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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Stability of streamwise vortices

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Khorrami, M. K.↗
NASA NTRS1950

An introduction to the physical aspects of helicopter stability

In order to provide engineers interested in rotating-wing aircraft, but with no specialized training in stability theory, some understanding of the factors that influence the flying qualities of the helicopter, an explanation is made of both the static stability and the stick-fixed oscillation in hovering and forward flight in terms of fundamental physical quantities. Three significant stability factors -- static stability with angle of attack, static stability with speed, and damping due to a pitching or rolling velocity -- are explained in detail.

Gessow, Alfred↗
NASA NTRS1985

Stability of an oscillating boundary layer

Levchenko and Solov'ev (1972, 1974) have developed a stability theory for space periodic flows, assuming that the Floquet theory is applicable to partial differential equations. In the present paper, this approach is extended to unsteady periodic flows. A complete unsteady formulation of the stability problem is obtained, and the stability characteristics over an oscillating period are determined from the solution of the problem. Calculations carried out for an oscillating incompressible boundary layer on a plate showed that the boundary layer flow may be regarded as a locally parallel flow.

Levchenko, V. Y.↗
NASA NTRS1989

Transition in hypersonic boundary layers

Linear stability theory for hypersonic boundary layers is presented. The theory is used to study the effects of real gas (under the assumption of local chemical equilibrium) and small nose bluntness on hypersonic boundary layer stability. It is found that chemical reactions have a stabilizing effect on the first mode instability and a destabilizing effect on the second mode instability in hypersonic boundary layers. There is also a tendency for the second-mode instability to shift to lower frequencies. The effect of small nose bluntness is found to be stabilizing.

Malik, Mujeeb R.↗
NASA NTRS1974

The modified equation approach to the stability and accuracy analysis of finite-difference methods

The stability and accuracy of finite-difference approximations to simple linear partial differential equations are analyzed by studying the modified partial differential equation. Aside from round-off error, the modified equation represents the actual partial differential equation solved when a numerical solution is computed using a finite-difference equation. The modified equation is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations. The connection between 'heuristic' stability theory based on the modified equation approach and the von Neumann (Fourier) method is established. In addition to the determination of necessary and sufficient conditions for computational stability, a truncated version of the modified equation can be used to gain insight into the nature of both dissipative and dispersive errors.

Warming, R. F.↗
NASA NTRS1998

An Experimental Study of Pressure Oscillation in a Capillary Pumped Loop with Multiple Evaporators and Condensers

The heat transport capability of a capillary pumped loop (CPL) is limited by the pressure drop that its evaporator wick can sustain. The pressure drop in a CPL is not constant even under seemingly steady operation, but rather exhibits an oscillatory behavior. A hydrodynamic theory based on a mass-spring-dashpot model was previously developed to predict the pressure oscillation in a CPL with a single evaporator and a single condenser. The theory states that the pressure oscillation is a function of physical dimensions of the CPL components and operating conditions. Experimental data agreed very well with theoretical predictions. The hydrodynamic stability theory has recently been extended to predict the pressure oscillations in CPLs with multiple evaporators and multiple condensers. Concurrently, an experimental study was conducted to verify the theory and to investigate the effects of various parameters on the pressure oscillation. Four evaporators with different wick properties were tested using a test loop containing two condenser plates. The test loop allowed the four evaporators to be tested in a single-pump, two-pump or four-pump configuration, and the two condenser plates to be plumbed either in parallel or in series. Test conditions included varying the power input, the reservoir set point temperature, the condenser sink temperature, and the flow resistance between the reservoir and the loop. Experimental results agreed well with theoretical predictions.

Ku, Jen-Tung↗
NASA NTRS1981

Existence of a natural instability not predicted by theory and connected to a wall deformation in a laminar boundary layer

Natural instability related to negative wall deformation was studied. It was shown that natural instabilities which propagate in a laminar boundary layer of a flat plate are in agreement with stability theory. It is found that if a wall has a deformation, a second frequency does exist, which is not predicted and is twice the first frequency. This second instable frequency only appears if there is a negative velocity gradient. The phenomenon is located very closely to the wall and drops off rapidly when moved away from it.

