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NASA NTRS1988

Deformational models of rifting and folding on Venus

Features of presumed tectonic origin on Venus are reviewed, and lithospheric strength envelopes are derived based on laboratory measurements of the deformational properties of crustal and subcrustal rocks, extrapolated to conditions appropriate to Venus. Models for rifting and folding are developed that use this lithospheric structure and take into account both brittle and ductile yielding as well as finite elastic strength. For both rifting and folding, structures with characteristic widths and spacings are predicted whose size depends on the thickness of the lithosphere, density contrast, and elastic properties of the layer. Finally, the model predictions are compared with the widths and spacings of observed tectonic features, and it is concluded that they are consistent with a relatively strong mantle layer separated from a thin brittle surface layer by a ductile lower crust. These results allow constraints to be placed on the crustal thickness and thermal gradient on Venus.

Banerdt, W. Bruce↗

NASA NTRS1995

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

Johnson, Arthur R.↗

NASA NTRS1994

Transverse shear stresses and their sensitivity coefficients in multilayered composite panels

A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

NASA NTRS1970

The dynamics of oceanic fronts. Part 1: The Gulf Stream

The establishment and maintenance of the mean hydrographic properties of large scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density. The full time dependent diffusion and Navier-Stokes equations for a constant Coriolis parameter are used in this study. Scaling analysis reveals three independent length scales of the problem, namely a radius of deformation or inertial length scale, Lo, a buoyance length scale, ho, and a diffusive length scale, hv. Two basic dimensionless parameters are then formed from these length scales, the thermal (or more precisely, the densimetric) Rossby number, Ro = Lo/ho and the Ekman number, E = hv/ho. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on E alone for problems of oceanic interest. Under this scaling, the solutions are similar for all Ro. It is also shown that 1/Ro is a measure of the frontal slope. The governing equations are solved numerically and the scaling analysis is confirmed. The solution indicates that an equilibrium state is established. The front can then be rendered stationary by a barotropic current from a larger scale along-front pressure gradient. In that quasisteady state, and for small values of E, the main thermocline and the inclined isopycnics forming the front have evolved, together with the along-front jet. Conservation of potential vorticity is also obtained in the light water pool. The surface jet exhibits anticyclonic shear in the light water pool and cyclonic shear across the front.

Kao, T. W.↗

NASA NTRS1999

Waves in Radial Gravity Using Magnetic Fluid

Terrestrial laboratory experiments studying various fluid dynamical processes are constrained, by being in an Earth laboratory, to have a gravitational body force which is uniform and unidirectional. Therefore fluid free-surfaces are horizontal and flat. Such free surfaces must have a vertical solid boundary to keep the fluid from spreading horizontally along a gravitational potential surface. In atmospheric, oceanic, or stellar fluid flows that have a horizontal scale of about one-tenth the body radius or larger, sphericity is important in the dynamics. Further, fluids in spherical geometry can cover an entire domain without any sidewall effects, i.e. have truly periodic boundary conditions. We describe spherical body-force laboratory experiments using ferrofluid. Ferrofluids are dilute suspensions of magnetic dipoles, for example magnetite particles of order 10 nm diameter, suspended in a carrier fluid. Ferrofluids are subject to an additional body force in the presence of an applied magnetic field gradient. We use this body force to conduct laboratory experiments in spherical geometry. The present study is a laboratory technique improvement. The apparatus is cylindrically axisymmetric. A cylindrical ceramic magnet is embedded in a smooth, solid, spherical PVC ball. The geopotential field and its gradient, the body force, were made nearly spherical by careful choice of magnet height-to-diameter ratio and magnet size relative to the PVC ball size. Terrestrial gravity is eliminated from the dynamics by immersing the "planet" and its ferrofluid "ocean" in an immiscible silicone oil/freon mixture of the same density. Thus the earth gravity is removed from the dynamics of the ferrofluid/oil interface and the only dynamically active force there is the radial magnetic gravity. The entire apparatus can rotate, and waves are forced on the ferrofluid surface by exterior magnets. The biggest improvement in technique is in the wave visualization. Fluorescing dye is added to the oil/freon mixture and an argon ion laser generates a horizontal light that can be scanned vertically. Viewed from above, the experiment is a black circle with wave deformations surrounded by a light background. A contour of the image intensity at any light sheet position gives the surface of the ferrofluid "ocean" at that "latitude". Radial displacements of the waves as a function of longitude are obtained by subtracting the contour line positions from a no-motion contour at that laser sheet latitude. The experiments are run by traversing the forcing magnet with the laser sheet height fixed and images are frame grabbed to obtain a time-series at one latitude. The experiment is then re-run with another laser-sheet height to generate a full picture of the three-dimensional wave structure in the upper hemisphere of the ball as a function of time. We concentrate here on results of laboratory studies of waves that are important in Earth's atmosphere and especially the ocean. To get oceanic scaling in the laboratory, the experiment must rotate rapidly (4-second rotation period) so that the wave speed is slow compared to the planetary rotation speed as in the ocean. In the Pacific Ocean, eastward propagating Kelvin waves eventually run into the South American coast. Theory predicts that some of the wave energy should scatter into coastal-trapped Kelvin waves that propagate north and south along the coast. Some of this coastal wave energy might then scatter into mid-latitude Rossby waves that propagate back westward. Satellite observations of the Pacific Ocean sea-surface temperature and height seem to show signatures of westward propagating mid-latitude Rossby waves, 5 to 10 years after the 1982-83 El Nino. The observational data is difficult to interpret unambiguously owing to the large range of motions that fill the ocean at shorter timescales. This series of reflections giving eastward, north- ward, and then westward traveling waves is observed cleanly in the laboratory experiments, confirming the theoretical expectations.

