Some Applications of Combined Asymptotics and Numerics in Fluid Mechanics and Aerodynamics

Malmuth, N.

doi:10.1007/978-94-011-1810-1_4

Cited by 2 publications

(1 citation statement)

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“…Related work on the equivalence and area rule appear in Oswatitisch & Keune (1955) and Whitcomb (1956), which correlate the aerodynamic characteristics of a full aircraft configuration to that of a body of revolution having the same cross-sectional area distribution along its length as the full airplane's. In Malmuth (1993), the area rule and equivalence rule have been systemized into a combined asymptotic and numerical method that can be used as a conceptual design tool. This approach reduces the three-dimensional drag shaping optimization problem to one in one less space dimension and is capable (in principle) of systematic refinement.…”

Section: Introductionmentioning

confidence: 99%

Wave drag due to lift for transonic airplanes

Cole

Malmuth

2005

Proc. R. Soc. A.

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SummaryLift dominated pointed aircraft configurations are considered in the transonic range. These are treated as lifting wings of zero thickness with aspect ratio of order one. An inner expansion which starts as Jones' theory is matched to a nonlinear outer transonic theory as in Barnwell's earlier work. New expressions for the wave drag due to the equivalent body are derived. Some examples of numerical calculations for different configurations are presented. IntroductionIn 1946, R. T. Jones (ref. 1) published a paper giving a formula for the lift and induced drag of "low aspect ratio pointed wings below and above the speed of sound". The work presented here, and earlier in the references cited below, represents an extension of Jones' ideas to the transonic range. It is reassuring that, under suitable circumstances, Jones' formula for the lift and induced drag not only continues to hold but is even valid for wings whose aspect ratio is order one. Under these circumstances, also shock waves and wave drag generally appear. The basic ideas of how this type of flow behaves are set out in the report of Barnwell (ref. 2). The principal result is that the lift produces a flow that looks, in the outer region, like the flow past an equivalent axisymmetric body. This physical effect shows up in the inner and outer expansions used by Barnwell. Cheng and Hafez used similar ideas to define the apparent body and general equivalence rule in a series of papers (ref. 3, 4). Cramer (ref. 5) also studied the problem (with zero thickness as is done here) and essentially verified the results of Cheng and Hafez.In this paper and ref. 6, we have also considered wing-like configurations with zero thickness and aspect ratio O(1) as in fig. 1. Thickness effects can be incorporated relatively easily. Inner and outer expansions are defined in essentially the same manner as Barnwell although the asymptotic matching is carried out in a different way using an intermediate limit. Then wave drag associated with the outer expansion is considered. Several computations and an optimization are carried out to show the effect of planform and longitudinal distribution of lift on the transonic wave drag.

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Section: Introductionmentioning

confidence: 99%