Gougat, P.↗
NASA NTRS1973

Research in plasma physics

Three aspects of barium ion cloud dynamics are discussed. First, the effect of the ratio of ion cloud conductivity to background ionospheric conductivity on the motion of barium ion clouds is investigated and compared with observations of barium ion clouds. This study led to the suggestion that the conjugate ionosphere participates in the dynamics of barium ion clouds. Second, analytic work on the deformation of ion clouds is presented. Third, a linearized stability theory was extended to include the effect of the finite extent of an ion cloud, as well as the effect of the ratio of ion cloud to ionospheric conductivities. The stability properties of a plasma with contra-streaming ion beams parallel to a magnetic field are investigated. The results are interpreted in terms of parameters appropriate for collisionless shock waves. It is found that this particular instability can be operative only if the up-stream Alfven Mach number exceeds 5.5.

Source record↗
NASA NTRS2013

Crystal Shape Evolution in Detached Bridgman Growth

Detached (or dewetted) Bridgman crystal growth defines that process in which a gap exists between a growing crystal and the crucible wall. Existence of the gap provides several advantages, including no sticking of the crystal to the crucible wall, reduced thermal and mechanical stresses, reduced dislocations, and no heterogeneous nucleation by the crucible. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus. The effect of a tapered crucible on dynamic stability is also described

Volz, M. P.↗
NASA NTRS2013

Crystal Shape Evolution in Detached Bridgman Growth

Detached (or dewetted) Bridgman crystal growth defines that process in which a gap exists between a growing crystal and the crucible wall. Existence of the gap provides several advantages, including no sticking of the crystal to the crucible wall, reduced thermal and mechanical stresses, reduced dislocations, and no heterogeneous nucleation by the crucible. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus. The effect of a tapered crucible on dynamic stability is also described.

Volz, M. P.↗
NASA NTRS2013

Evolution of the Shape of Detached GeSi Crystals in Microgravity

A series of GeSi crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. An objective of these experiments is to understand the mechanisms of detached Bridgman growth, a process in which a gap exists between the growing semiconductor crystal and the crucible wall. Crystals grown without wall contact have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus.

Volz, M. P.↗
NASA NTRS2013

Evolution of the Shape of Detached GeSi Crystals in Microgravity

A series of GeSi crystal growth experiments are planned to be conducted in the Low Gradient Furnace (LGF) onboard the International Space Station. An objective of these experiments is to understand the mechanisms of detached Bridgman growth, a process in which a gap exists between the growing semiconductor crystal and the crucible wall. Crystals grown without wall contact have superior quality to otherwise similar crystals grown in direct contact with a container, especially with respect to impurity incorporation, formation of dislocations, and residual stress in crystals. Numerical calculations are used to determine the conditions in which a gap can exist. According to crystal shape stability theory, only some of these gap widths will be dynamically stable. Beginning with a crystal diameter that differs from stable conditions, the transient crystal growth process is analyzed. In microgravity, dynamic stability depends only on capillary effects and is decoupled from heat transfer. Depending on the initial conditions and growth parameters, the crystal shape will evolve towards the crucible wall, towards a stable gap width, or towards the center of the crucible, collapsing the meniscus.

Volz, M. P.↗
NASA NTRS1987

The fully nonlinear development of Goertler vortices in growing boundary layers

The fully nonlinear development of small wavelength Goertler vortices in a growing boundary layer is investigated using a combination of asymptotic and numerical methods. The starting point for the analysis is the weakly nonlinear theory of Hall (1982b) who discussed the initial development of small amplitude vortices in a neighborhood of the location where they first become linearly unstable. That development is unusual in the context of nonlinear stability theory in that it is not described by the Stuart-Watson approach. In fact the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction. Here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state. Surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means. It is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer. In fact the system obtained by writing down the equations for the fundamental component of the vortex generate a differential equation for the basic state. Thus the mean flow adjusts so as to make these large amplitude vortices locally neutral. Moreover in the region where the vortices exist the mean flow has a square-root profile and the vortex velocity field can be written down in closed form. The upper and lower boundaries of the region of vortex activity are determined by a free-boundary problem involving the boundary layer equations. In general it is found that this region ultimately includes almost all of the original boundary layer and much of the free-stream. In this situation the mean flow has essentially no relationship to the flow which exists in the absence of the vortices.

