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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS1939

Some notes on the numerical solution of shear-lag and mathematically related problems

The analysis of box beams with shear deformation of the flanges can be reduced to the solution of a differential equation. The same equation is met in other problems of stress analysis. No analytical solutions of this equation can be given for practical cases, and numerical methods of evaluation must be used. Available methods are briefly discussed. Two numerical examples show the application of the step-by-step method of integration to shear-lag problems.

Kuhn, Paul↗
NASA NTRS1952

Solutions of laminar-boundary-equations which result in specific-weight-flow profiles locally exceeding free-stream values

Revised solutions of the laminar-boundary-layer equations for cases which involved cooling at the wall combined with large pressure gradients in the main stream produced specific-weight-flow profiles which locally exceeded free-stream values. Heat-transfer and friction coefficients, boundary-layer thicknesses, and velocity, temperature, and specific-weight-flow distributions resulting from the revised solutions are presented for Euler numbers of 0.5 and 1, stream-to-wall temperature ratios of 2 and 4, and cooling-air flow rates through porous walls designated by flow parameters of 0, -0.5, and -1.

HEAT TRANSFER, AERODYNAMIC↗
NASA NTRS1947

Voltera's Solution of the Wave Equation as Applied to Three-Dimensional Supersonic Airfoil Problems

A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformly loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the triangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application.

Heslet, Max A↗
NASA NTRS1952

Hydrodynamic impact of a system with a single elastic mode I : theory and generalized solution with an application to an elastic airframe

Solutions of impact of a rigid prismatic float connected by a massless spring to a rigid upper mass are presented. The solutions are based on hydrodynamic theory which has been experimentally confirmed for a rigid structure. Equations are given for defining the spring constant and the ratio of the sprung mass to the lower mass so that the two-mass system provides representation of the fundamental mode of an airplane wing. The forces calculated are more accurate than the forces which would be predicted for a rigid airframe since the effect of the fundamental mode on the hydrodynamic force is taken into account. In a comparison of the theoretical data with data for a severe flight-test landing impact, the effect of the fundamental mode on the hydrodynamic force is considered and response data are compared with experimental data.

Mayo, Wilbur L↗
NASA NTRS1955

Exact solutions of laminar-boundary-layer equations with constant property values for porous wall with variable temperature

Exact solution of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is assumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionless boundary-layer thicknesses, and convective heat-transfer coefficients are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes.

Donoughe, Patrick L↗
NASA NTRS1993

Determination of trace elements in triglycine sulfate solutions

Ten elements were divided into 2 groups. The elements in the first group included iron, nickel, chromium, manganese, copper, and gold. The elements in the second group included zinc, cobalt, lead, cadmium, and gold. Five ppm of each element in each group was spiked in a 1 percent triglycine sulfate (TGS) solution. Glycine was removed with 1-naphthyl isocyanate in ether medium. The glycine derivative 1-naphthyl isocyanate glycine was removed by filtration, and the filtrates were analyzed for the different elements. Analysis of these elements was performed by using the 5100 Perkin-Elmer Atomic Absorption Spectrophotometer. The result of these experiments was the observation that there was a decrease in the concentration of chromium and gold, which was interpreted to be due to the chelation of these elements by the derivative 1-naphthyl isocyanate glycine. Further research is needed to determine the concentration of other elements in triglycine sulfate (TGS) solutions. These elements will include lithium, sodium, rubidium, magnesium, calcium, strontium, barium, aluminum, and silicon. These are the most likely elements to be found in the sulfuric acid used in manufacturing the TGS crystal. Moreover, we will extend our research to investigate the structural formula of the violet colored chelated compounds, which had been formed by interaction of the derivative 1-naphthyl isocyanate glycine with the different elements, such as gold, chromium.

