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  • 1
    Publication Date: 2013-08-31
    Description: The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite element solution of the Boussinesq equations coupled with computed-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with Prandtl number of one and for cylinders with aspect ratio (Lambda) (defined as the height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curve for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous evolution of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and lambda are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Lambda or = Lambda * approximately 0.80 or by a limit point for Lambda Lambda *. The transition between these two modes may be described by the theory of multiple limit point bifurcation.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NAS 1.26:173626 , NASA-CR-173626
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  • 2
    Publication Date: 2013-08-31
    Description: The relative ablative performance of uncoated silicone-modified reinforced carbon composite (RCC) and uncoated shuttle baseline RCC substrates was investigated. The test specimens were 13 plies (5.3 to 5.8 millimeters) thick and had a 25-millimeter-diameter test face. Prior to arc tunnel testing, all specimens were subjected to a heat treatment simulating the RCC coating process. During arc tunnel testing, the specimens were exposed to cold wall heating rates of 178 to 529 kilowatts/sq m and stagnation pressures ranging from 0.015 to 0.046 atmosphere at Mach 4.6 in air, with and without preheating in nitrogen. The results show that the ablative performance of uncoated silicone-modified RCC substrates is significantly superior to that of uncoated shuttle baseline RCC substrates over the range of heating conditions used. These results indicate that the silicone-modified RCC substrate would yield a substantially greater safety margin in the event of complete coating loss on the shuttle orbiter.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-TN-D-8358 , L-11095
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  • 3
    Publication Date: 2016-03-09
    Description: A screen mesh artery supported concentrically within the evaporator section of a heat pipe liquid channel retains liquid in the channel. Continued and uniform liquid feed to the heat pipe evaporation section (20) during periods of excessive heat transfer is assured. The overall design provides high evaporation and condensation film coefficients for the working fluid by means of the circumferential grooves in the walls of the vapor channel, while not interfering with the overall heat transport capability of the axial groove. The design has particular utility in zero-g environments.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 4
    Publication Date: 2011-08-19
    Description: The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 29; 2788-279
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  • 5
    Publication Date: 2011-08-18
    Description: A liquid drop held captive between parallel disks that are differentially rotated is a model for the swirling flows induced by crystal rotation in the floating-zone process for growing semiconductor materials. An asymptotic analysis for a cylindrical drop is presented that elucidates the structure of the axisymmetric cellular motions caused by disk rotation at low Reynolds number. Variations of meniscus shape induced by these flows are described in the limit of small capillary number. Most cellular flow fields break the bifurcation point that corresponds to the Plateau-Rayleigh limit for the length of a static drop into two disjoint shape families and lower the maximum stable drop length. This effect is studied by a singular bifurcation analysis.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 126; Jan. 198
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  • 6
    Publication Date: 2011-08-17
    Description: Shapes and stability of surface-tension-endowed drops rotating rigidly at fixed angular momentum are calculated by finite-element analysis. A new family of asymmetric two-lobed drop shapes is discovered that branches from, and rejoins, the Pik-Pichak family of symmetric two-lobed shapes. The computations are verified for axisymmetric and symmetric two-lobed drop shape by comparison with previous approximations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters; 45; July 21
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  • 7
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    Publication Date: 2011-08-17
    Description: Equilibrium shapes and stability of rotating drops held together by surface tension are found by computer-aided analysis that uses expansions in finite-element basis functions. Shapes are calculated as extrema of appropriate energies. Stability and relative stability are determined from curvatures of the energy surface in the neighborhood of the extremum. Families of axisymmetric, two-, three-, and four-lobed drop shapes are traced systematically. Bifurcation and turning points are located and the principle of exchange of stabilities is tested. The axisymmetric shapes are stable at low rotation rates but lose stability at the bifurcation to two-lobed shapes. Two-lobed drops isolated with constant angular momentum are stable. The results bear on experiments designed to further those of Plateau (1863).
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 8
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    Publication Date: 2011-08-19
    Description: The bifurcation diagram corresponding to the Eckhaus stability curve has been constructed for the one-dimensional Swift-Hohenberg equation in a finite domain. Finite-amplitude solutions with particular spatial wavelength recover linear stability, as predicted by the Eckhaus curve, after a sequence of secondary bifurcations from the branch of solutions with this wavelength. No connectivity between the primary-solution branches is admissible if the stability predicted by this bifurcation diagram is to correspond to the prediction of the Eckhaus analysis. The Eckhaus curve does not exist if nonlinear couplings destroy this pattern. This is demonstrated by analysis of a coupled pair of Swift-Hohenberg equations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters (ISSN 0031-9007); 63; 2048-205
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  • 9
    Publication Date: 2011-08-19
    Description: The nonlinear dynamics of nonaxisymmetric inviscid charged conducting drops near the Rayleigh charge limit (R = 4) is investigated analytically. It is shown that only axisymmetric spheroid drops bifurcate from the sphere family when the charge is increased, that oblate spheroids at R greater than 4 are unstable to nonaxisymmetric disturbances governing drop breakup, and that prolate spheroids at R less than 4 are unstable only to axisymmetric disturbances tending to increase the length of the drop along its symmetry axis. The effects of external electric fields and rigid-body rotation are also analyzed, and the solutions for the amplitude equations at R just less than 4 (equivalent to the dynamical equations of the Henon-Heiles Hamiltonian) are explored.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630); 410; 1838,; 209-227
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  • 10
    Publication Date: 2011-08-18
    Description: Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Re sub c. The slope of the locus of Re sub c for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio for exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 144; 403-418
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