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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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Improved Data Reduction Algorithm for the Needle Probe Method Applied to In-Situ Thermal Conductivity Measurements of Lunar and Planetary Regoliths

The needle probe method (also known as the' hot wire' or 'line heat source' method) is widely used for in-situ thermal conductivity measurements on soils and marine sediments on the earth. Variants of this method have also been used (or planned) for measuring regolith on the surfaces of extra-terrestrial bodies (e.g., the Moon, Mars, and comets). In the near-vacuum condition on the lunar and planetary surfaces, the measurement method used on the earth cannot be simply duplicated, because thermal conductivity of the regolith can be approximately 2 orders of magnitude lower. In addition, the planetary probes have much greater diameters, due to engineering requirements associated with the robotic deployment on extra-terrestrial bodies. All of these factors contribute to the planetary probes requiring much longer time of measurement, several tens of (if not over a hundred) hours, while a conventional terrestrial needle probe needs only 1 to 2 minutes. The long measurement time complicates the surface operation logistics of the lander. It also negatively affects accuracy of the thermal conductivity measurement, because the cumulative heat loss along the probe is no longer negligible. The present study improves the data reduction algorithm of the needle probe method by shortening the measurement time on planetary surfaces by an order of magnitude. The main difference between the new scheme and the conventional one is that the former uses the exact mathematical solution to the thermal model on which the needle probe measurement theory is based, while the latter uses an approximate solution that is valid only for large times. The present study demonstrates the benefit of the new data reduction technique by applying it to data from a series of needle probe experiments carried out in a vacuum chamber on JSC-1A lunar regolith stimulant. The use of the exact solution has some disadvantage, however, in requiring three additional parameters, but two of them (the diameter and the volumetric heat capacity of the probe) can be measured and the other (the volumetric heat capacity of the regolith/stimulant) may be estimated from the surface geologic observation and temperature measurements. Therefore, overall, the new data reduction scheme would make in-situ thermal conductivity measurement more practical on planetary missions.

JSC-1A↗
NASA NTRS1992

Crack-mouth displacements for semielliptical surface cracks subjected to remote tension and bending loads

The exact analytical solution for an embedded elliptical crack in an infinite body subjected to arbitrary loading was used in conjunction with the finite element alternating method to obtain crack-mouth-opening displacements (CMOD) for surface cracks in finite plates subjected to remote tension. Identical surface-crack configurations were also analyzed with the finite element method using 20-noded element for plates subjected to both remote tension and bending. The CMODs from these two methods generally agreed within a few percent of each other. Comparisons made with experimental results obtained from surface cracks in welded aluminum alloy specimens subjected to tension also showed good agreement. Empirical equations were developed for CMOD for a wide range of surface-crack shapes and sizes subjected to tension and bending loads. These equations were obtained by modifying the Green-Sneddon exact solution for an elliptical crack in an infinite body to account for finite boundary effects. These equations should be useful in monitoring surface-crack growth in tests and in developing complete crack-face-displacement equations for use in three-dimensional weight-function methods.

Raju, Ivatury S.↗
NASA NTRS1961

An Analysis of Exact and Approximate Equations for the Temperature Distribution in an Insulated Thick Skin Subjected to Aerodynamic Heating

The problem of calculating the temperature distribution in an insulated slab is investigated. Exact and approximate solutions are obtained, and the results are compared to determine the ranges of applicability of the approximations. The approximations are found to be within 5 percent of the exact solution when the ratio of the thermal capacitance of the metal to that of the insulation and the ratio of the conductance of the metal to that of the insulation are sufficiently large. The roots of the characteristic equation of the exact solution are generally applicable to the two-slab heat-transfer problem and are tabulated up to the first nine roots.

Harris, Robert S., Jr.↗
NASA NTRS1990

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Hall, Philip↗
NASA NTRS1959

Details of Exact Low Prandtl Number Boundary-Layer Solutions for Forced and For Free Convection

A detailed report is given of exact (numerical) solutions of the laminar-boundary-layer equations for the Prandtl number range appropriate to liquid metals (0.003 to 0.03). Consideration is given to the following situations: (1) forced convection over a flat plate for the conditions of uniform wall temperature and uniform wall heat flux, and (2) free convection over an isothermal vertical plate. Tabulations of the new solutions are given in detail. Results are presented for the heat-transfer and shear-stress characteristics; temperature and velocity distributions are also shown. The heat-transfer results are correlated in terms of dimensionless parameters that vary only slightly over the entire liquid-metal range. Previous analytical and experimental work on low Prandtl number boundary layers is surveyed and compared with the new exact solutions.

