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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

System noise analysis of the dumbbell tethered satellite for gravity-gradient measurements

An analysis of the dumbbell gravity gradiometer concept for measuring short wavelength variations in the earth's gravity gradient is presented. Variations in the gradient are recorded by measuring tension variations in a vertically stabilized satellite consisting of heavy masses connected by a long wire or rod. Tension noise arises from the excitation of various mechanical oscillations of the system. The principal noise sources that were identified are fluctuations in atmospheric drag heating and drag force resulting from density variations and winds. Approximate analytical expressions are presented for the tension noise as a function of the system design parameters for various possible configurations. Computer simulations using numerical integration were performed to study the tension noise for several sample cases. Three designs consistent with Shuttle launch capabilities are discussed.

Colombo, G.↗
NASA NTRS1991

Analysis of the fluid flow and heat transfer in a thin liquid film in the presence and absence of gravity

The hydrodynamic and thermal behavior of a thin liquid film flowing over a solid horizontal surface is analyzed for both plane and radially spreading flows. The situations where the gravitational force is completely absent and where it is significant are analyzed separately and their practical relevance to a micro-gravity environment is discussed. In the presence of gravity, in addition to Reynolds number, the Froude number of the film is found to be an important parameter that determines the supercritical and subcritical flow regimes and any associated hydraulic jump. A closed-form solution is possible under some flow situations, whereas others require numerical integration of ordinary differential equations. The approximate analytical results are found to compare well with the available two-dimensional numerical solutions.

Rahman, M. M.↗
NASA NTRS1983

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗
NASA NTRS1984

Application of numerical optimization to rotor aerodynamic design

Based on initial results obtained from the performance optimization code, a number of observations can be made regarding the utility of optimization codes in supporting design of rotors for improved performance. (1) The primary objective of improving the productivity and responsiveness of current design methods can be met. (2) The use of optimization allows the designer to consider a wider range of design variables in a greatly compressed time period. (3) Optimization requires the user to carefully define his problem to avoid unproductive use of computer resources. (4) Optimization will increase the burden on the analyst to validate designs and to improve the accuracy of analysis methods. (5) Direct calculation of finite difference derivatives by the optimizer was not prohibitive for this application but was expensive. Approximate analysis in some form would be considered to improve program response time. (6) Program developement is not complete and will continue to evolve to integrate new analysis methods, design problems, and alternate optimizer options.

Pleasants, W. A., III↗
NASA NTRS1986

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Liou, M.-S.↗
NASA NTRS1993

A variable-order laminated plate theory based on the variational-asymptotical method

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Lee, Bok W.↗
NASA NTRS1997

Thermal Radiation Effects Analyzed in Translucent Composite and Thermal Barrier Coating

Ceramic parts and coatings are needed to withstand high temperatures in advanced aircraft engines. In hot environments, such as in the combustion chambers of these engines, infrared and visible radiation can penetrate into some ceramics and heat them internally. The internal temperatures depend on radiative effects combined with heat conduction, and on convection and radiation at the material boundaries. Since engine temperatures are high, radiant emission can be large from within translucent parts and coatings, and this must be included in the analysis. Transient and steady-state behavior are both important. During a transient, radiant penetration provides more rapid internal heating than conduction alone, and the temperature distributions are usually considerably different than for steady-state conditions; this can produce transient thermal stresses. Analytical and numerical methods are being used at the NASA Lewis Research Center to predict transient temperatures and heat flows in translucent materials. A transient analysis was done for a composite of two translucent layers. The layer refractive indices were larger than 1, producing internal reflections at the boundaries and at the internal interface. In addition, steady-state results were computed for a two-layer composite with one layer opaque. The results were used to assess the importance of internal radiation in a zirconia thermal barrier coating on a cooled metal wall. Since the radiative transfer equations are rather complex, especially when internal scattering is included, approximate methods are being investigated that might be convenient for computer design programs. An approximate two-flux method was used and verified by comparisons with solutions that used exact radiative transfer relations. The two-flux equations include scattering without increasing solution difficulty.

Siegel, Robert↗
NASA NTRS1967

Matrix Analysis of Longitudinal and Torsional Vibrations in Nonuniform Multibranch Beams

Since longitudinal modes and frequencies provide basic data for dynamic analyses of arbitrary beam-like structures and since closed-form solutions for the modes are generally not feasible to obtain, an approximate method is developed for computing the natural frequencies and the corresponding mode shapes for a variable-section, unconstrained multibranch beam. A lumped mass analogy employing influence coefficients is used to represent the beam. The simultaneous equations of motion for the lumped mass system are derived in matrix form and algebraically manipulated to yield a classical eigenvalue equation solvable by standard procedures. The orthogonality relationship of the natural modes is derived and used to form the basis of an orthogonal sweeping process for determination of modes above the fundamental. Numerical examples including an application to a solid-fuel launch system are presented. Also, a detailed discussion is devoted to the theoretical verifications of the approximate modes and frequencies.

