SEARCH · Search NASA

Results for “FREE BOUNDARY”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

NASA NTRS1985

Measurement of damping of graphite epoxy materials

The design of an experiment to measure the damping of a cylindrical graphite-epoxy specimen with a three point support and a knife edge support is described as well as equipment used in tests conducted to determine the influence of the support at the two ends of the specimen and to simulate an idealized free-free boundary condition at the two edges. A curve fitting technique is being used to process the frequency response data obtained. Experiments conducted on the thin plate specimen also reveal the influence of the end support condition on the damping ratio of the specimen. The damping ratio values measured for both specimens appear to be strongly influenced by the shape of the specimen and appear to depend on length and fiber orientation as well as the presence of discontinuities such as sharp bends, corners, and notches.

Crocker, M. J.↗

NASA NTRS1985

Measurement of damping of graphite expoxy materials

During this period damping measurements were made on the cylindrical graphite epoxy specimen using the forced-vibration test method. The specimen was carefully mounted directly on the shaker through the supporting ring and the impedance head. This was done to simulate an idealized free-free boundary condition at the two edges. The damping ratio value and the natural frequency (first mode) obtained in this experiment were 0.13% and 508.75 Hz respectively. In order to check the damping induced by the supporting ring, measurements were made with the top half of the ring removed. The specimen then was supported only by the bottom half of the ring (half ring). It was observed that the natural frequency of the specimen (first mode) increased of a value of 552.5 Hz due to the influence of the reduced mass of the supporting ring. But the damping ratio value obtained was the same as that obtained with full supporting ring, namely 0.13%.

Crocker, M. J.↗

NASA NTRS1985

Measurement of damping of graphite epoxy materials

Work on a damping measurement test apparatus is discussed. The device is designed to excite tube specimens in a vacuum chamber. Also some experiments were conducted on a tube specimen to confirm previously reported results. A table of data showing the results of forced vibration tests using a half ring and a free-free boundary is given. The main purpose was to study the effect of the frequency resolution on the damping ratio measurements.

Crocker, M. J.↗

NASA NTRS1985

A higher-order shear deformation theory of laminated elastic shells

A higher-order shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers. The theory is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces of the shell. The Navier-type exact solutions for bending and natural vibration are presented for cylindrical and spherical shells under simply supported boundary conditions.

Reddy, J. N.↗

NASA NTRS1986

On the Lagrangian Method for Steady and Unsteady Flow

A new and general Lagrangian formulation of fluid motion is given in which the independent variables are three material functions and a Lagrangian time, which differs for different fluid particles and is distinct from the Eulerian time. For steady flow it requires only three independent variables - the Lagrangian time and two stream functions - in contrast with the conventional Lagrangian formulation which apparently still requires four independent variables for describing a steady flow. This places the Lagrangian formulation for steady flow on the same footing as the Eulerian. For unsteady flow, the new formulation includes the conventional formulation as a special case when the Lagrangian time is identified with the Eulerian time and when the material functions are taken to be the fluid particle's position at some given time. The distinction between the Lagrangian and Eulerian time, however, is found useful in applications, e.g., to problems involving a free boundary.

Hui, W. H.↗

NASA NTRS1986

Transitions to chaos in two-dimensional double-diffusive convection

The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity tau is less than 1 and the solutal Rayleigh number Rs is sufficiently large. Solutions have been obtained for two representative values of tau. For tau = 0.316, R(s) = 10,000, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number R(T) is increased. At higher values of R(T), the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As R(T) is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for tau = 0.1 by varying R(T) for several different values of R(s). When R(s) is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As R(s) is increased, chaos appears in the neighborhood of these heteroclinic orbits. At higher values of R(s), chaos is found for a broader range in R(T). A truncated fifth-order model suggest that the appearance of chaos is associated with heteroclinic bifurcations.

Knobloch, E.↗

NASA NTRS1986

Time-dependent profiles of lava flows

This work investigates the combined effects of a time-dependent effusion rate and a spatially varying viscosity on the thickness profile of a flowing lava. Relatively simple governing equations are formulated as a primitive dynamical model for these two influences on lava flow morphology. Free boundary solutions for the profile of the flow and its extent are presented and analyzed for different boundary conditions at the source of the flow and several models for the spatial dependence of the viscosity. The results presented here suggest that time dependence in the flow depth at the source and the form of the viscosity variation are significant influences on the morphology and dimensions of lava flows. Moreover, this analysis implies that time-dependent source conditions may contribute to the scatter in plots of eruption rate versus flow length and disparities between field and laboratory estimates of lava viscosity.

Baloga, Stephen↗

NASA NTRS1987

Thermosolutal convection during directional solidification. II - Flow transitions

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

Mcfadden, G. B.↗

NASA NTRS1987

The configuration of slow-mode shocks

A simple method for computing blunt-body flows containing slow shocks is presented. The method is based on the solution of a free-boundary problem for the shock configuration that matches a postshock potential flow to a uniform preshock flow. The method is applied to shocks arising from flow about spherical and paraboloidal obstacles. The results of a parametric study of shock formation as a function of sonic and Alfven Mach numbers showed that when either Mach number decreased, the standoff distance increased. The results should give estimates of the location and the configuration of slow shocks, provided that two as yet unverified assumptions are correct: (1) that the standoff distance and the slow-shock configuration along the stagnation streamline are not affected significantly by portions of the shock still forming far upstream of the shock nose, and (2) that fast-mode waves propagating at small angles to the magnetic field do not significantly affect the formation of the slow shock.

