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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

An exact closed form solution for constant area compressible flow with friction and heat transfer

The well-known differential equation for the one-dimensional flow of a compressible fluid with heat transfer and wall friction has no known solution in closed form for the general case. This report presents a closed form solution for the special case of constant heat flux per unit length and constant specific heat. The solution was obtained by choosing the square of a dimensionless flow parameter as one of the independent variables to describe the flow. From this exact solution, an approximate simplified form is derived that is applicable for predicting subsonic flow performance characteristics for many types of constant area passages in internal flow. The data included in this report are considered sufficiently accurate for use as a guide in analyzing and designing internal gas flow systems.

Sturas, J. I.↗
NASA NTRS1972

Thermally stable polyimides from solutions of monomeric reactants

A method for preparing thermally stable resin-fiber-reinforced composites by using solutions of appropriate monomers is described. Solutions containing a dimethyl ester of an aryl tetracarboxylic acid, the monomethyl ester of nadic acid, and an aryl diamine were used to impregnate graphite fibers. Composites fabricated from these prepregs exhibited excellent thermo-oxidative stability and retention of mechanical properties at 315 C (600 F). These results compare favorably to those obtained from composites made from amide-acid prepolymers capped with reactive alicyclic rings. Monomeric solutions provide excellent shelf life and improved solubility compared to amide-acid prepolymer solutions.

Serafini, T. T.↗
NASA NTRS1971

A thin-shock-layer solution for nonequilibrium, inviscid hypersonic flows in earth, Martian, and Venusian atmospheres

An approximate inverse solution is presented for the nonequilibrium flow in the inviscid shock layer about a vehicle in hypersonic flight. The method is based upon a thin-shock-layer approximation and has the advantage of being applicable to both subsonic and supersonic regions of the shock layer. The relative simplicity of the method makes it ideally suited for programming on a digital computer with a significant reduction in storage capacity and computing time required by other more exact methods. Comparison of nonequilibrium solutions for an air mixture obtained by the present method is made with solutions obtained by two other methods. Additional cases are presented for entry of spherical nose cones into representative Venusian and Martian atmospheres. A digital computer program written in FORTRAN language is presented that permits an arbitrary gas mixture to be employed in the solution. The effects of vibration, dissociation, recombination, electronic excitation, and ionization are included in the program.

Grose, W. L.↗
NASA NTRS1972

Spectral reflectance of selected aqueous solutions for water quality applications

The relative specular reflectances of individual aqueous solutions having a particular chemical salt content were measured in the 2 to 20 micrometers region of the infrared component or radiant flux. Distilled water was the reflectance standard. The angle of incidence was 70.03 deg plus or minus 0.23 deg. Absolute reflectances of the solutions for the same polarization and angle of incidence were computed by use of the measured relative reflectances, one of the Fresnel equations, and the optical constants of distilled water. Phase shift and phase difference spectra were obtained by respectively applying a Kramers-Kronig dispersion analysis to the absolute and relative reflectance spectra. The optical constants of the solutions were determined by algorithms commonly associated with the Kramers-Kronig analysis. Spectral signatures that qualitatively and quantitatively characterize the solute and that show structure of the infrared bands of water were noted in the phase difference spectra. The relative and absolute reflectances, the phase shift and phase difference spectra and the optical constants are presented in graphical form. Application of these results to remote sensing of the chemical quality of natural waters is discussed briefly.

Querr, M. R.↗
NASA NTRS1972

Application of thermodynamics to silicate crystalline solutions

A review of thermodynamic relations is presented, describing Guggenheim's regular solution models, the simple mixture, the zeroth approximation, and the quasi-chemical model. The possibilities of retrieving useful thermodynamic quantities from phase equilibrium studies are discussed. Such quantities include the activity-composition relations and the free energy of mixing in crystalline solutions. Theory and results of the study of partitioning of elements in coexisting minerals are briefly reviewed. A thermodynamic study of the intercrystalline and intracrystalline ion exchange relations gives useful information on the thermodynamic behavior of the crystalline solutions involved. Such information is necessary for the solution of most petrogenic problems and for geothermometry. Thermodynamic quantities for tungstates (CaWO4-SrWO4) are calculated.

Saxena, S. K.↗
NASA NTRS1971

Thermodynamic properties of carbon in b.c.c. and f.c.c. iron-silicon-carbon solid solutions.

The equilibrium between hydrogen-methane gas mixtures and Fe-Si-C solid solutions has been investigated both as a function of temperature and carburizing gas composition. The thermodynamic properties of the carbon atoms in both b.c.c. and f.c.c. solid solution have been derived from the equilibrium measurements. The results found have been compared with those of earlier investigations and with the predictions of recent theoretical models on ternary solid solutions containing both substitutional and interstitial solute atoms.

Chraska, P.↗
NASA NTRS1971

Simultaneous solution for the masses of the principal planets from analysis of optical, radar, and radio tracking data.

The Jet Propulsion Laboratory has developed a set of computer programs known as the Solar System Data Processing System (SSDPS) which is employed in improving the ephemerides of the major planets and for improving the values of several associated astronomical constants. A group of solutions for the masses of the major planets, together with the AU and radii of Mercury, Venus, and Mars, is presented. These solutions based upon optical, radar, and spacecraft radio tracking data are preliminary. The relative power of radar and radio tracking data vis-a-vis purely optical data in a solution is shown. The problems which could arise by adopting solutions based upon a single data type are demonstrated.

