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In the present paper, the two-dimensional problem of the wave motion produced in a heavy fluid of finite depth by the horizontal rectilinear and uniform motion of a solid body of arbitrary shape immersed under the surface of the fluid is considered by the method of N. E. Kochin.
TMF is based on imposing a controlled phase-shift in a train of electromagnets, forming a stack. Thus, the induced magnetic field can be considered to be travelling along the axis of the stack. The coupling of this traveling wave with an electrically conducting fluid results in a basic flow in a form of a single axisymmetric roll. The magnitude and direction of this flow can be remotely controlled. Furthermore, it is possible to localize the effect of this force field though activating only a number of the magnets. This force field generated in the fluid can, in principle, be used to control and modify convection in the molten material. For example, it can be used to enhance convective mixing in the melt, and thereby modify the interface shape, and macrosegregation. Alternatively, it can be used to counteract thermal and/or solutal buoyancy forces. High frequency TMF can be used in containerless processing techniques, such as float zoning, to affect the very edge of the fluid so that Marangoni flow can be counter balanced. The proposed program consists of basic fundamentals and applications. Our goal in conducting the following experiments and analyses is to establish the validity of TMF as a new tool for solidification processes. Due to its low power consumption and simplicity of design, this tool may find wide spread use in a variety of space experiments. The proposed ground based experiments are intended to establish the advantages and limitations of employing this technique. In the fundamentals component of the proposed program, we will use theoretical tools and experiments with mercury to establish the fundamental aspects of TMF-induced convection through a detailed comparison of theoretical predictions and experimental measurements of flow field. In this work, we will conduct a detailed parametric study involving the effects of magnetic field strength, frequency, wave vector, and the fluid geometry. The applications component of this work will be focused on investigating the effect of TMF on the following solidification and pre-directional solidification processes: (1) Bridgman growth of Ga:Ge with the goal of counteracting the buoyancy-driven convection; (2) Mixing of Pb-Ga and Pb-Sn alloys with the aim of initiating and maintaining a uniform melt prior to solidification processing; and (3) Float Zone growth with the aim of identifying, through simulations and model experiments, conditions needed to counteract Marangoni flow in a microgravity environment. The proposed research has strong relevance to microgravity research and the objectives of the NRA. TMF can provide a unique and accurate mechanism for generation and control of desirable flow patterns for microgravity research. These attributes have significant relevance to 1) Alloy mixing prior to solidification in a microgravity environment. TMF can provide this mixing with a low level of power consumption; (2) TMF can offset the deleterious effects of Marangoni convection in microgravity containerless processing. Thus, TMF can be instrumental in further understanding this phenomena; (3) Generation of controlled flows will allow the investigation of the effect of these flows on growth morphology and growth kinetics; and (4) On Earth, TMF has the potential to significantly counter-balance thermosolutal convection, thereby creating conditions similar to those obtained in microgravity. Once demonstrated, this new tool for use in solidification has the strong potential to find applications in a host of microgravity material research projects.
A number of important physics effects on the stability of relatively high-n (n is the toroidal mode number) peeling-ballooning modes (PBMs) are investigated based on an equilibrium reconstructed from a NSTX discharge, utilizing extended magnetohydrodynamic (MHD) eigenvalue solvers. For a given toroidal mode number n, multiple branches of instabilities are computed, with the total number of unstable branches roughly linearly scaling with n. Most of the unstable branches are located in the plasma core region, but edge-localized branches, i.e., PBMs, are also identified at higher n-numbers. For the single-fluid-wise most unstable PBM with n = 19, stabilizing/destabilizing effects due to various physics beyond ideal MHD are systematically investigated. Plasma toroidal flow is found to be weakly stabilizing. Local flow shear is generally stabilizing as well, with the degree of stabilization depending on the initial growth rate (without flow shear) of the mode. The plasma resistivity can strongly destabilize the PBM within the single-fluid framework. Anisotropic thermal transport, strong parallel sound wave damping, as well as two-fluid effects are all stabilizing to the mode. In particular, diamagnetic stabilization (within the two-fluid model) is found to be very strong for this mode.
We review our current knowledge of ULF waves in planetary foreshocks. Most of this knowledge comes from observations taken within a few Earth radii of the terrestrial bow shock. Terrestrial foreshock ULF waves can be divided into three types, large amplitude low frequency waves (approximately 30-s period), upstream propagating whistlers (1-Hz waves), and 3-s waves. The 30-s waves are apparently generated by back-streaming ion beams, while the 1-Hz waves are generated at the bow shock. The source of the 3-s waves has yet to be determined. In addition to issues concerning the source of ULF waves in the foreshock, the waves present a number of challenges, both in terms of data acquisition, and comparison with theory. The various waves have different coherence scales, from approximately 100 km to approximately 1 Earth radius. Thus multi-spacecraft separation strategies must be tailored to the phenomenon of interest. From a theoretical point of view, the ULF waves are observed in a plasma in which the thermal pressure is comparable to the magnetic pressure, and the rest-frame wave frequency can be moderate fraction of the proton gyro-frequency. This requires the use of kinetic plasma wave dispersion relations, rather than multi-fluid MHD. Lastly, and perhaps most significantly, ULF waves are used to probe the ambient plasma, with inferences being drawn concerning the types of energetic ion distributions within the foreshock. However, since most of the data were acquired close to the bow shock, the properties of the more distant foreshock have to be deduced mainly through extrapolation of the near-shock results. A general understanding of the wave and plasma populations within the foreshock, their interrelation, and evolution, requires additional data from the more distant foreshock.
