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At least 19 records

An application of Floquet theory to prediction of mechanical instability

The problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative, and it is shown that if the hub is considered to be nonisotropic, the equations of motion have periodic coefficients which cannot be eliminated. The Floquet transition matrix method is shown to be an effective way of dealing with the nonisotropic hub and nonisotropic rotor situation. Time history calculations are examined and shown to be inferior to the Floquet technique for determining system stability. It is shown that instabilities which occur when one blade damper is inoperative may consist of nearly pure blade motion or they may be similar to the classical mechanical instability.

Hammond, C. E.↗

An application of Floquet theory to prediction of mechanical instability

The problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative. It is shown that, if the hub is considered to be nonisotropic, the equations of motion have periodic coefficients which cannot be eliminated. However, if the hub is isotropic, the equations can be transformed to a rotating frame of reference and the periodic coefficients eliminated. The Floquet transition matrix method is shown to be an effective way of dealing with the nonisotropic hub and nonisotropic rotor situation. Time history calculations are examined and shown to be inferior to the Floquet technique for determining system stability.

Hammond, C. E.↗

Secondary instability mechanisms in compressible, axisymmetric boundary layers

Secondary instability mechanisms in compressible, axisymmetric boundary layers are analyzed using spectrally-accurate mean-flow and stability codes. Results show that subharmonic disturbances are the most dangerous secondary disturbances in an environment with a low to moderate intensity of the primary disturbance. The relation between spatial and temporal analyses of the secondary disturbance is explored at Mach 1.6 along a flat plate and Mach 6.8 along a cone. Spatial direct numerical simulations are utilized to confirm the quantitative predictions from spatial secondary instability theory.

Ng, Lian L.↗

Experimental and theoretical investigation of boundary-layer instability mechanisms on a swept leading edge at Mach 3.5

A brief outline of the experimental and theoretical investigation of boundary layer instability mechanisms on a swept leading edge at Mach 3.5 is presented. Transition is affected by wind tunnel noise only when roughness is present. Local bar-R sub * Reynolds number and k/eta sub * are useful correlation parameters for a wide range of free stream Mach numbers. Stability theory is in good agreement with the experimental cross flow vortex wavelength. These conclusions are briefly discussed.

Creel, Theodore R., Jr.↗

On the Gortler vortex instability mechanism at hypersonic speeds

The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point the viscosity of the fluid is taken to be a linear function of temperature and real-gas effects are ignored. It is shown that the flow is susceptible to Gortler vortices and that they are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value. The vortices decay exponentially in both directions away from this layer and are most unstable when their wavelength is comparable with the depth of the adjustment layer. The non-uniqueness of the neutral stability curve associated with incompressible Gortler vortices is shown to disappear at high Mach numbers if the appropriate fast streamwise dependence of the instability is built into the disturbance flow structure. It is shown that in the hypersonic limit wall-cooling has a negligible effect on the stability of a fluid with a given value of the Chapman constant.

Hall, Philip↗

On the Goertler vortex instability mechanism at hypersonic speeds

The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point, the viscosity of the fluid is taken to be a linear function of temperature and real-gas effects are ignored. It is shown that the flow is susceptible to Goertler vortices and that they are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value. The vortices decay exponentially in both directions away from this layer and are most unstable when their wavelength is comparable with the depth of the adjustment layer. The nonuniqueness of the neutral stability curve associated with incompressible Goertler vortices is shown to disappear at high Mach numbers if the appropriate 'fast' streamwise dependence of the instability is built into the disturbance flow structure. It is shown that in the hypersonic limit, wall-cooling affects the leading-order term in the expansion of the Goertler number which is independent of the wavenumber, and which is due to the curvature of the basic state but it has a negligible effect on the other terms which are dependent on the wavenumber.

Hall, Philip↗

On the Goertler vortex instability mechanism at hypersonic speeds

The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point real-gas effects are ignored and the viscosity of the fluid is taken to be related to the temperature either by Chapman's Law or by Sutherland's Law. It is shown that the flow is susceptible to Goertler vortices. If Chapman's Law is used the vortices are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value and the nonuniqueness of the neutral stability curve associated with incompressible Goertler vortices is shown to disappear at high Mach numbers if the appropriate 'fast' streamwise dependence of the instability is built into the disturbance flow structure. If, on the other hand, Sutherland's Law is used, the vortices are found to spread into an O(1) region and the concept of a unique neutral stability curve is not tenable because of the nonparallel effects. For both laws the leading order terms in the expansions of the Goertler number are independent of the wave number and are due to the curvature of the basic state.

Hall, P.↗

Will the real dynamic instability mechanism please be recognized!

There is a richness of flow mechanisms that can cause dynamic instability. Only after asking the right questions and carefully considering the answers can the fluid dynamic source of the observed dynamic instability be recognized. This is illustrated by two carefully chosen examples.

