Detachment Distance Research Articles

The influence of relaxation on shock detachment

By establishing that the length scale governing the detachment of a shock wave from a wedge is the distance from the leading edge to the sonic line, and by considering the view of observers with different length scales, it is predicted that the detachment distance increases gradually with wedge angle for relaxing flow and more rapidly in a perfect gas. Both of these features are confirmed by experiments in the free-piston shock tunnel. The influence of other length scales is discussed. The phenomenon is related to a relaxation effect in which a subsonic layer grows from the translational-rotational shock as the wedge inclination is increased beyond the frozen sonic point.

Shock detachment distance at near sonic speeds

Shock detachment distance at near sonic speeds

Application of the measurement of shock detachment distance at low supersonic speeds

Application of the measurement of shock detachment distance at low supersonic speeds

Flow-establishment times for blunt bodies in an expansion tube

Flow establishment results are presented as obtained from shock standoff distance, pressure, and heat transfer measurements in the Langley expansion tube. The models tested were flat-faced cylinders with varying radius and a sphere with a constant radius, and they were positioned at the acceleration section exit and tested in the open jet at zero angle of attack. The experimental results were obtained as spinoff from various studies using helium, air, and CO2 test gases at freestream velocities in the range 5-7 km/sec. Time histories of shock detachment distance illustrate that the shock formation about the smaller-radii flat-faced cylinders and the sphere is symmetrical, whereas a complex, asymmetric formation is observed for the larger-radii cylinders. Flow is shown to establish more readily about the sphere than a flat-faced cylinder of the same diameter. A quasi-steady flow exists about relatively large blunt models during two-thirds of the approximate 250-microsec expansion tube test period.

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.

Shock Detachment Distance for Flow around Cylinders and Spheres

Shock Detachment Distance for Flow around Cylinders and Spheres

Method of Intergal Relationsによる鈍頭物体まわりの流れの研究

Systematic calculations over blunt bodies of simple shapes are carried out for two-dimensional and axisymmetric flows at high Mach number. Emphasis is placed on detachment distance and accuracy of results obtained by Method of Integral Relations. And the relation between the accuracy and uniform flow Mach number was investigated.For flows at high Mach number, it was concluded that the sufficient accuracy was obtained even by the lowest approximation.The study of flow patterns for two-dimensional and axisymmetric bodies made it clear thatthis method is more suitable for axisymmetric bodies than two-dimensional bodies in the flows at higher Mach number.

The effect of wall temperature on the low Reynolds number hypersonic stagnation region shock layer

The effect of wall temperature on the behavior of the hypersonic stagnation region shock layer in incipient merged layer flow is described. The enthalpy function profile across the shock layer is obtained. The shock detachment distance is shown to be subjected to the compensating corrections of an “inflow” effect due to velocity slip and an “outflow” effect due to temperature jump, with the main contribution coming from the over-all density decrease due to wall heating. The net corrections render the shock detachment distance to remain relatively constant with K 2 for a fixed wall temperature, where K 2 is the rarefaction parameter. The ratio of heat flux behind the shock wave to that at the wall is shown to be independent of the wall temperature and is essentially the same as the corresponding ratio when slip effects are absent.

Dissociation effect on the hypersonic flow past a circular cylinder

The effects of dissociation of air on hypersonic flow past a circular cylinder at zero angle of incidence are considered under the assumptions that the shock wave is in the shape of a circular cylinder, the density ratio across the shock is constant, the flow behind the shock is at constant density and dissociation occurs only behind the shock wave. In the present paper, the velocity, pressure and drag coefficients, vorticity, shock detachment distance, stagnation point velocity gradient and sonic points on the shock and the surface have been obtained in the presence of dissociation. The results have been compared with the corresponding results obtained in the case when dissociation dose not occur and the corresponding results in the case of the sphere in the presence of dissociation.

Experimental investigation of shock wave detachment in real gases

A method is proposed for measuring the detachment distance of the forward shock wave from the surface of a free-flying blunt body. The effect of excitation of vibrational degrees of freedom of the gas on the position of the detached shock wave is investigated for air and carbon dioxide.

Stagnation-point heat transfer and shock- detachment distance for ellipsoids of revolution

Stagnation-point heat transfer and shock- detachment distance for ellipsoids of revolution

鈍頭物体の先端付近における非平衡流

Analyses have been made of the effects of coupled chemical and vibrational rate processes in external hypersonic flows at high enthalpy levels. Exact (numerical) solutions have been obtained by the inverse method for inviscid nitrogen gas flows over a circular cylinder under the conditions where nonequilibrium prevails through the nose region. The results illustrate the general importance of the coupling among the chemical and vibrational rate processes. In order to sustain a prominent effect of pre-shocknonequilibrium, values of shock wave detachment distance have been compared under the condition of the same total enthalpy.

Hypersonic flow past a sphere

The effects of dissociation or ionization of air on the analytical solution for hypersonic flow past a sphere are considered here, under certain assumptions. It has been assumed that the shock wave is in the shape of a sphere, that the density ratio across the shock is constant, that the flow behind the shock is at constant density and that dissociation or ionization only occurs behind the shock wave. Thus the effects of the compressibility of the air, variation of density ratio along the shock, and the department of the shock shape from being circular are not taken into account. Here the velocity, pressure, temperature, pressure coefficient and vorticity, etc., at any point between the shock and the surface of the sphere in the presence of dissociation or ionization are obtained. In addition, shock detachment distance, drag coefficient, stagnation point velocity gradient and sonic points on the shock and the surface have also been obtained. The results have been compared with the corresponding results obtained in the case when dissociation or ionization does not occur behind the shock.