It has been estimated that the noise levels in aircraft engine transmissions can be reduced by as much as 10 dB through the use of journal bearings. The potential benefits of lower noise levels include reduced wear, longer gear life and enhanced comfort for passengers and crew. Based on this concept the journal-thrust wave bearing was analyzed and its performance was evaluated. Numerical codes, developed over the past 30 years by Dr. Dimofte, were used to predict the performance of the bearing. The wave bearing is a fluid film bearing and therefore was analyzed using the Reynolds pressure equation. The formulation includes turbulent flow concepts and possesses a viscosity-temperature correction. The centrifugal growth of the bearing diameter and the deformation of the bearing under gear loads were also incorporated into the code. An experimental rig was developed to test the journal-thrust wave bearing.
Resources and tools for the modeling and simulation of low-temperature plasma (LTP) discharges are increasingly vital to progress in the field in order to properly characterize and study complex source designs and plasma chemistries beyond the scope of traditional diagnostics. Open-source software provides powerful platforms for this work and can enable community-driven LTP R&D. Within the Multiphysics Object-Oriented Simulation Environment (MOOSE) open-source framework [1], capabilities have been demonstrated in the areas of plasma fluids (Zapdos [2]), plasma chemistry (CRANE [3]), and general electromagnetic wave theory (Electromagnetic Library for Kinetics & fluids [ELK] [4]). ELK has since been coupled to Zapdos/CRANE to enable fully coupled electromagnetic plasma simulations. This talk will detail the continued validation efforts and discuss Zapdos-ELK-CRANE code coupling with various-low temperature plasma sources. The impact of fully coupled electromagnetics on process parameters (e.g., temperature and electron/ion energy) versus an electrostatic description will also be discussed. [1] Permann et al., SoftwareX, 11 (2020) 100430. [2] Lindsay et al., J. Phys. D: Appl. Phys. 49 (2016) 235204. [3] Keniley et al., Talk, GEC Session DT3.00002 (2019). [4] Icenhour et al., Talk, GEC Session RR1.00006 (2019). Acknowledgements: INL Graduate Fellowship Program, NSF SI2 Grant 1740300, U.S. Dept. of Energy Office of Science Graduate Student Research Program
Two crucial challenges faced in the design of ocean wave energy converters (WECs) are maintaining high capacity factors and remaining robust in everchanging, harsh ocean environments. This study introduces a novel mechanism for achieving reactive WEC control with a soft hydraulic power take-off, thereby addressing both challenges. The device of interest involves a hydraulic pump, constructed from a fluidic flexible matrix composite (F2MC), which is cyclically stretched by driving waves and pressurizes working fluid through a turbine-generator. This class of fiber-reinforced stretch hoses is established for ocean use as robust moorings and shock absorbers. The dynamic properties of the F2MC pump depend on internal pressure, which can be controlled by a continuously variable transmission between the turbine and generator, allowing the system to be adapted for better performance over a wide range of wave conditions. This work presents a dynamic model for operation and adaptive behavior of this power take-off system, experimentally validates components of the model, and performs dynamic simulations of the system that show increases in power production and capacity factor compared to non-adaptive operation for a variety of driving wave conditions. This work develops the basis for future large-scale experimental testing and controller design of this system.
A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high-fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not predicted by potential flow engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.
Unsteady spatial flow of compressible fluids - wing of finite span in presence of moving shock wave
To run both smoothly and efficiently, high-speed machines need stable, low-friction bearings to support their rotors. In addition, an oil-free bearing system is a common requirement in today's designs. Therefore, self-acting gas film bearings are becoming the bearing of choice in high-performance rotating machinery, including that used in the machine tool industry. Although plain journal bearings carry more load and have superior lift and land characteristics, they suffer from instability problems. Since 1992, a new type of fluid film bearing, the wave bearing, has been under development at the NASA Lewis Research Center in Cleveland, Ohio, by Dr. Florin Dimofte, a Senior Research Associate of the University of Toledo. One unique characteristic of the waved journal bearing that gives it improved capabilities over conventional journal bearings is the low-amplitude waves of its inner diameter surface. The radial clearance is on the order of one thousandth of the shaft radius, and the wave amplitude is nominally up to one-half the clearance. This bearing concept offers a load capacity which is very close to that of a plain journal bearing, but it runs more stably at nominal speeds.
