Sharp Pressure Gradient Research Articles

The Pressure and Deformation Profiles Between Two Normally Approaching Lubricated Cylinders

The pressure and deformation profiles between two colliding lubricated cylinders are obtained by solving the coupled, time-dependent elastohydrodynamic equations with an iterative procedure. The analysis includes several effects which were not considered in a previous solution by Christensen [4], namely, the effect of surface velocities due to local deformation, the effect of the lubricant compressibility, and the effect of a lubricant with composite pressure-viscosity coefficients. It is found that the local approach velocity plays an important role during final stages of normal approach. It causes the lubricant to be entrapped within the contact region, and both the pressure and deformation profiles appear to converge to the Hertzian profile. The use of a smaller pressure-viscosity coefficient at high pressures reduces the sharp pressure gradient at the center of the contact, and produces a much milder variation of load with respect to the film thickness. The effect of compressibility of the lubricant is found to be relatively small.

Dike filling by magma intrusion and by explosive entrainment of fragments

Two mechanisms of material transport in dikes, viz., flow of a viscous magma and explosive entrainment of fragments in a gas, are examined quantitatively. For magma intrusion the asymptotic behavior of the system is examined by investigating the heat and fluid flow problems separately. For a given set of physical and geometrical conditions, limiting values of variables consistent with the mechanism may be computed. For some dikes too narrow to be satisfactorily explained by the magma flow representation, properties of an alternative model are developed. This model postulates that on the formation of a deep fissure a very sharp pressure gradient would develop at its base. The pressure gradient would lead to the formation of a shock wave and explosive evolution of volatiles that would be accelerated to near sonic velocity and entrain substantial quantities of fragmental material.

Deformation of asymmetrically loaded, symmetrically prestressed orthotropic shells of revolution.

The helium injection causes the sharp pressure gradient representing the wake recompression shock to disappear for configurations B-4 and B-5, whereas nitrogen injection does not do this. This unanticipated result is confirmed by the schlieren photographs shown in Fig. 4. A cause for this phenomenon may be the much larger sonic speed in helium which may result in a subsonic type of recompression at the wake neck. Model B-l was tested with a nitrogen injection only. The injection effects were intermediate between those obtained with configurations B-3 and B-5. Some added details on injection results and on the effect of various afterbodies have been presented in Ref. 3.

Experiments on Interaction of Shock Waves and Cylindrical Bodies at Supersonic Speeds

INTRODUCTION While two-dimensional shock-wave reflections have received much attention, in most applications either the shock surface or the reflecting surface is curved. Elements of nonviscous theory for three-dimensional shock reflections by two of the present authors indicated the likelihood of anomalous reflection for configurations such as that of a plane shock impinging on a cylinder aligned with the free stream. This paper presents the highlights of the experimental investigation of this three-dimensional shock-cylinder configuration conducted in the University of Michigan Supersonic Wind Tunnel at a Mach Number of 1.90. One general result is the striking boundary-layer cross flow induced by the sharp pressure gradients across the reflection line on body surfaces. For the present configuration, the cross flow, in and outside of the boundary layer, results in a separated region on the lee side of the body. The effects of boundary-layer character and thickness and of shock strength on the overall flow and pressure fields are studied by means of body-pressure distributions and several visualization techniques. Implications of the present findings for practical applications are discussed.