Speaker
Description
Background of the study : The windward side of a re-entry vehicle needs to be protected by a heat shield, made of advanced thermal protection materials (TPMs) to overcome the tremendous amount of heat loads during planetary entry. Because in-flight testing of new TPMs is prohibitively expensive, the extreme heat loads imposed on a thermal protection shield during hypersonic re-entry are reproduced by placing a sample of a TPM in a hot jet of plasma. An important class of plasma wind tunnels is the ICP (inductively coupled plasma) facility which offers a large volume of contamination-free plasma for a considerable amount of time as it does not require electrodes to generate the plasma. As a result, ICPs are often preferred for testing of thermal protection systems for re-entry vehicles.
An important aspect in the modeling of ICPs is the possible impact of Non-Local Thermodynamic Equilibrium (NLTE) effects. Most of the ICP studies reported in the literature assume that LTE conditions prevail. This assumption, however, breaks down at low pressures due to lowering of collisional rates among gas particles. As a matter of fact, temperature and chemical composition distributions in low pressure ICPs may show significant departure from equilibrium. Under these circumstances, the availability of accurate NLTE kinetics models is of paramount importance. This task may be achieved, in theory, by adopting a State-to-State (StS) kinetics formulation. In Sts models each internal energy state is treated as a separate pseudo-species, thus allowing for taking into account non-Boltzmann distributions. State-to-State models provide a superior description compared to conventional multi-temperature (MT) models, which are based on Boltzmann distributions. Most StS models assume that the rotational and vibrational energy levels of molecules are populated according to Boltzmann distributions at their own temperatures, $T_r$ and $T_v$, respectively. These models solve the master equation only for the electronic levels thereby implicitly assuming small departures from Boltzmann ro-vibrational distributions. However, although the assumption of rotational equilibrium may be safely assumed for ICP applications, the same assumption does not hold for the vibrational states of molecules such as $\mathrm{N}_2$ and $\mathrm{N}_2^+$ and may need a vibronic state-to-state treatment. Also, the radiative effects inside the ICP facilities have largely been neglected in most of the ICP studies. There are hardly any literatures presenting a systematic study of radiative effects in ICPs.
The present work demonstrates a high-fidelity multi-physics computational framework to study non-equilibrium and radiative phenomena in inductively coupled plasma discharges. This framework couples the plasma flow solver HEGEL (High fidElity tool for maGnEto-gas-dynamics simuLations) with an electro-magnetic solver FLUX (Finite-element soLver for Unsteady electromagnetix) for the magneto-hydrodynamic modeling of the ICP. The framework is further coupled with a radiative transport solver MURP (MUlti-fidelity Radiation Package) for taking into account the radiative effects while modeling the ICP discharge.
Methodology : The dynamics of NLTE gaseous plasmas treated in this work are governed by the species mass, global momentum and energy, and vibronic energy equations which have been implemented in a finite-volume solver HEGEL which uses the PLATO (PLAsma in Thermodynamic nOn-equilibrium) library for evaluation of plasma-related quantities (e.g. thermodynamic properties,
etc.). The electromagnetic field inside ICPs are governed by the set of Maxwell's equations which are solved in a mixed finite-element solver FLUX. Radiative heat transfer in the ICP facility is investigated using the numerical code MURP which is a finite-volume radiative heat transfer solver encompassing self-consistent non-Boltzmann spectral modules ranging from line-by-line to reduced-order approaches for the accurate and efficient description of plasma's spectral properties desired in the present work. All the above mentioned solvers have been developed at the Center for Hypersonics (CHESS) at University of Illinois.
The governing equations for the plasma are coupled to those for the electromagnetic field via the Lorentz forces and Joule heating source terms. At the same time, the electric and magnetic field within the plasma are affected by the electrical conductivity of the latter. As a result, the two datasets (Lorentz forces and Joule heating for HEGEL, and electrical conductivity for FLUX) are passed at every fluid time-step to accurately capture the magneto-hydrodynamic phenomena occurring within an ICP. Similarily, HEGEL passes the species populations and the temperatures to MURP, while MURP feeds back the computed radiative losses as an energy source term to HEGEL. The required volume coupling between the above mentioned solvers is here realized using preCICE, an open source coupling library for partitioned multi-physics simulations. The electromagnetic equations are solved on a farfield mesh coinciding with the fluid mesh where only the torch section is meshed.
Results : Preliminary simulations have been performed using an electronic CR (collisional-radiative) model for Nitrogen [$e^-$, $N(1-7)$, $N_2(1-6)$, ${N_2}^+(1-5)$, $N^+$] plasma where we resolve the electronic-states by tightly coupling the electronic master equations with the conservation equations. The calculations have been done for 2D axi-symmetric torch configuration where cold Nitrogen gas is injected through a thin annular injector which gets heated by six parallel inductor coils. The operating conditions for the preliminary calculation are as followed : length of the torch 0.486m, torch radius 0.08m, pressure 1000 Pa, inductor power 50 KW, inductor frequency 0.45 MHz, inlet mass flow 6 g/s. The radial population distributions of the elctronic states of the chemical components at the mid-torch axial location show a significant amount of deviation from the populations obtained using Boltzmann distribution. The electronic state-to-state simulation results show the incapability of the conventional multi-temperature model in predicting the correct plasma physcis and suggest a need to do a more detailed study of ICPs using state-of-the-art CR models.
Conclusion : A high-fidelity multi-physics computational framework to study inductively coupled plasma discharges has been presented. Preliminary calculations using a multi-temperature model show a significant extent of non-equilibrium between the trans-rotational and the electron-electronic-vibrational modes at lower pressures. Furthermore, calculations performed using electronic CR model show a large deviation of the species populations from that obtained using Boltzmann distribution.
Future work will focus on using state-of-the-art vibronic CR models to simulate ICP discharges while taking into account the radiative effects via CFD-radiation coupling.
Summary
The present work demonstrates a high-fidelity multi-physics computational framework to study non-equilibrium and radiative phenomena in inductively coupled plasma discharges. This framework couples the plasma flow solver HEGEL (High fidElity tool for maGnEto-gas-dynamics simuLations) with an electro-magnetic solver FLUX (Finite-element soLver for Unsteady electromagnetix) for the magneto-hydrodynamic modeling of the ICP. The framework is further coupled with a radiative transport solver MURP (MUlti-fidelity Radiation Package) for taking into account the radiative effects while modeling the ICP discharge. Preliminary calculations using a multi-temperature model show a significant extent of non-equilibrium between the trans-rotational and the electron-electronic-vibrational modes. Furthermore, calculations performed using electronic CR model show a large deviation of the species populations from that obtained using Boltzmann distribution.