Ohlsen, D. R.↗

NASA NTRS1994

Recent deformation rates on Venus

Constraints on the recent geological evolution of Venus may be provided by quantitative estimates of the rates of the principal resurfacing processes, volcanism and tectonism. This paper focuses on the latter, using impact craters as strain indicators. The total postimpact tectonic strain lies in the range 0.5-6.5%, which defines a recent mean strain rate of 10(exp -18)-10(exp -17)/s when divided by the mean surface age. Interpretation of the cratering record as one of pure production requires a decline in resurfacing rates at about 500 Ma (catastrophic resurfacing model). If distributed tectonic resurfacing contributed strongly before that time, as suggested by the widespread occurrence of tessera as inliers, the mean global strain rate must have been at least approximately 10(exp -15)/s, which is also typical of terrestrial active margins. Numerical calculations of the response of the lithosphere to inferred mantle convective forces were performed to test the hypothesis that a decrease in surface strain rate by at least two orders of magnitude could be caused by a steady decline in heat flow over the last billion years. Parameterized convection models predict that the mean global thermal gradient decreases by only about 5 K/km over this time; even with the exponential dependence of viscosity upon temperature, the surface strain rate drops by little more than one order of magnitude. Strongly unsteady cooling and very low thermal gradients today are necessary to satisfy the catastrophic model. An alternative, uniformitarian resurfacing hypothesis holds that Venus is resurfaced in quasi-random 'patches' several hundred kilometers in size that occur in response to changing mantle convection patterns.

Grimm, Robert E.↗

NASA NTRS1992

Continuation of tailored composite structures of ordered staple thermoplastic material

