# Unresolved problems

Suction force:

Compared to lower flight speeds, the efficiency of leading edge suction in supersonic flow is reduced. Basically the effect should be correlated to the Mach number components normal to the leading edge, trailing edge, maximum thickness line etc. Following M. Mann and H. Carlson (67]. it should be correlated to free stream Mach number

Reasons for loss of suction force are:

• Low – pressures generate suction forces, but reduce density. This diminishes efficiency of suction forces, especially in combination with shock losses. These arc compressibility efTects which should be related to normal Mach numbers.

• Supersonic trailing edges inhibit circulation efficiency and so reduce suction force recovery. For supersonic leading edges suction force is lost.

• The flow field in the vicinity of the wing is governed by radiation processes. These processes arc not axactly modeled by numerical calculations: lincari/ed theory docs not течкі effects of local Mach number variations and therefore is unable to produce the correct radiation directions (characteristics). Most nonlinear methods respect for the local Mach numbers, but do not exactly model radiation; so numerical diffusion smears out radiation transport.

• Supersonic wings arc mainly designed for minimum wave drag. This leads to nearly conical flow situations. At higher Mach numbers with smaller Mach angles this introduces strong pressure gradients in spanwise direction, i. e. normal 10 the free stream direction. Boundary layer flow tends to follow local pressure gradients; so, boundary layer air will accumulaie in the low pressure valleys on the w ing and may modify the designed low wave drag pressure distributions. This effect should strongly depend on Reynolds number and might be stronger in low Reynolds wind tunnel tests than in free flight. This effect is mainly related to free stream Mach number

Radiation in CFD solutions:

Linearized theory does not model cfTccts from local Mach number variations. Usual CFD methods do respect these, but only marginally model radiation properties Numerical stability is achieved usually by addition of numerical viscosity. Without proper modelling of radiation properties, though, random contributions arc introduced into the solution or valid contributions arc assumed to be zero Upwind schemes should model radiation, but most upwind schemes are basically one-dimensional and cannot model radiation direction, like all the upwind schemes which only fulfill the eigenvalue sign; i. e. they approximate the radiation direction by an accuracy of up to ±90* Only CFD methods which are carefully based on the method of characteristics provide good radiation properties, but these methods usually arc not suited for universal CFD codes, especially for their rather inflexible handling of complicated geometries. A challenge remains to improve the tools for supersonic CFD

Physical drug contributions:

To improve the aerodynamic design of an aircraft, it is very helpful! to know the different contributors fo physical drag-

• Wave drag (radiated energy plus entropy generated by shocks)

• induced drag

• friction drag

• separation drag

For subsonic flow and linearized supersonic flow, methods exist largely based on far field balances, c. g. (68]. but for nonlinear supersonic flow the far field results are poor because of inexact radiation models. Also, surface integration accuracy is more difficult to achieve; only friction drag can easily be extracted.

Supersonic laminar flow:

This technology is still a big challenge, for both theoretical predictions and even more for experimental verification With aerodynamic efficiency improvements by successful lami – narisanon promising to be very high, a special book chapter is devoted to that field

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