Hypersonic Magneto-Fluid-Dynamic Compression in Cylindrical Inlet

Hypersonic magneto-fluid-dynamic interaction has been successfully performed as a virtual leading-edge strake and a virtual cowl of a cylindrical inlet. In a side-by-side experimental and computational study, the magnitude of the induced compression was found to be depended on configuration and electrode placement. To better understand the interacting phenomenon the present investigation is focused on a direct current discharge at the leading edge of a cylindrical inlet for which validating experimental data is available. The present computational result is obtained by solving the magneto-fluid-dynamics equations at the low magnetic Reynolds number limit and using a nonequilibrium weakly ionized gas model based on the drift-diffusion theory. The numerical simulation provides a detailed description of the intriguing physics. After validation with experimental measurements, the computed results further quantify the effectiveness of a magnet-fluid-dynamic compression for a hypersonic cylindrical inlet. At a minuscule power input to a direct current surface discharge of 8.14 watts per square centimeter of electrode area produces an additional compression of 6.7 percent for a constant cross-section cylindrical inlet

Implementation of the classical plasma–fluid model for simulation of dielectric barrier discharge (DBD) actuators in OpenFOAM

To simulate the coupled plasma and fluid flow physics of dielectric-barrier discharge, a plasma–fluid model is utilized in conjunction with a compressible flow solver. The flow solver is responsible for determining the bulk flow kinetics of dominant neutral background species including mole fractions, gas temperature, pressure and velocity. The plasma solver determines the kinetics and energetics of the plasma species and accounts for finite rate chemistry. In order to achieve maximum reliability and best performance, we have utilized state-of-the-art numerical and theoretical approaches for the simulation of DBD plasma actuators. In this respect, to obtain a stable and accurate solution method, we tested and compared different existing numerical procedures, including operator-splitting algorithm, super-timestepping, and solution of the Poisson and transport equations in a semi-implicit manner. The implementation of the model is conducted in OpenFOAM. Four numerical test cases are considered in order to validate the solvers and to investigate the drawbacks/benefits of the solution approaches. The test problems include single DBD actuator driven by positive, negative and sinusoidal voltage waveforms, similar to the ones that could be found in literature. The accuracy of the results strongly depends to the choice of time step, grid size and discretization scheme. The results indicate that the super-time-stepping treatment improves the computational efficiency in comparison to explicit schemes. However, the semiimplicit treatment of the Poisson and transport equations showed better performance compared to the other tested approaches.info:eu-repo/semantics/publishedVersio

INVESTIGATION OF LANGMUIR PROBES IN NON-MAXWELLIAN PLASMA USING PARTICLE-IN-CELL (PIC) MODELING

This dissertation explores the development of a capability for simulating the plasma dynamics of Langmuir probes (LP) in complex plasmas where the velocity distributions are non-equilibrium and the electron energy spectrum is non-Maxwellian with respect to laboratory and space experiments. The results of this investigation are interpreted to give recommendations for design and use of LPs. This work is conducted using computational techniques to create the exact plasma conditions of the experimental testing environments. The investigations address the following topics: development of a technique to model non-Maxwellian physics, modification of a baseline-technique and optimization of it for this application, creation of three-dimensional PIC code to include non-Maxwellian physics, evaluation of effectiveness of enhanced PIC simulations, demonstration of use of enhanced PIC code to conduct and simulate LP experiments in non-ideal conditions such as in the EP thruster. Major results can be summarized as follows: PROBEPIC (PIC code) is modified for interpreting data obtained using an electrostatic-probe in an ion-beam to implement OML (thick-sheath) and SL (thin-sheath) current-collection theories. PROBEPIC was modified to model the non-Maxwellian plasmas, and test-cases are presented to validate the simulation against published empirical data. General equations for current-collection and I-V curves for cylindrical, planar and spherical LP in isotropic and anisotropic non-Maxwellian plasmas are examined. Distribution functions are introduced as a method of measuring the deviation from Maxwellian. Existing non-Maxwellian techniques (i.e., Druyvesteyn, bi-Maxwellian) were modified to model the environment around LP in an EP system. The EEDF has been investigated with LP to overcome some limitations of Druyvesteyn method. The EEDF changes from Druyvesteyn to bi-Maxwellian with decreasing pressure. Therefore, bi-Maxwellian method was also implemented in the system to obtain utmost results in modelling non-isotropic plasmas. This innovative model, which was then integrated into PROBEPIC, was used to simulate operation of LP in a series of validation and demonstration cases. The effective-Te, n, and Vp were obtained from the LP simulations, and I-V traces were created. The code can predict the high-energy ions, and experimental measurement of the EEDF, providing useful information for the development of a state-of-the-art new plasma and EP diagnostic capabilities