The search for the cost effective composite structure has motivated the investigation of several approaches to develop composite structure from innovative material forms. Among the promising approaches is the conversion of a planar sheet to components of complex curvature through sheet forming or stretch forming. In both cases, the potential for material stretch in the fiber direction appears to offer a clear advantage in formability over continuous fiber systems. A framework was established which allows the simulation of the anisotropic mechanisms of deformation of long discontinuous fiber laminates wherein the matrix phase is a viscous fluid. Predictions for the effective viscosities of a hyper-anisotropic medium consisting of collimated, discontinuous fibers suspended in viscous matrix were extended to capture the characteristics of typical polymers including non-Newtonian behavior and temperature dependence. In addition, the influence of fiber misorientation was also modeled by compliance averaging to determine ensemble properties for a given orientation distribution. A design tool is presented for predicting the effect of material heterogeneity on the performance of curved composite beams such as those used in aircraft fuselage structures. Material heterogeneity can be induced during manufacturing processes such as sheet forming and stretch forming of thermoplastic composites. This heterogeneity can be introduced in the form of fiber realignment and spreading during the manufacturing process causing radial and tangential gradients in material properties. Two analysis procedures are used to solve the beam problems. The first method uses separate two-dimensional elasticity solutions for the stresses in the flange and web sections of the beam. The separate solutions are coupled by requiring that forces and displacements match section boundaries. The second method uses an approximate Rayleigh-Ritz technique to find the solutions for more complex beams. Analyses are performed for curved beams of various cross-sections loaded in pure bending and with a uniform distributed load. Preliminary results show that the geometry of the beam dictates the effect of heterogeneity on performance. The role of heterogeneity is larger in beams with a small average radius-to-depth ration, R/t, where R is the average radius of the beam and t is the difference between the inside and outside radii. Results of the anlysis are in the form of stresses and displacements and are compared to both mechanics of materials and numerical solutions obtained using finite element analysis.

Santare, Michael H.↗

NASA NTRSDate not supplied

Using Digital Image Correlation for Material Testing at Cryogenic Temperatures

Recent efforts were made to parametrize an aluminum alloy at cryogenic temperatures to calibrate finite element models simulating material deformation. Digital image correlation (DIC) was used to measure material properties using front/back strains of specimens during tensile tests. Data acquired from DIC was compared to physical extensometer measurements. Two camera pairs (front and back) were mounted via aluminum extrusion to the exterior of an environmental chamber of a hydraulic test stand. Images were taken through single-pane optical glass windows of the environment chamber. Positive pressure bags encased the cameras, attaching to the perimeter of the glass to keep out moisture and prevent windows from frosting. Figure 1 shows the environmental setup and the camera setup during cryogenic testing. Some of the challenges during testing at cryogenic temperatures include the gaseous flow of liquid nitrogen in the optical path of the mounted cameras, frost buildup on the windows as seen in Figure 1b, and frost on the test coupon. The temperature gradient present during the introduction of liquid nitrogen into the chamber can increase the projection error of images captured of the specimen. Figure 2 shows the estimated projection error from DIC as a function of temperature during the cool down process. This presentation addresses some of the concerns and observations when using DIC for testing at cryogenic temperatures using methods of isolated camera system and techniques for maintaining the glass panel clear from frost.

Joseph Cochran↗

NASA NTRS2002

Thermostructural Analysis of Carbon Cloth Phenolic Material Tested at the Laser Hardened Material Evaluation Laboratory

RSRM nozzle liner components have been analyzed and tested to explore the occurrence of anomalous material performance known as pocketing erosion. Primary physical factors that contribute to pocketing seem to include the geometric permeability, which governs pore pressure magnitudes and hence load, and carbon fiber high temperature tensile strength, which defines a material limiting capability. The study reports on the results of a coupled thermostructural finite element analysis of Carbon Cloth Phenolic (CCP) material tested at the Laser Hardened Material Evaluation Laboratory (the LHMEL facility). Modeled test configurations will be limited to the special case of where temperature gradients are oriented perpendicular to the composite material ply angle. Analyses were conducted using a transient, one-dimensional flow/thermal finite element code that models pore pressure and temperature distributions and in an explicitly coupled formulation, passes this information to a 2-dimensional finite element structural model for determination of the stress/deformation behavior of the orthotropic fiber/matrix CCP. Pore pressures are generated by thermal decomposition of the phenolic resin which evolve as a multi-component gas phase which is partially trapped in the porous microstructure of the composite. The nature of resultant pressures are described by using the Darcy relationships which have been modified to permit a multi-specie mass and momentum balance including water vapor condensation. Solution to the conjugate flow/thermal equations were performed using the SINDA code. Of particular importance to this problem was the implementation of a char and deformation state dependent (geometric) permeability as describing a first order interaction between the flow/thermal and structural models. Material property models are used to characterize the solid phase mechanical stiffness and failure. Structural calculations were performed using the ABAQUS code. Iterations were made between the two codes involving the dependent variables temperature, pressure and across-ply strain level. Model results comparisons are made for three different surface heat rates and dependent variable sensitivities discussed for the various cases.