Hall, Philip↗
NASA NTRS1990

Effects of forebody geometry on subsonic boundary-layer stability

As part of an effort to develop computational techniques for design of natural laminar flow fuselages, a computational study was made of the effect of forebody geometry on laminar boundary layer stability on axisymmetric body shapes. The effects of nose radius on the stability of the incompressible laminar boundary layer was computationally investigated using linear stability theory for body length Reynolds numbers representative of small and medium-sized airplanes. The steepness of the pressure gradient and the value of the minimum pressure (both functions of fineness ratio) govern the stability of laminar flow possible on an axisymmetric body at a given Reynolds number. It was found that to keep the laminar boundary layer stable for extended lengths, it is important to have a small nose radius. However, nose shapes with extremely small nose radii produce large pressure peaks at off-design angles of attack and can produce vortices which would adversely affect transition.

Dodbele, Simha S.↗
NASA NTRS2019

Effects of Wall Cooling on Supersonic Modes in High-Enthalpy Hypersonic Boundary Layers over a Cone

High-enthalpy hypersonic boundary-layer transition plays an important role in many entry/descent vehicles. Aerothermodynamic performance of these vehicles strongly depends on the transition location on the surface. However, detailed transition flow physics in these chemically reacting boundary layers are poorly understood and transition estimates during the design phase rely heavily on empirically-derived transition criteria such as 𝑹𝒆(𝜽)/𝑴(𝒆). One of the most intriguing characteristics in hypersonic boundary layers is the presence of unstable supersonic modes, first identified in the 1990s. Due to a recent surge in hypersonic applications, there has been renewed interest in studying the flow physics of supersonic modes using either theory or direct numerical simulations. This paper investigates the rise of supersonic modes in a high-enthalpy hypersonic flow over a 𝟓° half-angle cone at various wall temperatures using both quasiparallel linear stability theory and linear PSE. It was found that supersonic modes exist in all wall temperature conditions including the adiabatic wall case. Cooler wall temperature causes the second Mack mode to become an unstable supersonic mode naturally downstream of the upper-branch neutral location when the wall is sufficiently cooled. In terms of the integrated growth, the second mode is still the dominant mode. Nonetheless, supersonic modes can cause additional series of relatively weaker growth than that of the second mode beyond the peak amplitude location. According to the present linear PSE results, contrary to what was speculated in the literature, supersonic-mode pressure disturbance structure radiated into the freestream is nonacoustic in nature and the formation of unstable supersonic modes is mainly associated with the synchronization of phase speed between the instability and acoustic waves in a nonp ayer, not due to nonlinear modal interaction as suggested in the literature.

Chang, Chau-Lyan↗
NASA NTRS1994

Effect of crossflow on Goertler instability in incompressible boundary layers

Linear stability theory is used to study the effect of crossflow on Goertler instability in incompressible boundary layers. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. It is shown that the crossflow stabilizes Goertler disturbances by reducing the maximum growth rate and shrinking the unstable band of spanwise wave numbers. On the other hand, the effect of concave wall curvature on crossflow instability is destabilizing. Calculations show that the changeover from Goertler to crossflow instabilities is a function of Goertler number, pressure gradient, and sweep angle. The results demonstrate that Goertler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressure gradient and sweep can be combined by defining a crossflow Reynolds number. Thus, the changeover from Goertler to crossflow instability takes place at some critical crossflow Reynolds number whose value increases with Goertler number.

Zurigat, Y. H.↗
NASA NTRS1972

Origin of strong magnetic fields.

A possible mechanism by which extremely strong magnetic fields in neutron stars and white dwarfs could originate involves the existence of thermodynamic equilibrium states (LOFER states) of an electron gas. The essence of the stability theory of a LOFER state is discussed. The extended electronic system considered is in contact with a thermal bath in the presence of an external magnetic field. It is found that it is not necessary to require absolute stability in order to realize a LOFER state in nature.

Canuto, V.↗