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Uncontrolled ow separation in nozzles of rocket engines is not desired because it can lead to dangerous lateral forces. Different origins for side loads were identi ed in the past. Meanwhile, it is proven that in thrust-optimized or parabolic nozzles, a major side load occurs as a result of the transition of separation pattern from free shock separation to restricted shock separation and vice versa. Reasons for the transition between the separation patterns are discussed, and the cap-shock pattern, which is identi ed to be the cause of this transition, is closely analyzed. It turns out that this pattern can be interpreted as an inverse Mach re ection of the internal shock at the nozzle axis. To prove the transition effect as main side-load driver, a subscale test campaign has been performed. Two different nozzle contours, a thrust-optimized and a truncated ideal nozzle with equal performance data, were tested. Highest side loads were measured in the thrust-optimized nozzle, when the separation pattern changes from free to restricted shock separation. Side loads measured in the truncated ideal nozzle were only about one-third as high as in the thrust-optimized nozzle.Nomenclature I sp = speci c impulse l = length p a = ambient pressure p c = chamber pressure p w = wall pressure r t = throat radius x = length°= ratio of speci c heats " = area ratio µ = ow de ection angle across oblique shock Á = ow angle

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The impetus toward development of a hydrogen-fueled scramjet engine to accelerate aerospace vehicles at hypersonic speeds has focused attention on the need to model accurately the uid-thermal-structural interaction of such engines. The proposed method is able to solve coupled thermal problems by computing high-speed turbulent and compressible ow elds including multidimensional heat conduction in adjacent walls. To achieve a completely conservative couplingat the uid-structural interface, the same nite element method is applied to both the uid and the structural equations. The use of the surface energy-balance equation with the boundary integral formulation yields a stable solution procedure for steady-state computationsof the stiff problem. For the computationof the heat transfer inside a supersonic combustion chamber, the nonreactive gas ow solver is extended by an energy source term to simulate the heat addition due to the combustion process. The code is tested and applied to a combustor and test conditions experimentally investigated within the framework of the joint German-Russian cooperation on scramjet technology. Nomenclature a = speed of sound c p = speci c heat at constant pressure D = damping operator E = total energy e = speci c energy F = viewing factor for surface radiation F¯= ux in direction ofḡ O2 = mass fraction of oxygen H = source term h = speci c enthalpy h = heat transfer coef cient k = turbulent kinetic energy M = Mach number M = mass matrix M L = lumped mass matrix N = form function Pr = Prandtl number p = pressure q = turbulent velocity P q = heat ux density R = speci c gas constant Re = Reynolds number S e = element pressure switch S ®¯= velocity gradient tensor T = temperature U = conserved variables u ® = velocity component in direction of ® x ® = Cartesian coordinates 0 = computational boundary ± ®¯= Kronecker delta ² s ¾ = radiation emission coef cient times Stefan-Boltzmann constant . Student Member AIAA. † Professor, Institute for Space Propulsion,DLR Lampoldshausen, Langer Grund; wolfgang.koschel@dlr.de. Senior Member AIAA. · = isentropic exponenţ = thermal conductivity ¹ = viscosity º = Runge-Kutta level ½ = density ¾ = stress tensor Ä = computational domain ! = speci c rate of turbulent diffusion Subscripts and Superscripts d = diffusive e = element F = uid I; J = global node number i; j = local element node number k= turbulent uctuation of variable u w = wall ;¯= partial derivative with respect to xĪ ntroduction T HE high demands on the capability and performance of future engine components promote the development of new analysis and design methods for engine systems. Those methods combine classically separated elds of interest such as aerodynamic and structural analyses to reduce the margin of error introduced by the analysis. Until recently, combined methods of solution for uidstructural interaction have mainly been applied to the sizing of the thermal protection system, 1 to improving the prediction of heat resistance for turbine blades, 2 or to the analysis of thermal loads ...