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Results for “Hydrodynamic Stability Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1980

Sunspots and the physics of magnetic flux tubes. X - On the hydrodynamic instability of buoyant fields

The hydrodynamics of cylindrical buoyant bubbles (magnetic flux tubes) in an atmosphere is examined. Their dynamical stability is considered, with particular attention to the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The instabilities are sufficient to cause fragmentation in the absence of some strong stabilizing effect such as surface tension or an internal azimuthal magnetic field. The results of the stability analysis are first applied to rising gas bubbles in liquids. Then, since agreement with the experimental data is found, the results are applied to the similar problem of the rising magnetic flux in the sun. Magnetic flux tubes in a fluid velocity field are intrinsically unstable, unless twisted. With the known dynamical limits on the degree of twisting, an upper limit on the diameter of the order of a few hundred kilometers is found for the stability of individual flux tubes in the photosphere. Observations show that tubes, except when clustered to form sunspots, are generally not larger than this amount. Therefore, it is suggested that the hydrodynamic instability of larger tubes is a prime cause of their absence from the solar photosphere.

Tsinganos, K. C.↗
NASA NTRS2000

Viscous Analysis of Pulsating Hydrodynamic Instability and Thermal Coupling Liquid-Propellant Combustion

A pulsating form of hydrodynamic instability has recently been shown to arise during liquid-propellant deflagration in those parameter regimes where the pressure-dependent burning rate is characterized by a negative pressure sensitivity. This type of instability can coexist with the classical cellular, or Landau form of hydrodynamic instability, with the occurrence of either dependent on whether the pressure sensitivity is sufficiently large or small in magnitude. For the inviscid problem, it has been shown that, when the burning rate is realistically allowed to depend on temperature as well as pressure, sufficiently large values of the temperature sensitivity relative to the pressure sensitivity causes like pulsating form of hydrodynamic instability to become dominant. In that regime, steady, planar burning becomes intrinsically unstable to pulsating disturbances whose wave numbers are sufficiently small. This analysis is extended to the fully viscous case, where it is shown that although viscosity is stabilizing for intermediate and larger wave number perturbations, the intrinsic pulsating instability for small wave numbers remains. Under these conditions, liquid-propellant combustion is predicted to be characterized by large unsteady cells along the liquid/gas interface.

Margolis, Stephen B.↗
NASA NTRS1975

Design and application of squeeze film dampers for turbomachinery stabilization

The steady-state transient response of the squeeze film damper bearing was investigated. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived; the steady-state equations were used to determine the damper equivalent stiffness and damping coefficients. These coefficients are used to find the damper configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The effects of end seals and cavitated fluid film are included. The transient analysis of rotor-bearing systems was conducted by coupling the damping and rotor equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed.

Gunter, E. J.↗
NASA NTRS2000

Viscous and Thermal Effects on Hydrodynamic Instability in Liquid-Propellant Combustion

A pulsating form of hydrodynamic instability has recently been shown to arise during the deflagration of liquid propellants in those parameter regimes where the pressure-dependent burning rate is characterized by a negative pressure sensitivity. This type of instability can coexist with the classical cellular, or Landau, form of hydrodynamic instability, with the occurrence of either dependent on whether the pressure sensitivity is sufficiently large or small in magnitude. For the inviscid problem, it has been shown that when the burning rate is realistically allowed to depend on temperature as well as pressure, that sufficiently large values of the temperature sensitivity relative to the pressure sensitivity causes the pulsating form of hydrodynamic instability to become dominant. In that regime, steady, planar burning becomes intrinsically unstable to pulsating disturbances whose wavenumbers are sufficiently small. In the present work, this analysis is extended to the fully viscous case, where it is shown that although viscosity is stabilizing for intermediate and larger wavenumber perturbations, the intrinsic pulsating instability for small wavenumbers remains. Under these conditions, liquid-propellant combustion is predicted to be characterized by large unsteady cells along the liquid/gas interface.

Margolis, Stephen B.↗
NASA NTRS1982

Coronal closed structures. IV - Hydrodynamical stability and response to heating perturbations

The response of magnetically confined atmospheres to perturbations in the temperature and density distribution, and the local heating rate by means of a one-dimensional time-dependent hydrodynamical code, which incorporates the full energy, momentum and mass conservation equations is studied. These studies extend the linear instability analysis of Habbal and Rosner (1979) into the finite-amplitude regime, and generalize the confined atmosphere models of Serio et al., to the time-dependent domain. The results show that closed coronal atmospheres are stable against finite-amplitude perturbations if the chromospheric response is taken into account; and observed correlated increases in coronal density and temperature can only be achieved under quiescent conditions by increasing the heat deposition rate relatively more in the chromosphere than in the corona.