Lieske, J. H.↗
NASA NTRS1971

Numerical solution for propagation of coupled longitudinal and transverse waves normal to the applied magnetic field in a three-fluid medium.

The solution was obtained without approximating the dispersion relation. This was made possible by the use of a computer method for carrying out the extremely large number of algebraic manipulations involved. The three-fluid model employed accounts for the interaction of the electron, ion, and neutral species. The solution for the e-folding distance describes the damping characteristics of each wave mode. Each of the e-folding solutions corresponds to one of the phase velocity solutions.

Mcclendon, R. W.↗
NASA NTRS1973

Exact analytical solution to a transient conjugate heat-transfer problem

An exact analytical solution is found for laminar, constant-property, slug flow over a thin plate which is also convectively cooled from below. The solution is found by means of two successive Laplace transformations when a transient in the plate and the fluid is initiated by a step change in the fluid inlet temperature. The exact solution yields the transient fluid temperature, surface heat flux, and surface temperature distributions. The results of the exact transient solution for the surface heat flux are compared to the quasi-steady values, and a criterion for the validity of the quasi-steady results is found. Also the effect of the plate coupling parameter on the surface heat flux are investigated.

Sucec, J.↗
NASA NTRS1973

Cracking of Ti-6Al-4V in methanol solutions containing sulfates.

Whether cracking of unnotched Ti-6Al-4V specimens occurs in methanol containing H2SO4, Li2SO4, or Fe2(SO4)3 is a function of the age of the solution and the concentration of the sulfate. With H2SO4 concentrations of 0.10 N to 0.25 N, the methanol solutions lose their ability to crack the specimens with time after mixing and prior to exposure. The aging time required to inhibit the cracking varies inversely with the water content of the solution. With larger quantities of H2SO4, 0.5 N and 1 N, no cracking is observed. Interpretations of Raman spectroscopic studies of the aging solution suggests that the nature of the O-H group may play a role in the crack initiation or inhibiting mechanism.

Haney, E. G.↗
NASA NTRS1974

Spherical means of solutions of partial differential equations in a conical region

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Ting, L.↗
NASA NTRS1973

First-order corrections to approximate solutions to two-point boundary-condition problems

A method, applicable to real time guidance, is developed for accurate solution to exo-atmospheric space flight optimization problems. In principle the method is applicable to many other two-point boundary-condition (TPBC) problems. The first step of the method is the iterative solution (using a shooting method) of a TPBC problem with differential equations simplified so that they may be solved analytically by means of a single closed-form solution over each stage of the flight. The second step is the addition of a closed-form correction to the solution to the TPBC problem obtained in the first step. The correction accounts (to first-order accuracy) for the errors due to the aforementioned simplifications. Numerical results are given for several orbital injection problems.

Andrus, J. F.↗
NASA NTRS1975

Numerical solution of the Navier-Stokes equations for arbitrary two-dimensional multi-element airfoils

Abstracts are presented on a method of numerical solution of the Navier-Stokes equation for the flow about arbitrary airfoils, using a numerically generated curvilinear coordinate system having a coordinate line coincident with the body contour. Results of continuing research are reported and include: application of the Navier-Stokes solution in the vorticity-stream function formulation to a number of single airfoils at Reynolds numbers up to 2000; programming of the Navier-Stokes solution for multiple airfoils in the primitive variable formulation; testing of the potential flow solution of multiple bodies; and development of a generalized coordinate system program.

Thompson, J. F.↗
NASA NTRS1975

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Baldwin, B. S.↗
NASA NTRS1975

Nonlinear acoustic behavior at a caustic - An approximate analytical solution

The present paper discusses an approximate analytical solution to the nonlinear behavior of a discontinuous acoustic signal near a caustic. The Seebass transformation (1970) is refined to provide results which satisfy the governing equation to any prescribed accuracy, except across the shock wave produced by reflection of the simple wave at the caustic. The solution is approximate in the sense that the basic equation is satisfied wherever the solution is continuous but can satisfy only one of the two jump conditions at the reflected shock. The results give essential geometric features of the exact solution and provide a quantitative estimate of the strength of the so-called superboom.

Gill, P. M.↗
NASA NTRS1975

Solutions for incompressible separated boundary layers including viscous-inviscid interaction

Numerical solutions are presented for the laminar and turbulent boundary-layer equations for incompressible flows with separation and reattachment. The separation angularity is avoided by using an inverse technique in which the displacement thickness is prescribed and the pressure is deduced from the resulting solution. The turbulent results appear qualitatively correct despite the use of a two-layer eddy-viscosity model which is generally assumed appropriate only for mild-pressure-gradient flows. A new viscous-inviscid interaction technique is presented in which the inviscid flow is solved inversely by prescribing the pressure from the boundary-layer solution and deducing the new displacement thickness from the solution of a Cauchy integral. Calculations are presented using this interaction procedure for a laminar flow in which separation and reattachment occur on a solid surface.

Carter, J. E.↗
NASA NTRS1975

Spherical means of solutions of partial differential equations in a conical region

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Ting, L.↗
NASA NTRS1975

On relative periodic solutions of the planar general three-body problem

We describe two relatively simple reductions to order 6 for the planar general three-body problem. We also show that this reduction leads to the distinction between two types of periodic solutions: absolute or relative periodic solutions. An algorithm for obtaining relative periodic solutions using heliocentric coordinates is then described. It is concluded from the periodicity conditions that relative periodic solutions must form families with a single parameter. Finally, two such families have been obtained numerically and are described in some detail.

Broucke, R.↗