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Theoretical analysis of pressure distribution, load capacity, attitude angle, and friction force for eccentric Rayleigh step journal bearing - infinite length solution
The effects of steady and time-dependent residual accelerations on representative melt and solution crystal growth systems have been investigated using numerical models. For the melt growth system, it was found that the lateral nonuniformity in crystal composition, depending on the particular operating conditions, can be very sensitive to the orientation of the steady component of the residual gravity vector down to 10 to the -6th g. Oscillatory residual accelerations (g-jitter) were found to lead to transients in the dopant distribution. For the solution growth, longtime simulations showed that at 10 to the -5th g, and the cooling rates used in Spacelab 3 experiments, diffusive transport dominates only in the beginning. Convective transport becomes increasingly significant after 3 to 5 hours, depending on the orientation of the crystal in the residual gravity field.
Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.
Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.
Integral transform methods for analytic solutions to current and potential distribution on disk in infinite plane for four limiting cases
Deep space exploration, especially that of Mars, is on the horizon as the next big challenge for space exploration. Nuclear propulsion, through which high thrust and efficiency can be achieved, is a promising option for decreasing the cost and logistics of such a mission. Work on nu- clear thermal engines goes back to the days of the NERVA program. Currently, nuclear thermal propulsion is under development again in various forms to provide a superior propulsion system for deep space exploration. The authors have been working to develop a concept nuclear thermal engine that uses a grooved ring fuel element as an alternative to the traditional hexagonal rod design. The authors are also studying the use of carbide fuels. The concept was developed in order to increase surface area and heat transfer to the propellant. The use of carbides would also raise the operating temperature of the reactor. It is hoped that this could lead to a higher thrust to weight nuclear thermal engine. This paper describes the modeling of neutronics, heat transfer, and fluid dynamics of this alternative nuclear fuel element geometry. Fabrication experiments of grooved rings from carbide refractory metals are also presented along with material characterization and interactions with a hot hydrogen environment. Results of experiments and associated analysis are desired densities with some success in material distribution and reaching a solid solution. Future work is needed to improve distribution of material, minimize oxidation during the milling process, and de ne a fabrication process that will serve for constructing grooved ring fuel rods for large system tests.
Deep space exploration, especially that of Mars, is on the horizon as the next big challenge for space exploration. Nuclear propulsion, through which high thrust and efficiency can be achieved, is a promising option for decreasing the cost and logistics of such a mission. Work on nuclear thermal engines goes back to the days of the NERVA program. Currently, nuclear thermal propulsion is under development again in various forms to provide a superior propulsion system for deep space exploration. The authors have been working to develop a concept nuclear thermal engine that uses a grooved ring fuel element as an alternative to the traditional hexagonal rod design. The authors are also studying the use of carbide fuels. The concept was developed in order to increase surface area and heat transfer to the propellant. The use of carbides would also raise the operating temperature of the reactor. It is hoped that this could lead to a higher thrust to weight nuclear thermal engine. This paper describes the modeling of neutronics, heat transfer, and fluid dynamics of this alternative nuclear fuel element geometry. Fabrication experiments of grooved rings from carbide refractory metals are also presented along with material characterization and interactions with a hot hydrogen environment. Results of experiments and associated analysis are discussed. The authors demonstrated success in reaching desired densities with some success in material distribution and reaching a solid solution. Future work is needed to improve distribution of material, minimize oxidation during the milling process, and define a fabrication process that will serve for constructing grooved ring fuel rods for large system tests.
An examination is made to identify appropriate times to include weakly relativistic wave dispersion in calculations of auroral zone electron distributions. Two dispersion relations are examined. First, solutions are found for a ring distribution of particles around a cold ambient plasma. The solutions are found only for modes near the electron gyrofrequency. A trapped mode which is decoupled from the freely propagating R-X mode of cold plasmas is found to be the most unstable mode. Wave dispersion is examined with a spherically symmetric Dory-Guest-Harris (DGH) distribution, which describes a shell distribution that has a peak momentum larger than the thermal spread. The trapped mode is again found to be the most unstable. The analysis indicates it is beneficial to include relativistic effects whenever calculating auroral plasma distributions, and that a simple model will have sufficient accuracy.
A solution-adaptive grid algorithm has been developed for use in two and three dimensions. The algorithm uses a transformation from the cartesian coordinate system to a general coordinate space, which will be defined as a parallelepiped. A weighting function for adaption of the grid is developed that will allow adaption to the gradients of any combination of dependent variables in the flow. The adaption is carried out in the parametric space and a simple inverse mapping to return the new parametric space to the physical space is derived. The concept used to relocate the grid-points in the parametric space is based on the center of mass of distributed weights. Solution-adaptive results are presented for various laminar flows in two dimensions and for mathematical weighting functions in three dimensions.
In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.
A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.
The high-velocity tail of the electron distribution has been calculated by solving the high-velocity form of the Landau equation for a thermal structure representative of a flaring coronal loop. These calculations show an enhancement of the tail population above Maxwellian for electrons moving down the temperature gradient. The results obtained are used to test the reliability of the BGK approximation. The comparison shows that the BGK technique can estimate contributions to the heat flux from the high-energy tail to within an order of magnitude.
Increasing numbers of distributed generators in the electric power distribution networks require developing a control strategy to optimize solutions in real time. Linearized optimal distribution flow development has seen growth and acceptance in the distribution systems literature for efficiently modeling the \glspl{opf} for distribution systems. This paper examines the implementation and integration procedure for linearized optimal distribution flow federate to \gls{oedisi} platform. Specifically, we discuss i) the usage of the \gls{oedisi} platform, ii) obtaining a tractable solution using developed \gls{opf} federate, and iii) validation of solutions and bench-marking the \gls{oedisi} platform with developed \gls{opf} federate using OpenDSS. In brief, we demonstrate how a general linearized optimal distribution flow federate can be developed and integrated with a co-simulation environment to mimic real-world examples. The efficacy of the proposed method is demonstrated using the IEEE 123-bus test system under different scenarios to obtain a tractable solution and compare its results.
Charts for solution of radial distribution flow equations used in axial flow compressor design
Solution of angular distribution of outgoing thermal radiation from planetary atmosphere, using Chandrasekhar diffuse scattering and transmission functions
Steam filament solution determines velocity distribution due to potential flow in the blade-to-blade plane of the radial impeller. This is used to determine the mass-averaged relative fluid angle, which is in turn used in an axisymmetric program to obtain steam surfaces of the assumed axisymmetric flow.
Numerical solution of current distribution, wave propagation constant and propagation mode cut-off frequencies on periodic linear array
Nonlinear boundary value problems of an infinite elastic-plastic plate with a circular hole subjected to pure tension and pure shear at infinity are solved by a method involving Fourier series and finite difference. On the basis of these solutions, the validity of Neuber's relationship between the stress and strain concentration factors for the plane stress problems is examined and a generalized Stowell formula for the stress concentration factor is proposed for problems in which the applied loading may be pure shear as well as pure tension and, furthermore, other stress states. By the same method of solution, the stress distributions around a rigid circular cylindrical inclusion embedded in an infinite rigid-plastic matrix subjected to uniform transverse pure shear and tension are obtained.