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A simplified model of an electromagnetic filamentation instability that arises when two counterstreaming electron beams pass through a uniform ion background is treated by statistical mechanical techniques borrowed from fluid turbulence theory. Accumulation of magnetic energy at long wavelengths is predicted, as observed in the numerical simulations of Lee and Lampe.
Oscillatory instability in shape of solid/liquid interface geometry observed in heat-transfer experiments in long, thin vertical cylinder filled with succinonitrile. Novel fluid flow configuration with cylindrical symmetry developed to permit detailed heat flow experiments in geometry also mathematically tractable.
Computer programming was completed for digital acquisition of temperature and velocity data generated by the Geophysical Fluid Flow Cell (GFFC) during the upcoming Spacelab 3 mission. A set of scenarios was developed which covers basic electro-hydrodynamic instability, highly supercritical convection with isothermal boundaries, convection with imposed thermal forcing, and some stably stratified runs to look at large-scale thermohaline ocean circulations. The extent to which the GFFC experimental results apply to more complicated circumstances within the Sun or giant planets was assessed.
Turbulent sublayer streaks are studied with the aid of a simplified theoretical model. In this the nonlinear activity is assumed to be intermittent and to act locally in space during a very short initial time so as to set up the initial conditions for the subsequent linear and inviscid evolution of the resulting three-dimensional flow disturbance. The mean shear flow is taken as a parallel one and a correction for the long-tern effects of viscosity is applied. A model for the initial nonlinear phase is chosen to represent the local Reynolds stresses that would be produced by a patch of local inflectional instability. The streamwise dimension of the resulting eddy is found to grow linearly with time in accordance with the algebraic instability mechanism (Landahl 1980). The associated Reynolds shear stress is expressible in a simple manner in terms of the liftup of the fluid elements and is suggestive of an algebraic-type Reynolds stress model similar to, but not identical to, that of Prandtl's (1925) mixing-length theory.
This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.
The basic kinetic and thermodynamic concepts of crystal growth will be revisited in view of recent AFM and interferometric findings. These concepts are as follows: 1) The Kossel crystal model that allows only one kink type on the crystal surface. The modern theory is developed overwhelmingly for the Kessel model; 2) Presumption that intensive step fluctuations maintain kink density sufficiently high to allow applicability of Gibbs-Thomson law; 3) Common experience that unlimited step bunching (morphological instability) during layer growth from solutions and supercooled melts always takes place if the step flow direction coincides with that of the fluid.
While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have recently developed a time-dependent renormalization approach to stabilize such reduced models. In the current work, we extend this framework by introducing a parameter that controls the time-decay of the memory of such models and optimally selecting this parameter based on limited fully resolved simulations. First, we demonstrate our framework on the inviscid Burgers equation whose solution develops a finite-time singularity. Our renormalized reduced order models are stable and accurate for long times while using for their calibration only data from a full order simulation before the occurrence of the singularity. Furthermore, we apply this framework to the 3D Euler equations of incompressible fluid flow, where the problem of finite-time singularity formation is still open and where brute force simulation is only feasible for short times. Our approach allows us to obtain for the first time a perturbatively renormalizable model which is stable for long times and includes all the complex effects present in the 3D Euler dynamics. We find that, in each application, the renormalization coefficients display algebraic decay with increasing resolution, and that the parameter which controls the time-decay of the memory is problem-dependent.
An analytical technique for the prediction of the effects of rigid baffles on the stability of liquid propellant combustors is presented. This analysis employs both two and three dimensional combustor models characterized by concentrated combustion sources at the chamber injector and a constant Mach number nozzle. An eigenfunction-matching method is used to solve the linearized partial differential equations describing the unsteady flow field for both models. Boundary layer corrections to this unsteady flow are in a mechanical energy dissipation model to evaluate viscous and turbulence effects within the flow. An integral instability relationship is then employed to predict the decay rate of the oscillations. Results of this analysis agree qualitatively with experimental observations and show that sufficient dissipation exists to indicate that the proper mechanism of baffle damping is a fluid dynamic loss. The response of the dissipation model to varying baffle blade length, mean flow Mach number, oscillation amplitude, baffle configuration, and oscillation mode is examined.
