Conical Shock Research Articles

Ducted propagation of Concorde-generated shock waves

Measurements with an array of low-frequency microphones are compared to ray calculations, describing the long range propagation of acoustic energy from the shock cone of the Concorde SST. This energy is ducted between the surface and the strong sound velocity gradient of the upper stratosphere. The measured pressure signatures are composed of one to five distinct wave groups arriving over a period of minutes; the number and sequence of arrivals is different for the Dulles-bound and JFK-bound airplanes. With respect to arrival time and azimuth of phase propagation, we find close correspondence between the highest amplitude wave groups and the refracted arrival predicted by ray calculations. Subsidiary wave groups apparently result from the diffracted ’’ground’’ wave and from volume scattering of acoustic energy into shadow zones.

The Effects of Sonic Boom on the Ecological Environment

It is expected that the number of military and civil aircraft operating supersonically all over the world may remain the same during the next decade. The problem of sonic boom, which has been by-passed for military aircraft through the assignment of specially allocated ranges for supersonic operation, is still with us and is likely to influence the operation of supersonic transport (SST) aircraft, the Concorde and the Tupolev 144. Concorde is still short of reaching the break-even point, despite the large traffic gain registered on the routes to North and South America. The problem is to get overland routes; the difficulties encountered by the UK in the discussions with India and Malaysia for the establishment of a London–Bahrain–Singapore route are well known.Before presenting the effects of the sonic boom on the ecology it may be well to summarize the nature and the main features of this phenomenon.(i) The N-wave signature. A complex body like an aircraft, moving in supersonic flight, generates a pattern of local shock waves which tend to coalesce in two main shock cones, the front (or bow) and tail, as the distance from the aircraft increases. A shock wave is a discontinuity surface for the thermodynamic characteristics of the fluid, the most important being the static pressure jump responsible for the N-shaped pressure signature characteristic of the sonic boom. Other parameters are of minor importance to the environment. A shock signature is denned by the following parameters:

The Axisymmetric Impingement of Supersonic Air Jets on Cones

SummaryThis paper reports an experimental investigation into the impingement of three jets from a convergent, conically divergent nozzle on to three cones of apex angles 120°, 90° and 60°. The exit Mach number of the nozzle was 2.2 and the jets were produced by operating with ratios of nozzle lip pressure to ambient pressure of 1, 1.2 and 2. The cones were arranged symmetrically in the jets at nozzle to apex distances of 0, 1 and 2 times the nozzle exit diameter. Surface pressures and shadowgraph pictures are presented. The most striking feature of the flows is the shock pattern produced by the interaction between the cone shock and the jet shock. This pattern can take a wide variety of forms depending on the structure of the free jet and strongly influences the form of the surface pressure distribution. For the most part, the flows can be explained on the basis of inviscid behaviour.

Axisymmetric accretion near compact objects

Similarity solutions relevant to axisymmetric gas flows about compact objects are developed on the assumptions that the gravitating object is a point mass and the flow region of interest is much smaller than the accretion radius. Gasdynamic equations are given for steady adiabatic flow with azimuthal symmetry in a point gravitational field, conditions are placed on physically appropriate solutions, and asymptotic solutions near the accretion axis are considered. The equations are integrated numerically to determine the value of the shock cone angle and the variation of flow parameters within the entire shock cone. The significance of the specific heat ratio is examined, and the origin of the shock front is discussed. It is found that axisymmetric accreting solutions occur only for a specific heat ratio less than 5/3 in all but one case and that the shock angle depends on that ratio, with shock detachment indicated when the ratio equals 5/3. The results also confirm a tendency to form a high-density region around the accretion axis.

A NUMERICAL METHOD FOR SUPERSONIC CONICAL FLOW WITHOUT AXIAL SYMMETRY

In this paper a numerical method for supersonic conical flow without axial symmetry was developed as follows: the governing equations for conical flow without axial symmetry were derived from a pair of stream functions of conical flow and a vorticity equation, and were transformed into Stocker & Mauger's coordinate system. By this method the numerical solutions were also presented for the supersonic flow past conical bodies which produced elliptic conical, nearly conical, and pseudo-triangular conical shock waves, and were compared with other investigator's solutions.