Tadros, Shawky H.↗
NASA NTRS1993

A multi-level solution algorithm for steady-state Markov chains

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Horton, Graham↗
NASA NTRS1994

Fluid-loading solutions and plasma volume: Astro-ade and salt tablets with water

Fluid loading with salt and water is a countermeasure used after space flight to restore body fluids. However, gastrointestinal side effects have been frequently reported in persons taking similar quantities of salt and water in ground-based studies. The effectiveness of the Shuttle fluid-loading countermeasure (8 gms salt, 0.97 liters of water) was compared to Astro-ade (an isotonic electrolyte solution), to maintain plasma volume (PV) during 4.5 hrs of resting fluid restriction. Three groups of healthy men (n=6) were studied: a Control Group (no drinking), an Astro-ade Group, and a Salt Tablet Group. Changes in PV after drinking were calculated from hematocrit and hemoglobin values. Both the Salt Tablet and Astro-ade Groups maintained PV at 2-3 hours after ingestion compared to the Control Group, which had a 6 percent decline. Side effects (thirst, stomach cramping, and diarrhea) were noted in at least one subject in both the Astro-ade and Salt Tablet Groups. Nausea and vomiting were reported in one subject in the Salt Tablet Group. It was concluded that Astro-ade may be offered as an alternate fluid-loading countermeasure but further work is needed to develop a solution that is more palatable and has fewer side effects.

Fortney, Suzanne M.↗
NASA NTRS1993

Solution of mixed convection heat transfer from isothermal in-line fins

Transient and steady state combined natural and forced convective flows over two in-line finite thickness fins (louvers) in a vertical channel are numerically solved using two methods. The first method of solution is based on the 'Simple Arbitrary Lagrangian Eulerian' (SALE) technique which incorporates mainly two computational phases: (1) a Lagrangian phase in which the velocity field is updated by the effects of all forces, and (2) an Eulerian phase that executes all advective fluxes of mass, momentum and energy. The second method of solution uses the finite element code entitled FIDAP. In the first part, comparison of the results by FIDAP, SALE, and available experimental work were done and discussed for steady state forced convection over louvered fins. Good agreements were deduced between the three sets of results especially for the flow over a single fin. In the second part and in the absence of experimental literature, the numerical predictions were extended to the transient transports and to the opposing flow where pressure drop is reversed. Results are presented and discussed for heat transfer and pressure drop in assisting and opposing mixed convection flows.

Khalilollahi, Amir↗
NASA NTRS1993

A comparative study of computational solutions to flow over a backward-facing step

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Mizukami, M.↗
NASA NTRS1993

Numerical solution of flame sheet problems with and without multigrid methods

Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.

Douglas, Craig C.↗
NASA NTRS1993

Multi-grid domain decomposition approach for solution of Navier-Stokes equations in primitive variable form

The new multigrid (or adaptive) pseudospectral element method was carried out for the solution of incompressible flow in terms of primitive variable formulation. The desired features of the proposed method include the following: (1) the ability to treat complex geometry; (2) high resolution adapted in the interesting areas; (3) requires minimal working space; and (4) effective in a multiprocessing environment. The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of fine-grid and coarse-grid subdomains with the inter-overlapping area. Next, it is necessary to implement the Schwarz alternating procedure (SAP) to exchange the data among subdomains, where the coarse-grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine-grid subdomain to the coarse-grid subdomain is conducted. The strategy behind the coarse-grid correction is to adopt the operator of the divergence of the velocity field, which intrinsically links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique with the least storage requirement, i.e. O(N(exp 3)) in 3-D and O(N(exp 2)) in 2-D. Numerical results of both driven cavity and jet flow will be presented in the paper to account for the versatility of the proposed method.

Ku, Hwar-Ching↗
NASA NTRS1994

Direct observation of crystal growth from solution using optical investigation of a growing crystal face

The first technical report for the period 1 Jan. 1993 till 31 Dec. 1993 for the research entitled, 'Direct observation of crystal growth from solution using Optical Investigation of a growing crystal Face' is presented. The work on the project did not start till 1 June 1993 due to the non-availability of the required personnel. The progress of the work during the period 1 June 1993 till the end of 1993 is described. Significant progress was made for testing various optical diagnostic techniques for monitoring crystal solution. Some of the techniques that are being tested are: heterodyne detection technique, in which changes in phase are measured as a interferometric function of time/crystal growth; a conventional technique, in which a fringe brightness is measured as a function of crystal growth/time; and a Mach-Zehnder interferometric technique in which a fringe brightness is measured as a function of time to obtain information on concentration changes. During the second year it will be decided to incorporate the best interferometric technique along with the ellipsometric technique, to obtain real time in-situ growth rate measurements. A laboratory mock-up of the first two techniques were made and tested.

