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At least 865 records · Page 48

Relationship between transition and modes of instability in supersonic boundary layers

The relationship between the predicted transition location and the first and second modes of instability in two-dimensional supersonic boundary-layer flow on a flat plate is examined. Linear stability theory and the N-factor criterion are used to predict transition location. The effect of heat transfer is also studied; the results demonstrate that the transition reversal phenomenon can be explained by the opposite effect of cooling on the first and second modes of instability. Compressibility of destabilizing at free-stream Mach numbers of 2 to 3.5. The predicted transition location is due to the oblique first modes of instability, up to free-stream Mach numbers between 6 and 6.5. At higher Mach numbers, the predicted transition location is due to a combination of two-dimensional first and second modes of instability.

Masad, Jamal A.↗

Effects of flows on viscous and resistive MHD stability

In many solar applications the viscosity appears to be more important than resistivity. In order to discuss the instabilities in solar conditions, an idealized configuration is considered in which the plasma is flowing in the z-direction along the magnetic field B sub 0 with a velocity V sub 0. As far as the velocity is concerned two different velocity profiles, with different hydrodynmaic stability properties are discussed. The results are summarized.

Einaudi, Giorgio↗

Streaming sausage, kink and tearing instabilities in a current sheet with applications to the earth's magnetotail

This paper investigates the growth rates and eigenmode structures of the streaming sausage, kink, and tearing instabilities in a current sheet with a super-Alfvenic flow. The growth rates and eigenmode structures are first considered in the ideal incompressible limit by using a four-layer model, as well as a more realistic case in which all plasma parameters and the magnetic field vary continuously along the direction perpendicular to the magnetic field and plasma flow. An initial-value method is applied to obtain the growth rate and eigenmode profiles of the fastest growing mode, which is either the sausage mode or kink mode. It is shown that, in the earth's magnetotail, where super-Alfvenic plasma flows are observed in the plasma sheet and the ratio between the plasma and magnetic pressures far away from the current layer is about 0.1-0.3 in the lobes, the streaming sausage and streaming tearing instabilities, but not kink modes, are likely to occur.

Lee, L. C.↗

Nonlinear Evolution and Breakdown of Azimuthally Compact Crossflow Vortex Pattern over a Yawed Cone

Hypersonic boundary-layer flows over a circular cone at moderate angle of incidence can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to the more efficient excitation of stationary crossflow vortices by surface roughness, a possible path to transition in such flows corresponds to rapid amplification of the high-frequency secondary instabilities of finite amplitude stationary crossflow vortices. In the present paper, the previous analyses of crossflow instability over a 7- degree half-angle, yawed circular cone in a Mach 6 free stream have been extended to the nonlinear evolution of azimuthally localized crossflow vortex packets and the amplification characteristics and nonlinear breakdown of high-frequency secondary instabilities associated with those packets. A comparison between plane marching PSE and direct Navier-Stokes simulations (DNS) reveals favorable agreement in regard to mode shapes, most amplified disturbance frequencies, and N-factor evolution. In contrast, the quasi-parallel predictions are found to result in severe underprediction of the N-factors. The direct numerical simulations also indicate that the breakdown of secondary instabilities in a 3D hypersonic boundary layer shares certain common features with the previous computations of crossflow transition over subsonic swept wings.

Vortex structure↗

Magnetohydrodynamic Instabilities in a Simple Gasdynamic Mirror Propulsion System

The gasdynamic mirror has been proposed as a concept which could form the basis of a highly efficient fusion rocket engine. Gasdynamic mirrors differ from most other mirror type plasma confinement schemes in that they have much larger aspect ratios and operate at somewhat higher plasma densities. To evaluate whether a gasdynamic mirror could indeed confine plasmas in a stable manner for long periods of time, a small scale experimental gasdynamic mirror was built and tested. The objective of this experiment was to determine ranges of mirror ratios and plasma densities over which gasdynamic mirror could maintain stable plasmas. Theoretical analyses indicated that plasma magnetohydrodynamic instabilities were likely to occur during subsonic to supersonic flow transitions in the mirror throat region of the gasdynamic mirror. The experimental evidence based upon data derived from the Langmuir probe measurements seems to confirm this analysis. The assumption that a gasdynamic mirror using a simple mirror geometry could be used as a propulsion system, therefore, appears questionable. Modifications to the simple mirror concept are presented which could mitigate these MHD instabilities.