Ericsson, L. E.↗

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Xu, Jian-Jun↗

The Goertler vortex instability mechanism in three-dimensional boundary layers

The two dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

Hall, P.↗

The Goertler vortex instability mechanism in three-dimensional boundary layers

The two-dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three-dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two-dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three-dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

Hall, P.↗

Jet fuel instability mechanisms

The mechanisms of the formation of fuel-insoluble deposits were studied in several real fuels and in a model fuel consisting of tetralin in dodecane solution. The influence of addition to the fuels of small concentrations of various compounds on the quantities of deposits formed and on the formation and disappearance of oxygenated species in solution was assessed. The effect of temperature on deposit formation was also investigated over the range of 308-453 K.

Daniel, S. R.↗

Boundary-layer instability mechanisms on a swept-leading edge at Mach 3.5

Correlations have been made in NASA Langley's Mach 3.5 Pilot Quiet Tunnel for the transitions occurring from laminar to turbulent flow, in the cases of 45-deg and 60-deg swept cylinders. While freestream noise variations had no effect on boundary layer transition, the addition of boundary layer trips to the leading edges led to transition at lower Re numbers, depending on both trip height and wind tunnel noise level. Also presented are the results of compressible linear stability calculations for the boundary layer of an infinite swept cylinder; Tollmien-Schlichting waves are found to be amplified in the attachment line boundary layer.

Creel, T. R., Jr.↗

Shear coaxial injector instability mechanisms

Although stable operating regimes for cryogenic coaxial injectors have been empirically determined, there is no knowledge of the spray characteristics corresponding to stable operation, or the physical processes which produce the atomization patterns that result in stable or unstable operation. The current engineering method for determining the stable operating regime of a cryogenic coaxial injector is the 'hydrogen temperature ramping' method, however there is no definitive knowledge of whether the hydrogen temperature influences the chamber stability by decreasing the injected gas velocity, by affecting a recirculation region at the base of the LOX Post, or by changing the pressure drop across the injector, allowing chamber pressure oscillations to couple to the fuel feed system. Results for the injector response from a linearized lumped-element model are presented as a function of temperature and frequency. LDV measurements in the recess region at the base of the LOX post show reverse flow indicative of a recirculation region. Finally, Phase Doppler Particle Analyzer (PDPA) measurements of droplet size and velocity distributions are discussed for a coaxial injector element similar to the SSME preburner element operating with water and air at atmospheric pressure and liquid and gaseous nitrogen at 20 bars.

Kaltz, T.↗

Shear coaxial injector instability mechanisms

There is no definitive knowledge of which of several concurrent processes ultimately results in unstable combustion within liquid rocket chambers employing shear coaxial injectors. Possible explanations are a detrimental change in the atomization characteristics due to a decrease in the gas-to-liquid velocity ratio, a change in the gas side injector pressure drop allowing acoustic coupling to the propellant feed system or the disappearance of a stabilizing recirculation region at the base of the LOX post. The aim of this research effort is to investigate these proposed mechanisms under conditions comparable to actual engine operation. Spray characterization was accomplished with flash photography and planar laser imaging to examine the overall spray morphology and liquid jet breakup processes and with a PDPA to quantify the spatial distribution of droplet size and mean axial velocity. A simplified stability model based on the Rayleigh criterion was constructed for the flow dynamics occurring within the chamber and injector to evaluate the potential coupling between the chamber and injector acoustic modes and was supported by high frequency measurements of chamber and injector pressure oscillations. To examine recirculation within the LOX post recess, velocity measurements were performed in the recess region by means of LDV. Present experiments were performed under noncombusting conditions using LOX/GH2 stimulants at pressures up to 4 MPa.

Puissant, C.↗

Instability Mechanisms of Thermally-Driven Interfacial Flows in Liquid-Encapsulated Crystal Growth

During the past year, a great deal of effort was focused on the enhancement and refinement of the computational tools developed as part of our previous NASA grant. In particular, the interface mollification algorithm developed earlier was extended to incorporate the effects of surface-rheological properties in order to allow the study of thermocapillary flows in the presence of surface contamination. These tools will be used in the computational component of the proposed research in the remaining years of this grant. A detailed description of the progress made in this area is provided elsewhere. Briefly, the method developed allows for the convection and diffusion of bulk-insoluble surfactants on a moving and deforming interface. The novelty of the method is its grid independence: there is no need for front tracking, surface reconstruction, body-fitted grid generation, or metric evaluations; these are all very expensive computational tasks in three dimensions. For small local radii of curvature there is a need for local grid adaption so that the smearing thickness remains a small fraction of the radius of curvature. A special Neumann boundary condition was devised and applied so that the calculated surfactant concentration has no variations normal to the interface, and it is hence truly a surface-defined quantity. The discretized governing equations are solved subsequently using a time-split integration scheme which updates the concentration and the shape successively. Results demonstrate excellent agreement between the computed and exact solutions.

Haj-Hariri, Hossein↗