ALBERT

Description: Low Reynolds number flow of a conducting fluid past a sphere is considered. The classical Stokes solution is modified by a magnetic field which, at infinity, is uniform and in the direction of flow of the fluid. The formula for the drag is found to be [Formula omitted] Where DS is the Stokes drag and M is the Hartmann number. © 1957, Cambridge University Press. All rights reserved.

Description: An investigation is made of the effect of a small disturbance on the flow in a complete rarefaction wave, for example, the flow produced by the rupture of a membrane originally separating a compressible gas from a vacuum. The perturbation arises from a rigid boundary slightly inclined to the direction of flow. The growth of the perturbed region is studied and the pressure field is calculated for diatomic gases. The nature of the expanding boundary of the perturbed region is investigated. Arguments are put forward which suggest that this boundary can be a weak shock in certain circumstances. A second shock may also appear in some cases, following the first and of greater strength. In an appendix the solutions are extended to monatomic gases and to fluids with an adiabatic index of 2. The latter results are suitable for a comparison with hydraulic experiments. © 1957, Cambridge University Press. All rights reserved.

Description: Experiments with Perspex nozzles, which were arranged to discharge vertically downwards and in which the convergent part was followed by a short divergency, showed that at low swirls the flow was unstable. When the swirl was sufficiently large for an air core to be established, its effective magnitude was estimated from measurements, at the throat, of the core diameter and of the wall pressure. The former were in closer accord with inviscid theory than the latter. The results are presented in terms of dimensionless discharge and swirl coefficients. Measurements of core diameter and wall pressure were also made throughout one of the nozzles and compared with the theory. Reversed axial flow in the upper part of the nozzles was easily produced, and the limits of its appearance were determined. Low pressure tests with the reservoir top alternately submerged and uncovered revealed that the top had a marked influence on the nature of the flow in the nozzle; and measurements of the tangential and axial velocities in the upper part of the nozzle proved the inviscid theory to be seriously in error at high swirls. For purposes of comparison, similar experiments were performed on a convergent nozzle. © 1957, Cambridge University Press. All rights reserved.

Description: A dispersed shock wave may be defined as one in which finite changes occur over distances large compared to the mean free path in the gas. In contrast a shock wave in air extends over only a few mean free paths. When internal motions in a molecule are excited rather slowly by collisions, as is the case for molecular vibration, the shock wave may be partly dispersed; then, the sharp shock front is followed by a diffuse tail leading to complete thermal equilibrium. Alternatively, it may be fully dispersed, so that adjustments in the energy in all the degrees of freedom proceed slowly and in parallel. The purpose of this note is to point out that within a narrow speed range, from a shock Mach number of 1 to 1.042, shocks in carbon dioxide are fully-dispersed in the above sense. Such waves have been observed experimentally using a shock tube and interferometer. The possible existence of such waves was first pointed out by Bethe & Teller (1941) purely as a matter of academic interest. This note treats the problem in the same spirit.

Description: An unbounded parallel flow, consisting of a linear shear layer between uniform streams, is investigated for stability. A conventional eigenvalue problem is formulated, and solved by both analytical and numerical methods. The region of instability in the plane of Reynolds number R and disturbance wave number α is determined, and typical growth rates in the unstable region are computed. Unstable disturbances are found at all values of R. Results for αR 〉 100 are found to agree closely with inviscid theory results. An analytic method useful for αR 〈 1 is developed. The extent to which the present results can be applied to the laminar boundary layer between free streams is discussed. © 1957, Cambridge University Press. All rights reserved.

Description: The structure of a plane shock wave moving through a completely ionized plasma of protons and electrons is calculated. It is assumed that the two species of particles behave as two gases, each separately in a quasi-equilibrium state corresponding generally to two different temperatures. Navier-Stokes type equations with coefficients of viscosity and thermal conductivity appropriate to the two species are solved by numerical iteration. For very strong shocks it is found that both the velocity of electrons and protons and the temperature of the protons change in a distance about twice the mean path for momentum transfer between protons in the hot (shocked) gas. The electron temperature changes in about eight of these mean free paths, causing a relatively wide zone of hot electrons at low density ahead of the usual velocity shock-front. The density and temperature gradients of protons and electrons create an electric field. © 1957, Cambridge University Press. All rights reserved.

Description: An approximate solution is devised for the one-dimensional motion following the impact of a shock wave on a wall which is free to move. The approximate solution neglects changes in entropy occurring through the reflected and transmitted shocks, thus reducing the problem to one of a simple wave type. The asymptotic behaviour of the system is considered and it is shown by exact physical argument that the transmitted shock eventually attains the same strength as the incident shock and that the reflected shock ultimately decays to a sound wave. An experimental investigation of the interaction was made, using thin walls of cellulose acetate, in a shock tube at an incident shock Mach number of 1·50. Agreement between the theoretical and experimental results, especially for the path followed by the wall, was found to be good. © 1957, Cambridge University Press. All rights reserved.

Description: This paper is concerned with the rates at which atoms and molecules react in the air that flows over a body flying through the atmosphere at hypersonic speeds. Using air as a working fluid, a series of shock tube experiments were carried out to provide information about these rates. Mach angle measurements were made to determine the state of the gas in three situations of interest. Flow over flat plates was used to determine the state of the gas behind the incident normal shock; temperatures in the gas that passed through the shock varied between 2000 and 6000°:K and densities between standard and 1/80 of standard density. Flow over wedges was employed to decelerate the flow behind the incident shock to a small supersonic Mach number; here temperatures downstream of the oblique shock increased, at most, 2000°:K above the free stream value. A Prandtl-Meyer expansion was used to cool rapidly the dissociated gas, so that the recombination process could be investigated; temperatures dropped at most 2500°:K and the densities varied between standard and 1/200 of the standard value. In some cases, the initial degree of dissociation of air was over 45%. The results (figure 11) indicate that the dissociation and recombination relaxation times of the chemical species found in air are very fast, when compared to the time it takes a particle of gas to flow either around a blunt body in hypersonic flight or past smtill models in shock tubes. Thus the shock tube is shown to be an instrument capable of supplying air at high temperatures in thermodynamic equilibrium (figure 5). In the case of a non-melting blunt body of about 1 ft. diameter flying through the atmosphere at hypersonic speeds, the present results imply that, when the gas behind the detached shock is in thermodynamic equilibrium, the flow will also be in equilibrium as it expands around the body, provided its speed is greater than 10 000 ft./sec at altitudes below 180 000 ft. (figure 12). © 1957, Cambridge University Press. All rights reserved.