Clayton, J. Louie↗

NASA NTRS1993

The importance of properties in modeling

Casting and welding of superalloys, stainless steel and titanium alloys are processes which can be improved through modeling of heat flow, fluid flow, residual stress development, and microstructural evolution. These simulations require inputs of thermophysical data, some of which involves the partially or totally liquid state. In particular, these processes involve melting, flow in the liquid, and solidification. Modeling of such processes can lead to an improved understanding of defects such as shrinkage, inclusions, cracks, incomplete filling (or penetration), macrosegregation, improper grain structure, and deviations from dimensional specifications. Effective modeling can shorten process development time and improve quality. An approach to these problems is to develop efficient models; validate through correlations with thermal, distortion, and microstructural data; run parametric studies; extract knowledge based rules; and apply to adaptive closed loop control systems. With the appropriate pre- and post-processing, such analyses can be made 'user friendly'. This would include graphical user interfaces as well as realistic images and color maps. In such form, these models can be used for sensitivity analyses, which are useful in defining appropriate sensors and in the development of control strategies. Such modeling can be done at several levels, e.g., the MARO level, modeling large scale phenomena such as heat and fluid flow or material deformation; the MICRO level, modeling the development of dendrites, grains or precipitates; or at the NANO level, modeling point defects, dislocations, stacking faults, etc. There are many computational issues associated with these simulations, e.g. computational efficiency and accuracy. In addition, there are many materials issues, not the least of which is the availability of accurate high temperature thermophysical data for complex alloys. This would include latent heat of fusion, temperature dependent heat capacity and thermal conductivity (for liquid and solid), viscosity, surface tension, thermal expansion, mechanical properties, etc. Preliminary data is frequently gathered from the literature; however, this is often not available for modern alloys. If additional data are required, measurements can be used; however, these are costly, time consuming and can be erroneous due to a lack of testing standards or impure materials. Microstructural predictors can be extracted from thermal information, e.g. cooling rate and thermal gradient; the prediction of microstructure is dependent on solidus and liquidus temperature, mushy zone permeability, the solidification curve, volume changes, phase transformations, alloying effects (such as surface tension or viscosity), mold/metal reactions, metal/environment reactions, etc. Defect maps may be needed to predict the onset of shrinkage, hot cracking or 'freckling'. Constants may be needed for stress relaxation, dendrite coarsening, vaporization, etc. Visualization was used as a tool to better comprehend complex data sets associated with the analysis of directional solidification (including crystal growth) and welding. Examples include not only isotherms, but also cooling rate, growth rate and thermal gradient. The latter two are not single valued scalars, but rather time and space dependent vector fields. Efficient models were developed for both casting and welding to predict heat flow and the relationship to dendrite and grain growth. These codes include many of the non-linear effects, e.g. radiation, which dominate these processes. The home-built FDM code(s) were designed to be useful not only to the scientist, but also to the process engineer. Special output can be requested to compare directly to experimental data. Visualization procedures were developed to visualize critical results, e.g. fusion zone width at the surface opposite that where the arc is applied ('penetration'). Both elaborate and simplified distortion analyses were carried out. It is clear that extensive mechanical property data are critical in order to accurately predict residual stress patterns. A scheme is currently being developed to integrate these modeling tools into a set of control algorithms; however, the success of this approach is critically dependent on the availability of accurate high temperature thermophysical data.