Stability experiments were carried out in 4-cm-thick, salt-stratified fluid layer by heating from below and cooling from above. The bottom boundary was rigid while the top was either free or rigid. The initial solute Rayleigh number varied from 2.5 x 10(exp 6) to 4.6 x 10(exp 7). For the rigid-free case, at initial solute Rayleigh numbers R(sub s) greater than 5.4 x 10(exp 6), thermal Marangoni instabilities were observed to onset along the free surface at a relatively low thermal Rayleigh number, R(sub t). The convection was very weak, and it had almost no effect on the concentration and temperature distributions. Double-diffusive instabilities along the top free surface were observed to onset at a higher R(sub t), with much stronger convection causing changes in the concentration and temperature distributions near the top. At a yet higher R(sub t), double-diffusive convection was observed to onset along the bottom boundary. Fluid motion in the layer then evolved into fully developed thermal convection of a homogeneous fluid without any further increase in the imposed Delta T. For layers with R(sub s) less than 5.4 x 10(exp 6), Marangoni and double-diffusive instabilities onset simultaneously along the free surface first, while double-diffusive instabilities along the bottom wall onset at a higher R(sub t).
This manuscript presents verification cases that are developed to study the electrothermal instability (ETI). Specific verification cases are included to ensure that the unit physics components necessary to model the ETI are accurate, providing a path for fluid-based codes to effectively simulate ETI in the linear and nonlinear growth regimes. Two software frameworks with different algorithmic approaches are compared for accuracy in their ability to simulate diffusion of a magnetic field, linear growth of the ETI, and a fully nonlinear ETI evolution. The nonlinear ETI simulations show early time agreement, with some differences emerging, as noted in the wavenumber spectrum, late into the nonlinear development of ETI. Here, a sensitivity study explores the role of equation-of-state (EOS), vacuum density, and vacuum resistivity. EOS and vacuum resistivity are found to be the most critical factors in the modeling of nonlinear ETI development.
The capability of producing complex, high performance metal parts on demand has established laser powder bed fusion (LPBF) as a promising additive manufacturing technology, yet deeper understanding of the laser-material interaction is crucial to exploit the potential of the process. By simultaneous in-situ synchrotron x-ray and schlieren imaging, we probe directly the interconnected fluid dynamics of the vapour jet formed by the laser and the depression it produces in the melt pool. The combined imaging shows the formation of a stable plume over stable surface depressions, which becomes chaotic following transition to a full keyhole. We quantify process instability across several parameter sets by analysing keyhole and plume morphologies, and identify a previously unreported threshold of the energy input required for stable line scans. The effect of the powder layer and its impact on process stability is explored. These high-speed visualisations of the fluid mechanics governing LPBF enable us to identify unfavourable process dynamics associated with unwanted porosity, aiding the design of process windows at higher power and speed, and providing the potential for in-process monitoring of process stability.
The LANL ASC Arbitrary Lagrange/Eulerian (ALE) code, FLAG, is being used to model experiments conducted under this grant in order to understand the physics limiting high-current conduction and thermal plasma production. This includes the effects of nonlinear magnetic diffusion (NLMD), the magnetic Rayleigh-Taylor (MRT) instability, and the electro-thermal instability (ETI). FLAG is a multi-dimensional, unstructured-grid, multi-material, multi-temperature, shockphysics code with a single-fluid, resistive magnetohydrodynamics (MHD) package. Equations-ofstate (EOS), conductivity, material-strength, and melt can be treated with a variety of analytic or tabular models.
