Journal of Computational Engineering

Volume 2016, Article ID 8401249, 14 pages

http://dx.doi.org/10.1155/2016/8401249

## Computationally Efficient Assessments of the Effects of Radiative Transfer, Turbulence Radiation Interactions, and Finite Rate Chemistry in the Mach 20 Reentry F Flight Vehicle

Department of Chemical Engineering, University of North Dakota, P.O. Box 7101, Harrington Hall Room 323, 241 Centennial Drive, Grand Forks, ND 58202-7101, USA

Received 8 March 2016; Revised 13 May 2016; Accepted 16 May 2016

Academic Editor: Minvydas Ragulskis

Copyright © 2016 Gautham Krishnamoorthy and Lauren Elizabeth Clarke. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Effects of finite rate chemistry, radiative heat transfer, and turbulence radiation interactions (TRI) are assessed in a fully coupled manner in simulations of the Mach 20 Reentry F flight vehicle. Add-on functions were employed to compute a Planck mean absorption coefficient and the temperature self-correlation term (for TRI effects) in the optically thin shock layer. Transition onset was induced by specifying a wall roughness height at the experimentally observed transition location. The chemistry was modeled employing eight elementary reactions and an equilibrium approach allowing species to relax towards their chemical equilibrium values over the process characteristic time scale. The wall heat fluxes in the turbulent region, density, and velocity profiles compared reasonably well against measurements as well as similar calculations reported previously. The density predictions were more sensitive to the choice of modeling options than the velocities. The radiative source term magnitude agreed closely with its measurements deduced from shock tube experiments. The TRI model predicted a 60% enhancement in emission due to temperature fluctuations in the turbulent boundary layer. While the variations in density and velocity predictions among the models diminished along the length of the body, the O and NO prediction variations extended well into the turbulent boundary layer.

#### 1. Introduction

Planetary entry vehicles are subjected to significant aerothermal heating as they dissipate their kinetic energy into the atmosphere of their destination planet. The very high velocity of an earth bound reentry vehicle causes viscous dissipation and the formation of a shock wave resulting in very high air-temperatures surrounding the vehicle. Intense thermochemical processes occur in the region between the body surface and the shock. The molecules in the surrounding air dissociate and might be far from their equilibrium state [1, 2]. These reactions may be further catalyzed by the products resulting from the decomposition and ablation of the vehicle’s thermal protection system (TPS). For earth reentry, the concentrations of N and O and their recombination to produce NO molecules surrounding the vehicle in particular have been determined to be important towards determining the shock and boundary layer characteristics and for providing more reliable TPS sizing requirements [3, 4]. Further, at certain reentry conditions radiative transfer can contribute both to the surface heat fluxes and to the cooling of the shock and boundary layers surrounding the vehicle depending on the spectral emission and absorption properties of the surrounding molecules [5, 6]. Computational Fluid Dynamics (CFD) through a coupled modeling of nonequilibrium, reacting flows with radiative heat transfer can yield valuable insights into the flow characteristics within these hypersonic flight environments [7, 8]. However, due to the fact that radiative heat transfer calculations are inherently expensive as a result of its strong spatial, directional, and wave-length dependencies [9, 10], the radiation field is often computed in a 1D domain. Further, the coupling between the radiation and the thermal field is accomplished in a loose coupling/decoupled manner [11]. These approaches are justified by facts that, at high reentry velocities, the radiative heat flux to the stagnation point is significant. The shock stand-off distance is small compared with the nose radius of vehicles, and a spatial change of physical properties is much more severe in the direction normal to the shock than in the tangential direction. Since it is well known from simulations of combustion phenomena that a strong coupling between the fluid dynamics and radiative heat transfer is necessary to accurately predict the concentrations of minor species such as O, N, and NO [12, 13], this may hold true in hypersonic flows as well. Similarly, combustion simulations have also examined and highlighted the importance of turbulence-chemistry and turbulence radiation interaction (TRI) models on these minor specie concentrations [14, 15]. Therefore, the primary goals of this paper are as follows:(1)To demonstrate a simple methodology for providing initial assessments of radiative transfer and TRI effects in a computationally efficient manner in hypersonic flow simulations for an optically thin shock layer.(2)To provide an initial assessment of fully taking into account radiative transfer and TRI effects on the density, velocity, and O and NO predictions surrounding a hypersonic vehicle.(3)To assess the differences between employing finite rate chemistry and equilibrium based thermochemical models on the density, velocity, and O and NO predictions surrounding the vehicle [16, 17].

The hypersonic flow scenario specifically chosen for the purpose is the Reentry F flight vehicle which is a cone with a 5-degree half angle with a small spherical nose tip (Figure 1) [18]. This has been a valuable dataset for evaluating the predictions of several CFD codes. The criteria that make this a good test case for this investigation are as follows:(1)The gas temperature was found to be more than 6000 K at the nose tip with dissociation of oxygen and nitrogen occurring. Further dissociation of oxygen in the boundary layer was observed as a result of viscous dissipation resulting in temperatures around 3000 K [19]. The high temperatures make it a good test case to investigate the sensitivity of the predictions to equilibrium chemistry, finite rate chemistry, and radiation models.(2)At an altitude of 24.4 km (which is the conditions investigated in this study), the laminar to turbulence transition occurred at about 62.5% the total wall length translating to 2.5 m along the length of the simulated vehicle. This implies a significant interplay between turbulence, chemistry, and radiative transfer spanning the remaining 1.5 m of the simulated cone providing sufficient length of the domain to investigate the effects of TRI on the flow field.(3)Local thermodynamic equilibrium (LTE) can be assumed at this altitude. When shock passes through air, the energy goes initially into the translational energy of the molecules and is later redistributed into the rotational and vibrational energy levels. At 24.4 km this energy redistribution rapidly results from collisions but can be much slower at higher altitudes. However, LTE is a good approximation at altitudes between 15 km and 45 km [20]. Therefore, this alleviates the need to solve separate transport equations for the rotational and vibrational temperatures and subsequently use a geometric average of those temperatures to estimate the reaction rates, radiative transfer.(4)In general, the pathlines (the path followed by a fluid element) after the strongly dissociating shock layer will determine the chemical composition at any given location [2]. Therefore, at large distances downstream of the bow shock the chemistry is assumed to relax towards equilibrium. Considering the large length of the vehicle (4 m), the differences between the finite rate and equilibrium predictions can be quantified and the validity of this assumption can be assessed at a number of locations along the body including the turbulent boundary layer.(5)The availability of numerical results encompassing this scenario from previous investigators is needed to assess the validity of our simulation techniques.