Summary
M ∞Design of SCLFC airfoils increases by undercutting the front and rear lower surface and using upper surface pressure distributions with an extensive flat rooftop at low supersonic speeds, preceeded by a supersonic pressure minimum (located far upstream to delay double shock formation at M ∞ < M ∞ Design ) and followed by a steep subsonic rear pressure rise with suction. Conservatively high supersonic bubbles at M ∞ Design and a rapid transition from the flat rooftop to the rear pressure rise minimize off-design discontinuities in the rear part of the supersonic zone.
Relatively sharp leading edges, combined with boundary layer crossflow cancellation in the acceleration and deceleration zones in the leading edge area essentially eliminate boundary layer croosflow instability in the upper surface rooftop area of swept SC LFC wings. Similar boundary layer crossflow cancellation minimizes crossflow instability on the lower surface. A steep rear pressure rise with suction eases boundary layer crossflow in this area. Compressibility strongly alleviates TS-type boundary layer instability on the upper surface to allow substantial suction interuptions across the main wing structure.
The inherently small low drag C L — range of SC LFC airfoils, resulting from Mach wave reflections within the supersonic zone, increases by deflecting a trailing edge cruise flap. Weak off-design shocks develop at higher C L ’s with flap down, requiring distributed suction in the shock area for 100% laminar flow. Alternately, these may be cancelled by active contour correctors.
Cruise flaps raise the low drag C L — range further by lowering the peak Mach number of the front pressure minimum and increasing the separation between the flap hinge and the rear end of the supersonic zone by extending the trailing edge.
In addition to flap deflection, the shockfree low drag C L — range increases substantially by proportionally adjusting the upper surface camber according to the desired C L .
The lift loss due to early transition decreases by extending the trailing edge, lowering the aft loading and applying suction in the rear pressure rise area.
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Abbreviations
- A:
-
Boundary layer disturbance amplitude
- A O :
-
Initial disturbance amplitude
- \({C_{{D_\infty }}} \) :
-
Equivalent profile drag coefficient of low drag suction wing
- C L :
-
Lift coefficient
- \( {C_{{m_{c/4}}}} \) :
-
Airfoil pitching moment (with respect to c/4)
- \( {C_p} = \frac{{2p}}{{\rho U_\infty ^2}} \) :
-
Surface static pressure coefficient
- \( \vartriangle {C_p} = \frac{{2\Delta p}}{{\rho U_\infty ^2}} \) :
-
Nondimensional surface static pressure jump across off-design flow discontinuities and shocks
- \( {C_Q} = \frac{{{\rho _{wall}}{\upsilon _o}}}{{{\rho _{amb.}}{U_{flight}}}} \) :
-
Nondimensional suction mass-flow coefficient
- c:
-
Airfoil chord
- h:
-
Height of supersonic bubble
- l:
-
Length of supersonic bubble
- M:
-
Local Mach number (normal to leading edge)
- M ∞ :
-
Free-stream Mach number
- n = ln(A/A O ):
-
logarithmic growth factor of amplified boundary layer disturbances
- Re c :
-
Wing chord Reynolds number
- \( R{e_n} = \frac{{{w_{\max }}{\delta _{0.1}}}}{v} \) :
-
Boundary layer cross flow Reynolds number (based on w max and boundary layer thickness δ 0.1 where w = 0.1 × w max)
- t/c :
-
Airfoil thickness ratio
- U ∞ :
-
Free-stream velocity (normal to leading edge)
- U flight :
-
Flight speed
- υ o :
-
Equivalent area suction velocity
- w:
-
Boundary layer crossflow velocity
- \( X = {\left( {\frac{{{W_{\max }}{\delta _{0.1}}}}{v}} \right)_{stab.limit}} \) :
-
Boundary layer crossflow stability limit Reynolds number
- x:
-
Chordwise distance
- y:
-
Vertical coordinate
- ∆y :
-
Contour difference between airfoils X782,X927 with respect to airfoil X63T18S
- α :
-
Effective wing angle of attack
- β 0.115 :
-
Deflection of 0.115 chord trailing edge cruise flap
- φ :
-
Wing sweep angle
- v :
-
Kinematic viscosity
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Pfenninger, W., Viken, J., Vemuru, C.S., Volpe, G. (1988). All Laminar Supercritical LFC Airfoils with Natural Laminar Flow in the Region of the Main Wing Structure. In: Liepmann, H.W., Narasimha, R. (eds) Turbulence Management and Relaminarisation. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83281-9_26
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