NASA's effort for the thermal environmental control of the Space Station Freedom is directed towards the design, analysis, and development of an Active Thermal Control System (ATCS). A two phase, flow through condenser/radiator concept was baselined, as a part of the ATCS, for the radiation of space station thermal load into space. The proposed condenser rejects heat through direct condensation of ATCS working fluid (ammonia) in the small diameter radiator tubes. Analysis of the condensation process and design of condenser tubes are based on the available two phase flow models for the prediction of flow regimes, heat transfer, and pressure drops. The prediction formulas use the existing empirical relationships of friction factor at gas-liquid interface. An attempt is made to study the stability of interfacial waves in two phase annular flow. The formulation is presented of a stability problem in cylindrical coordinates. The contribution of fluid viscosity, surface tension, and transverse radius of curvature to the interfacial surface is included. A solution is obtained for Kelvin-Helmholtz instability problem which can be used to determine the critical and most dangerous wavelengths for interfacial waves.
Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.
Internal fluid flows are subject not only to self-sustained oscillations of the purely hydrodynamic type but also to the coupling of the instability with the acoustic mode of the surrounding cavity. This situation is common to turbomachinery, since flow instabilities are confined within a flow path where the acoustic wavelength is typically smaller than the dimensions of the cavity and flow speeds are low enough to allow resonances. When acoustic coupling occurs, the fluctuations can become so severe in amplitude that it may induce structural failure of engine components. The potential for catastrophic failure makes identifying flow-induced noise and vibration sources a priority. In view of the complexity of these types of flows, this report was written with the purpose of presenting many of the methods used to compute frequencies for self-sustained oscillations. The report also presents the engineering formulae needed to calculate the acoustic resonant modes for ducts and cavities. Although the report is not a replacement for more complex numerical or experimental modeling techniques, it is intended to be used on general types of flow configurations that are known to produce self-sustained oscillations. This report provides a complete collection of these models under one cover.
This report describes the work done by SciberNet, Inc. during the month of January. During this time, we primarily worked on further analysis of the results presented at the AGU as well as writing them up for publication. Using large scale simulations, we showed that the magnetopause during the southward IMF case is quite irregular with varying thickness, and has a complex flow pattern owing to the nonlinear effects of the convective flow superimposed on the flows generated in the reconnection layer. We used inflow-outflow boundary conditions to examine the kinetic nature of the discontinuities that are formed in the reconnection layer and concluded that nonlocal effects play a major role in the formation of such discontinuities and can alter their properties from the usual structures expected from 1-D simulations or from fluid theories. Finally, we used our 3-D simulations to examine the nonlinear interaction of the tearing mode with the Kelvin-Helmholtz instability. We showed that this interaction leads to the generation of a large core field which is observed both in the magnetotail as well as the magnetopause.
Combustion instabilities in gas turbine engines are most frequently encountered during the late phases of engine development, at which point they are difficult and expensive to fix. The ability to replicate an engine-traceable combustion instability in a laboratory-scale experiment offers the opportunity to economically diagnose the problem (to determine the root cause), and to investigate solutions to the problem, such as active control. The development and validation of active combustion instability control requires that the causal dynamic processes be reproduced in experimental test facilities which can be used as a test bed for control system evaluation. This paper discusses the process through which a laboratory-scale experiment was designed to replicate an instability observed in a developmental engine. The scaling process used physically-based analyses to preserve the relevant geometric, acoustic and thermo-fluid features. The process increases the probability that results achieved in the single-nozzle experiment will be scalable to the engine.
Nuclear fusion appears to be the most promising concept for producing extremely high specific impulse rocket engines. One particular fusion concept which seems to be particularly well suited for fusion propulsion applications is the gasdynamic mirror (GDM). This device would operate at much higher plasma densities and with much larger LD ratios than previous mirror machines. Several advantages accrue from such a design. First, the high LA:) ratio minimizes to a large extent certain magnetic curvature effects which lead to plasma instabilities causing a loss of plasma confinement. Second, the high plasma density will result in the plasma behaving much more Re a conventional fluid with a mean free path shorter than the length of the device. This characteristic helps reduce problems associated with "loss cone" microinstabilities. An experimental GDM device is currently being constructed at the NASA Marshall Space Flight Center to provide an initial assessment of the feasibility of this type of propulsion system. Initial experiments are expected to commence in the late fall of 2000.