Aerothermoelastic response of a panel under a high speed turbulent boundary layer using direct numerical simulation

Abstract

The interaction between a thin panel and a Mach 2.25 turbulent boundary layer is investigated using a high-accuracy, high-fidelity approach for the simulation of coupled fluid-structure problems. The solid solution is found by integrating the conservation of momentum equation using a non-linear 3D finite element solver, and the direct numerical simulation of the turbulent boundary layer uses a finite-difference compressible NavierStokes solver. The evolution of the panel response progresses from the emergence of low amplitude traveling bending waves to a larger amplitude standing wave type motion. Panel defections exceed 25 wall units into the boundary layer and produce compression waves that oscillate with the panel motion. Turbulence statistics are shown to be modified by the presence of the compliant panel. A large dependence on coupling configuration is shown.= thermodynamic pressure T = thermodynamic temperature ρE = total energy, = ρe + 1 2 ρu i u i ρe = internal energy, = p/(γ − 1) τ = stress tensor, τ ij = µ(∂u i /∂x j + ∂u j /∂x i ) + λ∂u k /∂x k δ ij C = specific heat capacity (J/kgK) γ = gas ratio of specific heats, = C p /C v k = thermal conductivity µ, λ = first and second coefficients of fluid viscosity q j = fluid heat flux vector, = −k∂T /∂x j x = spatial coordinates in current configuration, = (x, y, z) T ξ = computational coordinates, = (ξ, η, ζ) T δ 99 = boundary layer visual thickness δ * = boundary layer displacement thickness θ = boundary layer momentum thickness t = time t = traction ǫ = convergence value B = solid configuration X = spatial coordinates in reference configuration, = (X, Y, Z) T φ = solid domain coordinate transformation, = (φ 1 , φ 2 , φ 3 ) T F = solid domain coordinate deformation gradient, = ∂x/∂X Θ = solid domain temperature β = thermal stretch ratio σ = Cauchy stress tensor P = first Piola-Kirchhoff stress tensor δu = virtual displacement, = (δu 1 , δu 2 , δu 3 ) T δW = virtual work J = JacobianSubscript i, j = direction index w = wall n = normal ref = reference condition 0 = solid reference configuration