Sparrow, E. M.↗
NASA NTRS1990

A two-step iterative method for evolving nonlinear acoustic systems to a steady-state

A new approach for evolving two-dimensional nonlinear acoustic systems with flow to a steady state is presented. The approach is a two-step iterative method which is tested on a benchmark acoustic problem for which an exact analytical solution is available. Results are also calculated for a nonlinear acoustic problem for which an exact analytical solution is not known. Results indicate that the two-step method represents a powerful, efficient, and stable method for evolving two-dimensional acoustic systems to a steady state, and that the method is applicable to any number of spatial dimensions and to other hyperbolic systems. It is noted that for the benchmark problem only a single iteration on the method is required when the transient and steady-state field are of the same order of magnitude; however, four iterations are required when the steady-state field is several orders of magnitude smaller than the transient field. This method requires six iterations before achieving a steady state for the nonlinear test problem.

Watson, Willie R.↗
NASA NTRS1991

Exact and explicit optimal solutions for trajectory planning and control of single-link flexible-joint manipulators

An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.

Chen, Guanrong↗
NASA NTRS1994

Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.

Liu, Jiwen↗
NASA NTRS1991

Using trees to compute approximate solutions to ordinary differential equations exactly

Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

Grossman, Robert↗
NASA NTRS1991

Implementation of wall boundary conditions for transpiration in F3D thin-layer Navier-Stokes code

Numerical boundary conditions for mass injection/suction at the wall are incorporated in the thin-layer Navier-Stokes code, F3D. The accuracy of the boundary conditions and the code is assessed by a detailed comparison of the predictions of velocity distributions and skin-friction coefficients with exact similarity solutions for laminar flow over a flat plate with variable blowing/suction, and measurements for turbulent flow past a flat plate with uniform blowing. In laminar flow, F3D predictions for friction coefficient compare well with exact similarity solution with and without suction, but produces large errors at moderate-to-large values of blowing. A slight Mach number dependence of skin-friction coefficient due to blowing in turbulent flow is computed by F3D code. Predicted surface pressures for turbulent flow past an airfoil with mass injection are in qualitative agreement with measurements for a flat plate.

Kandula, M.↗
NASA NTRS1974

Aligned magnetohydrodynamic solution for solar wind flow past the earth's magnetosphere

Exact numerical solutions of the MHD equations for a perfect dissipationless gas with aligned magnetic field are given for conditions representative of steady supersonic solar wind flow past an axisymmetric model of the earth's magnetosphere. The solution is based on use of a transformation that relates without approximation the equations of magnetohydrodynamics to those of gasdynamics of a pseudogas that has an unusual equation of state. The results confirm the applicability of the previously existing gasdynamic solutions for the typically modest intensities of the interplanetary magnetic field that lead to Alfven Mach numbers of about 10 or greater. For smaller values, however, significant effects are indicated with the flanks of the bow wave moving away from the earth and the nose moving toward the earth. The results are consistent with direct observations in space.

Spreiter, J. R.↗
NASA NTRS1980

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

Redekopp, L. G.↗
NASA NTRS1976

A high order theory for uniform and laminated plates

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.

Lo, K. H.↗
NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗
NASA NTRS1977

Simple analytical solutions for spherically symmetric production and modulation of energetic solar particles

Exact analytical solutions are presented for the standard time-independent spherically symmetric convection-diffusion-adiabatic deceleration equation governing the transport of cosmic rays in the interplanetary medium for the case in which particles are produced with spherical symmetry at the sun. It is assumed that the solar-wind speed is constant and radial, and that the spatial diffusion coefficient has a power-law dependence on momentum. The Green's function describing the modulation of a monoenergetic production of particles is presented. The solutions provide a useful basis for the study of time-integrated properties of energetic solar-flare particle spectra.

Gross, M. W.↗
NASA NTRS1972

Bounding filter - A simple solution to lack of exact a priori statistics.

Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.

Nahi, N. E.↗
NASA NTRS1976

A higher order panel method for linearized supersonic flow

A higher order panel method using linearly varying source and quadratically varying doublet distributions for computing linearized supersonic flow over arbitrary wings and bodies is described. With tangential mass flux boundary conditions on circular cones at angles of attack, the source panel method gave pressure distributions which are in excellent agreement with exact nonlinear theory. The numerical source panel method was demonstrated to be very stable by randomly panelling an axially symmetric body. For wings with thickness and camber, both the source and doublet panel methods yield excellent agreement with exact linearized solutions. Computational experiments indicate that the use of exact surface paneling in lieu of linearized boundary conditions for wings provides better agreement with higher order theory and with experiment.

Ehlers, F. E.↗