Giamei, A. F.↗

NASA NTRS2007

Experimental Evaluation of an Isolated Synthetic Jet IN Crossflow

The second case for this workshop builds upon the isolated synthetic jet of Case 1 by adding a crossflow, with no streamwise pressure gradient, for the developing jet to interact with. Formally, Case 2 examines the interaction of a single, isolated, synthetic jet and a fully turbulent zero-pressure gradient boundary layer. The resulting flow has many of the characteristics that need to be modeled with fidelity if the results of the calculations are to serve as the basis for research and design with active flow control devices. These include the turbulence in the boundary layer, the time-evolution of the large vortical structure emanating from the jet orifice and its subsequent interaction with and distortion by the boundary layer turbulence, and the effect of the suction cycle on the boundary layer flow. In a synthetic jet, the flow through the orifice and out into the outer flowfield alternates between an exhaust and a suction cycle, driven by the contraction and expansion of a cavity internal to the actuator. In the present experiment, the volume changes in the internal cavity are accomplished by replacing one of the rigid walls of the cavity, the wall opposite the orifice exit, with a deformable wall. This flexible wall is driven by a bottom-mounted moveable piston. The piston is driven electro-mechanically. The synthetic jet issues into the external flow through a circular orifice. In the present experiment, this orifice has a diameter of 0.250 inches (6.35 mm). The flow is conceptually similar to that documented in Schaeffler [1]. To document the flow, several measurement techniques were utilized. The upstream boundary conditions (in-flow conditions), and several key phase-averaged velocity profiles were measured with a 3-component laser-Doppler velocimetry system. Phase-averaged velocity field measurements were made with both stereo digital particle image velocimetry and 2-D digital particle image velocimetry as the primary measurement system. Surface pressure measurements were made utilizing an electronically scanned pressure system.

Schaeffler, Norman W.↗

NASA NTRS2000

Reduction of Effective Acceleration to Microgravity Levels

Acceleration due to earth's gravity causes buoyancy driven convection and sedimentation in solutions. In addition. pressure gradients occur as a function of the height within a liquid column. Hence gravity effects both equilbria conditions and phase transitions as a result of hydrostatic pressure gradients. The affect of gravity on the rate of heat and man transfer in solutal processes can be particularly important in polymer processing due to the high sensitivity of polymeric materials to processing conditions. The term microgravity has been coined to describe an environment in which the affects of gravitational acceleration am greatly reduced. It may seem odd to talk in term of reducing the effects of gravitational acceleration since gravitational attraction is a basic property of matter. However, die presence of gravity on in situ processing or measurements can be negated by achieving conditions in which the laboratory, or more specifically the container of the experimental materials, a subjected to the same acceleration as the materials themselves. With regard to the laboratory reference frame, there is virtually no force on the experimental solutions. This is difficult to achieve but can be done. A short review of Newtonian physics provides an explanation on both how processes we affected by gravity and how microgravity conditions are achieved. The fact that fluids deform when subject to a force bid solids do not indicates that solids have a structure able to exert an opposing force that negates an externally applied force. Liquids deform when a force is applied, indicating that a liquid structure cannot completely negate an applied force. Just how easily a liquid resists deformation is related to its viscosity. Spaceflight provides an environment in which the laboratory reference frame i.e. the spacecraft and all the equipment therein an experiencing virtually identical forces. There is no solid foundation underneath such a laboratory, so the laboratory accelerates according to the force of gravity as do the experimental fluids within the lab. Hence, the magnitude of the form excited by the laboratory on the experimental solutions within are greatly reduced. When compared with a laboratory on the ground and averaged over time, the fluids in a spaceflight laboratory experience approximately a 10 (sup -6)decrease in acceleration relative to their laboratory reference frame hence the term microgravity.

Downey, James P.↗

NASA NTRS1995

Sensitivity Analysis of Wing Aeroelastic Responses

Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency, and torsional frequency is calculated analytically. A strip theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model and solved as an eigenvalue problem to determine the critical speed of the wing. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming.

