Speaker
Description
- Introduction
The reentry of space debris is a major safety concern. Since only part of the debris are destroyed in the atmosphere, it is essential to be able to characterize the size, number and impact zone of the remaining fragments. Estimating the survivability of an object and its trajectory requires an accurate knowledge of the aerothermodynamics of the shock layer surrounding it.
At high altitudes and low freestream densities, the flow is in the transitional regime and shows rarefaction effects while maintaining a strong chemical activity. This highly non-equilibrium configuration may be simulated using the Direct Simulation Monte Carlo method. To achieve a reliable description of the interplay between chemical processes and the non-Boltzmann population of excited levels, one must resort to using detailed chemical models. In state-to-state models, each level is considered a distinct species (or rather “pseudo-species”) and followed individually. The resulting distribution provides valuable information to assess non-equilibrium radiative effects.
The application of such models proves to be difficult. The range of concentration of the various excited states spans over orders of magnitude. Most of them act as trace species, which are problematic for particle methods. Indeed, in a typical DSMC study, each simulated particle represents billions of real gas particles, so that the computation is affordable. If trace species are present, this ratio must be decreased to keep enough simulated particles of each species and have meaningful samples. The higher the number of species (i.e. levels) and their energy, the higher the computational penalty, making the computational cost of a state-to-state simulation prohibitive. One must then consider indirect strategies, such as the one presented in this work.
- Computational method
Boccelli et al. [1] have developed a Lagrangian reactor approach to refine the thermochemical description of pre-existing aerodynamic calculations using improved chemical models. It allows introducing an arbitrary number of new species and chemical processes. These are described by a rate equation using temperature-dependent reaction rates. It can therefore cope with any number of trace species, being free of statistical noise issues associated with DSMC.
The basic assumption underlying the method is that the trace species have a weak influence on the bulk flow. One may therefore decouple the computation of these species kinetics, and a simplified chemical scheme in the aerodynamic simulation suffices to obtain the main features of the flow. The method seems especially appropriate for the computation of electronically excited states kinetics: given typical shock layers temperatures, these are produced in small amounts merely influencing the global density and velocity fields.
The decoupled high-fidelity chemical simulation is overlaid on the flow field. Assuming steady-state and neglecting diffusion, the advection terms in the different governing equations are written as derivatives with respect to the streamline curvilinear abscissa. The resulting equations are ordinary differential equations solved with a forward marching method along each streamline. This allows for a substantial speedup with respect to a coupled approach.
The procedure involves three successive steps:
(1) Perform a baseline simulation with only major species and chemical processes;
(2) Extract aerodynamic quantities $u(s)$, $ρ(s)$, $T_{m}(s)$, $x_{i}(s)$ along one or more streamlines ($s$ is the curvilinear abscissa, $i$ the species index and $m$ denotes the internal energy mode);
(3) Solve the species mass conservation and the energy modes conservation equations along the streamlines with refined chemistry.
In the Lagrangian solver, the flow is modelled with a two-temperature $T$-$T_{v}$ model. The rotational mode is assumed to be in equilibrium with translation at temperature $T$, while the vibrational mode in equilibrium at $T_{v}$; free electrons are coupled to vibration. Since a state-to-state description of the electronic levels is adopted, no equation is needed for the electronic energy mode; it only requires to solve a mass conservation equation for each level.
- Kinetic models
The baseline simulation employs a mixture comprised of the neutral species N$_{2}$, O$_{2}$, N, O and NO. The chemical model includes dissociation and exchange (Zel’dovich) reactions, implemented through the TCE model. Relaxation of the molecules rotational and vibrational energy is handled with the usual empirical models.
The detailed Lagrangian-reactor based computation makes use of the CoRaM state-to-state model developed at CORIA [2]. It takes into account numerous electronic levels of N$_{2}$, O$_{2}$, N, O, NO and their ions. The kinetic scheme covers the related excitation/deexcitation processes by heavy particle and electron impact as well as chemical reactions (dissociation/recombination, ionisation/recombination, exchange, dissociative recombination/associative attachment, etc.).
- Application
The test case is a 2D air flow around a 20 cm diameter cylinder. Freestream temperature and pressure are $T_{\infty}$ = $T_{v, \infty}$ = 200 K and $p_{\infty}$ = 1.38 Pa. The Mach number is 26 ($V_{\infty}$ = 7.5 km/s) and the Knudsen number based on the diameter is 0.01. These conditions are typical of those experienced by debris at an altitude of 80 km.
Acknowledgements:
J. Am. wishes to acknowledge the support of L. Walpot, European Space Agency and C.N.E.S. (Centre National d’Etudes Spatiales).
References:
[1] S. Boccelli, F. Bariselli, B Dias & T. Magin. Lagrangian diffusive reactor for detailed thermochemical computations of plasma flows (to be published).
[2] J. Annaloro & A. Bultel, Vibrational and electronic collisional-radiative model in air for Earth entry problems, Phys. Plasmas, 21, 123512, 2014.
Summary
Non-equilibrium chemistry and radiation in the shock layer of hypersonic entry flows are greatly influenced by electronically excited species. The computation of these species in the transitional regime using the DSMC method is a challenging task owing to their low concentration. A strategy to deal with such flows is presented. A Lagrangian reactor approach is adopted to compute the population of excited species, starting from a baseline solution provided by a prior DSMC simulation. The method allows for an arbitrary refinement of the chemical model to take into account trace species and is particularly suitable for state-to-state computations.
