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Document describes method for determining minimum leak rate to which soap-solution leak detectors sensitive. Bubbles formed at smaller leak rates than previously assumed. In addition to presenting test results, document discusses effects of joint-flange configurations, properties of soap solutions, and correlation of test results with earlier data.
A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.
An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flow.
The problem of hydrodynamic stability and the transition from laminar to turbulent flows are reformulated by seeking numerical solutions of the full, unapproximated Navier-Stokes equations. This method differs significantly from the well known Orr-Sommerfeld equation approach. The oncoming laminar flow is disturbed by forced, time dependent perturbations. The magnitudes of these perturbations are arbitrary. Then, the ensuing spatial and temporal development of the imposed perturbations on the basic flow is calculated by direct numerical solutions of the time dependent Navier-Stokes equations. One of the main advantages of this method is its ability to simulate nonlinear processes. As a specific application of this technique to SSME (Space Shuttle Main Engine) flow configurations, computer programs have been written for the two dimensional flow over a backward facing step. This numerical code will be tested for operational use as part of a continued research collaboration effort with the NASA/MSFC counterparts.
The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.
Crystals of high morphological quality are grown by dissolution of a substance to be grown into the crystal in a suitable solvent under high pressure, and by subsequent slow, time-controlled reduction of the pressure of the resulting solution. During the reduction of the pressure interchange of heat between the solution and the environment is minimized by performing the pressure reduction either under isothermal or adiabatic conditions.
A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.
Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.
Two buffers were explored for testing: low ionic strength electrophoresis buffer with and without density gradient material. It was found that the electrophoresis routine was better tolerated when Ficoll was present. The results of a viability study of primary human fetal kidney (HFK-1) cells at the first passage are shown. Cell strain HFK-1 was used in several experiments at the first and second passage. The HFK consisted mainly of fibroblasts, and HFK-1 has a high epithelioid cell content. The chromosomes of HFK were examined and found to be euploid. The stock medium for cell electrophoresis is described. In this solution density gradient solutes such as sucrose and Ficoll are dissolved to bring the osmolarity to 0.30. Its ionic strength is less than 0.01M, and its conductivity is usually 0.0011 mho/cm. Methods for viability determination included direct microscopic counting of the percent cells attached and spread within 24 hr of plating test cultures or electrophoretically separated fractions. The Cytograf viability assay concept was tested, and shown that blue stained cells scatter less light into the 0.8 to 3.3 deg angular interval than do unstained cells.
The flow around a thin elliptic cone at Mach number 2 and angle of attack 10 deg is simulated numerically, comparing the results obtained using a fine grid and the Navier-Stokes (NS) equations with those obtained using both coarse and fine grids and the Euler (E) equations. On the coarse grid, the E results are found to reproduce roughly the NS predictions of leading-edge separation and primary and secondary vortices on the leeward surface, but the E solution on the fine NS grid (showing no separation and a crossflow-shock-induced vorticity) reveals this agreement to be spurious. The fine-grid E prediction is shown to be a valid solution of the E equations, indicating their unsuitability as approximators of viscous flow. The imposition of a Kutta condition on the E computation is found to be ineffective in correcting this discrepancy.
A method for the calculation of the flow field of a helicopter rotor blade in hover is presented. The approach uses a finite volume solution of the three dimensional Euler equations for the blade near field. In the Euler solver the velocity field is decomposed into two parts. One is the induced velocity of the vortex wake extending below the blade, found from a free wake calculation procedure. The other part is the unknown additional velocity field of the rotor blade. This approach eliminates numerical diffusion of the rolled up wake vorticity due to truncation error and artificial viscosity. Also, the effects of the far wake are included in the limited computational domain. Solutions are presented for an isolated wing and a model helicopter rotor and compared to experiment.
An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flows.
In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.
This paper develops a hierarchical type solution scheme which can handle the field equations associated with nonlinear finite element simulations. The overall procedure possesses various levels of application namely degree of freedom, nodal, elemental, substructural as well as global. In particular iteration, updating, assembly and solution control occurs at the various hierarchical levels. Due to the manner of formulation, the degree of matrix inversion depends on the size of the various hierarchical partitioned groups. In this context, degree of freedom partitioning requires no inversion. To benchmark the overall scheme, the results of several numerical examples are presented.
Mickens (1981, 1984) has considered analytic techniques for obtaining approximate solutions to one-dimensional nonlinear oscillatory systems x(double-dot) + x = lambda f(x, x/dot/, lambda) where lambda is a small positive parameter and f is a nonlinear polynomial function of its arguments. However, in certain cases there is interest in the analysis of physical systems for which the nonlinear function f(x, x/dot/, lambda) is singular for finite values of x or x(dot). The present investigation is concerned with the use of existing approximate analytic schemes to obtain solutions to singular nonlinear oscillatory differential equations.
The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.
Closed-form solutions are derived for a class of tracking problems including a linear optimal regulator and a prefilter for a time-invariant plant. The solutions for the prefilter equation and state trajectory coupled by the Riccati equation are exponentially related to the stability matrix of the plant. A computational procedure is presented in recursive form when the desired output state dynamics is assumed linear and time-invariant. Several examples are given for illustration.
A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.