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Model calculations and graphical presentation of acoustic velocities in two-phase mixtures of some cryogenic fluids
Theoretical and experimental aspects are summarized for single crystal, silicon photovoltaic devices made by forming a grating pattern of p/n junctions on the light receiving surface of the base crystal. Based on the general semiconductor equations, a mathematical description is presented for the photovoltaic properties of such grating-like structures in a two dimensional form. The resulting second order elliptical equation is solved by computer modeling to give solutions for various, reasonable, initial values of bulk resistivity, excess carrier concentration, and surface recombination velocity. The validity of the computer model is established by comparison with p/n devices produced by alloying an aluminum grating pattern into the surface of n-type silicon wafers. Current voltage characteristics and spectral response curves are presented for cells of this type constructed on wafers of different resistivities and orientations.
Experimental measurements of the mean and turbulent velocity field in a water flow, turn-around-duct is documented. The small radius of curvature duct experiments were made over a range of Reynolds numbers (based on a duct height of 10 cm) from 70,000 to 500,000. For this particular channel, the flow is dominated by the inertia forces. Use of the local bulk velocity to non-dimensionalize the local velocity was found to limit Reynolds number effects to the regions very close to the wall. Only secondary effects on the flow field were observed when the inlet or exit boundary conditions were altered. The flow over the central two-thirds of the channel was two-dimensional. Mean tangetial and radial velocities, streamlines, pressure distributions, surface shear stress; tangential, radial and lateral turbulent velocities and the Reynolds turbulent shear values are tabulated in other reports. It is evident from the experimental study that a complex numerical modeling technique must be developed to predict the flow in the turn-around-duct. The model must be able to predict relaminarization along the inner-convex-wall. It must also allow for the major increase in turbulence produced by the outer-concave-wall.
Herein this paper forms, optimizes, and evaluates three numerical approaches for characterizing mean velocities in far wake region behind ocean current turbines. These approaches are derived from wake models originally developed for wind turbines and are referred here as the Larsen/Larsen, Larsen/Ainslie, and Jensen/Ainslie approaches based on the researchers originally credited with developing the expressions for dependence of the mean wake velocity on centerline and/or radial locations. The numerical coefficients utilized by these approaches are optimized to best match Computational fluid dynamics (CFD) generated wake velocity data. After optimizing the coefficients, this study finds that the Larsen/Ainslie and Jensen/Ainslie approaches best match the CFD generated flow data, with Larsen/Ainslie being the best match for an ambient turbulence intensity (TI) of 3% and Jensen/Ainslie being the best match for TIs of 6 and 9%.
The essential ingredients and the effectiveness of several levels of turbulent-flow partial differential equation models are considered. Zero-equation models use only the partial differential equation (pde) for the mean velocity field and do not employ turbulence pde's. One-equation models make use of an additional pde relating to the turbulence velocity scale. Attention is also given to two-equation models, stress-equation models, and large eddy simulations. Large-eddy simulations are concerned with a three-dimensional time-dependent numerical computation of the large-scale turbulence.
Global Positioning System (GPS) measurements spanning approximately 3 years have been used to determine velocities for 7 sites on the Australian, Pacific and Antarctic plates. The site velocities agree with both plate model predictions and other space geodetic techniques. We find no evidence for internal deformation of the interior of the Australian plate. Wellington, New Zealand, located in the Australian-Pacific plate boundary zone, moves 20 +/- 5 mm/yr west-southwest relative to the Australian plate. Its velocity lies midway between the predicted velocities of the two plates. Relative Euler vectors for the Australia-Antarctica and Pacific-Antarctica plates agree within one standard deviation with the NUVEL-1A predictions.
The objective of the present work is to extend the probability density function (PDF) tubulence model to compressible reacting flows. The proability density function of the species mass fractions and enthalpy are obtained by solving a PDF evolution equation using a Monte Carlo scheme. The PDF solution procedure is coupled with a compression finite-volume flow solver which provides the velocity and pressure fields. A modeled PDF equation for compressible flows, capable of treating flows with shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed. Two super sonic diffusion flames are studied using the proposed PDF model and the results are compared with experimental data; marked improvements over solutions without PDF are observed.