Peres, G.↗
NASA NTRS1997

Hydrodynamic Instability in an Extended Landau/Levich Model of Liquid-Propellant Combustion at Normal and Reduced Gravity

The classical Landau/Levich models of liquid-propellant combustion, despite their relative simplicity, serve as seminal examples that correctly describe the onset of hydrodynamic instability in reactive systems. Recently, these two separate models have been combined and extended to account for a dynamic dependence, absent in the original formulations, of the local burning rate on the local pressure and temperature fields. The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed either numerically or analytically in various limiting parameter regimes. In the present work, a formal asymptotic analysis, based on the realistic smallness of the gas-to-liquid density ratio, is developed to investigate the combined effects of gravity and other parameters on the hydrodynamic instability of the propagating liquid/gas interface. In particular, an analytical expression is derived for the neutral stability boundary A(p)(k), where A(p) is the pressure sensitivity of the burning rate and k is the wavenumber of the disturbance. The results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for negative values of A(p). In the limiting case of weak gravity, it is shown that hydrodynamic instability in liquid-propellant combustion is a long-wave instability phenomenon, whereas at normal gravity, this instability is first manifested through O(1) wavenumber disturbances. it is also demonstrated that, in general, surface tension and the viscosity of both the liquid and gas phases each produce comparable stabilizing effects in the long-wavenumber regime, thereby providing important modifications to previous analyses in which one or more of these effects were neglected.

Margolis, S. B.↗
NASA NTRS1998

Hydrodynamic Instability in an Extended Landau/Levich Model of Liquid-Propellant Combustion at Normal and Reduced Gravity

The classical Landau/Levich models of liquid-propellant combustion, despite their relative simplicity, serve as seminal examples that correctly describe the onset of hydrodynamic instability in reactive systems. Recently, these two separate models have been combined and extended to account for a dynamic dependence, absent in the original formulations, of the local burning rate on the local pressure and temperature fields. The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed either numerically or analytically in various limiting parameter regimes. In the present work, a formal asymptotic analysis, based on the realistic smallness of the gas-to-liquid density ratio, is developed to investigate the combined effects of gravity and other parameters on the hydrodynamic instability of the propagating liquid/gas interface. In particular, an analytical expression is derived for the neutral stability boundary A(sub p)(k), where A(sub p) is the pressure sensitivity of the burning rate and k is the wavenumber of the disturbance. The results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for critical negative values of A(sub p). In the limiting case of weak gravity, it is shown that hydrodynamic instability in liquid-propellant combustion is a long-wave instability phenomenon, whereas at normal gravity, this instability is first manifested through O(1) wavenumber disturbances. It is also demonstrated that, in general, surface tension and the viscosity of both the liquid and gas phases each produce comparable stabilizing effects in the large-wavenumber regime, thereby providing important modifications to previous analyses in which one or more of these effects were neglected.

Margolis, Stephen B.↗
NASA NTRS1980

Variations on a spherically symmetrical accretion flow

Spherically symmetrical accretion onto a compact gravitating object is considered from a purely hydrodynamical viewpoint while disregarding heating and cooling processes. The study derives the radial perturbation equation, expresses it in a Eulerian form which is simpler than the Lagrangian form considered, for example, by Balazs (1972), and discusses the relation between the two formulations. This perturbation equation is used for the stability analysis of standing waves as well as for the study of short wavelength traveling waves which are a generalization of Parker's (1966) traveling wave solutions in the sense that they are not restricted to isothermal flows. These traveling waves can cause fluctuations in the mass accretion rate to grow large, but will not drive the unperturbed solution away from its assumed stationary profile. The waves conserve the total energy contained in the perturbation.

Petterson, J. A.↗
NASA NTRS1989

On wave stability in relativistic cosmic-ray hydrodynamics

Wave stability of a two-fluid hydrodynamical model describing the acceleration of cosmic rays by the first-order Fermi mechanism in relativistic, cosmic-ray-modified shocks is investigated. For a uniform background state, the short- and long-wavelength wave speeds are shown to interlace, thus assuring wave stability in this case. A JWKB analysis is performed to investigate the stability of short-wavelength thermal gas sound waves in the smooth, decelerating supersonic flow upstream of a relativistic, cosmic-ray-modified shock. The stability of the waves is assessed both in terms of the fluid velocity and density perturbations, as well as in terms of the wave action. The stability and interaction of the short-wavelength cosmic-ray coherent mode with the background flow is also studied.

