Inviscid–viscous interaction in a high supersonic flow is studied on the triple-deck scales to delineate the wall-temperature influence on the flow structure in a region near a laminar separation. A critical wall-temperature rangeO(Tw*) is identified, in which the pressure–displacement relation governing the lower deck departs from that of the classical (Stewartson, Messiter, Neiland) formulation, and below which the pressure–displacement relation undergoes still greater changes along with drastic scale changes in the triple deck. The reduced lower-deck problem falls into three domains: (i) supercritical (Tw* [Lt ]Tw), (ii) transcritical (Tw=O(Tw*)) and (iii) subcritical (Tw[Lt ]Tw*). Readily identified is a parameter domain overlapping with the Newtonian triple-deck theory of Brown, Stewartson & Williams (1975), even though the assumption of a specific-heat ratio approaching unity is not required here. Computational study of the compressive free-interaction solutions and solutions for a sharp-corner ramp are made for the three wall-temperature ranges. Finite-difference equations for primitive variables are solved by iterations, employing Newton linearization and a large-band matrix solver. Also treated in the program is the sharp-corner effect through the introduction of proper jump conditions. Comparison with existing numerical results in the supercriticalTwrange reveals a smaller separation bubble and a more pronounced corner behaviour in the present numerical solution. Unlike an earlier comparison with solutions by interactive-boundary-layer methods for ramp-induced pressure with separation, the IBL results do approach closely the triple-deck solution atRe= 108in a Mach-three flow, and the differences atRe= 106may be attributed in part to the transcritical temperature effect. Examination of the numerical solutions indicates that separation and reattachment on a compressive ramp cannot be effectively eliminated/delayed by lowering the wall temperature, but loweringTwdrastically reduces the triple-deck dimension, and hence the degree of upstream influence.
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.
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 Lighthill's (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.
The asymptotic theory of a high-aspect-ratio wing in an incompressible flow is generalized to an oscillating lifting surface with a curved centreline in the domain where the reduced frequency based on the half-span is of order unity. The formulation allows applications to lightly loaded models of lunate-tail swimming and ornithopter flight, provided that the heaving displacement does not far exceed the mean wing chord. The analysis include the quasi-steady limit, in which the crescent-moon wing problem considered earlier by Thurber (1965) is solved and several aerodynamic properties of swept wings are explained.Among the important three-dimensional and unsteady effects are corrections for the centreline curvature and for the spanwise components of the locally shed vortices. Comparison of the lift distributions obtained for model lunate tails with data computed from the doublet-lattice method (Albano & Rodden 1969) lends support to the asymptotic theory.
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