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Increasingly agile manoeuvre is an advantage in the flight of aircraft, missiles and aerial vehicles, but the principles of accelerating aerodynamics in the transonic regime are only now being fully investigated. This study contributes to the understanding of shock and separation effects on drag during axial acceleration, using a simple geometric configuration. Unsteady shock wave behavior was numerically investigated for an axisymmetric cone-cylinder using a commercial solver and the Moving Reference Frame acceleration technique. This acceleration technique was validated using unsteady numerical and experimental methods. The cone-cylinder was accelerated from Mach number 0.6 to Mach number 1.2 at 100g constant and deceleration was from Mach number 1.2 until Mach number 0.6 at –100g constant. Three cone angles were tested for the cone-cylinder with uniform cylinder diameter. Acceleration through the transonic Mach regime was characterised by a delayed and gradual shock wave development when compared to steady state, demonstrating a clear flow history effect. Deceleration through the transonic Mach regime was characterised by shock wave propagation from the base to the nose. New flow structures appeared during deceleration that do not have counterparts in the steady state, including shock interactions and propagating expansion-compression features. Gross changes in the unsteady drag coefficient curves for each cone-angle are explained with reference to unsteady shock wave behaviour for accelerating and decelerating motion.

There is a dearth of information on the reflection of very weak shock waves on curved surfaces; and particularly a distinct lack of experimental data at Mach numbers below 1.03. A previous study at Mach numbers between 1.03 and 1.05 showed that there are variations in the accepted reflection evolution on curved surfaces. That work indicated the existence of an apparent regular refection pattern in the curved shock wave reflection evolution which is also predicted for very much weaker waves in acoustic studies. To improve spatial resolution, the current study is performed in a large shock tube with a test section height of 450 mm using a 520 mm radius curved test piece with zero initial ramp angle. Imaging is primarily using shadowgraphy and high-speed photography. Experiments concentrated on tests in a range of $$1.007 \le M \le 1.09$$ with some tests at higher values. No shear layer is evident at the lower Mach numbers as for von Neumann and weak Mach reflection patterns. Transitioned regular reflection appears to cease at incident Mach numbers below 1.07. A reflection pattern resembling a regular reflection exists in the transition between the three-shock patterns and transitioned regular reflection.

The flow field which results from an expansion wave entering a cavity from an upstream tube, and the focusing effect which occurs, is investigated. Different cavity geometries, different expansion wave pressure ratios and different expansion wave widths are explored. As the expansion wave propagates into the cavity it induces flow in the opposite direction and back down the walls. The flow experiences compression as it flows out back into the tube because of the concave surface of the cavity it encounters. This can result in the formation of shock waves which can propagate back up into the cavity. Very low pressure and temperature regions can develop because of the focusing action of the expansion. A convenient way of generating an expansion wave numerically and/or experimentally is in a shock tube. This consists of a tube divided into two compartments, one at high pressure and one at low pressure separated by a frangible diaphragm. On bursting the diaphragm, a shock wave travels in one direction and an expansion in the other towards the cavity. Whilst ideal boundary conditions can be imposed in numerical simulation laboratory experiments are complicated by the diaphragm being curved and having a finite opening time. The effect of an initially curved diaphragm is briefly considered. The expansion wave pressure ratio was altered by changing the initial pressure ratio across the diaphragm. For an initially high pressure ratio, supersonic flow can occur behind the trailing edge of the expansion wave which has a marked influence on the flow. The width of the wave is dependent on the distance of the diaphragm from the cavity and also has a significant influence on the flow. As the width of the wave increases and the density gradient decreases, focusing effects becomes significantly weaker. Correspondence between experiment and simulation is examined.

