Shock Tube Flow Research Articles

Some Investigations of Shock Tube Flow : On the Propagation Behavior of the Initial Shock Front

Propagation behavior of initial shock front in a shock tube is investigated at moderate shock strength. Experimental result on the shock speed suggests the following flow model. At early stage of the diaphragm opening, a compression wave races into the driven gas, and it generates and intensifies a shock front. Once the maximum speed is achieved, the shock front gradually diminishes in intensity, overtaken by a rarefaction wave. A platinum wire heat gage is also used to confirm the validity of this flow model. The formation distance is more than 20 times the tube diameter, and becomes longer at larger diaphragm pressure ratio and lower driven gas pressure. Deviation of the maximum shock speed from the theoretically calculated speed depends mainly on the formation distance. The formation distance and the maximum Mach number are better correlated to diaphragm pressure ratio when parametrized by driven gas pressure. As a general remark the formation distance significantly affects the shock tube experiments as well as the shock Mach number does.

Direct shock tube measurements of oxygen-atom recombination rates

Oxygen-atom recombination rates have been measured over the temperature range 3000 to 3800 K using a method which affords direct control over the recombination process stimulated in a rapidly expanded sample of gas in a shock tube. A knife edge ‘trap’ was placed in the shock tube channel in order to provide partial reflection of incident shock waves. Density variations in the expanded gas region were measured with a quantitative interferometric chronometer by using the helium-neon laser as a light source. Simultaneous pressure measurements enable the relaxation effect to be detected from a comparison of the local change of pressure with the density variations. A strong temperature dependence for the recombination rate coefficients with the oxygen molecule as the dominant catalyst was obtained in the limits (2·0 to 0·4) × 10 15 cm 6 mole −2 sec −1 at 3000 to 3800 K respectively. The data agree well with recombination rates evaluated from dissociation rate measurements. Some gas dynamic applications of the results to quasi-stationary expanded shock tube flow analysis are discussed. Measured decay distances of the recombination relaxation in rarefaction waves generated in non-equilibrium flows around a corner are in accordance with the recombination rate data.

Compressible Boundary Layer-Inviscid Flow Interactions in Entrance Region of Internal Flows

The coupling between the inviscid flow and the compressible boundary layer in the developing entrance region for internal flows is analyzed by solving the particular inviscid flow-boundary layer interaction problem. The interaction problem is solved by postulating certain series forms of solutions for the inviscid region and the boundary layer. The boundary-layer equations and inviscid-flow equations are perturbed to third order and each generated equation is solved numerically. In order to preserve the universality of each of the perturbed boundary-layer equations, the perturbation parameter is described by an integral equation which is also solved in series form. The final results describing the interaction problem are then constructed for any given conditions by forming the three series to a consistent order of magnitude. This technique of coordinate perturbation is generalized to show how it may be applied to the entrance regions of pipe flows, including mass injection or suction, and also to the laminar boundary layers in shock tube flows. It demonstrates analytically the manner in which the boundary layer and inviscid flow interact and create a streamwise pressure gradient. In particular, the interaction problem which occurs in shock tube flows is solved in detail by the use of this generalized method, as an example.

Studies in expanded shock tube flows I. Probe studies of the expansion process

An apparatus for expanding high-temperature flows behind incident shock waves is de­scribed. Various types of probes for studying the low-density flows are examined and the performance of a double electrostatic probe is investigated in some detail. The characteristics of the signals obtained are interpreted in terms of the high temperature of the shock-heated gas and the expansion process. The properties of the molecular beam generated by the expan­sion are discussed.

Studies in expanded shock tube flows II. Interpretation of ion density profiles

Ion density profiles have been obtained in expanded shock tube flows from incident shock waves in argon and in air. The rate of increase of ion density and the ‘plateau’ level of ion density have been measured for shock waves in argon over the temperature range, 3670 to 10730°K, and in air over the range 2260 to 3790°K. The Arrhenius temperature coefficients obtained are much smaller than the ionization potentials of the major species involved and the results are interpreted in terms of a multi-step process involving impurity ionization. The changes in the physical properties associated with the flow through the expansion and their effect on the ‘freezing’ condition are also discussed. Evidence is also presented for vibra­tional equilibration during the expansion process.

Heat-transfer measurements with a catalytic flat plate in dissociated oxygen.

Heat-transfer measurements are presented which were obtained with catalytic and noncatalytic surfaces on a sharp flat plate. The experiments were made in a shock-tube flow of argon and dissociated oxygen, and are intended to provide a check on existing laminar boundary-layer theories. The design of the experiment is described, and the instrumentation and surface-conditioning requirements are discussed. Typical experimental data are presented to demonstrate the effects of shock-wave attenuation and other gasdynamic transients, and to show that these effects are negligible. The data obtained with the noncatalytic surface are compared with existing theories to demonstrate the importance of Prandtl number effects and variations in the p/j, product through the boundary layer. An approximate relation, based on an extension of Crocco's laminar boundary-layer theory, is given which accounts for these quantities and for surface recombination. It is found to be in good agreement with the data obtained with both the noncatalytic and the catalytic surfaces. The data obtained with both surfaces are used to infer the ambient atom concentration, as in diagnostic applications, and the inferred concentrations agree with those predicted using equilibrium theory with typical uncertainties of 5%.