Issac, Jason Cherian↗

NASA NTRS1995

A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow

A model of mantle convection which generates plate tectonics requires strain rate- or stress-dependent rheology in order to produce strong platelike flows with weak margins as well as strike-slip deformation and plate spin (i.e., toroidal motion). Here, we employ a simple model of source-sink driven surface flow to determine the form of such a rheology that is appropriate for Earth's present-day plate motions. In this model, lithospheric motion is treated as shallow layer flow driven by sources and sinks which correspond to spreading centers and subduction zones, respectively. Two plate motion models are used to derive the source sink field. As originally implied in the simpler Cartesian version of this model, the classical power law rheologies do not generate platelike flows as well as the hypothetical Whitehead-Gans stick-slip rheology (which incorporates a simple self-lubrication mechanism). None of the fluid rheologies examined, however, produce more than approximately 60% of the original maximum shear. For either plate model, the viscosity fields produced by the power law rheologies are diffuse, and the viscosity lows over strike-slip shear zones or pseudo-margins are not as small as over the prescribed convergent-divergent margins. In contrast, the stick-slip rheology generates very platelike viscosity fields, with sharp gradients at the plate boundaries, and margins with almost uniformly low viscosity. Power law rheologies with high viscosity contrasts, however, lead to almost equally favorable comparisons, though these also yield the least platelike viscosity fields. This implies that the magnitude of toroidal flow and platelike strength distributions are not necessarily related and thus may present independent constraints on the determination of a self-consistent plate-mantle rheology.

Bercovici, David↗

NASA NTRS1999

Paramagnetic Liquid Bridge in a Gravity-Compensating Magnetic Field

Magnetic levitation was used to stabilize cylindrical columns of a paramagnetic liquid in air between two solid supports. The maximum achievable length to diameter ratio R(sub max) was approx. (3.10 +/- 0.07), very close to the Rayleigh-Plateau limit of pi. For smaller R, the stability of the column was measured as a function of the Bond number, which could be continuously varied by adjusting the strength of the magnetic field. Liquid bridges supported by two solid surfaces have been attracting scientific attention since the time of Rayleigh and Plateau. For a cylindrical bridge of length L and diameter d, it was shown theoretically that in zero gravity the maximum slenderness ratio R (identically = L/d) is pi. The stability and ultimate collapse of such bridges is of interest because of their importance in a number of industrial processes and their potential for low gravity applications. In the presence of gravity, however, the cylindrical shape of an axisymmetric bridge tends to deform, limiting its stability and decreasing the maximum achievable value of R. Theoretical studies have discussed the stability and possible shapes of axisymmetric bridges. Experiments typically are performed in either a Plateau tank, in which the bridge is surrounded by a density-matched immiscible fluid, or in a space-borne microgravity environment. It has been shown, for example, that the stability limit R can be pushed beyond pi by using flow stabilization, by acoustic radiation pressure, or by forming columns in the presence of an axial electric field. In this work, magnetic levitation was used to simulate a low gravity environment and create quasi-cylindrical liquid columns in air. Use of a magnetic field permits us to continuously vary the Bond number B identically equal to (g)(rho)d(exp 2)/4(sigma), where g is the gravitational acceleration, rho is the density of the liquid, and sigma is the surface tension of the liquid in air. The dimensionless Bond number represents the relative importance of external forces acting on the liquid column to those due to surface tension. Our central result is that in a large magnetic field gradient we could create and stabilize columns of mixtures of water and paramagnetic manganese chloride tetrahydrate (MnCl2.4H2O), achieving a length to diameter ratio very close to pi.

Mahajan, Milind P.↗

NASA NTRS2004

Thermocapillary migration of a drop: an exact solution with Newtonian interfacial rheology and stretching/shrinkage of interfacial area elements for small Marangoni numbers

In this paper we analyze the effects of the following phenomena associated with the thermocapillary migration of a drop. The first is the influence of Newtonian surface rheology of the interface and the second is that of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the drop is in motion. The former occurs because of dissipative processes in the interfacial region, such as when surfactant molecules are adsorbed at the interface in sufficient concentration. The interface is typically modeled in this instance by ascribing to it a surface viscosity. This is a different effect from that of interfacial tension gradients arising from surfactant concentration gradients. The stretching and shrinkage of interfacial area elements leads to changes in the internal energy of these elements that affects the transport of energy in the fluids adjoining the interface. When an element on the interface is stretched, its internal energy increases because of the increase in its area. This energy is supplied by the neighboring fluids that are cooled as a consequence. Conversely, when an element on the interface shrinks, the adjoining fluids are warmed. In the case of a moving drop, elements of interfacial area are stretched in the forward half of the drop, and are shrunk in the rear half. Consequently, the temperature variation on the surface of the drop and its migration speed are modified. The analysis of the motion of a drop including these effects was first performed by LeVan in 1981, in the limit when convective transport of momentum and energy are negligible. We extend the analysis of LeVan to include the convective transport of momentum by demonstrating that an exact solution of the momentum equation is obtained for an arbitrary value of the Reynolds number. This solution is then used to calculate the slightly deformed shape of the drop from a sphere.

