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At least 37 records · Page 2
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NASA NTRS1994

Towards an MHD theory for the standoff distance of Earth's bow shock

An MHD theory is developed for the stand-off distance a(sub s) of the bow shock and the thickness delta(sub ms) of the magnetosheath, using the empirical Spreiter et al. relation delta(sub ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for delta(sub ms) and a(sub s). In general, however, MHD effects produce major differences from previous models, especially at low Alfven (M(sub A)) and sonic (M(sub S)) Mach numbers. The magnetic field orientation, M(sub A), M(sub S) and the ratio of specific heats gamma are all important variables of the theory. Three principal conclusions are reached. First, the gasdynamic and phenomenological models miss important dependances on field orientation and M(sub S) and generally provide poor approximations to the MHD results. Second, changes in field orientation and M(sub S) are predicted to cause factor of approximately 4 changes in delta(sub ms) at low M(sub A). Third, using Spreiter et al.'s value for k in the MHD theory leads to maximum a(sub s) values at low M(sub A) and nominal M(sub S) that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or breakdown in the Spreiter-like relation at very low M(sub A).

Cairns, Iver H.↗
NASA NTRS1994

Towards an MHD Theory for the Standoff Distance of Earth's Bow Shock

A magnetohydrodynamic (MHD) theory is developed for the standoff distance a(s) of the bow shock and the thickness Delta(ms) of the magnetosheath, using the empirical Spreiter et al. relation Delta(ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for Delta(ms) and As. In general, however, MHD effects produce major differences from previous models, especially at low Alfev (Ma) and Sonic (Ms) Mach numbers. The magnetic field orientation Ma, Ms and the ratio of specific heats gamma are all important variables of the theory. In contrast, the fast mode Mach number need play no direct role. Three principle conclusions are reached. First the gasdynamic and phenomenological models miss important dependences of field orientation and Ms generally provide poor approximations to the MHD results. Second, changes in field orientation and Ms are predicted to cause factor of approximately 4 changes in Delta(ms) at low Ma. These effects should be important when predicting the shock's location or calculating gramma from observations. Third, using Spreiter et al.'s value for k in the MHD theory leads to maxima a(s) values at low Ma and nominal Ms that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or a breakdown in the Spreiter-like relation at very low Ma.

Carins, Iver H.↗
NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗
NASA NTRS1976

System studies of coal fired-closed cycle MHD for central station power plants

This paper presents a discussion of the closed-cycle MHD results obtained in a recent study of various advanced energy-conversion power systems. The direct coal-fired MHD topping-steam bottoming cycle was established as the current choice for central station power generation. Emphasis is placed on the background assumptions and the conclusions that can be drawn from the closed-cycle MHD analysis. It is concluded that closed-cycle MHD has efficiencies comparable to that of open-cycle MHD. Its cost will possibly be slightly higher than that of the open-cycle MHD system. Also, with reasonable fuel escalation assumptions, both systems can produce lower-cost electricity than conventional steam power plants. Suggestions for further work in closed-cycle MHD components and systems are made.

Zauderer, B.↗
NASA NTRS1987

MHD aspects of magnetotail dynamics

The equations of ideal MHD represent the conservation of mass, momentum, and energy; thus, MHD must, in some broad sense, provide a correct description of large-scale structure of the earth's magnetosphere. However, steady-state, ideal MHD (the simplest description) allows only a static interaction between the solar wind and the magnetosphere. Hence an MHD theory of magnetospheric dynamics must involve unsteady flow turbulence, such as might be generated by Kelvin-Helmholtz turbulence at the magnetopause, and dissipative transport, such as reconnection, which violates ideal MHD. This brief review summarizes recent theoretical efforts to explore and extend the early MHD magnetospheric models of Axford and Petschek. Analytic calculations show that steady convection in the magnetotail is nearly impossible. Global magnetospheric simulations exhibit substorm reconnection phenomena for southward IMF and predict a novel convection pattern for northward IMF. Reconnection simulations show plasmoid formation and field-aligned current flows in the tail. The Kelvin-Helmholtz instability can provide a strong anomalous viscosity which can drive the viscous convection system.

Coroniti, F. V.↗
NASA NTRS1992

Heating of solar and stellar chromospheres and coronae by MHD waves

The two general classes of models that deal with the required heating of stellar chromospheres and coronae assume that outer stellar atmospheres are heated by hydrodynamic or by magnetohydrodynamic (MHD) waves and that these waves are generated by turbulent motions in the stellar convection zones. This paper considers the types of MHD waves and the source of these waves in stars like sun, the efficiency of the generation of MHD waves, and the manner of propagation and energy dissipation of MHD waves. It is shown that the basic criteria for the validity of any theory of MHD wave heating must account for the mean level of heating observed in stellar chromospheres and coronae, and for the range of radiative losses observed for a given spectral type. It is also required that the MHD wave heating theory accounts for the existence of inhomogeneities in stellar atmospheres. The results obtained indicate that magnetic tube waves might supply enough energy for the chromospheric and coronal heating and might also account for the observed range of variations of stellar radiative losses for a given spectral type.

