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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 631 records · Page 35
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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.↗
NASA NTRS1976

Integration-free interval doubling for Riccati equation solutions

Various algorithms are given for the case of constant coefficients. The algorithms are based on two ideas: first, relate the Re solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration free superlinearly convergent iterative solution to the algebraic RE. The algorithm, arranged in square-root form, is thought to be numerically stable and competitive with other methods of solving the algebraic RE.

Bierman, G. J.↗
NASA NTRS1977

Implicit approximate-factorization schemes for the efficient solution of steady transonic flow problems

Implicit approximate-factorization algorithms (AF) are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for a transonic flow field. This increase in computational efficiency is achieved with no appreciable increase in computer storage or coding complexity.

Ballhaus, W. F.↗
NASA NTRS1977

Solution of transient optimization problems by using an algorithm based on nonlinear programming

An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.

Teren, F.↗
NASA NTRS1977

Numerical solutions for viscous and potential flow about arbitrary two-dimensional bodies using body-fitted coordinate systems

A procedure for numerical solution of the time-dependent, incompressible Navier-Stokes equations for the flow about arbitrarily shaped two-dimensional bodies is given. This solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having a coordinate line coincident with the body contour regardless of its shape. The implicit solution utilizes the vorticity-stream function formulation with a false-position iterative adjustment of the surface vorticity in satisfaction of the no-slip boundary condition. Excellent agreement with the Blasius boundary layer solution is obtained for a semi-infinite flat plate. Results are presented for Reynolds numbers up to 2000 for several airfoils and a cambered rock.

Thames, F. C.↗
NASA NTRS1978

Numerical solution of the Navier-Stokes equations for super-sonic flows with strong shocks

The numerical solution of the full Navier-Stokes Equations for viscous flows with high Mach numbers and a strong detached bow shock was obtained. Two dimensional flows around a circular cylinder, and a circular cylinder with an aft-body in the form of a fairing, were considered. The solution of the compressible N.S. equations was accomplished by the method of finite differences. An implicit scheme of solution, the S.O.R., was used with the optimum acceleration parameters determined by trial and error. The tensor notation was used in writing the N-S Equations transformed into general curvilinear coordinates. The equations for the generation of the coordinate system were solved, followed by the solution of the N.S. equations, at the end of a set of given number of time steps. "Wiggles", constituted the one major problem that needed to be overcome. These oscillations give rise to quantities such as negative temperatures, which ultimately caused the computational program to break down. Certain dissipative finite-difference schemes damped these oscillations.

Devarayalu, K.↗
NASA NTRS1977

Integration-free interval doubling for Riccati equation solutions

Starting with certain identities obtained by Reid (1972) and Redheffer (1962) for general matrix Riccati equations (RE's), we give various algorithms for the case of constant coefficients. The algorithms are based on two ideas - first, relate the RE solution with general initial conditions to anchored RE solutions; and second, when the coefficients are constant, the anchored solutions have a basic shift-invariance property. These ideas are used to construct an integration-free, superlinearly convergent iterative solution to the algebraic RE. Preliminary numerical experiments show that our algorithms, arranged in square-root form, provide a method that is numerically stable and appears to be competitive with other methods of solving the algebraic RE.

Sidhu, G. S.↗
NASA NTRS1977

Solution of transient optimization problems by using an algorithm based on nonlinear programming

A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.

Teren, F.↗
NASA NTRS1977

Recursive analytical solution describing artificial satellite motion perturbed by an arbitrary number of zonal terms

An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.

Mueller, A. C.↗