Rheology/methods↗

NASA NTRS1999

Constructing the Coronal Magnetic Field by Correlating Parameterized Magnetic Field Lines with Observed Coronal Plasma Structures

A method is presented for constructing the coronal magnetic field from photospheric magnetograms and observed coronal loops. A set of magnetic field lines generated from magnetogram data is parameterized and then deformed by varying the parameterized values. The coronal flux tubes associated with this field are adjusted until the correlation between the field lines and the observed coronal loops is maximized. A mathematical formulation is described which ensures that (1) the normal component of the photospheric field remains unchanged, (2) the field is given in the entire corona over an active region, (3) the field remains divergence-free, and 4electric currents are introduced into the field. It is demonstrated that a parameterization of a potential field, comprising a radial stretching of the field, can provide a match for a simple bipolar active region, AR 7999, which crossed the central meridian on 1996 November 26. The result is a non-force-free magnetic field with the Lorentz force being of the order of 10(exp -5.5) g per s(exp 2) resulting from an electric current density of 0.79 micro A per m(exp 2). Calculations show that the plasma beta becomes larger than unity at a strong non-radial currents requires low height of about 0.25 solar radii supporting the non-force-free conclusion. The presence of such strong non-radial currents requires large transverse pressure gradients fo maintain a magnetostatic atmosphere, required by the relatively persistent nature of the coronal structures observed in AR 7999. This scheme is an important tool in generating a magnetic field solution consistent with the coronal flux tube observations and the observed photospheric magnetic field.

Allen, Gary G.↗

NASA NTRSDate not supplied

In-Situ Detection of Process-Induced Porosity During Cure of Out-of-Autoclave Composites

