Abstract
It is a well-known fact to anyone concerned with the prediction and prevention of flutter and other aerodynamically induced instabilities that the transonic speed range more often than nob turns out to be the most critical one. In order to achieve an efficient, dynamically stable design one therefore needs to know oscillatory transonic air forces with good accuracy. Another more basic reason for studying unsteady transonic flow is to gain improved physical understanding of transonic flow in general. For example, a problem of fundamental importance in transonic flow is to study whether particular steady flow patterns are stable to small unsteady disturbances. The present paper will be mainly concerned with methods for predicting oscillatory forces. However, other more general unsteady transonic flows will also be considered briefly.
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Abbreviations
- A :
-
Aspect ratio
- b :
-
reference length (root chord)
- C Mα :
-
moment coefficient due to pitch
- C Mq + C Mα :
-
coefficient of damping in pitch
- C p :
-
= |C p | e iϕp, pressure coefficient
- c :
-
speed of sound
- h :
-
function describing the location of wing surface
- k :
-
=ω b/U∞, reduced frequency
- l 11 :
-
= k11/eiϕ11, sectional coefficient of lift due to translation (see I)
- M :
-
Mach number
- r :
-
radial distance from x-axis
- S :
-
cross-sectional area of wing or body
- s :
-
Fourier variable
- t :
-
time
- U :
-
=1 + ϕx, (non-dimensional) component of velocity in free-stream direction
- u, v, w :
-
perturbation velocity component (for oscillatory perturbations the exponential time factor is usually deleted)
- V :
-
radial velocity component
- x, y, z :
-
cartesian coordinate system, the z-axis in the free-stream direction
- γ:
-
ratio of specific heats
- δ :
-
non-dimensional amplitude of motion
- ε:
-
non-dimensional small parameter measuring the overall deviation of the local Mach number from unity in the flow
- ϱ:
-
=\(\sqrt {n^2 + \zeta ^2 }\)
- ξ, η, ζ :
-
stretched Cartesian coordinates
- σ:
-
(Wing semispan)/(root chord)
- τ:
-
= k t
- ϕ :
-
non-dimensional perturbation velocity potential; for oscillatory flow ϕ = Re {φ e iωt }
- χ :
-
function appearing in the solution for the receding wave
- φ :
-
side-edge correction potential
- ω :
-
angular velocity of oscillation
- Ω :
-
function appearing in the solution for a delta wing
- i :
-
inner flow
- o:
-
outer flow
- 1:
-
for dependent variables: referring to mean steady flow; for independent variables: referring to integration variables
- ∞:
-
free stream
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© 1964 Springer-Verlag OHG., Berlin/Göttingen/Heidelberg
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Landahl, M.T. (1964). Linearized theory for unsteady transonic flow. In: Oswatitsch, K. (eds) Symposium Transsonicum. International Union of Theoretical and Applied Mechanics (IUTAM) / Internationale Union für Theoretische und Angewandte Mechanik (IUTAM). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88337-8_27
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DOI: https://doi.org/10.1007/978-3-642-88337-8_27
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