Emrich, William J., Jr.↗

Magnetotail instability

The stability of the geomagnetic tail is investigated on the basis of three dimensional resistive magnetohydrodynamic simulations, using different dynamic constraints and different initial equilibria. Different forms of the energy equation for isotropic pressure are found to have no significant effect on the dynamic growth of a resistive tearing instability, which is responsible for near Earth reconnection, plasmoid formation and ejection, and the generation of fast plasma flows. The constraints of a modified double adiabatic approach, however, can quench the tearing instability through the development of large, mirror type, anisotropies in the boundary regions of the plasma sheet, unless isotropization occurs on fast, nearly Alfvenic, time scales. The presence of a net cross tail magnetic field component B(sub yN) can reduce the growth of the instability without complete stabilization. An increase of B(sub z) from midnight toward the tail flanks, however, by more than a factor of about 3, apparently completely stabilizes the tearing mode. Stabilization and destabilization thus may depend on properties and constraints (and their release) in regions other than the neutral sheet where reconnection is initiated.

Birn, Joachim↗

Development of Computational Aeroacoustics Code for Jet Noise and Flow Prediction

Accurate prediction of jet fan and exhaust plume flow and noise generation and propagation is very important in developing advanced aircraft engines that will pass current and future noise regulations. In jet fan flows as well as exhaust plumes, two major sources of noise are present: large-scale, coherent instabilities and small-scale turbulent eddies. In previous work for the NASA Glenn Research Center, three strategies have been explored in an effort to computationally predict the noise radiation from supersonic jet exhaust plumes. In order from the least expensive computationally to the most expensive computationally, these are: 1) Linearized Euler equations (LEE). 2) Very Large Eddy Simulations (VLES). 3) Large Eddy Simulations (LES). The first method solves the linearized Euler equations (LEE). These equations are obtained by linearizing about a given mean flow and the neglecting viscous effects. In this way, the noise from large-scale instabilities can be found for a given mean flow. The linearized Euler equations are computationally inexpensive, and have produced good noise results for supersonic jets where the large-scale instability noise dominates, as well as for the tone noise from a jet engine blade row. However, these linear equations do not predict the absolute magnitude of the noise; instead, only the relative magnitude is predicted. Also, the predicted disturbances do not modify the mean flow, removing a physical mechanism by which the amplitude of the disturbance may be controlled. Recent research for isolated airfoils' indicates that this may not affect the solution greatly at low frequencies. The second method addresses some of the concerns raised by the LEE method. In this approach, called Very Large Eddy Simulation (VLES), the unsteady Reynolds averaged Navier-Stokes equations are solved directly using a high-accuracy computational aeroacoustics numerical scheme. With the addition of a two-equation turbulence model and the use of a relatively coarse grid, the numerical solution is effectively filtered into a directly calculated mean flow with the small-scale turbulence being modeled, and an unsteady large-scale component that is also being directly calculated. In this way, the unsteady disturbances are calculated in a nonlinear way, with a direct effect on the mean flow. This method is not as fast as the LEE approach, but does have many advantages to recommend it; however, like the LEE approach, only the effect of the largest unsteady structures will be captured. An initial calculation was performed on a supersonic jet exhaust plume, with promising results, but the calculation was hampered by the explicit time marching scheme that was employed. This explicit scheme required a very small time step to resolve the nozzle boundary layer, which caused a long run time. Current work is focused on testing a lower-order implicit time marching method to combat this problem.

Keith, Theo G., Jr.↗

Viscous nongeostrophic baroclinic instability

Calculations have been performed of the (linear) stability of a baroclinic flow to three-dimensional perturbations. Both the simple Eady basic state and the rotating Hadley cell of Antar and Fowlis are considered. The independent influences of the Richardson (Ri), thermal Rossby (baroclinicity), Ekman, and Prandtl numbers are examined, as well as the influences of the angle of orientation of the horizontal wave vector and the wavelength. It is shown that if the wavelength is allowed to vary freely, disturbances of the Eady type are preferred (i.e., have greatest growth rate) unless Ri and Ekman numbers are small enough and the thermal Rossby number is large enough. In the latter case, disturbances whose angles of orientation are almost symmetric and whose wavelengths are mesoscale are preferred. If, on the other hand, the wavelength is fixed at a mesoscale size, only the symmetric and almost symmetric modes have growth. By allowing the wave vector orientation to deviate from purely symmetric, it is noted that the region of instability (i.e., critical Ri) is increased, the extent of which is greater for longer wavelength. For Prandtl number = 1, permitting the angle to be nonsymmetric demonstrates the existence of two maxima in growth rate at opposite angles of orientation and with very different energetics. For Prandtl number far enough from one and for large enough dissipation, only one of these two modes has positive growth rates. Growing oscillatory modes were found for some cases.