Musielak, Z. E.↗
NASA NTRS1995

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Goossens, Marcel↗
NASA NTRS2000

MHD-Based Specification of Magnetotail Plasma and Fields: Possibilities and Limitations

Magnetohydrodynamics (MHD) constitutes the simplest comprehensive and self-consistent formulation of the properties of space plasmas. As such, it has been applied with large success to the dynamics of solar system plasmas. For the nightside region of the Earth, the magnetotail, MHD simulations have led to new understanding of the structure and dynamics of the plasmas, in response to both changes in boundary conditions as well as internal dynamical processes. As a result, substantial knowledge of the structure and dynamics of the nightside region have been accumulated. In basic MHD conservation laws on magnetospheric structure, as well as the role of non-MHD processes in the initiation and evolution of dynamical processes of the magnetotail. This presentation will consist of three parts, the first of which addresses the basic constraints on magnetotail structure as well as their consequences for magnetotail specification and forecasting. We will then review some examples of magnetotail structural changes brought about by solar-wind-like boundary conditions. Last, we consider the role of non-MHD processes in magnetotail specification and forecasting. The emphasis here will be on inclusion of these processes into MHD models, and their impact on the overall structure and dynamics.

Hesse, M.↗
NASA NTRS2002

The Delta(dot) B = O Constraint vs. Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. On the other hand, the MHD equations can be derived from basic principles in either conservative or non-conservative form. The non-conservative system has a better conditioned eigensystem. The Delta(dot)B = 0 constraint of the A4HD equations is only an initial condition constraint. One does not need the Delta(dot)B condition to close the MHD system. We formulate our new low dissipative high order scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the Delta(dot)B condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗
NASA NTRSDate not supplied

Impact of Magnetohydrodynamic (MHD) Induced Drag on High Ballistic Coefficient Aerocapture at Neptune

This paper presents analyses illustrating the benefits of magnetohydrodynamic (MHD) drag force control for a capsule performing aerocapture at Neptune relative to the same capsule utilizing conventional aerodynamic-only control across a range of design and flight conditions. MHD technology utilizes an onboard mag-net to create a magnetic field that interacts with the ionized plasma surrounding the capsule at hypersonic velocities, thus creating an electron current and inducing a Lorentz force used to increase capsule drag. The study assumes a 4.57-meterMars Science Laboratory (MSL) 70-degree sphere-cone capsule aerodynamic shape arrives hyperbolically at Neptune and aerocaptures into a synchronous Tri-ton orbit (3986 km x 430,000 km orbit inclined 157 degrees) that offers repeated flyby opportunities. Hyperbolic arrival velocity and the capsule entry mass (i.e., ballistic coefficient) are varied over a wide range of values to study the impact of these variables on key flight performance and sizing parameters. Results show reduced heat rates, heat loads, and thermal protection system mass for MHD cases at all conditions, with the benefit of MHD relative to conventional aerodynamic-only options increasing as ballistic coefficient increases, suggesting the payoff for MHD is significantly better for high-mass entry system design concepts with high ballistic coefficients.

Entry Descent and Landing↗
NASA NTRS1985

A Leaky Waveguide Model for MHD Wave Driven Winds from Coronal Holes

Magnetohydrodynamic (MHD) waves, driven by the large scale convective motions of the photosphere are suggested as a possible source of additional acceleration for the stellar wind. Most of the turbulent power in a coronal hole is carried by MHD waves with periods of a few hundred seconds or longer. This is evident from direct observations of turbulence in the solar photosphere, as well as in situ observations of turbulence in the solar wind. But waves with periods this long have wavelengths which are typically as large as the transverse scale of the coronal hole flux tube itself. For these waves boundary effects are important and the coronal hole must be treated as a waveguide. The propagation of MHD waves using this waveguide approach is discussed. The simple model presented demonstrates that coronal holes can act as waveguides for MHD waves. For typical solar parameters the waves are compressible and can generate a wave tensile force which tends to cancel at least part of the wave pressure force. This effect tends to decrease the efficiency of MHD wave acceleration.

Davila, J. M.↗
NASA NTRS1985

An MHD model of the earth's magnetosphere

It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.

Wu, C. C.↗
NASA NTRS1995

Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.

