used to explore the flowfield. The main purpose of the experiments was to determine the shape and position of the inboard shock wave and of the conical sonic line, the latter being the locus of points where the conical Mach number is equal to unity. The conical Mach number was derived as the Mach number of the local velocity component normal to a ray through the apex of the delta wing. A comparison of measurements performed in different planes normal to the root chord showed that the flow may be considered as conical. The obtained results suggest that the conical sonic line and the inboard shock wave meet in a point well inside the central region of the flowfield (in this region the influence of both the left half and the right half of the delta wing is felt). The results agree very well with numerical calculations using a shock capturing technique. A flow model is discussed based on the present investigation.

Approximate analytic solution for the position and strength of shockwaves about cones in supersonic flow

Approximate solution for position and strength of shock waves about cones in steady supersonic flow

The Displacement of the Nose Shock Wave from a Pitot Tube under a Streamwise Velocity Gradient

Summary:—The pressure reading of a pitot tube in a supersonic flow corresponds to the position of the nose shock wave. Results of measurements of the shock stand-off distance are presented for three different streamwise Mach number gradients and for a uniform flow. These results are compared with existing theoretical values.

ELECTRICAL RESISTANCE AND SHEATH POTENTIAL ASSOCIATED WITH A COLD ELECTRODE

The boundary-layer resistance and the difference in sheath potentials between a pair of electrodes were measured in a shock tube. Using a small, square electrode and a strip electrode flush with the wall of the shock tube, the electric current could be drawn across the shock tube was measured as a function of the shock wave position for several applied voltages and load resistances. All measurements were made in air at a shock speed of 4.35 mmn/ mu sec and an initial pressure of 1 mm Hg. In the range of applied voltages considered, the boundary-layer resistance was not a function of the current level. The change in the sheath potential was of the order of several volts. A continumm theory is developed to predict the boundary-layer resistance for small current levels and the sheath potential. The sheath solution is separated from the convective compressible boundary-layer problem where ambipolar diffusion dominates. In the sheath, the transport equations for ions and electrons in and electric field are solved numerically. Resulting integrals for the dimensionless boundary-layer resistance and sheath potential are evaluated, both in the sheath and in more » the compressible boundary layer, to obtuin results that can be compared with experiment. Values of the resistance obtained, assuming the ionization reaction to be frozen, are not in agreement with experiment. Reasonable agreement between theory and experiment is obtained for the magnitude of the sheath potential. (auth) « less

Some Comments “On The Effect of Shock-Induced Turbulent Separation on the Shock-Wave Position in a Nozzle”

In Ref. 1, Professor D. W. Holder describes a very interesting experiment pertaining to shock wave position and boundary layer separation in supersonic nozzles at low Mach numbers (M ⩽ 1·4). A closer examination of this experiment indicates that the results may only be applicable in the Mach number range of M < 1·48, not in the range of M> 1·48.

On the Effect of Shock-Induced Turbulent Separation on the Shock-Wave Position in a Nozzle

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Continuous Oscillographic Method for Measuring the Velocity and Conductivity of Stable and Transient Shocks in Solid Cast Explosives

The continuous monitoring of the position and relative conductivity of reactive shock waves in confined cast explosives is made possible by a new technique. A fine Nichrome wire is cast within and parallel to the long axis of the sample. A record of its resistance during detonation serves to locate the ionization front associated with detonation. The measurement is recorded on an oscillograph. From the photograph of this record, instantaneous detonation velocities are measured to within ±2%. Attenuation of the initiating shock causes a delay in the establishment of a stable detonation in the acceptor. The distance and time required for this transition is confined charges can be measured. The simultaneous use of independent Nichrome and copper wire sensors furnishes additional information about the conductivity of the predetonation zone. Failure of a propagating detonation can also be studied; this permits the measurement of critical diameters, i.e., that diameter below which detonation will not propagate in an unconfined charge. Examples of each use are presented.

The Shock Pattern of a Wing-Body Combination, Far from the Flight Path

SummaryThe position and strength of the front shock wave at large distances from a wing-body combination, are deduced from the linear theory for the combination, using a method developed by Whitham. The combination consists of a body of revolution and a wing which has thickness and is lifting. The effects of interference between the flow over the body and the flow over the wing are included. In any direction the flow far from the wing-body combination is equivalent to the flow past a body of revolution determined from the configuration of the combination. The modified formulae for unsteady flow are given and some results are evaluated for the combination of a body of revolution and a delta wing with subsonic leading edges.