Computational Aspects of Nonsimilar Solutions of the Rarefied Leading Edge on a Cone Wesley

viscous layer is modeled after that of Yasuhara with modified external pressure field and boundary conditions. The original freestream boundary conditions of Yasuhara and the classical Rankine-Hugoniot conditions downstream of the conical shock are replaced by matching the mass flux, the tangential shear, velocity components, and state variables at the shock wave-viscous layer interface. Attention is given to the details of the initial data profiles. We also note the finite-difference form of the model equations which are required for the generation of a solution which is physically acceptable and mathematically selfconsistent. Heat transfer rate and viscous shear at the surface of the cone are computed. First-order corrections for shock curvature, velocity slip, and temperature jump at the cone surface are not considered in this paper. The proposed method does provide a straightforwar d means for including these effects.1 The following relations can be obtained by integrating the zeroth order conservation equations for the shock structure and applying the freestream boundary conditions: p°v°=-smds

Numerical simulation of flow during compression of cylindrical samples by a glancing detonation wave

The parameters of shock waves created in cylindrical samples of various materials during detonation of explosive charges surrounding them have been determined experimentally [1–3]. It was established that in a number of materials the reflection of a conical shock wave from the symmetry axis of a sample leads to the formation of a Mach triple shock-wave configuration which gives rise to a complex flow pattern in the region beyond the shock waves. Analytic study of irregular reflection is a complex problem. Solutions obtained under various assumptions about the nature of the flow are presented in papers reviewed in [4]. In the present paper, axisymmetric flow of detonation products (DP) and sample material in the region adjacent to the detonation front is determined from the solution of a two-dimensional, time-dependent problem in gasdynamics by the finite-difference method [5].

Holographic Studies of Shock Waves Within Transonic Fan Rotors

NASA has funded two separate contracts to apply pulsed laser holographic interferometry to the detection of shock patterns in the outer span regions of high tip speed transonic rotors. The first holographic approach used ruby laser light reflected from a portion of the centerbody just ahead of the rotor. These holograms showed the bow wave patterns upstream of the rotor and the shock patterns just inside the blade row near the tip. Much of the region of interest was in the shadow of the blade leading edge and could not be visualized. The second holographic approach, on a different rotor, used light transmitted diagonally across the inlet annulus past the centerbody. This approach gave a more extensive view of the region bounded by the blade leading and trailing edges, by the part span shroud and by the blade tip. These holograms showed the passage shock emanating from the blade leading edge and a moderately strong conical shock originating at the intersection of the part span shroud leading edge and the blade suction surface. Due to a limited viewing angle, the bow waves upstream of the rotor could not be observed, and only limited details of the trailing edge shocks were obtained. The results of these studies were promising. Reasonable details of the shock patterns were obtained from holograms which were made without extensive rig modifications. These studies indicated several advancements that would give even better results. Larger viewing windows, and holographic plates would permit a wider viewing angle and give much more coverage of the regions of interest. Shorter time delay for double-pulsed holograms is also desirable. This would minimize blade movement and give clearer holograms. With these improvements of technique effective visualization of shock configurations at least outboard of part span shrouds should be possible. Accurate definition of shock configurations will aid in attainment of improved transonic fan and compressor rotors.

Reynolds-shear-stress measurements in a compressible boundary layer within a shock-wave-induced adverse pressure gradient

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer-thickness Reynolds number were 4 and 105, respectively. The adverse pressure gradient was induced by an externally generated, conical shock wave.Mean and time-averaged fluctuating-flow data, including the experimental Reynolds shear stresses and experimental turbulent heat-transfer rates, are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed.From the results of the investigation, it is concluded that the shock-wave/boundary-layer interaction significantly alters the shear-stress characteristics of the boundary layer.