Frank, Adam↗
NASA NTRS1999

Towards Integrated Pulse Detonation Propulsion and MHD Power

The interest in pulse detonation engines (PDE) arises primarily from the advantages that accrue from the significant combustion pressure rise that is developed in the detonation process. Conventional rocket engines, for example, must obtain all of their compression from the turbopumps, while the PDE provides additional compression in the combustor. Thus PDE's are expected to achieve higher I(sub sp) than conventional rocket engines and to require smaller turbopumps. The increase in I(sub sp) and the decrease in turbopump capacity must be traded off against each other. Additional advantages include the ability to vary thrust level by adjusting the firing rate rather than throttling the flow through injector elements. The common conclusion derived from these aggregated performance attributes is that PDEs should result in engines which are smaller, lower in cost, and lighter in weight than conventional engines. Unfortunately, the analysis of PDEs is highly complex due to their unsteady operation and non-ideal processes. Although the feasibility of the basic PDE concept has been proven in several experimental and theoretical efforts, the implied performance improvements have yet to be convincingly demonstrated. Also, there are certain developmental issues affecting the practical application of pulse detonation propulsion systems which are yet to be fully resolved. Practical detonation combustion engines, for example, require a repetitive cycle of charge induction, mixing, initiation/propagation of the detonation wave, and expulsion/scavenging of the combustion product gases. Clearly, the performance and power density of such a device depends upon the maximum rate at which this cycle can be successfully implemented. In addition, the electrical energy required for direct detonation initiation can be significant, and a means for direct electrical power production is needed to achieve self-sustained engine operation. This work addresses the technological issues associated with PDEs for integrated aerospace propulsion and MHD power. An effort is made to estimate the energy requirements for direct detonation initiation of potential fuel/oxidizer mixtures and to determine the electrical power requirements. This requirement is evaluated in terms of the possibility for MHD power generation using the combustion detonation wave. Small scale laboratory experiments were conducted using stoichiometric mixtures of acetylene and oxygen with an atomized spray of cesium hydroxide dissolved in alcohol as an ionization seed in the active MHD region. Time resolved thrust and MHD power generation measurements were performed. These results show that PDEs yield higher I(sub sp) levels than a comparable rocket engine and that MHD power generation is viable candidate for achieving self-excited engine operation.

Litchford, Ron J.↗
NASA NTRS1999

Review of Recent Results in Global MHD Modeling: ISTP Project Scientist for Theory and Ground-Based Observations

Global MHD (magnetohydrodynamic) simulations have shown a remarkable ability to describe the global dynamics of geospace. The limitations of the physical approximations underlying MHD would seem to limit the effectiveness of these codes, since kinetic and hybrid effects should manifest themselves by cross-scale coupling from microscales to mesoscales to global scales. However three effects appear to allow the codes to operate much more successfully than one would at first believe. They are:(l) the globally self-consistent nature of the codes with very well defined exterior boundary conditions (the solar wind) which allows the proper intercommunication between magnetospheric regions on MHD scales, (2) the control by global dynamics of the boundary layer locations where micro and meso scale processes operate, and (3) the critical role of numerical diffusion and with a sufficiently high resolution grid, the use of an empirical resistivity term, which if set at a level where the major magnetosphere boundaries properly calibrate against their observed locations, appear to well represent the effects of kinetic and hybrid processes on the global dynamics. The effectiveness of the global MHD codes, which have been developed under the ISTP mission, in describing Wind, Polar and Geotail observations, as well as ground-based observations are described. Particular emphasis is placed upon the Polar imaging data which when combined with ground-based data and global MHD-based synthetic aurora and convection patterns provide a powerful tool in understanding the final link in the solar-terrestrial chain: coupling into the atmosphere and ionosphere.

Curtis, Steven↗
NASA NTRS2000

Global MHD Simulations of Space Plasma Environments: Heliosphere, Comets, Magnetospheres of Plants and Satellites

Magnetohydrodynamics (MHD) provides an approximate description of a great variety of processes in space physics. Accurate numerical solutions of the MHD equations are still a challenge, but in the past decade a number of robust methods have appeared. Once these techniques made the direct solution of MHD equations feasible, a number of global three-dimensional models were designed and applied to many space physics objects. The range of these objects is truly astonishing, including active galactic nuclei, the heliosphere, the solar corona, and the solar wind interaction with planets, satellites, and comets. Outside the realm of space physics, MHD theory has been applied to such diverse problems as laboratory plasmas and electromagnetic casting of liquid metals. In this paper we present a broad spectrum of models of different phenomena in space science developed in the recent years at the University of Michigan. Although the physical systems addressed by these models are different, they all use the MHD equations as a unifying basis.

Kabin, K.↗
NASA NTRS2002

Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

Yee, H. C.↗