A Two-dimensional Hybrid-Direct Kinetic Model of a Hall Thruster

The goal of this dissertation is to improve the state-of-the art modeling approaches available for simulating the discharge plasma in a Hall effect thruster (HET). A HET is a space propulsion device that utilizes electrical energy to ionize and accelerate propellant, generating thrust. The device features a cross-field configuration, whereby the transverse magnetic field traps electrons, and the axial electric field electrostatically accelerates ions out of the thruster channel. This configuration enables desirable thruster performance characteristics typically characterized by a relatively high specific impulse (1000-3000 s) and a high thrust density (a few Newtons per square meter). High fidelity computational models are useful to investigate the physical processes that govern the HET's performance, efficiency, and lifetime limitations. The non-equilibrium nature of the plasma transport should be resolved so that the flow can be accurately characterized. A grid-based direct kinetic (DK) simulation is capable of modeling the non-equilibrium state of plasma without the numerical noise that is inherent to particle-based methods since the velocity distribution functions (VDFs) are obtained in a deterministic manner. As the primary objective of this work, a two-dimensional, hybrid-DK simulation of the discharge plasma in a HET is developed. As a secondary objective, a plasma sheath, one of the important physical structures that form in the discharge plasma of a HET near the channel walls, is examined via a two-dimensional full DK simulation that highlights slight spatial differences in the sheath as a result of electrically disparate, adjacent wall materials. The memory storage requirements and computational load for the parallelized DK simulation grow with additional species, physical space dimensions, and velocity space dimensions. Some of these numerical limitations are encountered within this work. The hybrid-DK HET model utilizes a quasi-one-dimensional fluid electron algorithm in conjunction with a two-dimensional DK method to simulate the motion of neutral atoms and ions in a HET channel and near-field plume. Upon its development, the hybrid-DK simulation is benchmarked against results obtained from a two-dimensional hybrid-particle-in-cell (PIC) simulation with an identical fluid electron algorithm. To achieve agreement between the simulation results, a boundary condition for the DK model that satisfies particle conservation at the wall boundaries is developed, and electron model boundary conditions that provide solution stability are sought and utilized. For both high-frequency and low-frequency oscillations, the two simulations show good agreement for both time-averaged and dynamic plasma properties. Statistical noise tends to randomize plasma oscillations in the PIC simulation results, whereas the DK results exhibit coherent oscillatory behavior. Furthermore, results indicate that the DK simulation is capable of responding to small changes in electron dynamics, which is promising for future work. The DK plasma sheath simulation models a two-dimensional plasma sheath that highlights slight spatial differences inside the sheath as a result of electrically disparate, adjacent materials. To accomplish this goal, a quasi-one-dimensional sheath model is first built in a two-dimensional framework, boundary conditions are developed, and results are verified against theoretical expectations. Then, the full two-dimensional plasma sheath is modeled. The proof-of-concept model shows that two-dimensional effects are present in the vicinity of the discontinuous plasma potential at the wall, and electron and ion VDFs both clearly exhibit changes due to these effects.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162983/1/astridr_1.pd

Fully Coupled Fluid and Electrodynamic Modeling of Plasmas: A Two-fluid Isomorphism and a Strong Conservative Flux-coupled Finite Volume Framework

Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models both analytically and numerically. This dissertation alleviates these challenges by investigating new frameworks that facilitate efficient modeling of plasmas beyond the MHD description. Two investigations are performed: first, an isomorphism is constructed between the two-fluid plasma model and the Maxwell equations. This permits a set of unified Maxwell equations for both the electrodynamic and hydrodynamic behavior, but introduces an analogous notion of charge and current density for a fluid, which must be modeled to solve the new equations. We examine the homogeneous case (where these sources vanish), and then discuss iterative approaches and empirical modeling of the sources. We calculate some simple source models for fluid problems, including Blasius boundary layer flow. We demonstrate solution approaches using Green\u27s functions methods and the method of images, for which a closed-form solution to Blasius boundary layer flow is achieved. The second investigation recasts the single-fluid model into a strong conservative form. This permits the coupled Navier-Stokes and full Maxwell equations to be written exactly, but with no source terms present, which tend to cause numerical instability during simulation. The removal of the source terms is shown to improve the stability and robustness of the equations, but at the cost of introducing a significantly more complicated eigenstructure; we present the new eigenstructure for this system of equations and demonstrate an effective Riemann solver and flux splitting approach. Validation tests including magnetohydrodynamic problems, radio wave propagation tests and plasma instabilities and turbulence are presented

Modeling of Electron Transpiration Cooling for Leading Edges of Hypersonic Vehicles

The development of aeronautics has been largely driven by the passion to fly faster. From the flight of the Wright Flyer that flew 48 km/hr to the recent advances in hypersonic flight, most notably NASA's X-43A that flew at over 3 km/s, the velocity of flight has steadily increased. However, as these hypersonic speeds are reached and increased, contradicting aerothermodynamic design requirements present themselves. For example, a hypersonic cruise vehicle requires sharp leading edges to decrease the drag in order to maximize the range. However, the aerodynamic performance gains obtained by having a sharp leading edge come at the cost of very high, localized heating rates. There is currently no ideal way to manage these heating loads for sustained hypersonic flight, especially as flight velocities continue to increase. An approach that has been recently proposed involves using thermo-electric materials on these sharp leading edges to manage the heating loads. When exposed to high convective heating rates, these materials emit a current of electrons that leads to a cooling effect of the surface of the vehicle called electron transpiration cooling (ETC). This dissertation focuses on developing a modeling approach to investigate this phenomenon. The research includes developing and implementing an approach for ETC into a computational fluid dynamics code for simulation of hypersonic flow that accounts for electron emission from the surface. Models for space-charge-limited emission are also developed and implemented in order to accurately determine the level of emission from the surface. This work involves developing analytic models and assessing them using a direct-kinetic plasma sheath solver. Electric field effects are also implemented in the modeling approach, which accounts for forced diffusion and Joule heating. Finally, the modeling approach is coupled to a material response code in order to model the heat transfer into the material surface. Using this modeling approach, ETC is investigated as a viable technology for a wide range of hypersonic operating conditions. This includes altitudes between 30 and 60 km, freestream velocities between 4 and 8 km/s, and leading edge radii between 1 mm and 10 cm. The results presented in this study show that ETC can reduce the leading edge temperature significantly for certain conditions, most notably from 3120 to 1660 K for Mach 26 flight for a sharp leading edge (1 cm). However, at lower velocities, the cooling effect can be diminished by space-charge limits in the plasma sheath. ETC is shown to be most effective at cooling hotter surfaces (e.g. high freestream velocities and sharp leading edges) and the level of ionization in the flowfield can help the emission overcome space-charge limits. The modeling approach is assessed using experiments from the 1960s where thermionic emission was investigated as a mode of power generation for reentry vehicles. The computational results produce a wide range of emitted current due to the uncertainty in the freestream conditions and material properties, but they still agree well with the experiments. Overall, this work indicates that ETC is a viable method of managing the immense heat loads on sharp leading edges during hypersonic flight for certain conditions and motivates future work in the area both computationally and experimentally.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138537/1/hanquist_1.pd