二次元鈍頭物体前方の衝撃波層におよぼす磁場の影響について

On the assumption that the flow field near the stagnation point in the cylindrical shock layer is incompressible, inviscid and having a constant conductivity, the standoff distance of detached shock wave ahead of two-dimensional blunt bodies in the hypersonic flow under the influence of magnetic field is analyzed.Using a conical electromagnetic shock tube of 90m/mφ, detachment distances in front of two dimensional models as well as an axially symmetric model are measured with a rotating mirror camera and condenser banks to make magnetic field.Comparison is made concerning to the relation of nondimensional distance Δ/ΔNM to the value of Q at the stagnation point or Q*.Experimental values of Δ/ΔNM show rather good agreement with the theoretical results in the two dimensional case as well as the axially symmetric case.

Waves in an elastic medium generated by a point source moving in an overlying fluid medium

Elastic waves coupled to atmospheric compressional waves radiated from a supersonic moving point source are considered. The point source has the form. $$\operatorname{Re} [(vt - z\cos \alpha )^2 - r^2 \sin ^2 \alpha ]^{ - 1/2} fort > zcos\alpha /v,0< \alpha \leqslant \frac{\pi }{2},$$ describing a conic shock wave whose vertex is moving uniformly with a velocity δ, δ=v/cosα>v. An exact expression is derived for the motion of an elastic half-space excited by the moving point source in an overlying fluid half-space.

Photoelectrons and solar wind/lunar limb interaction

It is suggested that boundary conditions for solar wind/lunar limb interactions are active. The ‘whole-Moon’ limb does not evoke a shock cone because warm (≃13 eV/electron) solar wind electrons are replaced by cool (≲2 eV/electron) photoelectrons that are ejected from the generally smooth areas of the lunar terminator illuminated at glazing angles by the Sun. A localized volume of low thermal pressure is created in the solar wind by these cool photoelectrons. The solar wind expands into this turbulence-suppressive volume without shock production. Conversely, directly illuminated highland areas exchange hot photoelectrons (> 20 eV/electron) for warm solar wind electrons. The hot electrons generate a localized pressure increase (Δp) in the adjacent solar wind flow which evokes a shock streamer in the solar wind. Shock streamers are identifiable by a coincident increase in the magnitude (ΔB ∼ Δp) of the solar wind magnetic field immediately external to the lunar wake. Shock occurrence is controlled by lunar topography, solar activity in the hard ultraviolet (> 20 eV), solar wind electron density and thermal velocity, and the intensity of the solar wind magnetic field.

Resonant coupling of ocean Rayleigh waves to atmospheric shock waves from Apollo rockets

Trains of seismic waves with periods between 25 and 12 sec commence at Bermuda 17 min after lift-off of Apollo (Saturn 5) rockets from Cape Kennedy, Florida. The signal, which is identified as Rayleigh mode and first shear mode waves, persists for as long as 7 min. Generation of the entire train is shown to be possible by resonant coupling to the rocket shock cone as it travels across the sea surface at phase velocities appropriate to the different wave periods observed. Arrival time for each phase can be accounted for by the time required for the rocket to reach resonant speed plus the time required for the shock to reach the surface from a height of about 175 km plus the seismic travel time at the appropriate group velocity. The long duration of the signal results from the fact that successively later arrivals have been generated earlier along the rocket trajectory.

Transition and Hot-wire Measurements in Hypersonic Helium Flow

Experiments have been performed to determine the influence of freestream disturbances on boundary-layer transition on sharp cones in a hypersonic wind tunnel. A constant current hot-wire anemometer was used to measure freestream and cone shock layer disturbances in two hypersonic helium tunnels. Comparison of these freestream and shock layer hot-wire measurements indicates that the disturbance level in percentage of local mean properties remains essentially unchanged by the cone shock. Transition Reynolds number was found to vary inversely with facility sound disturbance level and also to be strongly dependent on local Mach number.