Webb, G. M.↗
NASA NTRS1980

Instability thresholds for flexible rotors in hydrodynamic bearings

Two types of fixed pad hydrodynamic bearings (multilobe and pressure dam) were considered. Optimum and nonoptimum geometric configurations were tested. The optimum geometric configurations were determined by using a theoretical analysis and then the bearings were constructed for a flexible rotor test rig. It was found that optimizing bearings using this technique produces a 100% or greater increase in rotor stability. It is shown that this increase in rotor stability is carried out in the absence of certain types of instability mechanisms such as aerodynamic crosscoupling. However, the increase in rotor stability should greatly improve rotating machinery performance in the presence of such forces as well.

Allaire, P. E.↗
NASA NTRS1998

Hydrodynamic Instability in an Extended Landau/Levich Model of Liquid-Propellant Combustion

The classical Landau/Levich models of liquid propellant combustion, which serve as seminal examples of hydrodynamic instability in reactive systems, have been combined and extended to account for a dynamic dependence, absent in the original formulations, of the local burning rate on the local pressure and/or temperature fields. The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed in various limiting parameter regimes. In the present work, a formal asymptotic analysis, based on the realistic smallness of the gas-to-liquid density ratio, is developed to investigate the combined effects of gravity, surface tension and viscosity on the hydrodynamic instability of the propagating liquid/gas interface. In particular, a composite asymptotic expression, spanning three distinguished wavenumber regimes, is derived for both cellular and pulsating hydrodynamic neutral stability boundaries A(sub p)(k), where A(sub p) is the pressure sensitivity of the burning rate and k is the disturbance wavenumber. For the case of cellular (Landau) instability, the results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for critical negative values of A(sub p). In the limiting case of weak gravity, it is shown that cellular hydrodynamic instability in this context is a long-wave instability phenomenon, whereas at normal gravity, this instability is first manifested through O(l) wavenumber disturbances. It is also demonstrated that, in the large wavenumber regime, surface tension and both liquid and gas viscosity all produce comparable stabilizing effects in the large-wavenumber regime, thereby providing significant modifications to previous analyses of Landau instability in which one or more of these effects were neglected. In contrast, the pulsating hydrodynamic stability boundary is found to be insensitive to gravitational and surface-tension effects, but is more sensitive to the effects of liquid viscosity, which is a significant stabilizing effect for O(l) and higher wavenumbers. Liquid-propellant combustion is predicted to be stable (i.e., steady and planar) only for a range of negative pressure sensitivities that lie between the two types of hydrodynamic stability boundaries.

Margolis, Stephen B.↗
NASA NTRS1990

Instability of a supersonic shock-free elliptic jet

A comparison of the measured and the computed spatial stability properties of an aspect ratio 2, supersonic, shock free, elliptic jet is presented. The shock free nature of the elliptic jet furnishes a perfect test of the validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with the linear hydrodynamic stability theory. Aerodynamic and acoustic data are measured to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. The measured mean velocity profiles are employed to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles utilized in the stability analysis. It is shown that the measured frequency associated with peak amplitude noise radiation agrees with that frequency predicted to dominate the large scale structure near the end of the potential core.

Baty, Roy S.↗
NASA NTRS1974

Water impact analysis of space shuttle solid rocket motor by the finite element method

Preliminary analysis showed that the doubly curved triangular shell elements were too stiff for these shell structures. The doubly curved quadrilateral shell elements were found to give much improved results. A total of six load cases were analyzed in this study. The load cases were either those resulting from a static test using reaction straps to simulate the drop conditions or under assumed hydrodynamic conditions resulting from a drop test. The latter hydrodynamic conditions were obtained through an emperical fit of available data. Results obtained from a linear analysis were found to be consistent with results obtained elsewhere with NASTRAN and BOSOR. The nonlinear analysis showed that the originally assumed loads would result in failure of the shell structures. The nonlinear analysis also showed that it was useful to apply internal pressure as a stabilizing influence on collapse. A final analysis with an updated estimate of load conditions resulted in linear behavior up to full load.

Buyukozturk, O.↗
NASA NTRS1992

A new direction in hydrodynamic stability: Beyond eigenvalues

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and looking for unstable eigenvalues of the linearized problem, but the results agree poorly in many cases with experiments. Nevertheless, it has become clear in recent years that linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis can be obtained by considering the 'pseudospectra' of the linearized problem, which reveals that small perturbations to the smooth flow in the form of streamwise vortices may be amplified by factors on the order of 10(exp 5) by a linear mechanism, even though all the eigenmodes are stable. The same principles apply also to other problems in the mathematical sciences that involve non-orthogonal eigenfunctions.