The solution was obtained without approximating the dispersion relation. This was made possible by the use of a computer method for carrying out the extremely large number of algebraic manipulations involved. The three-fluid model employed accounts for the interaction of the electron, ion, and neutral species. The solution for the e-folding distance describes the damping characteristics of each wave mode. Each of the e-folding solutions corresponds to one of the phase velocity solutions.
An experimental study of shock wave interference heating on a cylindrical leading edge representative of the cowl of a rectangular hypersonic engine inlet at Mach numbers of 6.3, 6.5, and 8.0 is presented. Stream Reynolds numbers ranged from 0.5 x 106 to 4.9 x 106 per ft. and stream total temperature ranged from 2100 to 3400 R. The model consisted of a 3" dia. cylinder and a shock generation wedge articulated to angles of 10, 12.5, and 15 deg. A fundamental understanding was obtained of the fluid mechanics of shock wave interference induced flow impingement on a cylindrical leading edge and the attendant surface pressure and heat flux distributions. The first detailed heat transfer rate and pressure distributions for two dimensional shock wave interference on a cylinder was provided along with insight into the effects of specific heat variation with temperature on the phenomena. Results show that the flow around a body in hypersonic flow is altered significantly by the shock wave interference pattern that is created by an oblique shock wave from an external source intersecting the bow shock wave produced in front of the body.
Shock-wave boundary-layer interactions (SWBLI) pose unique challenges for the slender airframes and sharp control surfaces characteristic of high-speed airbreathing aircraft. Spikes in pressure and thermal loading have been shown to occur in SWBLI regions; thus, predicting their location and behavior proves critical for assuring aircraft structural integrity and fatigue resilience. SWBLIs frequently lead to severe turbulent boundary-layer separation and corresponding unsteady motions characterized by a wide range of frequencies. Low-frequency motion has been shown to couple with the structure of a compliant panel, and turbulent boundary layers thus present a particular danger for thin control surfaces. Previous studies have shown that the thermal loading on a compliant panel in a ramp-induced SWBLI may have a signi cant impact on the panel vibrations. A multitude of studies has investigated the heating on rigid structures, but a charactrization of the heating effects on compliant structures is necessary to fully understand the fluid-thermal-structural interactions (FTSI) occurring in ramp-induced SWBLIs. This studuses infrared thermography and high-frequency Kulite pressure transducers to examine the heating loads on rigid and compliant ramps at various angles and flow conditions at Mach 6.
Shock-wave boundary-layer interactions (SWBLI) pose unique challenges for the slender airframes and sharp control surfaces characteristic of high-speed airbreathing aircraft. Spikes in pressure and thermal loading have been shown to occur in SWBLI regions; thus, predicting their location and behavior proves critical for assuring aircraft structural integrity and fatigue resilience. SWBLIs frequently lead to severe turbulent boundary-layer separation and corresponding unsteady motions characterized by a wide range of frequencies. Low-frequency motion has been shown to couple with the structure of a compliant panel, and turbulent boundary layers thus present a particular danger for thin control surfaces. Previous studies have shown that the thermal loading on a compliant panel in a ramp-induced SWBLI may have a signi cant impact on the panel vibrations. A multitude of studies has investigated the heating on rigid structures, but a charactrization of the heating effects on compliant structures is necessary to fully understand the fluid-thermal-structural interactions (FTSI) occurring in ramp-induced SWBLIs. This studuses infrared thermography and high-frequency Kulite pressure transducers to examine the heating loads on rigid and compliant ramps at various angles and flow conditions at Mach 6.
A collisionless fluid model of a plasma is presented and solved to first order in the cold, high frequency limit. From this model, a homogeneous system of linear equations is obtained for a harmonic electric field perturbation from which the Appleton-Hartree equation is derived. Moreover, the polarization states of electromagnetic waves in cold, collisionless plasmas are examined. Complete sets of equations governing the reflection and transmission of electromagnetic waves in both non magnetized and magnetized plasmas are obtained. In solving the boundary problem, the Booker quartic is derived and the nature of its roots discussed.
The method of pseudocompressibility is being tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite-difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibility for solving the pressure field, coupled with an implicit, approximate-factorization scheme. This coupling is known as the pseudocompressibility method. The pseudocompressibility method introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. However, these waves limit the time-accuracy of the computations. The effects of these waves are analyzed and criteria are set for choosing the pseudocompressibility parameters that govern the pressure wave speed. Test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.
The method of pseudocompressibility is tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibiity for solving the pressure field, coupled with an implicit, approximate factorization scheme. This coupling is known as the pseudocompressibility method and introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. These waves, however, limit the time accuracy of the computations. The effects of these waves are analysed and criteria are set for choosing the pseudocompressibility parameter that governs the pressure wave speed; test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.