Abstract
Within the framework of research on unsteady flows performed at ONERA, a calculation method of two- dimensional unsteady flows in which the effects of the unsteady boundary layers on the profile are taken into account has been developed in incompressible and in transonic regime.
The methods used are briefly described. The results obtained show, by comparison with results of inviscid flow calculations, the influence of viscous effects on unsteady pressure distributions, on total force coefficients and on shock-wave intensity and location.
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Abbreviations
- ρ:
-
density
- M∞ :
-
Mach number at infinity upstream
- c:
-
chord
- τ:
-
thickness-to-chord ratio
- ∝:
-
incidence of the profile
- δm :
-
mean flap deflection
- δi :
-
amplitude of flap oscillations
- f=w/2π:
-
oscillation frequency
- \({\text{k = wc}}/2\sqrt {\infty } {\mkern 1mu} = {\mkern 1mu} \pi f{\text{c}}/\sqrt {\infty }\) :
-
reduced frequency
- p:
-
instantaneous pressure
- Δp:
-
pressure fluctuation
- \({\text{cp}} = \Delta {\text{p}}/\frac{1}{2}{{\rho }_{\infty }}\sqrt {{{{\infty }^{2}}}} {{\delta }_{i}}\) :
-
instantaneous (or steady) pressure coefficient
- \({\text{cp}} = \Delta {\text{p}}/\frac{1}{2}{{\rho }_{\infty }}\sqrt {{{{\infty }^{2}}}}\) :
-
unsteady pressure coefficient
- Cp1 :
-
modulus of the first harmonic of the pressure coefficient
- K *p :
-
value of Kp for Mℓ=1
- Czδ :
-
unsteady lift coefficient (value of Cz1 for δ i =1 radian)
- Cmδ :
-
unsteady pitching moment coefficient
- Cmcδ :
-
unsteady hinge moment coefficient
- ϕ:
-
phase angle
- ϕ1:
-
phase angle of first harmonic
- Re :
-
Reynolds number,relative to chord c
- δ:
-
boundary layer thickness
- U:
-
longitudinal component of velocity in the boundary layer
- θ=∫ δ0 eu(1−U/Ue)/ρeUedy :
-
boundary layer momentum thickness
- δ1=∫ δ0 (1−ρU/ρeUe edy :
-
boundary layer displacement thickness
- δ3∫ δ0 ρU(1−U2/U 2e )/ρ/eUedy:
-
kinetic energy thickness(H32=δ3/θ)
- δρ=∫ δ0 (1−ρ/ρe)dy :
-
boundary layer density thickness
- H=δ1/θ:
-
boundary layer shape factor
- cf :
-
local skin friction coefficient
References
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© 1981 Springer-Verlag, Berlin, Heidelberg
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Desopper, A. (1981). Influence of the Laminar and Turbulent Boundary Layers in Unsteady Two-Dimensional Viscous- Inviscid Coupled Calculations. In: Michel, R., Cousteix, J., Houdeville, R. (eds) Unsteady Turbulent Shear Flows. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81732-8_14
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DOI: https://doi.org/10.1007/978-3-642-81732-8_14
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