Previous work has shown that heat transfer into a plane conducting surface affects shock wave reflection properties. In the more complex reflection case of a curved surface the situation would be different because of the increased number of reflection patterns, with a rapid change in reflection geometry as the wave propagates up the surface. Test pieces of different thermal conductivities (0.19 W/mK and 401 W/mK) and hydraulically smooth surfaces are used on both convex and concave cylindrical surfaces. The test pieces are placed in identical positions on either side of a plane of symmetry and at the same incident angles in a shock tube. Tests are performed at incident shock Mach numbers of 1 . 22 M 1 . 5 and imaged using high-speed shadowgraph photography. The images are analyzed both quantitatively through reflection angle measurements and qualitatively by searching for asymmetry. Both the qualitative and quantitative measurements clearly indicate that the thermal conductivity of the surface affects the reflection patterns due to the complex transient thermal environment. Asymmetry in the reflection patterns is found at all Mach numbers. In contrast to the plane wall case the lack of theory limits comparison, where in that case it was shown that the lower the thermal conductivity the closer the experimental results approached the ideal adiabatic case. Similar comparisons in the relationship of reflection types between different materials are found in the current case. The findings could be refined by using higher imaging frame rates and spatial resolution, and sophisticated numerical modeling.

Most computational fluid dynamics simulations are, at present, performed in a body-fixed frame, for aeronautical purposes. With the advent of sharp manoeuvre, which may lead to transient effects originating in the acceleration of the centre of mass, there is a need to have a consistent formulation of the Navier–Stokes equations in an arbitrarily moving frame. These expressions should be in a form that allows terms to be transformed between non-inertial and inertial frames and includes gravity, viscous terms, and linear and angular acceleration. Since no effects of body acceleration appear in the inertial frame Navier–Stokes equations themselves, but only in their boundary conditions, it is useful to investigate acceleration source terms in the non-inertial frame. In this paper, a derivation of the energy equation is provided in addition to the continuity and momentum equations previously published. Relevant dimensionless constants are derived which can be used to obtain an indication of the relative significance of acceleration effects. The necessity for using computational fluid dynamics to capture nonlinear effects remains, and various implementation schemes for accelerating bodies are discussed. This theoretical treatment is intended to provide a foundation for interpretation of aerodynamic effects observed in manoeuvre, particularly for accelerating missiles. Funding agencies: DRDB [KT466921, KT528944, KT470887]

In the conventional von Neumann theoretical treatment of two-dimensional shock wave reflection off a surface, it is assumed that the flow is inviscid and that the reflecting surface is perfectly smooth, rigid, non-porous, and adiabatic. These theoretical predictions have been found to be good predictions of reflection over a significant range where regular reflection exists and for a limited range around Mach 2 for strong shocks in the case of Mach reflection. However, experiments on regular reflection have shown that this pattern persists to a small extent beyond what the theory predicts. This effect has been ascribed to the development of a viscous boundary layer behind the point of reflection, and some studies have been done on the effect of surface roughness on reflection topology. The possibility of thermal effects and heat transfer from the shock-heated gas to the wall and on the boundary layer has, on the other hand, been almost totally neglected. To study this, two surfaces of different conductivities have been placed at the same angle, symmetrically in a shock tube, and impacted by a single plane shock wave and the reflection patterns examined. Tests were conducted over a range of Mach numbers between 1.28 and 1.4, and incident shock wave angles between \(36^\circ \) and \(70^\circ \) covering both regular and Mach reflection. Both quantitative and qualitative tests show that there is a difference in the angles between the reflected waves and the reflecting surfaces based on the material thermal conductivity. In the quantitative tests the value of this angle was larger for materials with a lower thermal conductivity, and vice versa. A material, such as aluminium, with mid-range thermal conductivity had angles that lay within the limits of the two extreme values for glass and copper. The qualitative images supported these findings, showing asymmetry in reflection topography, with the intersection of the two reflected shock waves lying closer to the material with a higher thermal conductivity.

