The forces on wing-fuselage combinations in supersonic flow

1960 ◽  
Vol 8 (2) ◽  
pp. 210-226 ◽  
Author(s):  
Joseph H. Clarke
Keyword(s):  
Supersonic Flow ◽  
Reverse Flow ◽  
Mathematical Physics ◽  
Reciprocity Relation ◽  
Hyperbolic Problems ◽  
Aerodynamic Forces ◽  
Relative Ease ◽  
Special Cases

Reverse-flow relations are used to provide convenient expressions for the aerodynamic forces which act on a general wing-fuselage combination in supersonic flow. The drag, lift, spanwise and chordwise lift distributions, and wing moments are treated. Consideration is given to available methods and results, including tables, which apply to the wing-fuselage interference problem, and reverse-flow relations are then employed to effect desirable changes in the detining force expressions by introducing wings or fuselages in the reverse flow. It is shown that the aerodynamic forces can be determined from a solution for the pressure on only the fuselage surface within the domain of dependence of the wing, this region being selected on the basis of relative ease of computation. In some cases the simplification achieved is quite substantial. Certain results in the literature arise naturally as special cases. The reverse-flow theorem is re-examined in the light of the procedure considered, and it is found to be inapplicable in one respect. The difficulty is circumvented by constructing an acceptable configuration which is equipollent to the prescribed one. It appears that the method given is applicable in other linear hyperbolic problems in mathematical physics when bulk or gross information is required and a suitable reciprocity relation can be constructed.

scholarly journals Reverse flow and supersonic interference

1959 ◽  
Vol 6 (2) ◽  
pp. 272-288 ◽  
Author(s):  
Joseph H. Clarke
Keyword(s):  
Spatial Distribution ◽  
Supersonic Flow ◽  
Flow Field ◽  
Reverse Flow ◽  
Flow Reversal ◽  
Analytic Proof ◽  
Perturbation Velocity ◽  
Horseshoe Vortices ◽  
Linearized Theory ◽  
Drag And Lift

First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.

Supersonic Flow Past Bodies of Revolution with Thin Wings of Small Aspect Ratio

1951 ◽  
Vol 3 (1) ◽  
pp. 61-79 ◽  
Author(s):  
P. M. Stocker
Keyword(s):  
Supersonic Flow ◽  
Aspect Ratio ◽  
The Body ◽  
Supersonic Stream ◽  
List Type ◽  
Body Of Revolution ◽  
Small Aspect Ratio ◽  
Flow Past ◽  
Special Cases ◽  
Ratio Set

SummaryThe method developed by G. N. Ward for the treatment of slender pointed bodies in a uniform supersonic stream is applied to three special cases. (i)Supersonic flow past a body of revolution with thin wings of symmetrical section and of small aspect ratio at zero incidence.(ii)Supersonic flow past a body of revolution with plane wings of small aspect ratio set at incidence to the body, the whole being at incidence to the stream.(iii)Supersonic flow past a body of revolution with a plane fin of small aspect ratio set at incidence, the whole being at incidence to the stream.The pressure distribution on the wing has been calculated for a special case of (i) and is given in the Appendix.

Laminar boundary-layer reattachment in supersonic flow

1979 ◽  
Vol 90 (2) ◽  
pp. 289-303 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Bluff Body ◽  
Fundamental Problem ◽  
Reverse Flow ◽  
Correct Choice ◽  
Flow Profile ◽  
Local Flow ◽  
Boundary Layer Equations ◽  
Lower Deck

A rational theory is developed to describe the reattachment of a laminar shear layer in supersonic flow. In the neighbourhood of reattachment the flow develops a threetiered or ‘triple-deck’ structure analogous to that which occurs at a point of separation (Stewartson & Williams 1969) and, as in the separation problem, the local flow pattern may be found independently of the flow in the surrounding regions. The fundamental problem of the reattachment triple deck reduces to the solution of the incompressible boundary-layer equations in the lower deck, which is of streamwise and lateral dimensions O(R−⅜) and O(R−⅝), where R [Gt ] 1 is a representative Reynolds number for the flow. Pressure variations in this region are O(R−¼). Asymptotic solutions in terms of x, the scaled streamwise lower-deck variable, are derived to confirm the transition from a reverse flow profile at x = 0+, through reattachment, to a forward flow as x → ∞, the attainment of the required asymptotic form downstream (as x → ∞) being shown to depend crucially upon the correct choice of the finite part of the pressure in the lower deck at x = 0+. The lower-deck solution is singular at x = 0+ and assumes a complicated multi-structured form which is shown to match upstream with the solution in a largely inviscid region of dimension O(R−½) where the pressure is O(1) and the major part of the flow reversal takes place. Solutions are presented for reattachment at a wall and for symmetric reattachment behind a wedge or bluff body. In the former case the results also explain the apparent ignorance of upstream conditions in the expansive triple-deck solution formulated by Stewartson (1970) in the context of supersonic flow around a convex corner.

