The method of characteristics is used to calculate the unsteady one-dimensional flow produced by the convection of a temperature disturbance, contained between two contact surfaces, in high subsonic flow through a nozzle. The results show the development of the pressure disturbances which are associated with the force perturbation needed to accelerate the temperature disturbance at the same rate as the surrounding gas and propagate in both the upstream and downstream directions. Using a simple flow model, expressions for the mean pressure disturbances are derived and shown to be in good agreement with numerical solutions. Other numerical solutions which show the effect of changing the various flow parameters and the nozzle shape are presented. In all of the cases considered, the pressure disturbances caused by a 10 % change in the inlet temperature are significantly large and may be an important part of ‘excess’ noise.
Application of a wake roll-up method coupled with the vortex lattice method and approximate expressions for the receiver fuselage effect have been used to determine the induced loads on a Hercules receiver aircraft behind a KC10 tanker. The induced loads depend strongly on the vertical position of the receiver wing and fin relative to the tanker wing wake. In the case of steady sideslip there is a large decrease in the directional stability of the receiver as quantified by the gradient of the rudder angle versus sideslip. This is due mainly to the combined effects of the yawing moments due to bank, yaw and side displacements. Minimum directional stability corresponds to the tip of the receiver fin intersecting the tanker wing wake. The associated aileron angle is two to three times the value in free air in agreement with flight test data. Solution of the linearized equations of motion gives three lateral characteristic oscillations for the air-to-air refuelling case. These include the usual Dutch roll oscillation, a highly damped rolling oscillation and a divergent oscillation involving mainly bank and side displacements.
The momentum integral method of Klineberg is shown to provide a good description of the major characteristics of two-dimensional laminar viscous-inviscid interactions a t hypersonic speeds. Surface pressure and heat-transfer-rate measurements were made for sharp compression and expansion corners at Mach 12.2 and are compared with the theoretical predictions. The agreement is found to be good for attached, incipient and fully separated flows.Some theoretical comparisons between methods based on the Klineberg formulation are made which suggest that the full boundary-layer equations are well described using integral methods that incorporate the energy equation. It is further shown that the properties associated with the stability of the governing differential equations are mathematical properties of the analytical model and should not be associated with any physical characteristics of the boundary layer.A correlation of hypersonic, cold-wall, incipient separation data is also presented.
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