Scramjet powered hypersonic vehicles represent the next critical step toward achieving NASA's vision for Highly Reliable Reusable Launch Systems (HRRLS), affordable space access, planetary re-entry systems, and global reach vehicles. The design of such vehicles is a very interdisciplinary and highly complex problem. As such, the development of varying fidelity mathematical models for assessing overall stability and performance during the design process is very important. In particular, developing "low-order" models with "sufficient fidelity" to capture control-centric phenomena becomes vital in early stages of vehicle design. Historically, the early stage vehicle design process never incorporated control related considerations. The design obtained by such practice is not optimal and can often lead to poor design from a stability and performance view point. This paper presents control-relevant modeling efforts which will facilitate quick iterative control analysis and design during early stages of vehicle design. The paper is intended to be of an introductory nature and presents the high level modeling framework and associated challenges. An example linear 6 DOF model with some representative analysis is also given to demonstrate the applicability of the tool suite.
A theoretical study is made of periodic spanwise disturbances in nominally two-dimensional reattaching laminar and turbulent separated flows. A compressible small disturbance flow analysis of the local vortex instability mechanism involved is made emphasizing the three-dimensional heat-transfer effects including blowing or suction through the surface. It is shown that Reynolds analogy does not apply between the disturbance skin friction and heat transfer. The corresponding thermal response of the wall surface is also analyzed taking into account the spanwise heat conduction within the underlying surface materials; it is governed by the characteristic ratio of boundary layer heat transfer to the spanwise heat conduction. The theoretical predictions are in good agreement with experimental observations.
NomenclatureB = stagnation point inviscid velocity gradient (du e /dx) s C p = constant pressure specific heat / = similarity solution stream function g = total enthalpy ratio, H/H S h,H = static and total enthalpy, respectively [H=h + (u 2 /2)] k = thermal conductivity M = Mach number p -static pressure q = heat-transfer rate T = absolute static temperature w,f,w =streamwise, normal and sidewash velocity components inx,y,z directions, respectively x,y,z =streamwise coordinates measured from reattachment line, distance normal to surface and spanwise distance, respectively Y = compressibly-transf ormed y (d Y=p 0 dy) a = inverse wavelength parameter (2?r/X) a = a^v 0s /B 8 = boundary-layer thickness rj -similarity coordinate = Y\lB/p w^w X = spanwise wavelength of disturbance pattern H -coefficient of viscosity 6 = nondimensional wall temperature function [Eq. (11)] = kinematic viscosity = density = shear stress v P T Subscripts e g 1 0 s w = effective edge of boundary layer = gas side of wall = perturbation values in first approximation = basic two-dimensional reattaching flow = stagnation or reattachment line conditions = wall surface
An approximate analytical theory of the onset of viscous effects on hypersonic body nose shock standoff distance is developed. Boundary layers displacement, shock layer vorticity and longitudinal curvature effects are all included, as are the influence of both shock layer density ratio and arbitrary body surface temperature. Validating comparisons with both CFD results and experimental data are also presented.
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