The aerodynamic forces on an aerofoil in non-uniform unsteady motion in a closed tunnel

1957 ◽  
Vol 250 (977) ◽  
pp. 247-278 ◽  
Keyword(s):  
Harmonic Oscillation ◽  
Elliptic Functions ◽  
Detailed Examination ◽  
Unsteady Motion ◽  
Physical Plane ◽  
Aerodynamic Forces ◽  
Jacobian Elliptic Functions ◽  
First Order ◽  
Inviscid Incompressible Fluid ◽  
Special Cases

The two-dimensional unsteady motion of an aerofoil, situated midway between parallel walls, and moving through an inviscid, incompressible fluid, is investigated. A completely general upwash distribution is taken, and expressions are obtained for the pressure on the aerofoil surface and the lift and moment about the mid-chord point. By a conformal transformation involving Jacobian elliptic functions the physical plane is mapped into a rectangle, and the theory is based on a solution of Laplace’s equation satisfying certain given boundary conditions on this rectangle. Special cases are considered in which the upwash is ( a ) sudden upgust, and ( b ) a harmonic oscillation. Detailed examination is made of a rigid-body aerofoil performing translational and rotational harmonic oscillations. The aerodynamic forces are expressed in terms of dimensionless ‘air-load coefficients’, which are then compared with corresponding coefficients for an aerofoil in an infinitely deep stream. The air-load coefficients are obtained in a form which readily enables first-order corrections for wall interference to be evaluated. It is shown that the formulae derived are at variance with corresponding results obtained by other authors using different methods.

How animals glide: from trajectory to morphology

2015 ◽  
Vol 93 (12) ◽  
pp. 901-924 ◽  
Author(s):  
John J. Socha ◽  
Farid Jafari ◽  
Yonatan Munk ◽  
Greg Byrnes
Keyword(s):  
Performance Metrics ◽  
Flapping Flight ◽  
The Body ◽  
Aquatic Environments ◽  
Aerodynamic Forces ◽  
Relative Ease ◽  
Ecological Roles ◽  
And Control ◽  
Glide Paths

Animals that glide produce aerodynamic forces that enable transit through the air in both arboreal and aquatic environments. The relative ease of gliding compared with flapping flight has led to a large diversity of taxa that have evolved some degree of flight capability. Glide paths are curved, reflecting the changing forces on the animal as it progresses through its aerial trajectory. These changing forces can be under control of the glider, which uses specific aspects of anatomy to modulate lift, drag, and rotational moments on the body. However, gliders share no single anatomical or behavioral feature, and some species are unspecialized for gliding, producing aerodynamic forces using posture and orientation alone. Animals use gliding in a broad range of ecological roles, suggesting that multiple performance metrics are relevant for consideration, but we are only beginning to understand how gliders produce and control their flight from takeoff to landing. In this review, we focus on the physical aspects of how glide trajectories are produced, and additionally discuss the range of morphologies and postures that are used to control aerial movements across the broad diversity of animal gliders.

scholarly journals Integrable systems connected with black holes

2019 ◽  
pp. 89-93
Author(s):  
H. Demirchian
Keyword(s):  
Black Holes ◽  
Shock Waves ◽  
Gravitational Waves ◽  
Integrable Systems ◽  
Mathematical Physics ◽  
Theory Of Relativity ◽  
Test Particles ◽  
Special Cases ◽  
A New Technique ◽  
Definition Of

We studied some important questions in general relativity and mathematical physics mainly related to the two most important solutions of the theory of relativity - gravitational waves and black holes. In particular, the work is related to astrophysical shock waves, gravitational waves, black holes, integrable systems associated with them as well as their quantum equivalents. We studied the effects of null shells on geodesic congruences and suggested a general covariant definition of the gravitational memory effect. Thus, we studied observable effects that astrophysical shock waves can have on test particles after cataclysmic astrophysical events. We studied the geodesics of massive particles in Near Horizon Extremal Myers-Perry (NHEMP) black hole geometries. This is the space-time in the vicinity of the horizon of higher dimensional rotating black holes. Thus, this work can have applications for studying accretions of black holes. The system is also important in mathematical physics as it describes integrable (in special cases superintegrable) system, where the constants of motion are fully studied. On the other hand, the quantum counterparts of this and other integrable systems are studied as well and a new technique is suggested for geometrization of these systems.

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