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Sunspot structure from two dimensional radiative transfer analysis of center limb intensity profiles made at several heliocentric angles
A three-dimensional finite element analysis was performed for a biaxially loaded composite laminate (with a centered hole) consisting of several fiber-reinforced composite layers each with a specified fiber orientation. The detailed stress distribution around the hole was determined. Also, the locations of initial damage zones due to different failure mechanisms were indicated.
This paper describes a practical approach using a general purpose lumped-parameter computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels including electro-viscous effects due to the existence of electrical double layer (EDL). In this study, an empirical formulation for calculating an effective viscosity of ionic solutions based on dimensional analysis is described to account for surface charge and bulk fluid conductivity, which give rise to electro-viscous effect in microfluidics network. Two dimensional slit micro flow data was used to determine the model coefficients. Geometry effect is then included through a Poiseuille number correlation in GFSSP. The bi-power model was used to calculate flow distribution of isotropically etched straight channel and T-junction microflows involving ionic solutions. Performance of the proposed model is assessed against experimental test data.
The boundary element method (BEM) is used to compute fillet stress concentration in spur gear teeth. The results are shown to compare favorably with analogous results obtained using the finite element method (FEM). A partially supported thin rim gear is studied. The loading is applied at the pitch point. A three-dimensional analysis is conducted using both the BEM and FEM (NASTRAN). The results are also compared with those of a two-dimensional finite element model. An advantage of the BEM over the FEM is that fewer elements are needed with the BEM. Indeed, in the current study the BEM used 92 elements and 270 nodes whereas the FEM used 320 elements and 2037 nodes. Moreover, since the BEM is especially useful in problems with high stress gradients it is potentially a very useful tool for fillet stress analyses.
Hypersonic flow over spherical dome protuberances was investigated to determine increased pressure and heating loads to the surface. The configuration was mathematically modeled in a time-dependent three-dimensional analysis of the conservation of mass, momentum (Navier-Stokes), and energy equations. A boundary mapping technique was used to obtain a rectangular parallelepiped computational domain, a MacCormack explicit time-split predictor-corrector finite difference algorithm was used to obtain solutions. Results show local pressures and heating rates for domes one-half, one, and two boundary layer thicknesses high were increased by factors on the order of 1.4, 2, and 6, respectively. Flow over the lower dome was everywhere attached while flow over the intermediate dome had small windward and leeside separations. The higher dome had an unsteady windward separation region and a large leeside separation region. Trailing vortices form on all domes with intensity increasing with dome height. Discussion of applying the results to a thermally bowed thermal protection system are presented.
Hypersonic flow over spherical dome protuberances was investigated to determine increased pressure and heating loads to the surface. The configuration was mathematically modeled in a time-dependant three-dimensional analysis of the conservation of mass, momentum (Navier-Stokes), and energy equations. A boundary mapping techique was used to obtain a rectangular parallelepiped computational domain, and a MacCormack explicit time-split predictor-corrector finite difference algorithm was used to obtain solutions. Results show local pressures and heating rates for domes one-half, one, and two boundary layer thicknesses high were increased by factors on the order of 1.4, 2, and 6, respectively. However, because lee-side pressure and thermal loads were reduced the two lower height domes did not experience any net increase in total loads. The total loads on the higher dome were increased by twenty-five percent. Flow over the lower dome was everywhere attached while flow over the intermediate dome had small windward and leeside separations. The higher dome had an unsteady windward separation region and a large leeside separation region. Trailing vortices form on all domes with intensity increasing with dome height. Discussions of applying the results to a thermally bowed thermal protection system are presented.
A three dimensional elastoplastic finite element micromechanical model was developed to study the state of stress around a broken fibers in a unidirectional composite. A boron/aluminum composite consisting of 50 percent by volume of fibers in a square array and subjected to an axial loading is taken as a specific example. This loading in the fiber direction is applied in small increments, by prescribing increments of boundary displacement, until the first failure occurs. The effect of reduced material properties of the aluminum matrix material at elevated temperature is also studied. The results are presented in the form of stress contours and stress-strain plots.
An approach to predicting the effects of free stream turbulence on turbine vane and blade heat transfer is described. Four models for predicting the effects of free stream turbulence were in incorporated into a Navier-Stokes CFD analysis. Predictions were compared with experimental data in order to identify an appropriate model for use across a wide range of flow conditions. The analyses were compared with data from five vane geometries and from four rotor geometries. Each of these nine geometries had data for different Reynolds numbers. Comparisons were made for twenty four cases. Steady state calculations were done because all experimental data were obtained in steady state tests. High turbulence levels often result in suction surface transition upstream of the throat, while at low to moderate Reynolds numbers the pressure surface remains laminar. A two-dimensional analysis was used because the flow is predominately two-dimensional in the regions where free stream turbulence significantly augments surface heat transfer. Because the evaluation of models for predicting turbulence effects can be affected by other factors, the paper discusses modeling for transition, relaminarization, and near wall damping. Quantitative comparisons are given between the predictions and data.