Performance and Limitations of Shock Tubes with Imploding Detonation Drivers

Strong shock waves have been generated in a diaphragm shock tube using an imploding detonation driver of conical geometry. In comparing the performance of the conical driver to a Chapman–Jouguet detonation driver we have found that the conical driver provides comparable Mach numbers at considerably smaller ratios of driver to test gas filling pressures. For example Mach 10 was reached at a pressure ratio of 25 in the conical driver while a ratio of 100 is required to produce Mach 10 in a Chapman–Jouguet driver. In theory the Mach number available from a conical driver is expected to increase without bounds as the ratio of driver cone base to test tube diameter. A simplified model for this scaling is discussed and compared with experimental data. In addition an investigation of Mach number and shock attenuation versus cone slant angle is carried out in order to optimize the driver geometry.

Boundary Layer Closure in the Conical Shock Tube

The characteristics of the shock front produced in the Naval Ordnance Laboratory explosive driven conical shock tube differ both from those of its free-air analog and those of the shock in a conventional shock tube. The presence of walls makes it different from a free-air spherical explosion shock; the fact that it is in a diverging rough-walled cone makes it different from the conventional tube shock. Measurements of dynamic pressure and opacity of the gases behind the front and light output from the explosion gases were made near the wall of a conical tube at various distances from the site of an explosion. Results are interpreted in terms of turbulent boundary layer closure.

Aerodynamics of a Slender Cone with Asymmetric Nose Bluntness at Mach 14

T effect of nose shape asymmetries on the aerodynamics of a 10° cone (d= 5 in) was studied in ARL's 20-in.-hypersonic wind tunnel (M^ = 14.2, pt = 1500 psi, Tt = 2000°R, Re^d = 2.3 x 10, TJTt = 0.3, y = 1.4). Surface pressures were measured at various angles of attack and sideslip. Schlieren pictures were taken with a special nose model at several roll attitudes. Stability derivatives were measured by the free oscillation technique at the reduced frequency cod/IV^ « 0.003. The results are summarized and some conclusions relating to flight dynamics are drawn. Figure 1 shows a sketch of model A and the pressure distribution over the afterbody. The asymmetry of the nose tip is the result of a planar cut 40° off the x-z plane. The projected frontal area of the cut is approximately ^% of the base area. The schlieren picture on the left-hand side of Fig. 2 shows the shock contour in the x-y plane near the nose of model A. The plot below is a cross section of model and shock at the axial station l/L = 0.2. In the neighborhood of $ = 270°, the observed shock nearly coincides with the sharp cone shock, as given by the expression

Mach reflection parameters for plexiglas cylinders

The “collapsing air gap” method has been used to investigate the development and limiting parameters of the Mach reflection of a conical convergent shock in plexiglas cylinders arranged along the axis of a detonating explosive charge. The diameters of the cylindrical specimens varied from 15 to 100 mm. It is shown that on the stationary interval of development of the triple-shock configuration, where the velocity of the head wave is equal to the detonation velocity, there is a linear relationship between the diameter of the head wave, its radius of curvature, and the diameter of the cylinder.

Experimental investigation of the pressure profiles associated with the irregular reflection of a conical shock in plexiglas cylinders

Experimental investigation of the pressure profiles associated with the irregular reflection of a conical shock in plexiglas cylinders

Stress concentration in a cylindrical shell with an elliptical cutout

Equations (10) and (11) differ from the results of Lighthill and Whitham only by the appearance of the additional (7 + l)M*52/2j32 factor in the denominators. The validity of these equations easily can be checked by comparing results given by them with those obtained by numerically integrating the exact adiabatic equations of motion.3 The angular difference (e) between the shock cone and the undisturbed Mach cone is shown in Fig. 1 for two cone semiangles, 7.5° and 10°, as a function of Mach number. Results given by Eq. (11) are compared with those obtained from Whitham's formula2 and from cone tables.4 For the conditions illustrated, results from the present study show significantly better agreement with results from the cone tables, especially at the higher Mach numbers. As mentioned previously, any greater accuracy would have to be obtained by resorting to a uniformly valid second-order theory.