Wingate, Robert T.↗
NASA NTRS1994

Two-fluid simulations of galaxy formation

We investigate the formation of galaxies and larger structure with a simulation modeling two gravitationally coupled fluids representing dark matter and baryons. The baryon gas dynamics are calculated with a smoothed particle hydrodynamics (SPH) method, and the physics modeled includes thermal pressure, shock heating, and radiative cooling. We simulate a 16 Mpc periodic cube with 64(exp 3) particles in each fluid and 10% baryon mass fraction. We confirm, for the first time experimentally, disk formation as a natural consequence of hierarchical clustering in a large-scale cosmological environment. The majority of isolated galaxies exhibit centrifugally supported disks. A power-law relation between cold baryonic mass and maximum rotation velocity is found, M varies as nu(sub rot)(exp alpha) with alpha = 2.5 after correcting for differential numerical resolution. Both the spatial and velocity distributions of the simulated galaxies are biased with respect to the dark matter. A counts-in-cells analysis indicates that an unphysical degree of merging in the central cluster is likely responsible for the antibias signal in the correlation function. A robust, scale-dependent velocity bias is measured. The ratio of galaxy to dark matter pairwise velocity dispersions on a scale of 1 Mpc is 0.7. The amplitude is only mildly dependent on redshift or mass cutoff and scales with separation as r(exp 0.2). The degree to which these results depend on numerical parameters is discussed. Mass resolution plays a key role in controlling the resulting fraction of cold, dense baryons. The mass fraction associated with galaxies decreases by a factor of approximately greater than 3 when the mass per particle is increased by a factor 8. Photoionization and energy input from supernova will have to be included to determine more carefully the fraction of highly dissipated material and the characteristics of the stellar component of galaxies.

Evrard, August E.↗
NASA NTRS2008

Adjoint-Based Methodology for Time-Dependent Optimization

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Yamaleev, N. K.↗
NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) is described for fitting single-input single-output transfer function models to empirical frequency response data. The program is interactive in that the user specifies ``elementary factors'' (gain, delay, pure differentiators and integrators, and first- and second-order zeros and poles) by entering numerical values or moving sliders in a graphical user interface. A nonlinear optimization can then be performed to obtain maximum likelihood estimates of transfer function parameters and uncertainties to provide feedback on the modeling and refine estimates. Several examples are discussed, including the identification of aircraft pitch dynamics from simulation data and data reported in the literature, approximating Theodorsen's function of unsteady aerodynamics, and obtaining a reduced-order model of a computational fluid dynamics code describing the unsteady aerodynamics around an aeroelastic wing. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and simple system identification problems. The program was written in MATLAB and is planned for public release through the NASA Software Catalog.

System identification↗
NASA NTRS1985

Probabilistic Structural Analysis Theory Development

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Burnside, O. H.↗
NASA NTRS2000

Numerical Calculation of the Drag Force Acting on an Insoluble Particle Moving in Front of a Solidifying Interface

The distribution of insoluble particles in a metal casting depends primarily on the interaction of the particles with the solid/liquid interface (SLI) during the solidification process. Whether a particle will be engulfed or continuously pushed by SLI is essentially determined by the balance of forces acting on the particle. An important component of this force balance is the drag force generated by the particle motion in front of the SLI. Previously developed mathematical models for particle/SLI interaction made use of steady-state solutions of this force provided by the lubrication theory. However, our numerical model based on the SLI tracking approach shows that not only the steady-state approach is inappropriate to model the interaction process but also that even at steady-state the theoretical solution underestimates the drag force. A regression analysis of steady-state numerical solutions for cylindrical particles moving normal to a flat SLI gave a relationship of the form F(sub d) (exp num) = (square root of 3) pi eta V(sub p)((R(sub p) / d) (exp 10 gamma/3)) as compared to the theoretical solution F(sub d) (exp theor) = 3 X (square root of 2) pi eta V(sub p)((R(sub p) / d) (exp 3/2)) where F(sub d) is the drag force, eta is the dynamic viscosity of the fluid, V(sub p) is the particle velocity, R(sub p) is the particle radius, gamma is Euler's constant (gamma is approximately equal to 0.577), and d is the width of the gap between the particle and the SLI. Model validation as well as the influence of the interface shape on the value of F(sub d) will also be discussed.