The Droplet Deformation and Breakup Model was used to predict deformation of droplets approaching the leading edge stagnation line of an airfoil. The quasi-steady model was solved for each position along the droplet path. A program was developed to solve the non-linear, second order, ordinary differential equation that governs the model. A fourth order Runge-Kutta method was used to solve the equation. Experimental slip velocities from droplet breakup studies were used as input to the model which required slip velocity along the particle path. The center of mass displacement predictions were compared to the experimental measurements from the droplet breakup studies for droplets with radii in the range of 200 to 700 mm approaching the airfoil at 50 and 90 m/sec. The model predictions were good for the displacement of the center of mass for small and medium sized droplets. For larger droplets the model predictions did not agree with the experimental results.
The Droplet Deformation and Breakup Model was used to predict deformation of droplets approaching the leading edge stagnation line of an airfoil. The quasi-steady model was solved for each position along the droplet path. A program was developed to solve the non-linear, second order, ordinary differential equation that governs the model. A fourth order Runge-Kutta method was used to solve the equation. Experimental slip velocities from droplet breakup studies were used as input to the model which required slip velocity along the particle path. The center of mass displacement predictions were compared to the experimental measurements from the droplet breakup studies for droplets with radii in the range of 200 to 700 mm approaching the airfoil at 50 and 90 m/sec. The model predictions were good for the displacement of the center of mass for small and medium sized droplets. For larger droplets the model predictions did not agree with the experimental results.
The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.
The instability wave noise generation model is used to study the instability waves in the two shear layers of an inverted velocity profile, supersonic, coaxial jet and the noise radiated from the dominant wave. The inverted velocity profile jet has a high speed outer stream surrounding a low speed inner stream and the outer shear layer is always larger than the inner shear layer. The jet mean flows are calculated numerically. The operating conditions are chosen to exemplify the effect of the coaxial jet outer shear layer initial spreading rates. Calculations are made for the stability characteristics in the coaxial jet shear layers and the noise radiated from the instability waves for different operating conditions with the same total thrust, mass flow and exit area as a single reference jet. Results for inverted velocity profile jets indicate that relative maximum instability wave amplitudes and far field peak noise levels can be reduced from that of the reference jet by having higher spreading rates for the outer shear layer, low velocity ratios, and outer streams hotter than the inner stream.
In this paper we develop a computational model for the mixing and transport of a dilute biomass slurry. The objective was to create a sufficiently simple and efficient model for biomass transport that can be coupled with reaction models for the study of conversion of cellulosic biomass into fermentable sugars. Our target system is 5%-by-mass ..alpha..-cellulose, which is our proxy for more complex lignocellulosic biomass. In the authors' previous work, an experimental investigation with ..alpha..-cellulose under two vane-mixer configurations showed a bifurcation between a settling regime, for which settling effects dominate, and a suspended regime, for which solids are mostly suspended. Here, a mixed-fluid model was chosen, for which the model for the mixture-velocity field is the incompressible Navier-Stokes equations under the Boussinesq approximation for buoyancy. Solids transport includes solids motion due to diffusion, settling, advection, and shear. Comparison of simulated and experimental results show good agreement in the suspended regime, and in capturing the bifurcation rate. While the model captured well the distribution of solids in the settling regime, the model was incapable of capturing the high torque values seen in experiments with vanishing mixer rotation rate.
Composite cure process induced residual strains and warping deformations in composite components present significant challenges in the manufacturing of advanced composite structure. As a part of the Manufacturing Process and Simulation initiative of the NASA Advanced Composite Project (ACP), research is being conducted on the composite cure process by developing an understanding of the fundamental mechanisms by which the process induced factors influence the residual responses. In this regard, analytical studies have been conducted on the cure process modeling of composite structural parts with varied physical, thermal, and resin flow process characteristics. The cure process simulation results were analyzed to interpret the cure response predictions based on the underlying physics incorporated into the modeling tool. In the cure-kinetic analysis, the model predictions on the degree of cure, resin viscosity and modulus were interpreted with reference to the temperature distribution in the composite panel part and tool setup during autoclave or hot-press curing cycles. In the fiber-bed compaction simulation, the pore pressure and resin flow velocity in the porous media models, and the compaction strain responses under applied pressure were studied to interpret the fiber volume fraction distribution predictions. In the structural simulation, the effect of temperature on the resin and ply modulus, and thermal coefficient changes during curing on predicted mechanical strains and chemical cure shrinkage strains were studied to understand the residual strains and stress response predictions. In addition to computational analysis, experimental studies were conducted to measure strains during the curing of laminated panels by means of optical fiber Bragg grating sensors (FBGs) embedded in the resin impregnated panels. The residual strain measurements from laboratory tests were then compared with the analytical model predictions. The paper describes the cure process procedures and residual strain predications, and discusses pertinent experimental results from the validation studies.
