H. K. Cheng

The separation vortex in the Weis-Fogh circulation-generation mechanism

The influence of leading-edge separation vortices on the Weis-Fogh (1973) lift- generation mechanism for insect hovering is investigated. The analysis employs a vortex-shedding model (Edwards 1954; Cheng 1954) and represents an extension of Lighthills (1973, 1975) analysis of an inviscid model without separated vortices. Results of the study compare reasonably well with observations on a laboratory model at high Reynolds number (Maxworthy 1979), confirming that vortex separation significantly enhances the initial circulation on each of the wings. Unlike the un- separated-model solution, this circulation was found to depend on the history of the wing motion and to increase with a large opening angle.

Lunate-tail swimming propulsion. Part 2. Performance analysis

The theory of an oscillating, high-aspect-ratio, lifting surface with a curved centreline (Cheng & Murillo 1984) is applied to a performance analysis of lunate-tail swimming propulsion. Thrust, power and propulsive efficiency are calculated for model lunate tails with various combinations of mode shapes and morphological features to ascertain the viability of the proportional-feathering concept, and to determine the influence of sweep and centreline curvature. One of the principal conclusions concerns the interchangeability of the heaving amplitude of the peduncle (identified with the major pitching axis) with the centreline sweep, and its effect on the propulsive efficiency, while maintaining the same thrust. Hydrodynamic reasons are also offered for the apparent preference for the crescent-moon fin shape over the V-shape at moderate sweep angles, and for the large sweep angles often found in V-shaped fins.

Transonic equivalence rule: a nonlinear problem involving lift

The inviscid transonic flow past a thin wing having swept leading edges, with smooth lift and thickness distributions, is shown to possess an outer nonlinear structure determined principally by a line source and a line doublet. Three domains (the thickness-dominated, the intermediate, and the lift-dominated), representing different degrees of lift control of the outer flow, are identified; a transonic equivalence rule valid in all three domains is established. Except in one domain, departure from the Whitcomb-Oswatitsch area rule is significant; the equivalent body corresponding to the source effect has an increased cross-sectional area depending nonlinearly on the lift. This nonlinear lift contribution results from the second-order corrections to the inner (Jones) solution, but produces effects of first-order importance in the outer flow. Of interest is an afterbody effect dependent on the vortex drag, which is not accounted for by the classical transonic small-disturbance theory.

Inviscid-viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling

The influence of wall temperatures on the flow structure in a region near a laminar separation is presently studied on the triple-deck scales, for the case of a high supersonic flows inviscid-viscous interactions. A critical wall-temperature range is identified whose lower deck pressure-displacement relation departs from that of the classical formulation; below it, the pressure-displacement relation undergoes still greater transformations in conjunction with drastic scale-changes in the triple deck. The reduced lower-deck problem falls into supercritical, transcritical, and subcritical domains. A computational study is conducted for the compressive free-interaction solutions, and solutions are obtained for a sharp-corner ramp in the three wall-temperature ranges.

Sonic-boom noise penetration under a wavy ocean: theory

Sonic-boom noise penetrating under a deep ocean is affected by its time-dependent interaction with the surface waves, which can significantly influence the perceived sound pressure level and tonal content of the disturbances at depth far greater than expected from the flat-ocean (Sawyers) model. The present theory assumes a small surface slope and a high water-to-air density ratio; the ocean surface in the analysis is modelled by a sinusoidal surface-wave train. The analysis shows that a distinct acoustic wave mode in the form of a packet of wavelets emerges in the sound field far below the surface and attenuates with increasing distance in a manner similar to the cylindrical spreading of monochromatic waves. The latter feature renders the surface waviness influence an effect of first-order importance, overwhelming the primary noise field at large depth. Detailed properties of the deep-water wave fields are examined and illustrated for the case of an incident N-wave, for which an explicit, analytic solution is obtained. The result reveals a similarity structure of the wave field with two distinct time scales and the invariance characteristics of the cylindrically spreading waves, in accord with the group-velocity concept of dispersive waves. An example is given of the interaction, illustrating the underwater waveform, sound-pressure and frequency levels.

The oblique wing as a lifting-line problem in transonic flow

A transonic-flow theory of thin, oblique wing of high aspect ratio is presented, which permits a delineation of the influence of wing sweep, the centre-line curvature, and other three-dimensional (3D) effects on the nonlinear mixed flow in the framework of small-disturbance theory. In the (parameter) domain of interest, the flow field far from the wing section pertains to a high subsonic, or linear sonic, outer flow, representable by a Prandtl–Glauert solution involving a swept, as well as curved, lifting line in the leading approximation. Among the 3D effects is one arising from the compressibility correction to the velocity divergence, absent in classical works; this effect also leads to a correction in the outer flow in the form of an oblique line source. More important is the upwash corrections which includes the influence of both the near and far wakes, as well as the local curvature of the centre-line. For straight oblique wings, local similarities exist in the 3D flow structure, permitting the reduced equations to be solved once for all span stations. An analogy also exists between the oblique-wing problem and that of a 2D transonic flow which is weakly time-dependent; this provides an alternative method of solving numerically the inner airfoil problem. Solutions to the reduced problem are demonstrated and compared with full-potential solutions for elliptic oblique wings involving high subcritical as well as slightly supercritical component flows.

On the gas dynamics of an intense explosion with an expanding contact surface

The structure of a strong blast wave under the influence of an expanding inner contact surface is studied asymptotically in the Newtonian limit:

Topographically generated cyclonic disturbance and lee waves in a stratified rotating fluid

\epsilon \equiv (\gamma - 1)/2\gamma \ll 1, \epsilon \dot{y}^2_s \gg a^2_{\infty}

AN AIRFOIL THEORY OF BIFURCATING LAMINAR SEPARATION FROM THIN OBSTACLES

. The theory treats the interaction of a shock layer and an inner flow region (the entropy wake) and reduces the problem to an ordinary differential equation for the shock radius. The pressure–volume relation of Cheng et al. (1961) is recovered and extended to a higher order of e. It is shown that, depending on the rate of growth of the contact surface, the shock layer may ‘reattach’ to the surface at large time. In a number of cases, the reattachment is approached in an oscillatory manner which leads to a period of non-uniformity. The associated problem of multiple time scales (treated in sequels to this paper) is identified.

The response of a stratified rapidly rotating flow to a pulsating topography

The flow about an obstacle in horizontal motion relative to a stratified Boussinesq fluid in a deep, rapidly rotating container is studied. Numerical and asymptotic analyses of the linearized boundary-value problems for a shallow topography are made to delineate the influence of stratification and ground topography on wave and flow structure, and to ascertain the presence of a solitary anticyclonic, or cyclonic, disturbance in the far field at high as well as low stratification. Although the analyses are restricted to the rapidly rotating case corresponding to a vanishingly small Rossby number, it is pointed out that the cyclonic feature remains a valid inviscid description in the far field except for an infinite Rossby number corresponding to no rotation.