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INTRODUCTION
A broad range of high-enthalpy and plasma technology applications exhibit thermochemical nonequilibrium effects, ranging from solar physics and thermal plasmas [1], combustion and plasma-assisted ignition [2], diagnostics [3], and materials technology in general. In aerospace applications, the radiative heat flux to the heat shield of planetary entry probes [4] depends on the populations of atomic and molecular internal energy levels, often out of equilibrium. In particular, many chemically reacting species are present in atmospheric entry flows for space vehicles reaching entry velocities higher than 10 km/s [5]. Aiming at deep space exploration, detailed chemical mechanisms become of primary importance to optimize the efficiency of electric propulsion devices [6].
The simulation of plasmas with atomic and molecular energy level populations out of thermochemical equilibrium requires a comprehensive modeling of all the elementary collisional and radiative processes involved. Detailed simulations are based on a large set of chemical species and their related chemical mechanism [7]. Coupling such mechanisms to flow solvers is computationally expensive and often limits their application to 1D simulations.
The simulation of non-trivial geometries becomes feasible by adopting strategies to lower the computational cost associated with chemistry modeling, while retaining a good level of physical realm; principal component analysis (PCA), energy levels binning and rate-controlled constrained-equilibrium (RCCE) being some possible approaches (see for example [8]). Yet, the problem remains complicated enough to run out of the current supercomputing capabilities when real-world applications or design loops are targeted.
A pragmatic way to address the problem still relies in strong simplifying assumptions.
The idea of decoupling flow and chemistry is sometimes used in the chemistry community to include detailed mechanisms into lower-fidelity baseline solutions [9].
In atmospheric entry plasmas, a Lagrangian method using a collisional-radiative reactor has been coupled to a flow solver [10] based on the 1D method proposed by Thivet to study the chemical relaxation past a shockwave [11]. Lagrangian tools, allowing for the refinement of an existing solution with very small computational effort, are based on fluid models.
The aim of this work is to develop a method for including detailed thermochemical effects into lower-fidelity baseline solutions through an efficient Lagrangian diffusive reactor. Our approach starts from a baseline solution for a plasma flow, by extracting the velocity and total density fields along its streamlines, and thus decoupling thermochemical effects from the flowfield. The main assumption is that fine details of the species energy level populations, as well as trace species in the mixture, do not severely impact the hydrodynamic features of the flow. This is the case for many applications, such as the aerodynamics of a jet, the location of a detached shock wave, or the trail behind a body flying at hypersonic speed. As long as the total energy transfer can be modeled by means of some effective chemical mechanism, a more detailed description of the thermo-chemical state of the plasma can be obtained by re-processing the baseline calculation using more species and chemical reactions.
The originality of this contribution consists in exploiting the Lagrangian nature of the proposed method, developing a general solution procedure based on an upwinded marching approach, adding rarefied, multi-dimensional, and dissipative effects. The consequence is a drastic boost in the computational efficiency, allowing to deal with a large number of chemical species.
We propose to develop a tool to obtain reasonably accurate predictions of the thermochemical state of a flow using an enlarged set of species and describing thermal nonequilibrium via multi-temperature, state-to-state, or collisional-radiative models. As a proof of concept, we account for radiation-flow coupling via escape factors. Reaching higher accuracies using detailed chemistry output of the Lagrangian reactor to solve the radiative transfer equation can be studied in a future work.
The presented strategy can be employed as a design tool to obtain information too expensive for a fully coupled approach. Alternatively, it can also be used for diagnostic purposes to promptly estimate the effect of different physico-chemical models into realistic simulations: this allows us to understand whether a simplified modeling can be suitable for the considered problem. Finally, with respect to particle-based flow simulations, such as those obtained with the Direct Simulation Monte Carlo Method (DSMC), the proposed method smooths out the noise and irregularities associated to the inherent stochastic approach, improving the prediction of minor species. Electronic energy levels, which would require a particularly detailed and computationally intensive approach otherwise, can also be easily computed.
The capabilities of the method are assessed against five problems, namely: (i) Chemical refinement, (ii) Thermal refinement, (iii) State-to-state refinement, (iv) 2D rarefied flow, and (v) Mass and energy diffusion.
In all the performed testcases, we investigate the accuracy of the thermochemical description and its computational cost.
References
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Bellemans A. et al., Reduction of a collisional-radiative mechanism for argon plasma based on principal component analysis, POP, Vol.22, 2015.
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Corbetta M. et al., CATalytic – Post Processor (CAT-PP), Computers & Chem. Eng., Vol. 60, 2014.
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Magin T. E. et al., Nonequilibrium radiative heat flux modeling for the Huygens entry probe, Journal of Geophysical Research: Planets, Vol. 111, 2006.
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Thivet F., Modeling of hypersonic flows in thermal and chemical nonequilibrium, PhD thesis, Ecole Centrale Paris, 1992.
Summary
The simulation of thermochemical nonequilibrium for atomic and molecular energy level populations in plasma flows requires comprehensive modeling of the elementary collisional and radiative processes involved. Coupling detailed chemical mechanisms to flow, solvers, is computationally expensive and often limits their application to 1D cases. We describe the development of an efficient Lagrangian reactor moving along streamlines of a multi-dimensional baseline flow simulation to introduce detailed thermochemical effects. The method is efficient and allows to the model both continuum and rarefied flows while including mass and energy diffusion. The solver is tested on normal shockwaves and 2D and axisymmetric blunt-body rarefied hypersonic flows, where the Lagrangian reactor shows able to drastically improve the baseline simulations at a very low computational cost. The solver is also immune from statistical noise, which strongly affects the accuracy of calculations obtained through the Direct Simulation Monte Carlo method, especially considering minor species in the mixture. Results demonstrate that the method enables applying detailed mechanisms to multidimensional solvers to study thermo-chemical nonequilibrium flows.