This report develops: (1) a refined approximate theory for the static and dynamic analyses of finite, laminated, composite, circular cylindrical shells with general boundary conditions; (2) an exact three-dimensional analysis of simply supported, laminated, composite, circular cylindrical shells, and (3) a thin-shell theory for laminated, composite, circular cylindrical shells. In the refined approximate theory the displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and transverse normal stress are included. A variational approach is followed to obtain the governing differential equations and boundary conditions. A general solution of the governing differential equations is also presented. The results obtained by using the refined approximate theory and the thin-shell theory are compared with the exact results for the case of free vibrations of simply supported, laminated, composite, circular cylindrical shells. The refined approximate theory is very accurate, even for thick shells with short nodal distances, whereas thin-shell theory is reasonably accurate only for thin shells at moderate nodal distances and wave number less than 2.
A method was developed for calculating the static performance of thrust augmenting ejectors by matching a viscous solution for the flow through the ejector to an inviscid solution for the flow outside the ejector. A two dimensional analysis utilizing a turbulence kinetic energy model is used to calculate the rate of entrainment by the jets. Vortex panel methods are then used with the requirement that the ejector shroud must be a streamline of the flow induced by the jets to determine the strength of circulation generated around the shroud. In effect, the ejector shroud is considered to be flying in the velocity field of the jets. The solution is converged by iterating between the rate of entrainment and the strength of the circulation. This approach offers the advantage of including external influences on the flow through the ejector. Comparisons with data are presented for an ejector having a single central nozzle and Coanda jet on the walls. The accuracy of the matched solution is found to be especially sensitive to the jet flap effect of the flow just downstream of the ejector exit.
We construct entangled states of gluons that scatter exactly as if they were gravitons. Operationally, these objects implement the double copy at the level of the wave function. Our analysis begins with a general ansatz for a wave function characterizing gluons in two copies of SU(N ) gauge theory. Given relatively minimal assumptions following from permutation invariance and dimensional analysis, the three- and four-particle wave functions generate scattering amplitudes that automatically coincide exactly with gravity, modulo normalization. For five-particle scattering the match is not automatic but imposing certain known selection rules on the amplitude is sufficient to uniquely reproduce gravity. The resulting amplitudes exhibit a color-dressed and permutation-invariant form of the usual double copy relations. We compute the entanglement entropy between the two gauge theory copies and learn that these states are maximally-entangled at large N. Moreover, this approach extends immediately to effective field theories, where Born-Infeld photons and Galileons can be similarly recast as entangled gluons and pions.
The all rocket mode of operation is a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. However, outside of performing experiments or a full three dimensional analysis, there are no first order parametric models to estimate performance. As a result, an axisymmetric RBCC engine was used to analytically determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and statistical regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, percent of injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inject diameter ratio. A perfect gas computational fluid dynamics analysis was performed to obtain values of vacuum specific impulse. Statistical regression analysis was performed based on both full flow and gas generator engine cycles. Results were also found to be dependent upon the entire cycle assumptions. The statistical regression analysis determined that there were five significant linear effects, six interactions, and one second-order effect. Two parametric models were created to provide performance assessments of an RBCC engine in the all rocket mode of operation.
Abnormal grain growth has been previously found to increase with the inclusion of large pores (∼60 µm in diameter) in 80 ppm calcium doped alumina. However, the two-dimensional analysis could not accurately describe the proximity of the abnormal grains and pores to establish a correlation. This study uses laboratory-based diffraction contrast tomography and x-ray computed tomography to spatially map the pores and abnormal grains in 3D. A preference towards the formation of abnormal grains near large pores is found when compared to all potential sites. This finding supports that the pores may be a nucleation site for complexion transitions that promote abnormal grain growth. The growth of the abnormal grains in a subsequent heat treatment at 1600°C for 16 hrs was also studied. The elongation along the principal axes is similar for both small and large grains, again supporting that abnormal grain growth was facilitated by a complexion transition.
Objectives of study were: investigation of temperature changes caused by welding arc with analysis of temperature distribution; development of system of mathematical statements describing thermal stresses and plastic strains during welding; and development of system of mathematical solutions and computer programs for one-dimensional analysis.
A mathematical model is presented for the description of axisymmetric laminar-jet diffusion flames. The analysis includes the effects of inertia, viscosity, diffusion, gravity and combustion. These mechanisms are coupled in a boundary layer type formulation and solutions are obtained by an explicit finite difference technique. A dimensional analysis shows that the maximum flame width radius, velocity and thermodynamic state characterize the flame structure. Comparisons with experimental data showed excellent agreement for normal gravity flames and fair agreement for steady state low Reynolds number zero gravity flames. Kinetics effects and radiation are shown to be the primary mechanisms responsible for this discrepancy. Additional factors are discussed including elipticity and transient effects.
This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.
The nonlinear saturation spectrum of parametric instabilities is shown to be restricted to discrete values of the propagation vector if spontaneous emission is neglected and a one-dimensional analysis is used. The purely growing instability is not excited for equal ion and electron temperatures if the power is less than 3.5 times the threshold power. The inadequacy of the present one-dimensional treatment is pointed out, and it is shown that waves with propagation vectors that are not parallel to the pump field must be present even if spontaneous emission is neglected.