Magnetically Driven Shock-Tube Flow Studies at High Velocities

An attempt to employ a magnetically driven shock tube as a tool for aerodynamic studies of high velocity and high enthalpy flows is described. Examples of results are given.

Fast-Response Total Thermal Radiation Detectors

The construction, calibration, and performance of thin-film heat-transfer gauges in a measurement of the total radiant intensity of air at superorbital entry conditions are discussed. It is shown that reliance on an electrical bridge calibration alone can cause erroneous results. Magnetic interference from the shock tube flow was identified and eliminated by model design and shielding. Thin-film gauges are shown to be fundamentally unsuited for total radiation measurements because of noise caused by vacuum ultraviolet irradiation. Pyroelectric thermal detectors avoid this difficulty and offer several other advantages over thin-film gauges. The basic equations and practical considerations in the use of pyroelectric gauges are discussed.

Ion Density Profiles behind Shock Waves in Air

Experimental results are reported for the ionization rate behind shock waves of Mach numbers between 7.2 and 9.2. The results were obtained using a hollow, total collector probe in combination with a 38-mm-diam, stainless steel shock tube designed to minimize the impurity level in the test gas. Good agreement was obtained with a theoretical result based on Lin and Teare's rate equations. Equilibrium ion densities in good agreement with theory were measured behind shocks of Mach number 7.2-12.8, with initial pressures between 0.5 and 40-mm Hg. The effects on the measurements of deviations from ideal shock tube flow were determined to be small. Ion densities measured range from 108 to 10 12 cm~3. At the higher ion densities there are large space charge effects inside the probe. Under these circumstances, proper operation of the probe still could be obtained provided the collector potential was not made too high. This implies that the mobility of the NO ions collected must be rather large. ON density profiles behind shock waves in air have been the subject of various recent investigations. Lin, Neal, and Fyfe1 made measurements in a low-density shock tube using microwave techniques and a magnetic induction device, in the range of shock Mach numbers Ms between 14 and 20. A theoretical analysis of their results based on chemical rate equations was given by Lin and Teare.2 Experimental results for even higher shock Mach numbers were reported by Wilson,3 who found that for shock Mach numbers above 27, electron densities become high enough so that electron impact reactions become dominant. At the lower temperature end experimental data have been obtained by Thompson, 4 who used a low-density shock tube in combination with microwave techniques, with infrared emission measurements, and with a hollow, total collector probe described by de Boer.5 The present investigation was undertaken in order to extend the range of measured profiles to still lower temperatures. At these temperatures, both the ion density and the ionization relaxation rate become much smaller, and it is impractical to use a low-density shock tube because the test time required is too long. A 38-mm-diam shock tube was used in combination with the hollow, total collector probe of Ref. 5. This probe has a very high sensitivity and can be used without difficulty in the regime of interest. The main problem to be overcome was the influence of impurities on the ionization rates. This problem could be solved by using great care in the experimental procedures.

Some Investigations of Shock Tube Flows : On the Propagation Behavior of the Initial Shock Front

Some Investigations of Shock Tube Flows : On the Propagation Behavior of the Initial Shock Front

Flow Nonuniformity in Shock Tubes Operating at Maximum Test Times

Shock tube flow nonuniformity is investigated in the limit where the shock and contact surface have reached their maximum separation. Ideal gases are considered. It is found that all fluid properties increase in value between the shock and contact surface. The nonuniformity is greatest when γ (ratio of specific heats) is large and Ms (shock Mach number) is low. For γ = 53 and Ms ≥ 3, the static temperature, density, and pressure increase by about 8, 12, and 20%, respectively; the stagnation temperature increases by about 35%, and the stagnation pressure, dynamic pressure, and stagnation point heat transfer increase by about a factor of 2. These results apply to turbulent as well as laminar boundary layers. The variation of flow properties with distance behind the shock, as well as particle time of flight, is given for both wholly laminar and wholly turbulent wall boundary layers. These results are particularly important for chemical rate and heat transfer studies.

Flow Modes in Electric Shock Tubes

Electric shock tube flow has been studied at low pressures, after cessation of the powering discharge, in a 4-in.-diam tube. Three modes of plasma flow down the tube are found: (1) a diffusion type of flow below 10 μ, (2) flow with a single luminous front, and (3) flow with a separated shock front and contact surface. The criterion for the appearance of flow with a separated shock wave appears to be Taylor stability of the contact surface. Since electric shock tube flow is always decelerating strongly, this occurs when the driver density becomes less than that of the shocked gas layer immediately ahead. As a result separated shock flow is more likely the weaker the powering discharge, the higher the ambient pressure, the less the erosion of the electrodes, and the further downstream one observes. These considerations are also found to be consistent with the observed behavior of a medium and a high-pressure shock tube.

