Closely Coupled Flowfield-Radiation Interactions During Hypersonic Reentry

Abstract

Q2A one-dimensional tangent slab radiative transport solver is developed to model radiation in nonequilibrium hypersonic flows. The solver is line-by-line accurate and (by making use of attached spectral databases) efficient, allowing for direct coupling to hypersonic computational fluid dynamics codes. Modifications to the spectral databases include a hybrid line-by-line-gray solver and a molecular cross-section method based on the assumption of a single representative temperature. These modifications decrease computational costs to allow for tight flow coupling hypersonic computational fluid dynamics solvers, but they maintain line-by-line accuracy. The radiation code is verified by comparison with nonequilibrium air radiation, an established radiation solver. The solver is then integrated into the continuum computational fluid dynamics solver data-parallel line relaxation, and coupled simulations are performed for the flowfields of the Stardust sample return capsule and the Orion crew exploration vehicle. NomenclatureB 1 = single-temperature upper state population parameter B 2 = single-temperature upper-lower state ratio parameter c = speed of light, m=s, or mass fraction E = total emission energy, W E b = blackbody emissive power, W=m 3 A E n = exponential integral of order n F = state rotational term energy G = state vibrational term energy h = Q3 Planck constant; 6:6261 10 34 J=s i = line index I b = blackbody function, or Planck function, W=m 3 A sr I = spectral intensity, W=m 3 A sr J = radiosity, W=m 2 J U = upper state rotational quantum number k = Boltzmann constant; 1:3807 10 23 J=K N = number density, m 3 n = number of cells n s = total number of species s q = heat flux, W=m 2 Q VR U = upper state total partition function S = source function W=m 3 A sr T = total temperature, K T e = free electron temperature, K T r = rotational temperature, K T t = translational temperature, K T v = vibrational temperature, K V = cell volume, m 3 v = velocity, m=s V U = upper state vibrational quantum number w = line width, Å X = x-cartesian coordinate, m Y = y-cartesian coordinate, m z = distance in body-normal direction, m = Goulard number, or radiative cooling parameter = wall emittance " = emission coefficient, W=m 3 A sr " c i = emission constant, W= A sr max = maximum absorption coefficient in spectral band, m 1 = absorption coefficient, m 1 = wavelength, Å = density, kg=m 3 = optical thickness = line shape function r q r = divergence of radiative heat flux, W=m 3 Subscripts a = atomic c = at line center, or convective e = electronic i = line index L = Lorentz width, lower state m = molecular r = radiative s = species index tot = sum over all species U = upper state V = Voigt width = at a given wavelength, or per unit wavelength 0 = at boundary 1 = term due to true absorption 2 = term due to induced emission 1 = freestream parameters

An efficient computational approach to hypersonic nonequilibrium radiation utilizing Gaussian Quadrature and Space Partition

“…On each discrete grid points, the kinematic, thermodynamic properties, and the composition of the flow medium are generated by solving the interdisciplinary governing equations consisting of the compressible Navier-Stokes equation, law of mass action, and the internal energy conservation equations for vibrational and electronic degrees of freedom. The governing equations system can be summarized as [4,[8][9][10][11][12][13];…”

“…An attractive approach for solving the RTE is exemplifying by the ray tracing technique derived from the Monte-Carlo method [6,7]. The sampling and generating the pertaining optical data is paramount for achieving a meaningful statistical assemble [8][9][10][11]. The stateof-the-art methodology in this scientific discipline is rather inefficient to meet an accuracy tolerance for a better understanding.…”

On binary scaling and ground-to-flight extrapolation in high-enthalpy facilities

“…With the development of CFD, the adiabatic heat flux q r ad can now be estimated and the Goulard number is thus better known in the literature (see for example [142,52,106]) under the following form:…”

“…It corresponds to the peak heating of Stardust, often considered as a benchmark for the Goulard number [52]. Overall, radiation coupling implies that a significant portion of the flow's internal energy is leaking in the form of radiation.…”

“…That renewed interest was also motivated by the availability of flight data from the atmospheric entry of probes such as Stardust (2006) 2005). The number of publications on the topic that can be found in the literature since the last decade illustrates the renewed interest of the scientific community for these issues (see for example [67,80,52,95,118,165,174,186,210]). …”