The stability coefficients for quasi-adiabatic pulsations for a model in thermal imbalance are evaluated using the dynamical energy (DE) approach, the total (kinetic plus potential) energy (TE) approach, and the small amplitude (SA) approaches. From a comparison among the methods, it is found that there can exist two distinct stability coefficients under conditions of thermal imbalance as pointed out by Demaret. It is shown that both the TE approaches lead to one stability coefficient, while both the SA approaches lead to another coefficient. The coefficient obtained through the energy approaches is identified as the one which determines the stability of the velocity amplitudes. For a prenova model with a thin hydrogen-burning shell in thermal imbalance, several radial modes are found to be unstable both for radial displacements and for velocity amplitudes. However, a new kind of pulsational instability also appears, viz., while the radial displacements are unstable, the velocity amplitudes may be stabilized through the thermal imbalance terms.
Planar measurements of the injection mole fraction distribution and the velocity field within a nonreacting model SCRAMJET combustor have been made using laser-induced iodine fluorescence. The combustor geometry investigated in this work is staged transverse injection of air into a Mach 2 freestream. A complete three-dimensional survey of the injectant mole fraction distribution has been generated and a single planar velocity measurement has been completed. The measurements reveal the dramatic effect of streamwise vortices on the mixing of the injectant in the near field of the injectors, as well as the rapid mixing generated by staging two field injectors. Analysis of the downstream decay of the maximum injectant mole fraction in this and other nonreacting combustor geometries indicates that the relative rate of injectant mixing well downstream of the injectors is independent of combustor geometry, combustor Mach number, and injectant molecular weight. Mixing within this region of the combustor is dominated by turbulent diffusion within the injectant plume. The transition of the dominant mixing mechanism, from vortex-driven mixing in the near field to turbulent diffusion in the far field, was found to occur in the region between 10 and 20 jet diameters downstream of the injectors.
Nuclear system thermal hydraulic analysis has historically relied on computationally inexpensive 1D codes. However, such tools are unable to capture multiscale multidimensional effects in large nuclear reactor enclosures. On the other hand, simulations with higher fidelity can be too expensive for such purposes. One of the ways to reduce computational cost is to perform simulations on a coarse grid, which, unfortunately, introduces large discretization errors. In this paper, two high-to-low data-driven approaches are investigated: (1) a coarse grid turbulence model to predict eddy viscosity and (2) correction of errors in coarse grid velocity fields. The approaches aim to reduce grid- and turbulence model-induced errors in coarse grid Reynolds-averaged Navier–Stokes (RANS) simulations. Two sources of high-fidelity data, RANS and large eddy simulations (LES), are explored. To extract the eddy viscosity from the LES data, an inverse optimization problem is solved. However, the LES eddy viscosity is shown to be comparable to the RANS eddy viscosity in terms of error reduction. Therefore, the directly available RANS eddy viscosity was used to develop a coarse grid data-driven turbulence model. Additionally, error correction in velocity is used to reduce the remaining uncertainties and bring the results closer to reality. In conclusion, the performance of the frameworks is demonstrated for a scaled upper plenum of a gas-cooled reactor facility.
Measurements were made in the wake of a swept wing model to study the structure of lift generated vortex wakes shed by conventional span loadings and by several span loadings designed to reduce wake velocities. Variations in the span loading on the swept wing generator were obtained by deflecting seven flap segments on each side by amounts determined by vortex lattice theory to approximate the desired span loadings. The resulting wakes were probed with a three component, hot wire probe to measure velocity, and with a wing to measure the rolling moment that would be induced on a following aircraft. The experimental techniques are described herein, and the measured velocity and rolling moments are presented, along with some comparisons with the applicable theories.
A theoretical model is presented of the effects of forward velocity of an aircraft at arbitrary subsonic speed on sound radiated from convecting monopole and dipole sources embedded in the jet flow. It is found that with increasing forward velocity there is a steadily increasing amplification (over the static case) of the sound radiated into the forward arc and a large reduction of the sound which is radiated into the rearward arc. The same trend is also shown to result when there is a reduction in the exhaust velocity, with, however, a further rise in amplification in the forward quadrant and a drop in attenuation in the aft quadrant.