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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Parallel flows with Soret effect in tilted cylinders

Henry and Roux (1986, 1987, 1988) have conducted extensive numerical studies on the interaction of Soret separation with convection in cylindrical geometry. Many of their solutions exhibit parallel flow away from end walls. Their parallel flow results can be matched by closed-form solutions. Solutions are nonunique in some parameter regions. Disappearance of one branch of solutions correlates with a sudden transition of Henry and Roux's results from a separated to a well-mixed flow.

Jacqmin, David↗
NASA NTRS1986

On self-preserving, variable-density, turbulent free jets

Published experimental data on incompressible, compresible, free binary, and confined binary turbulent axisymmetric jet flows are compiled and characterized, and the effect of varying turbulent diffusivity across the mixing region of a free jet is investigated analytically, applying the similarity-solution approach of So and Hwang (1986) to the self-preserving region. It is shown that closed-form solutions, represented by Gaussian error functions and having the turbulent Reynolds number and a profile-shape factor as free parameters, can be obtained if the turbulent diffusivities of momentum, mass, or heat are assumed to be different and to vary in both the streamwise and radial directions. An entrainment function uniquely related to the turbulent Reynolds number is derived, and good agreement between theoretical predictions and experimental measurements is demonstrated in graphs.

So, R. M. C.↗
NASA NTRS1987

A theory for turbulent curved wall jets

An attempt is made to formulate the simplest possible model for the flow of a wall jet emanating from a two dimensional source into quiescent surroundings in the presence of a wall of arbitrary shape. The method used self similar profiles for the mean velocity together with a simple eddy viscosity model. The streamwise and radial momentum equations are integrated across the wall jet flow to give an expression for the momentum balance including the effect of the pressure gradient induced by the rate of change of surface curvature. The streamwise momentum equation is also evaluated at the point of maximum velocity to provide a second equation and thereby permit a solution for the two unknown quantities, the jet half width and the maximum velocity. This approach provides approximate closed form solutions for the flow of the wall jet over surfaces of various shapes, and in particular permits a direct comparison with the available experimental results for plane, cylindrical or logarithmic spiral surfaces.

Roberts, Leonard↗
NASA NTRS1993

Trajectory optimization for the National aerospace plane

While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.

Lu, Ping↗
NASA NTRS1998

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗
NASA NTRS1999

Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Markley, F. Landis↗
NASA NTRS1972

Interpolation using surface splines.

A surface spline is a mathematical tool for interpolating a function of two variables. It is based upon the small deflection equation of an infinite plate. The surface spline depends upon the solution of a system of linear equations, and thus, will ordinarily require the use of a digital computer. The closed form solution involves no functions more complicated than logarithms, and is easily coded. Several modifications which can be incorporated are discussed.

Harder, R. L.↗
NASA NTRS1981

Radiative transfer theory for passive microwave remote sensing of random media

The radiative transfer theory is applied to a random medium for the case of passive remote sensing. A general numerical solution with Gaussian quadrature method is studied. For a medium with laminar structure or a medium with cylindrical structure, closed form solutions are obtained by solving the radiative transfer equations of a two-layer random medium. Numerical results for the general case and the two limiting cases are compared.

Chuang, S. L.↗
NASA NTRS1989

A study of composite plates with holes/inclusions

Delamination characterization of a plate with a hole/inclusion is presented. A closed form solution is developed to obtain stresses on the boundary of hole/inclusion in the plate. Once the location with the highest tangential stress is identified, a Finite Element Method analysis of a laminate under tensile loading is considered. The models are presented for the closed form and Finite Element Method. The examples are for (+ or - 35/0/90)s laminate of AS4/3501-6. Tensile, biaxial, and shear loads are considered.

Bense, Ronald↗
NASA NTRS1989

Gravitation- And Conduction-Driven Melting In A Sphere

Simplifying assumptions lead to approximate closed-form solution. Theoretical paper discusses melting of solid sphere in spherical container. Develops mathematical model of melting process, based in part on simplifying assumptions like those used in theories of lubrication and film condensation. Resulting equation for melting speed as function of melting distance solved approximately in closed form.

Bahrami, Parviz A.↗
NASA NTRS1991

Effect of damage on elastically tailored composite laminates

A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.

Armanios, Erian↗
NASA NTRS1972

Influence of discontinuity stresses on main propellant tankage of a space shuttle orbiter.

Derivation of a general closed-form solution for the calculation of local stresses in cylindrical axial load-carrying pressure vessels which are heavily stiffened in the axial direction and circumferentially restrained by closely spaced ring stiffeners. The ring stiffeners are treated as discrete stiffeners and are allowed to have a temperature variation throughout the radial extension of the stiffener and different material properties compared with those of the vessel.

Meyer, H.-R.↗
NASA NTRS1973

Effect of shear on duct wall impedance.

The solution to the equation governing the propagation of sound in a uniform shear layer is expressed in terms of parabolic cylinder functions. This result is used to develop a closed-form solution for acoustic wall impedance which accounts for both the duct liner and the presence of a boundary layer in the duct. The effective wall impedance can then be used as the boundary condition for the much simpler problem of sound propagation in uniform flow.

Goldstein, M.↗
NASA NTRS2016

Spiral Lamber's Problem with Generalized Logarithmic Spirals

Lambert’s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert’s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.\

Roa, Javier↗
NASA NTRS2002

Dynamics of a 4x6-Meter Thin Film Elliptical Inflated Membrane for Space Applications

Dynamic characterization of a thin film inflatable elliptical structure is described in detail. A two-step finite element modeling approach in MSC/NASTRAN is utilized, consisting of (1) a nonlinear static pressurization procedure used to obtain the updated stiffness matrix, and (2) a modal "restart" eigen solution that uses the modified stiffness matrix. Unique problems encountered in modeling of this large Hexameter lightweight inflatable arc identified, including considerable difficulty in obtaining convergence in the nonlinear finite element pressurization solution. It was found that the extremely thin polyimide film material (.001 in or 1 mil) presents tremendous problems in obtaining a converged solution when internal pressure loading is applied. Approaches utilized to overcome these difficulties are described. Comparison of finite element predictions for frequency and mode shapes of the inflated structure with closed-form solutions for a flat pre-tensioned membrane indicate reasonable agreement.

Casiano, Matthew J.↗
NASA NTRS1953

Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

SURFACE CONDITIONS - WING SECTIONS↗
NASA NTRS1954

Impingement of water droplets on wedges and double-wedge airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees r, free stream Mach numbers from 1.1 to 2.0, semiapex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

Serafini, John S↗
NASA NTRS1990

Analytical estimation for static deformation of wire ropes with fibrous core

This paper develops closed-form solutions for the extension of twisted wire ropes with fibrous cores which are subjected to axial forces as well as axial moments. The analytical results are compared with the corresponding numerical results obtained by Costello and Phillips. A close agreement between the two establishes validity of the analytical solutions. Finally, an expression for the effective rigidity modulus of wire ropes with fibrous core is obtained in terms of the helix angle and the number of helical wires in the rope for each of the two end conditions.

Kumar, K.↗