Shock detachment distance for blunt bodies in argon at low reynolds number

Shock detachment distance for blunt bodies in argon at low reynolds number

Rocket exhaust impingement on a ground surface

The impingement of a rocket jet, exhausting into a vacuum, onto a solid surface is examined using the Newtonian approximation to analyse the transonic region. The jet exhaust into an unbounded vacuum required for this analysis is simplified as a quasi-radial flow using an exact calculation as a basis. Two examples are calculated giving the shock detachment distance and the ground pressures as a function of the rocket altitude.

Experimental Effect of Bluntness and Gas Rarefaction on Drag Coefficients and Stagnation Heat Transfer on Axisymmetric Shapes in Hypersonic Flow

X« = mean free path behind sphere shock A = sphere shock standoff distance FQ = drag force m = mass a = acceleration T,nin = minimum activation temperature of paint = 400°K T = wall temperature n = spectral order number, 3, 5, 7 X = wavelength of light in Angstrom units Inverted hemispheres, circular discs (normal to stream), spheres, 26° total angle 0.368 blunt hemisphere cones, 18° totalangle sharp cones, and other axisymmetric shapes were run in a hyper velocity wind tunnel. Hypersonic drag coefficients at zero angle of attack were measured in the air velocity range, 7,00020,500 ft/sec and Knudsen number range, 0.0001-0.34. Drag coefficient is defined as drag for c<t/qA JL. Knudsen number is defined as 1/3 mean free path behind shock/sphere shock detachment distance. In the case of nonsphere shapes, the Knudsen number is denned as the Knudsen number of a sphere with the same base diameter. These drag coefficients cover the range of gasdynamics to free molecule flow and are given in graphical form. The drag coefficients were measured by means of a ballistic balance in millisecond intervals, and referenced to the drag coefficient of a sphere in the gasdynamics region, for a gamma of 1.4, of 0.92. Tunnel stagnation conditions of pressure, temperature, density, and pressure drop with time were measured directly. In the tunnel test section, velocity, q density, total pressure, and static pressure were measured directly. These experimental curves have been found useful in the analysis of complex shapes if the complex shapes can be easily broken down into simple components with small interactions between components. Heat-transfer distributions have also been obtained on these and other complex shapes in the hypervelocity wind tunnel, by means of a special paint which changes through several visible spectral orders within a heat transfer range of X10 for a single application. Heat transfer rates, so obtained, have been performed in the hypersonic gasdynamic and slip flow regions and are presented for spheres. These data, in the vorticity interaction region, agree with the data of Ferri and Zakkay.*

Blunt Body Viscous Layer with and without a Magnetic Field

The present paper is mainly concerned with the solution for the viscous flow in the shock layer about the stagnation region of a sphere in hypersonic flow. The Reynolds numbers considered are in a range too low to apply usual boundary layer theory within the shock layer, but are large enough that the shock wave may be regarded as a discontinuous surface. This viscous layer problem has been studied previously by Probstein. With the assumption of constant density in the shock layer an analytic solution is applied to this problem both with and without an applied magnetic field. This solution makes use of the fact that the ratio of the density ahead of the shock to that behind the shock (ε) is small. The solution has been found in analytic form to first order in ε. In the nonmagnetic case numerical results for both the shock wave detachment distance and skin friction are presented for a value of ε = 0.1 and they are shown to be in good agreement with the exact numerical calculations of Probstein and Kemp. Numerical results are also presented on the effect of an applied magnetic field on both the shock wave detachment distance and skin friction. It is found that for a fixed value of ε and Reynolds number the skin friction decreases and the detachment distance increases for increasing values of the magnetic field parameter S which is proportional to the magnetic pressure divided by the total pressure.

On the Numerical Calculation of Detached Bow Shock Waves in Hypersonic Flow

A method is described for calculating examples of hypersonic flow with a detached bow shock wave past a bluff axially symmetric body. The form of the shock wave is assumed, and the analysis is based on a Cauchy problem for the stream function in the subsonic region, where the motion is governed by a partial differential equation of elliptic type. Through analytic continuation into the complex domain, the Cauchy problem is reformulated in such a manner that it becomes properly set in the subsonic region. This leads to a stable scheme for computation of the flow by finite differences. Numerical examples at freestream Mach Number 5.8 are presented in which the flow is determined throughout the subsonic region, and, in particular, the detachment distance, the location of the sonic line, and the pressure distribution along the body are calculated. These results are in excellent agreement with experimental data obtained at the California Institute of Technology.

The High Speed Flow of Gas Around Blunt Bodies

SummaryA number of results derived by the author in earlier reports on the flow of air around blunt bodies moving at high speed are here collected in a unified analysis. The theory predicts in a satisfactory way the shock shape and detachment distance for two blunt bodies, a flat disc and a sphere. It is shown that the density ratio across a normal shock is a useful parameter, combining the effects of both the free stream Mach number and the ratio of specific heats.

Two-Dimensional Bow Shock Wave Detachment Distances

In the recent paper by Warren a summary was made of current data on two-dimensional bow shock wave detachment distances. It was shown that the experimental results of Griffith and Alperin, as well as the detachment distances computed by Vincenti and Wagoner, could be collapsed into a single curve by using Spreiter's Transonic Similarity Parameter. This has been confirmed by the present authors who have found that the experimental results for wedges obtained by Bryson also correlate favourably with the curve given by Warren (Fig. 3 of Ref. 4).The results of the foregoing workers have been for steady flow conditions. However, it has been noted by Lilleyet aliathat a steady shock wave pattern can be established in free flight only after steady motion has been maintained for a considerable (infinite) time. In general, the locus of detached bow shock waves depends on the time history of the motion whenever a body is accelerated from subsonic speed.