Composite materials offer unique benefits in aerospace applications, including high strength-to-weight ratio, and are becoming increasingly used by industry manufacturers. Current manufacturing and processing methods can lead to defects in the composites, which are identified after fabrication using inspection methods. This study utilized a high-temperature ultrasonic inspection system to detect process-induced porosity in an out-of-autoclave (OOA) composite panel during cure. In order to perform ultrasonic scans in-situ during cure, the system needed to be able to operate at oven temperatures up to 200 °C. There are no commercially available ultrasonic scanning systems that can operate continuously at these temperatures, so an enclosure was fabricated to insulate the ultrasonic system in the curing oven. The enclosure housed a MISTRAS® motorized X-Y raster scanner and contact transducer (Olympus® X2002). The Olympus® X2002 contact transducer is a continuous high-temperature delay line transducer with a center frequency of 2.25 MHz. In order to prevent the inside of the enclosure from reaching high temperatures, a sparge pipe inside the cooling enclosure was connected to a liquid nitrogen (LN2) tank outside of the oven via insulated hoses. The cooling system was automatically controlled by a temperature controller that was programmed to open a solenoid valve along the hose at 31 ℃ and close at 28 ℃ inside the cooling enclosure. When the solenoid valve was open, LN2 would flow from the LN2 tank and vaporize prior to reaching cooling enclosure. A U-shaped sparge pipe had holes drilled along its length to uniformly introduce cold nitrogen gas into the cooling enclosure. This prevented the motors from ever reaching the maximum desired operating temperature of 38 ℃. In the bottom of the enclosure, the tool plate was placed with the composite facing the outside of the enclosure, exposing it to the temperatures of the oven. The tool plate was 63.5 mm thick borosilicate glass, which was chosen for its low ultrasonic attenuation and moderate thermal conductivity. A thin layer of ultrasonic couplant was placed on the tool plate. The transducer sent and received ultrasonic waves through the tool plate into the composite. A MISTRAS® Remote UT System performed all wave generation, analog to digital conversion, and data acquisition and processing. The transducer was connected directly to the Remote UT System via a high-temperature BNC cable (CD International, RG-316). Polyimide insulated copper wire was used to connect the scanner to a 2-axis motor drive, which was connected to the Remote UT System. The motor drive and Remote UT System were located outside the industrial oven. A diagram of the ultrasonic system is shown in Figure 1. Figure 1: Diagram of ultrasonic in-situ defect detection system. In this study, a porosity gradient was introduced into the carbon fiber reinforced polymer (CFRP) composite through a misfit of the part and caul plate. A 24-ply quasi-isotropic ([0/90, ±45]12S) composite panel was laid up using Newport® AS4C-M/NB321 out-of-autoclave (OOA) plain weave (PW) prepreg (42% resin content, 195 g/m2). The first 16 plies were 203 mm × 203 mm. Ply drops were incorporated into the panel by decreasing the length of plies 17-24. The sizes of each ply are included in Table 1. All plies were centered along their length (x-axis) creating a trapezoidal type cross-section. Table 1: Ply sizes Plies Length (mm) Width (mm) 1-16 203 203 17-18 102 203 19-20 85 203 21-22 68 203 23-24 51 203 A 15-5 stainless steel caul plate (Size: 203 × 203 × 1.2 mm) was placed on the laminate. The composite and caul plate were vacuum bagged to the tool plate. Per the product datasheet, Newport 321 can be cured between 121 °C and 149 °C, depending on service temperature, with a hold for 90-120 minutes. Based on prior thermal testing of the cooling enclosure, the desired composite temperature cycle could be attained when the air temperature of the oven was ramped to 160 °C at a rate of 1.7 °C/min with a 3 hour hold. The extended hold was not necessary to cure the composite, but did allow for additional scans at the cure temperature during preliminary testing. The composite panel was under vacuum pressure for the entire cure cycle. Under vacuum, the caul plate deformed causing high and low pressure regions. The low-pressure regions formed high porosity in the composite part. The ultrasonic data collected showed that the inspection system was able to monitor the evolution of porosity within the composite throughout the cure cycle. Fifty scans of a 203 mm × 51 mm (8 in. × 2 in.) area of the composite were completed throughout the cure cycle. The scan speed was set to 43 mm/s in the x-direction and 36 mm/s in the y-direction, with a 1.0 mm/pixel resolution in both directions. Each scan took approximately five minutes to complete. Figure 2 shows C-scan amplitude data (top view) from one scan during the cure cycle. The color map indicates the maximum amplitude (%) measured with a time gate that contains reflections from the back surface (furthest from the transducer in contact with the caul plate) of the composite. Because porosity in the composite increases the ultrasonic attenuation in the composite part, a higher amplitude (red) indicates low porosity and a lower amplitude (blue) indicates high porosity. The regions where the caul plate was applying increased pressure (center and ends of the panel) resulted in reduced porosity, whereas the ply drop regions had reduced pressure and thus had higher porosity. Figure 2: Amplitude C-scan (top view) of OOA composite from one scan during the 160 °C temperature hold. Higher amplitude (red) indicates low porosity. Lower amplitude (blue) indicates high porosity. A B-scan is a two-dimensional image plotting the ultrasonic signals from a single y-position at every x-location of the composite panel. The travel time (μs) of the ultrasonic wave (representing the through-thickness location) is plotted along the y-axis, and the ultrasonic wave signal is represented as a contour map. Based on the B-scan data, the location of the defects with respect to the composite thickness was able to be determined. The ply drop regions had high porosity near the front (tool plate) surface of the composite (Figure 3). Figure 3: B-scan (cross-section view) of OOA composite from one scan during the 160 °C temperature hold. Using the data obtained from amplitude C-scans and B-scans throughout the cure cycle, the high and low porosity regions within the composite laminate were detected and localized with high spatial resolution. This paper will discuss the evolution of porosity content in the OOA composite during cure. OOA tests aided the transition of this system to an autoclave, which is the primary method of curing aerospace-grade thermoset composites.

Tyler B. Hudson↗