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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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The flight trajectory of aerospace vehicles subject to a class of path constraints is considered. The constrained dynamics is shown to be a natural two-time-scale system. Asymptotic analytical solutions are obtained. Problems of trajectory optimization and guidance can be dramatically simplified with these solutions. Applications in trajectory design for an aerospace plane strongly support the theoretical development.
Previous numerical and experimental studies indicate that the high-temperature heat pipe startup process is characterized by a moving hot zone with relatively sharp fronts. Based on the above observation, a flat-front model for an approximate analytical solution is proposed. A closed-form solution related to the temperature distribution in the hot zone and the hot zone length as a function of time are obtained. The analytical results agree well with the corresponding experimental data, and provide a quick prediction method for the heat pipe startup performance. Finally, a heat pipe limitation related to the frozen startup process is identified, and an explicit criterion for the high-temperature heat pipe startup is derived. The frozen startup limit identified in this paper provides a fundamental guidance for high-temperature heat pipe design.
The motion of a satellite subject to an inverse-square gravitational force of attraction and a perturbation due to the earth's oblateness as the J2 term is analyzed, and a uniform, analytic solution correct to first-order in J2, is obtained using a noncanonical approach. The basis for the solution is the transformation and uncoupling of the differential equations for the model. The resulting solution is expressed in terms of elementary functions of the independent variable (the 'true anomaly'), and is of a compact and simple form. Numerical results are comparable to existing solutions.
A continuum theory is utilized to represent the thermoelastic behavior of a thick walled composite cylinder that can be idealized as transversely isotropic. A multiaxial statement of the constitutive theory employed is presented, as well as the out of the plane of isotropy, plane stress, and plane strain reductions. The derived analytical solution presented is valid for a cylindrical tube or thin disk with a concentric hole, subjected to internal and/or external pressure and a general radial temperature distribution. A specific problem examined is that of a thick walled cylinder subjected to an internal and external pressure loading and a linear radial temperature distribution. The results are expressed in nondimensional form and the effects on the response behavior are examined for various material properties, fiber orientation and types of loadings.
A generalized Yaroshevskii's system of equations is derived for analyzing ballistic entry at supercircular speeds. By an artificial introduction of a small parameter, the nonlinear system can then be integrated by Poincare's method. It is pointed out that the second-order theory displays explicitly the influence of the ballistic coefficient, entry speed, and entry angle on exit conditions. The analytic solution is found to be in excellent agreement with the numerical solution. Using an explicit formula, the critical entry angle at which the vehicle fails to skip out can be predicted to within one hundredth of a degree.
Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.
NASA design teams have been investigating options for "detuning" Ares I to prevent oscillations originating in the vehicle solid-rocket main stage from synching up with the natural resonance of the rest of the vehicle. An experimental work started at NASA MSFC center in 2008 using a damping device showed great promise in damping the vibration level of an 8 resonant tank. However, the mechanisms of the vibration damping were not well understood and there were many unknowns such as the physics, scalability, technology readiness level (TRL), and applicability for the Ares I vehicle. The objectives of this study are to understand the physics of intriguing slosh damping observed in the experiments, to further validate a Computational Fluid Dynamics (CFD) software in propellant sloshing against experiments with water, and to study the applicability and efficiency of the slosh damper to a full scale propellant tank and to cryogenic fluids. First a 2D fluid-structure interaction model is built to model the system resonance of liquid sloshing and structure vibration. A damper is then added into the above model to simulate experimentally observed system damping phenomena. Qualitative agreement is found. An analytical solution is then derived from the Newtonian dynamics for the thrust oscillation damper frequency, and a slave mass concept is introduced in deriving the damper and tank interaction dynamics. The paper will elucidate the fundamental physics behind the LOX damper success from the derivation of the above analytical equation of the lumped Newtonian dynamics. Discussion of simulation results using high fidelity multi-phase, multi-physics, fully coupled CFD structure interaction model will show why the LOX damper is unique and superior compared to other proposed mitigation techniques.
This paper presents a new method for optimizing yaw maneuvers, which are the most common large maneuvers on the International Space Station (ISS). The goal of the maneuver optimization is to find a maneuver trajectory with minimal torques acting on the vehicle during the maneuver. Therefore, the thruster firings necessary to perform the maneuver are minimized. Reduction of thruster firings saves propellant and decreases structural loads and contamination of the vehicle critical elements, thus saving the service life of the thrusters and the vehicle itself. Equations describing the pitch and roll motion needed to counteract the major torques during a yaw maneuver are obtained. Also, a yaw rate profile is suggested. In the obtained optimized case, the torques are significantly reduced. The proposed approximate analytical solution does not require extensive computer resources and, therefore, can be implemented using software onboard the ISS. As a result, the maneuver execution will be automatic. This is one of the major benefits of the simplified solution presented in this paper with respect to existing computational approaches. The suggested maneuver optimization method can be used not only for the ISS, but for other space vehicles as well.
The distribution of ceramic particles in a metal matrix composite material depends primarily on the interaction of the particles with the solid/liquid interface during the solidification process. A numerical model that describes the evolution of the shape of the solid/liquid interface in the proximity of a foreign particle will presented in this paper. The model accounts for the influence of the temperature gradient and the Gibbs-Thomson and disjoining pressure effects. It shows that for the systems characterized by k(sub p) < k(sub L) the disjoining pressure causes the interface curvature to change its sign in the close-contact particle/interface region. It also shows that the increase of the temperature gradient diminishes the effect of the disjoining pressure. The analysis of the numerical results obtained for a large range of processing conditions and materials parameters has led to the development of an analytical solution for the critical velocity of pushing/engulfinent transition. The theoretical results will be discussed and compared with the experimental measurements performed under microgravity conditions.
Description of an analytic trajectory solution for low thrust out of ecliptic mission design based on the two-variable asymptotic expansion technique. A practical steering program utilizing normal thrusting symmetrical about the nodes is assumed. A two-term expansion yields an essentially exact solution of the problem which is in a form suitable for evaluation on small desk-top computers. It is shown that for a circular base orbit at 1 AU, a 15-kw solar electric system with a specific impulse of 3000 sec is capable of delivering an 1100-kg net payload to a heliographic latitude of about 63 deg.
A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.
Analytical representations of the solutions of Kolmogorov's forward (i.e., Fokker-Planck) and backward partial differential equations are obtained by employing Girsanov's (1960) transformation. The equations considered are restricted to those with the drift vector being the gradient of a function and the diffusion matrix being nonsingular and dependent upon time only.
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.
Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.
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.
An analytical satellite theory based on the regular, canonical Poincare-Similar (PS phi) elements is described along with an accurate density model which can be implemented into the drag theory. A computationally efficient manner in which to expand the equations of motion into a fourier series is discussed.
Derivation of an analytical expression for the ballistic density distribution in a planetary exosphere
An analytical model of transient heat transfer in living biological tissue is considered. The model includes storage, generation, conduction, and convective transport of heat in the tissue. Solutions for rectangular and cylindrical coordinates are presented and discussed. Transient times for reaching the ?locally fully developed' temperature profile were found to be of the order of 5 to 25 min. These transients are dominated by a geometrical parameters and, to a lesser extent, by a parameter representing the ratio of heat supplied by blood flow to heat conducted in the tissue.