Thermal Analysis of Fluid-Structural Interaction in High-Speed Engine Flowfields

Abstract

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 ...

Numerical analysis of a divergent duct with high enthalpy transonic cross injection

“…The wall is of uniform thickness and of the same material throughout. The wall is 16 mm thick and is not cooled during the experiment [9]. The geometry considered for analysis is the same as considered by Reinartz and Koschel [9] and is shown schematically in Fig.…”

“…The inlet flow conditions of the test case [9] without injection are: Mach number − 3.0, total pressure − 2.33 MPa, total temperature-1701 K and mass flow rate − 1.6 kg/s. The injection of hydrogen is simulated by injecting a cold air jet at a Mach number of 1.05 and a stagnation or total pressure of 1.6 MPa.…”

“…The static temperature of injection is taken to be 280 K. In the present study, three cases have been investigated for flow with cross/transverse injection of air at Mach numbers of 2.0, 2.5 and 3.0. For each case, the temperature of air at the inlet has been taken as 607.5 K [9]. The operating pressure has been taken as atmospheric.…”

“…The size of the mesh near the wall has to be fine enough to resolve the viscous sub layer. The number of cells generated is more than the number of cells considered in [9].…”

“…Analysis of fuel mixing in supersonic combustors has been carried out by some researchers [7−8]. The objective of the present study is to carry out a numerical investigation of high-speed flow fields through the supersonic combustor without fuel injection but with high enthalpy air injection, following the combined experimental and numerical work of Reinartz and Koschel [9].…”