Trefethen, Lloyd N.↗
NASA NTRS1985

Symposium on Numerical and Physical Aspects of Aerodynamic Flows, 3rd, California State University, Long Beach, CA, January 21-24, 1985, Proceedings

Among the topics discussed are hydrodynamic stability and turbulent transition, separated flow simulations employing finite difference methods, a quasi-simultaneous finite difference approach for strongly interacting flow, the Newton solution of coupled Euler and boundary layer equations, multielement airfoil aerodynamics, vorticity dynamics, the significance of the thin layer Navier-Stokes approximation, a comparison of interactive and Navier-Stokes calculations of separating boundary layer flows, and a Navier-Stokes analysis for the mechanism of shock wave/boundary layer interactions. Also discussed are transonic interactions of unsteady vortical flows, boundary layers on oscillating airfoils, a laser-interferometer skin friction meter, flow over surface-mounted semibluff bodies, computations for spinning and spin-stabilized supersonic projectiles, transition calculations in three-dimensional flows, the effect of projectile boattailing in transonic flow, flow characteristics of a body of revolution at incidence, the influence of the boundary layer on the leading edge flow of a swept wing, and an interactive scheme for three-dimensional transonic flows.

Source record↗
NASA NTRS1990

Theory of electrohydrodynamic instabilities in electrolytic cells

The paper develops the theory of the hydrodynamic stability of an electrolytic cell as a function of the imposed electric current. A new electrohydrodynamic instability is encountered when the current is forced to exceed the Nernst limit. The convection is driven by the volume force exerted by the electric field on space charges in the electrolyte. This intrinsic instability is found to be easily masked by extrinsic convection sources such as gravity or stirring. A linear stability analysis is performed and a dimensionless number Le is derived whose value determines the convection pattern.

Bruinsma, R.↗
NASA NTRS1987

Stability of a rigid rotor supported on oil-film journal bearings under dynamic load

Most published work relating to dynamically loaded journal bearings are directed to determining the minimum film thickness from the predicted journal trajectories. These do not give any information about the subsynchronous whirl stability of journal bearing systems since they do not consider the equations of motion. It is, however, necessary to know whether the bearing system operation is stable or not under such an operating condition. The stability characteristics of the system are analyzed. A linearized perturbation theory about the equilibrium point can predict the threshold of stability; however it does not indicate postwhirl orbit detail. The linearized method may indicate that a bearing is unstable for a given operating condition whereas the nonlinear analysis may indicate that it forms a stable limit cycle. For this reason, a nonlinear transient analysis of a rigid rotor supported on oil journal bearings under: (1) a unidirectional constant load, (2) a unidirectional periodic load, and (3) variable rotating load are performed. The hydrodynamic forces are calculated after solving the time-dependent Reynolds equation by a finite difference method with a successive overrelaxation scheme. Using these forces, equations of motion are solved by the fourth-order Runge-Kutta method to predict the transient behavior of the rotor. With the aid of a high-speed digital computer and graphics, the journal trajectories are obtained for several different operating conditions.

Majumdar, B. C.↗
NASA NTRS1984

The dynamic fission instability and the origin of the Moon

A theory for the formation of the Moon which involves the dynamic fission of a rapidly rotating protoplanet, which might then result in the formation of the Earth and the Moon is discussed. The fission hypothesis was originally based on analytic, linearized models of the growth of asymmetry in homogenous bodies. The fully nonlinear evolution of the dynamic instability in inviscid, compressible bodies was calculated by numerical techniques. It was found that the dynamic instability degenerates into the ejection of a ring of matter with a substantial fraction of the mass, leaving behind a central body with most of the mass. The linearized analytical approach and the numerical approach were used to show that dynamic fission probably does not occur in rocky protoplanets. The numerical calculations are performed with a fully three dimensional hydrodynamical code, which allows the nonlinear, time evolution of the instability to be followed. Sequences of uniformly rotating equilibria were constructed and are used as the initial models for the fission calculations. An initially imposed asymmetry consisting of a 10% binary perturbation in the density was found to disappear on the rotational period time scale. No dynamic instability occurred. This result are verified by including the velocity dissipation terms in the linearized analysis of the stability of a Maclaurin spheroid: the dynamic instability disappears when the simulated viscous dissipation terms are included. It is concluded that any rocky body, even with considerable partial melt or a molten core, should be stable to dynamic fission; any rotational instability that occurs can only result in equatorial mass loss.

Boss, A. P.↗