Ion-Density Profile of the Flow in an Electric Shock Tube

The ion-density profile of the flow in an electric shock tube is measured by using probe method and the results are discussed under the assumption that the ion flow is one-dimensional, isentropic and electrohydrodynamic. The measured profile is considered to consist of two parts: one is a uniform region, and the other is a trailing region. In the trailing region there exists slightly excess ion of the order of the square root of the ion density in the uniform region. The effect of recombination on the peak value of the probe signal is briefly discussed.

Axial Temperature Gradient Distribution and Its Effect on Shock Tube Flow

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Estimates of Shock-Tube Precursor Infrared Excitation

A simple analysis is given for pre-excitation of molecular species in shock-tube flows by precursor infrared radiation. Estimates of rough magnitudes are given under shocked-gas temperature and pressure conditions corresponding to a Mach 5.5 shock propagating into 200 Torr of a 5% test gas, 95% argon mixture. It is found that the effect is slight for species of moderate infrared emission, such as CO, while it may be of some significance for species of high infrared emission, such as CO2.

Small Perturbation Theory for Shock-Tube Attenuation and Nonuniformity

Closed form expressions are derived, based on the concept of self similarity, for evaluating small perturbations of shock tube flow due to the wall boundary layer. Ideal diaphragm rupture is assumed. Extensive numerical results are obtained for the perturbations induced by the boundary layer in the driven gas, assuming that the boundary layer is wholly laminar or wholly turbulent. The driven gas is taken to be air. Various driver gases are considered. Attenuation results are obtained for shock Mach numbers up to 20. It is shown that the effect of the driver gas boundary layer on perturbations in the driven gas is small for large diaphragm pressure ratios. The results indicate that a shock tube with an efficient driver, e.g., helium, should have less attenuation for a given shock Mach number than would an inefficient driver, e.g., air. The latter result disagrees with existing experimental data. The source of the discrepancy is not known.

Hot Flow Length and Testing Time in Real Shock Tube Flow

The influence of viscosity on the hot flow length l and the testing time τ in shock tubes is investigated for the laminar and turbulent cases. Considering the case where the influence of viscosity can be treated as a perturbation of the ideal flow, it is shown that Mirels' theory, which takes into account shock-wave attenuation and wave reflections, can easily be used to evaluate l and τ. The limitations of the present theory are discussed and the results compared with the previous investigations. For the laminar case, the type of solution obtained is similar to that of Roshko. A ``maximum'' hot flow length, whose significance is mathematical rather than physical, because of the breakdown of the perturbation theory, is found. This ``maximum'' length is approximately twice as large as the one Roshko obtains when using his empirical value of √3 for the boundary layer parameter β. For the testing time in the turbulent case, the results differ somewhat from Anderson's.

The distortion of a magnetic field by flow in a shock tube

Induced magnetic fields in shock-tube flows have been measured by previous authors, in order to determine the electrical conductivity of ionized gases. Distortion of the applied magnetic field was taken to be small. In the present work, the full magnetic field solution is developed for idealized boundary conditions. At a magnetic Reynolds number equal to 4 the distortion is found to be considerable, but the field is well represented by a solution correct to third order in magnetic Reynolds number. The axial field in a real shock-tube configuration was computed, and experimentally measured fields were found to agree reasonably with theory.

Effect of Boundary-Layer Growth in a Shock Tube on Shock Reflection from a Closed End

The pressure behind a shock wave propagating in a constant-area duct increases slightly with time as a result of the growing boundary layer. This rise is considerably magnified by the shock reflection from the closed end of the duct. Analysis of the local interaction of the reflected shock with the boundary layer yields information on the shock configuration, but the combined effects of the waves produced by the growing boundary layer along the entire shock tube must be considered to obtain the state of the gas behind the reflected shock. The theory of the flow field behind the incident shock is modified to allow for effects in addition to boundary-layer growth which cause deviations from an ideal shock-tube flow. Experimental observations of the pressure rise behind the reflected shock, obtained for shock pressure ratios up to about 4.5 are in satisfactory agreement with the computed results, and estimates for stronger shock waves are presented.

Testing Time and Contact-Zone Phenomena in Shock-Tube Flows

Measurements have been made in a shock tube of the hot-flow duration, the structure of the contact front, and the nature of the mixing zone. The flow duration was obtained by spectroscopically detecting the first arrival of the driver gas, and is observed to become vanishingly small with decreasing initial driven gas pressure. These data and the data of Roshko and Duff are compared with predictions of Roshko's (laminar) theory and the numerical example of Anderson's (turbulent) theory. Agreement with the one point of Anderson's prediction is surprisingly good, while the agreement with Roshko's theory ranges from excellent to unsatisfactory. Approximations in Roshko's treatment which contribute to the lack of correlation with the data obtained in the smaller diameter shock tubes of Duff and the present work are emphasized and a formulation of the flow model is developed which better predicts the actual shock-tube flow durations.