Wolfson, Richard↗

NASA NTRS1987

A general form for the dissipation length scale in turbulent shear flows

It has been found that, for a wide range of turbulent wall-bounded shear flows with mean velocity profile U(y), the scale length L-epsilon determining the dissipation is approximately described in terms of distance from the wall (y), the mean shear (dU/dy), and the variance of the normal component of turbulence (bar u-squared), by the formula: L-epsilon to the -1 power is approximately equal to (A sub B / y) + A sub S (dU/dy / square root of bar u-squared) where L-epsilon = epsilon/(bar u-squared) to the 3/2 power. To match with shear-free boundary layers, A sub B is approximately 0.27, and to match with the log layer, A sub S is approximately 0.46. The shear flows tested here were: boundary layers over a flat plate, sink flow, oscillatory flow, and channel flow. The use of the square root of bar u-squared as a velocity scale minimizes the effects of Reynolds number. However, the formula fails within a distance of order L-epsilon for the regions where dU/dy = 0.

Hunt, J. C. R.↗

NASA NTRS1987

Redesign of a supercritical wing in the presence of an engine nacelle

If an obstacle, such as an engine nacelle, is placed in the flow near a virtually shockless wing, shocks of substantial magnitude may appear on the wing. A source distribution method is presently employed in the modeling of an engine nacelle in compressible flow, through incorporation into a free-boundary supercritical wing design code. Code calculation results are presented which show the transonic shock to appear, on average, 10 percent forward of its position on the clean wing. Attention is also given to an associated method for the calculation of wave drag.

Ross, David S.↗

NASA NTRS1989

Penetrative convective flows induced by internal heating and mantle compressibility

Penetrative convective flows induced in a spherical shell by combined effects of internal heating and mantle compressibility are investigated using mathematical and numerical formulations for compressible spherical shell convection. Isothermal stress-free boundary conditions applied at the top and the bottom of the shell are solved using a time-dependent finite difference code in a temperature, vorticity, stream function formulation for Rayleigh numbers ranging from the critical Rc up to 2000 Rc. Results indicate that compressibility, together with internal heating, could be a mechanism capable of generating spontaneously layered convection and local melting in the mantle and that non-Boussinesq effects must be considered in interpretations of geophysical phenomena.

Machetel, Philippe↗

NASA NTRS1989

Measurement of damping of graphite epoxy composite materials and structural joints

The damping capacity of graphite epoxy materials and structural joints was evaluated. The damping ratio of different composite specimens and bonded joints were systematically evaluated under normal atmospheric conditions and in a vacuum environment. Free and forced vibration test methods were employed for measuring the damping ratios. The effect of edge support conditions on the damping value of a composite tube specimen was studied by using a series of experiments performed on the specimen with different edge supports. It was found that simulating a free-free boundary conditions by having no constraints at the ends gives the lowest value of the material damping of the composite. The accuracy of the estimation of the damping ratio value was improved by using a curve-fitting technique on the response data obtained through measurement. The effect of outgassing (moisture desorption) on the damping capacity was determined by measuring the damping ratio of the tube specimen in a vacuum environment before and after outgassing had occurred. The effects of high and low temperatures on the damping was also investigated by using a series of experiments on tube and beam specimens. An analytical model to study the vibrations of a bonded lap joint system was formulated. Numerical results were generated for different overlap ratios of the system. These were compared with experimental results. In order to determine the influence of bonded joints on the material damping capacity, experiments were conducted on bonded lap-jointed and double-butt-jointed specimens. These experimental results were compared with simple beam specimens with no joints.

Crocker, Malcolm J.↗

NASA NTRS1989

Load-shortening behavior of an initially curved eccentrically loaded column

To explore the feasibility of using buckled columns to provide a soft support system for simulating a free-free boundary condition in dynamic testing, the nonlinear load-shortening behavior of initially imperfect, eccentrically loaded slender columns is analyzed. Load-shortening curves are obtained for various combinations of load eccentricity and uniform initial curvature and are compared, for reference purposes, with the limiting case of the classical elastica. Results for numerous combinations of initial curvature and load eccentricity show that, over a wide range of shortening, an axially loaded slender column exhibits load-deflection compliance which is of the same order as that of a straight but otherwise identical cantilever beam under lateral tip loading.

Fichter, W. B.↗

NASA NTRS1991

A system-approach to the elastohydrodynamic lubrication point-contact problem

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed.

Lim, Sang Gyu↗

NASA NTRS1992

Penetrative convection - Parametrized expression for the growth rates

The equations determining the linear growth rate omega characterizing a convectively unstable fluid with Rayleigh number R(u) bounded below by an impenetrable free boundary and above by a convectively stable fluid with Rayleigh number R(s), are solved numerically. Using the analytical Rayleigh-Benard growth rate omega (RB) as a convenient functional form, it is possible to fit the numerical values for omega if the vertical wave number k(z) = n(pi) and the Rayleigh number R(RB) are taken to be functions of R(s), R(u), and the horizontal wave number k-perpendicular rather than n = integer as in the Rayleigh-Benard case. In addition, contrary to Rayleigh-Benard convection, in which the critical Rayleigh number is fixed, it is found that R super (cr) sub u is variable in the presence of a stable layer, (i.e., it depends on R(s)).

Savolainen, V.↗

NASA NTRS1992

A system-approach to the elastohydrodynamic lubrication point-contact problem

Lim, Sang G.↗

NASA NTRS1992

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Saunders, B. V.↗