Multi-physics modeling of electromagnetically driven surface plasma discharges

This dissertation presents the computational modeling of non-equilibrium plasma discharges on an electromagnetically driven surface and its application to plasma assisted combustion. We address challenges often encountered in high pressure plasma discharges such as the non-uniform formation of plasmas due to filamentations and show how they could be handled by using a particular type of metamaterial. A metamaterial in the present context is an artificial composite assembled with periodic elements smaller than an incident wavelength. Metamaterials have drawn significant interest in engineering communities during the past few decades due to their extraordinary electromagnetic (EM) characteristics, e.g., a negative refractive index, that cannot be naturally excited using conventional methods or materials. An interesting electrodynamic phenomenon associated with metamaterials is the possible surface wave excitation on the artificially engineered surfaces. In particular, by carefully designing the assembly of periodic elements consisting of conductors and dielectrics, a strongly localized surface wave mode known as a spoof surface plasmon polariton (SSPP) can be efficiently excited. The extraordinary electromagnetic property of SSPP is its ability to imitate the behaviors of a surface plasmon polariton (SPP) in a wide range of frequencies (GHz -THz) while SPP can exist only in the optical regime (100’s THz). In this study, our goal is to provide the in-depth analysis of the electrodynamics of SSPP, transients of surface plasma generation due to SSPP resonances, and to demonstrate the feasibility of using it for plasma assisted combustion. We have used multiple computational models that have been developed by our group and added necessary features to simulate the phenomena more accurately. In the first part of this work, we describe the numerical schemes employed for simulations. The computational tool consists of solvers for three different sets of equations: Maxwell’s equations for high frequency (HF) electromagnetics, plasma governing equations for discharge physics, and reactive Navier Stokes equations for combustion. Coupling of these equations must be done carefully due to the multi-scale nature of the high frequency plasma discharges and combustion. The length and time scales range from micrometers to centimeters and nanoseconds to milliseconds, respectively. We provide the details of the coupling of the equations as well as the discretization methods for each set of equations. In this work, one of chief contributions to improving the models is the implementation of an enhanced version of absorbing boundary condition (CFS-PML) for second order Maxwell’s equations. CFS-PML is especially suited for electromagnetic wave simulations that involve conductors which we demonstrate by solving a model problem for the verification of the code. In the second part, we present the computational study of argon surface plasma discharges generated by SSPP. The EM surface wave excitation is first analyzed in depth because the electromagnetic power absorption by electrons determines the transients of plasma breakdown. Electrodynamics of the SSPP excitation is investigated using broadband and monochromatic wave simulations. Instead of the infinite array of periodic elements, we have studied the metamaterial with a finite length for practical engineering applications. It is found that over a wide range of length scales from millimeters to centimeters, the EM waves always have a single node structure at resonance frequencies. The surface wave excited on the metasurface is characteristic of coupling between the cavity mode and surface wave mode. We refer to the resonance pertinent to such coupling as hybrid resonance. The shift of the hybrid resonance frequency is investigated in terms of varying dielectric permittivities, distances between perforations, and the whole lengths of the metasurfaces. Using an optimal configuration of the metasurface, the transients of the surface plasma generation due to the field intensification is studied. Interactions among the surface plasma, SSPP and the incident wave are presented. Multiple simulations show that even if the metasurfaces have different lengths, the transients of surface plasma formation are qualitatively identical at the hybrid resonance frequencies. Such scalability is one of the primary features of metamaterials that can be extended to the plasma discharge. In the third part, plasma assisted combustion induced by microwave sources is studied. Previous research in combustion engineering communities have addressed the importance of volumetric formation of flame kernel for successful combustion. Another key point in plasma assisted combustion is the volumetric generation of radical species in nanosecond timescale, which can significantly reduce the ignition delay for lean fuel-air mixtures. Motivated by the need for mechanisms that can generate combustion enhancing radicals over a large area, we have investigated the feasibility of using the SSPP generated surface plasmas for plasma assisted combustion. A kinetic mechanism of H₂ - air mixture that was previously established by our group is used for this study. A mixture with the equivalence ratio of 0.3 at the initial pressure and temperature of 1 atm and 1000 K is assumed, respectively. Fully coupled simulations show that the cm-scale plasma kernel can be efficiently transitioned into successful ignition and flame propagation with shortened ignition delay. In the last part, we discuss strategies to parallelize the simulation tools for high performance computing. The governing equations solved in this study are spatially discretized using either finite edge element method or cell-centered finite volume method. They require different approaches to achieve parallel scalability, and in particular, the Maxwell’s equations needs a special preconditioning technique to reduce computational time. The technique is known as nodal auxiliary space preconditioning whose theoretical background and performance on a supercomputer are presented. Additionally, the module which solves reactive Navier-Stokes equations is also parallelized to study large scale (centimeters) ignition phenomena. For both plasma-wave coupled solver and combustion solver, we discuss the details of MPI(Message Passing Interface)-based parallelization processes.