This study numerically and experimentally examines the resulting flow field of a shock wave passing through a pipe gap. The effects of gap geometry and shock Mach number variation are investigated. Incident shock Mach numbers of 1.3, 1.4, and 1.5 and gap widths of 25 and 50 mm were used, which correspond to 0.5 and 1.0 pipe inner diameters, respectively. For both cases, the incident shock wave propagated into the downstream pipe at much reduced strength. A strong expansion propagated into the upstream pipe causing a significant pressure drop from the initial post-shock pressure. Expansion waves at the outflow resulted in supersonic speeds as the flow entered the gap for Mach 1.4 and 1.5. A notable feature was the formation of a standing shock at the inlet to the downstream pipe for the higher two Mach numbers in both cases. Decreasing the gap width moved the standing shock closer to the downstream pipe. For the lowest Mach number of 1.3, no standing shock system was set up. The propagation conditions in the downstream pipe showed that the pressure is initially unsteady, but becomes more uniform, controlled by the developed wave system in the gap. For the flanged gap case, the flow within the gap is confined for much longer and hence produces more intense and complex flow feature interactions and an earlier transition to turbulence. The induced shock strength in the downstream pipe is independent of gap geometry and separation distance examined in this paper as verified by experimental pressure traces.

Previous detailed studies of the interaction of a shock wave with a perforated sheet considered the impact of a shock wave on a plate with regularly spaced slits giving area blockages of 60 and 67%, at various angles of incidence, and resulting in both regular and Mach reflection. The current work extends this study to a much wider variety of plate geometries. Blockage ratios of 20, 25, 33, 50, and 67 and inclinations of 45, 60, 75, and 90° to the shock wave were tested. Four different thicknesses of plate were tested at the same frontal blockage in order to assess the effects of gap guidance. Tests were conducted at two shock Mach numbers of 1.36 and 1.51 (inverse pressure ratios of 0.4 and 0.5). It is found that secondary reflected and transmitted waves appear due to the complex interactions within the grid gaps, and that the vortex pattern which is generated under the plate is also complex due to these interactions. The angle of the reflected shock, measured relative to the plate, decreases with plate blockage and the angle of inflow to the plate reduces with increasing blockage. By analysing the flow on the underside of the plate the pseudo-steady flow assumption is found to be a reasonable approximation. Both the pressure difference and the stagnation pressure loss across the plate are evaluated. It is found that over the range tested the plate thickness has a minimal effect.

Air ejectors are used for sorting materials by displacing selected items through the action of aerodynamic drag. Subsonic units are common in the marketplace. This paper explores the potential for the use of an overexpanded supersonic jet because of it having reduced lateral spread and giving significantly higher particle drag. Experiments have been conducted to explore the flow field associated with a pulsed supersonic jet impacting particles in different positions relative to the jet exit, and of various shapes. The forces acting on a typical particle are measured and schlieren photography is used to visualize the flow.

The reflection of very weak shock waves from concave curved surfaces has not been well documented in the past, and recent studies have shown the possible existence of a variation in the accepted reflection configuration evolution as a shock wave encounters an increasing gradient on the reflecting surface. The current study set out to investigate this anomaly using high-resolution photography. Shock tube tests were done on various concave circular and parabolic geometries, all with zero initial ramp angle. Although the results have limitations due to the achievable image resolution, the results indicate that for very weak Mach numbers, M S

AUTOROTATION is the rotation of an object in an airstream in the absence of any other driving force1. It is important in the fall characteristics of some tree fruits, the growth of hailstones, and the trajectories of objects separating from aircraft and spacecraft. Previous studies have concentrated on thin, flat plates rotating about an axis normal to the airstream, but in many applications— those relating to the free fall of bodies through air—the behaviour of bodies of more complex geometry is of interest. When these autorotate, a lift force is generated which can significantly alter the body's trajectory. Here I examine the autorotation of prisms whose cross-sections are regular polygons. Prisms of triangular section rotate fastest, but generate less lift than a flat plate. Only bodies with less than eight sides are found to show autorotational behaviour. In all of these cases, the lift forces generated are larger than those obtained from a spinning cylinder driven externally at the same rotation speed. Many devices have been proposed in the past that use as a propulsion mechanism the lift force developed on a driven rotating cylinder, perhaps the most spectacular being the Flettner rotorship which crossed the Atlantic in 19262. The use of polygonal bodies would have application in these cases, not only because of the higher lift generated but also because the energy required may be derived simply from the relative wind. There are thus also clear implications for wind-power devices.