Miller, T. L.↗

Propeller flow visualization techniques

Propeller flow visualization techniques were tested. The actual operating blade shape as it determines the actual propeller performance and noise was established. The ability to photographically determine the advanced propeller blade tip deflections, local flow field conditions, and gain insight into aeroelastic instability is demonstrated. The analytical prediction methods which are being developed can be compared with experimental data. These comparisons contribute to the verification of these improved methods and give improved capability for designing future advanced propellers with enhanced performance and noise characteristics.

Stefko, G. L.↗

Fate of very low-mass secondaries in accreting binaries and the 1.5-ms pulsar

It is shown analytically that the canonical stability postulate for low-mass binaries can be inaccurate when the secondary component mass is less than 0.02 solar mass. The adjustable evolutionary parameter h is demonstrated to have a value (in terms of the mass flow effects) of 2/3, less than which catastrophic instability and tidal disruption of the secondary might occur. The disrupted secondary would be reduced to a remnant significantly smaller in mass than the earth, and not be observable visually. Additionally, close passage by another star could accelerate or initiate the process. The model is applicable to the pulsar binary PSR1937+214, and is noted not to conflict with spin-up theories.

Ruderman, M. A.↗

Goertler instability of compressible boundary layers

The instability of the laminar compressible boundary-layer flows along concave surfaces is investigated. The linearized disturbance equations for the three-dimensional, counter-rotating, longitudinal-type vortices in two-dimensional boundary layers are presented in an orthogonal curvilinear system of coordinates. The basic approximation of the disturbance equations, which includes the effect of the growth of the boundary layer, is considered and solved numerically.

El-Hady, N. M.↗

A 3-dimensional mass conserving element for compressible flows

A variety of finite element schemes has been used in the numerical approximation of compressible flows particularly in underwater acoustics. In many instances instabilities have been generated due to the lack of mass conservation. Two- and three-dimensional elements are developed which avoid these problems.

Fix, G.↗

Numerical experiments on the stability of controlled boundary layers

Nonlinear simulations are presented for instability and transition in parallel water boundary layers subjected to pressure gradient, suction, or heating control. In the nonlinear regime, finite amplitude, 2-D Tollmein-Schlichting waves grow faster than is predicted by linear theory. Moreover, this discrepancy is greatest in the case of heating control. Likewise, heating control is found to be the least effective in delaying secondary instabilities of both the fundamental and subharmonic type. Flow field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer.

Zang, Thomas A.↗

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.↗

Non-linear evolution of a second mode wave in supersonic boundary layers

The nonlinear time evolution of a second mode instability in a Mach 4.5 wall-bounded flow is computed by solving the full compressible, time-dependent Navier-Stokes equations. High accuracy is achieved by using a Fourier-Chebyshev collocation algorithm. Primarily inviscid in nature, second modes are characterized by high frequency and high growth rates compared to first modes. Time evolution of growth rate as a function of distance from the plate suggests this problem is amenable to the Stuart-Watson perturbation theory as generalized by Herbert.

Erlebacher, Gordon↗

Stability of three-dimensional boundary layers

The present evaluation of three-dimensional flows notes that the presence of such disturbance sources as roughness could favor the stationary mode, and that end-conditions may inhibit traveling disturbances in the experiments reported; alternatively, the theory could be inadequate. In general, uncertainties remain as to the definition of transition in three dimensions. It remains important to ascertain whether the formation of three-dimensional structures and characteristic stages will occur, as in two-dimensional flow transition. The possibilities and mechanisms for secondary instabilities also remain to be determined.

Reed, Helen L.↗

On the three-dimensional instability of strained vortices

The three-dimensional (3-D) instability of a two-dimensional (2-D) flow with elliptical streamlines has been proposed as a generic mechanism for the breakdown of many 2-D flows. A physical interpretation for the mechanism is presented together with an analytical treatment of the problem. It is shown that the stability of an elliptical flow is governed by an Ince equation. An analytical representation for a localized solution is given and establishes a direct link with previous computations and experiments.

Waleffe, Fabian↗