Catalina, Adrian V.↗
NASA NTRS1974

Theoretical and observational analysis of spacecraft fields

In order to investigate the dipolar and nondipolar contributions of spacecraft magnetic fields, a simple magnetic field model is proposed. This model consists of a number N of randomly oriented dipoles of strength M sub k in a given volume. Two sets of formulas are presented that give the rms multipole field components, first, for isotropic orientations of the dipoles at given positions and second, for isotropic orientations of the dipoles distributed uniformly throughout a cube or sphere. The statistical results for a cube (8 cu m in size) together with individual examples computed numerically show the following features. Beyond about 2- to 3-m distance from the center of the cube the field is dominated by an equivalent dipole. The magnitude of the magnetic moment of the dipolar part is approximated by N to the 1/2 power times M for equal magnetic moments or generally by the Pythagorean sum of the dipole moments. The radial component tend to be greater than either of the transverse components for the dipole portion as well as for the nondipolar field contributions.

Neubauer, F. M.↗
NASA NTRS1977

Velocity and temperature distributions of coal-slag layers on magnetohydrodynamic generators walls

Approximate analytical expressions are derived for the velocity and temperature distributions in steady state coal slag deposits flowing over MHD generator walls. Effects of slag condensation and Joule heating are included in the analysis. The transport conditions and the slag temperature at the slag-gas interface are taken to be known parameters in the formulation. They are assumed to have been predetermined either experimentally or from the slag properties and the gas dynamic calculations of the free stream flow. The analysis assumes a power law velocity profile for the slag and accounts for the coupling between the energy and momentum conservation equations. Comparisons are made with the more exact numerical solutions to verify the accuracy of the results.

Pian, C. C. P.↗
NASA NTRS1981

Manufacturing in space: Fluid dynamics numerical analysis

Natural convection in a spherical container with cooling at the center was numerically simulated using the Lockheed-developed General Interpolants Method (GIM) numerical fluid dynamic computer program. The numerical analysis was simplified by assuming axisymmetric flow in the spherical container, with the symmetry axis being a sphere diagonal parallel to the gravity vector. This axisymmetric spherical geometry was intended as an idealization of the proposed Lal/Kroes growing experiments to be performed on board Spacelab. Results were obtained for a range of Rayleigh numbers from 25 to 10,000. For a temperature difference of 10 C from the cooling sting at the center to the container surface, and a gravitional loading of 0.000001 g a computed maximum fluid velocity of about 2.4 x 0.00001 cm/sec was reached after about 250 sec. The computed velocities were found to be approximately proportional to the Rayleigh number over the range of Rayleigh numbers investigated.

Robertson, S. J.↗
NASA NTRS2010

Simple Check Valves for Microfluidic Devices

A simple design concept for check valves has been adopted for microfluidic devices that consist mostly of (1) deformable fluorocarbon polymer membranes sandwiched between (2) borosilicate float glass wafers into which channels, valve seats, and holes have been etched. The first microfluidic devices in which these check valves are intended to be used are micro-capillary electrophoresis (microCE) devices undergoing development for use on Mars in detecting compounds indicative of life. In this application, it will be necessary to store some liquid samples in reservoirs in the devices for subsequent laboratory analysis, and check valves are needed to prevent cross-contamination of the samples. The simple check-valve design concept is also applicable to other microfluidic devices and to fluidic devices in general. These check valves are simplified microscopic versions of conventional rubber- flap check valves that are parts of numerous industrial and consumer products. These check valves are fabricated, not as separate components, but as integral parts of microfluidic devices. A check valve according to this concept consists of suitably shaped portions of a deformable membrane and the two glass wafers between which the membrane is sandwiched (see figure). The valve flap is formed by making an approximately semicircular cut in the membrane. The flap is centered over a hole in the lower glass wafer, through which hole the liquid in question is intended to flow upward into a wider hole, channel, or reservoir in the upper glass wafer. The radius of the cut exceeds the radius of the hole by an amount large enough to prevent settling of the flap into the hole. As in a conventional rubber-flap check valve, back pressure in the liquid pushes the flap against the valve seat (in this case, the valve seat is the adjacent surface of the lower glass wafer), thereby forming a seal that prevents backflow.

Willis, Peter A.↗
NASA NTRS1990

Numerical derivative techniques for trajectory optimization

The adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.

Hallman, Wayne P.↗