Lal, Ravindra↗
NASA NTRS1993

Numerical solutions of the complete Navier-Stokes equations

The objective of this study is to compare the use of assumed pdf (probability density function) approaches for modeling supersonic turbulent reacting flowfields with the more elaborate approach where the pdf evolution equation is solved. Assumed pdf approaches for averaging the chemical source terms require modest increases in CPU time typically of the order of 20 percent above treating the source terms as 'laminar.' However, it is difficult to assume a form for these pdf's a priori that correctly mimics the behavior of the actual pdf governing the flow. Solving the evolution equation for the pdf is a theoretically sound approach, but because of the large dimensionality of this function, its solution requires a Monte Carlo method which is computationally expensive and slow to coverage. Preliminary results show both pdf approaches to yield similar solutions for the mean flow variables.

Hassan, H. A.↗
NASA NTRS1994

Uniqueness of a solution of a steady state photochemical problem: Applications to Mars

Based on the conservation of chemical elements in chemical reactions, a rule is proved that the number of boundary conditions given by densities and/or non-zero velocities should not be less than the number of chemical elements in the system, and the components given by densities and velocities should include all elements in the system. Applications of this rule to Mars are considered. It is proved that a problem of CO2-H2O chemistry in the lower and middle atmosphere of Mars, say, in the range of 0-80 km does not have an unique solution, if only CO2 and H2O densities are given at the lower boundary, while all other boundary conditions are fluxes. Two models of this type are discussed. These models fit the same boundary conditions, are balanced with a relative uncertainty of 10(exp -4) for H2, and predict the O2, CO, and H2 mixing ratios which differ by order of magnitude. One more species density, e.g. that of O2, should be specified at the boundary to obtain the unique solution. The situation is better if the upper boundary is extended to the exobase where thermal escape velocities of H and H2 can be specified. However, in this case, either oxygen nonthermal escape rate or the O2 density at the surface should be given as the boundary condition. Two models of Mars' photochemistry, with and without nitrogen chemistry, are considered. The oxygen nonthermal escape rate of 1.2 x 10(exp 8) cm(exp -2) s(exp -1) is given at 240 km and is balanced with the total hydrogen escape rate within uncertainty of 1 percent for both models. Both models fit the measured O2 and CO mixing ratios, the O3 line absorption at 9.6 microns, and the O2 1.27 microns dayglow within the uncertainties of the measured values; although, the model without nitrogen chemistry fits better.

Krasnopolsky, V. A.↗
NASA NTRS1994

Preliminary solutions for the lunar gravity field from analysis of lunar orbiter tracking data

Knowledge of the gravitation field, in combination with surface topography, provides one of the principal means of inferring the internal structure of a planetary body. Previous analyses of the lunar gravitational field have been based on data from the Lunar Orbiters, the Apollo subsatellites, and the low altitude passes of the Apollo spacecraft. Recently, Konopliv et al. have reanalyzed all available Lunar Orbiter and Apollo subsatellite tracking data, producing a 60th degree and order solution. In preparation for the Clementine Mission to the Moon, we have also initiated a reanalysis of the Lunar Orbiter and Apollo subsatellite data. Our reanalysis takes advantage of advanced force and measurement modeling techniques as well as modern computational facilities. We applied the least squares collocation technique which stabilizes the behavior of the solution and high degree and order. The extension of the size of the field reduces the aliasing coming from the omitted portion of the gravitational field. This is especially important for the analysis of the tracking data from the Lunar Orbiters, as the periapse heights frequently ranged from 50 to 100 km.

Lemoine, F. G.↗
NASA NTRS1994

A note on the regularity of solutions of infinite dimensional Riccati equations

This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR and LQG control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smoothes solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement.

Burns, John A.↗