Aerodynamic Design of Unmanned and Scaled Supersonic ...

K. Yoshida and Y. Makino
drag under the limitation of design condition and planform constraints.
The key point of warp design is to suppress theoretical infinite load at leading edge. This
usually leads to a certain leading edge droop to achieve an attached flow condition, because
leading edge separation vortex is induced by local high angle of attack due to highly swept
leading edge. This is the second principle for reducing supersonic drag.
3) Area-Ruled Body
According to the supersonic slender body theory [5], wave drag due to volume of a
complete aircraft is generally related to so-called supersonic cross sectional area distribution.
This area means the projection of oblique cross sectional area of airplane cut by Mach cone
on a plane vertical to streamwise direction. The optimum axisymmetric body with the lowest
wave drag due to volume was already derived using this formulation. It was called “Sears-
Haack body”. If a wing and tails of a complete aircraft are specified, we suppose that fuselage
geometry should be improved to adjust total supersonic area distribution to that of Sears-
Haack body. It is very effective to reduce the wave drag due to total volume of the aircraft.
This improved fuselage is generally called area-ruled body. This rule is the third principle of
reducing supersonic drag, especially interference drag between wings, tails and fuselage [5].
4) Natural Laminar Flow Wing
It is well expected that an aerodynamic optimum combination of the pressure drag
reduction concepts mentioned above has large effect in reducing supersonic cruise drag.
However, it is not easy to obtain the maximum gain of drag reduction effect, because we must
consider several constraints that are not included in linear theory. Therefore, any other drag
reduction concept is necessary to improve the L/D of a future advanced SST.
Reducing friction drag is one of the candidates. A laminar airfoil design concept is usually
based on suppressing Tollmien-Schlichting (T-S) wave instability. For a low aspect ratio wing
with highly swept leading edge, transition due to cross-flow (C-F) instability is dominant at
forward part of the wing. First of all, an optimum pressure distribution must be found for
suppressing the C-F instability. The key point is to reduce the region generating cross-flow.
Cross-flow is produced by chordwise pressure gradient. At the front part of the wing, there is
always severe acceleration. Therefore, it is very effective to set narrow acceleration region.
This leads to a pressure distribution with steep gradient at front.
Since the T-S instability becomes dominant after mid-chord of the wing, gradual
acceleration is effective to suppress the T-S instability. Fortunately, most of SST planforms
have supersonic trailing edge and require no recovery of trailing edge pressure. As a result, it
was found that pressure distribution of the NLF wing had to have steep acceleration at front
and gradual acceleration from the front to the trailing edge. At the first step of the NLF wing
design, we already found an optimum pressure distribution to delay transition [6], using a
practical transition prediction method (SALLY code [7]) based on e N method [8].
As the next step, we must solve a so-called inverse design problem to achieve this pressure
distribution. Therefore, we developed an original CFD-based inverse method [9]. This inverse
method consists of iteration loop for the following two routines: i) flow estimation using a
CFD code, and ii) modifying the geometry based on the difference between target and each
5