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NASA NTRS1991

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Korte, John J.↗

NASA NTRS1976

The theory of the gravitational potential applied to orbit prediction

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program listings for computing the geopotential function and the components of its gradient. The use of the geopotential function is illustrated.

Kirkpatrick, J. C.↗

NASA NTRS1972

Stabilization of linear multivariable systems by output feedback.

A method is developed for improving the stability of linear multivariable systems using output feedback. The technique, which utilizes a gradient approach, has been mechanized in a digital computer program. Illustrative results are given for a seven-state two-feedback model of the Saturn V booster.

Mcbrinn, D. E.↗

NASA NTRS1974

The numerical calculation of laminar boundary-layer separation

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

Klineberg, J. M.↗

NASA NTRS1977

Effect of gravity-gradient torques on the dynamics of a spinning spacecraft with telescoping appendages

The effects of gravity-gradient torques during boom deployment maneuvers of a spinning spacecraft are examined with a combination of numerical and analytical methods. It is assumed that the spacecraft consists of a rigid central hub and movable rigid telescoping booms where the booms extend only along the hub principal axes. For the special case of symmetric deployment the stability boundaries are determined and a stability chart is used to study the system behavior. Possible cases of instability during this type of maneuver are identified.

Rajan, M.↗

NASA NTRS1986

Enhancing Centrifugal Separation With Electrophoresis

Separation of biological cells by coil-planet centrifuge enhanced by electrophoresis. By itself, coil-planet centrifuge offers relatively gentle method of separating cells under low centrifugal force in physiological medium that keeps cells alive. With addition of voltage gradient to separation column of centrifuge, separation still gentle but faster and more complete. Since separation apparatus contains no rotary seal, probability of leakage, contamination, corrosion, and short circuits reduced.

Herrmann, F. T.↗

NASA NTRS1982

The 3-D inelastic analysis methods for hot section components: Brief description

Advanced 3-D inelastic structural/stress analysis methods and solution strategies for more accurate yet more cost-effective analysis of components subjected to severe thermal gradients and loads in the presence of mechanical loads, with steep stress and strain gradients are being developed. Anisotropy, time and temperature dependent plasticity and creep effects are also addressed. The approach is to develop four different theories, one linear and three higher order theories (polynomial function, special function, general function). The theories are progressively more complex from linear to general function in order to provide streamlined analysis capability with increasing accuracy for each hot section component and for different parts of the same component according to the severity of the local stress, strain and temperature gradients associated with hot spots, cooling holes and surface coating cracks. To further enhance the computational effectiveness, the higher order theories will have embedded singularities (cooling passages, for example) in the generic modeling region. Each of the four theories consists of three formulation models derivable from independent theoretical formulations. These formulation models are based on: (1) mechanics of materials; (2) special finite elements; and (3) an advanced formulation to be recommended by the contractor.

Chamis, C. C.↗

NASA NTRS1985

Contributions on the Subject of Longitudinal Movements of Aircraft in Wind Shears

The effect of downburst-type wind shears on the longitudinal dynamic behavior of an unguided aircraft is simulated numerically on the basis of published meteorological data and the flight characteristics of an A300-B passenger jet. The nonlinear differential equations of the aircraft motion are linearized by conventional methods, and the wind effects are introduced via the linear derivatives of the wind components referred to the wind gradients to obtain simplified technical models of the longitudinal response to all possible types of constant-gradient wind shears during the first 20-60 sec. Graphs, maps, and diagrams are provided, and a number of accidents presumed to have involved wind shears are analyzed in detail.

Krauspe, P.↗

NASA NTRS1984

Convergent-tapered annular seals - Analysis and testing for rotordynamic coefficients

A combined analytical-computational method has been developed to calculate the pressure field and dynamic coefficients for tapered high-pressure annular seals. Completely developed turbulent flow is assumed in both the circumferential and axial directions, according to Hirs' (1973) bulk-flow turbulent-lubrication equations. In a numerical experiment with the method, a short bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients of the seal. Numerical results of the integration are compared with previous results for straight and tapered seals. It is found that direct stiffness and leakage coefficients increase in the present seal, while the remaining coefficients decrease. An optimal taper angle is shown to exist with respect to: (1) the direct stiffness and (2) the ratio of direct stiffness to leakage. On the basis of the optimal taper angle calculations, stiffness increases on the order of 40 to 50 percent are predicted. Experimental results for three taper angles are presented, and are found to be in good agreement with the theoretical predictions.

Childs, D. W.↗

NASA NTRS1989

Airborne measurements of stratospheric constituents over Antarctica in the austral spring 1987. I - Method and ozone observations

A Fourier transform spectrometer was flown aboard a DC-8 on 10 flights over Antarctica during August and September, 1987, as part of the Airborne Antarctic Ozone Experiment (AAOE). Observing the sun at infrared wavelengths, it was possible to determine the integrated column amount above the flight altitude for ozone and a number of other chemical species that are believed to be important in the perturbed chemistry of the 'ozone hole'. The paper describes the method, the observations, the data analysis procedure, and the ozone results. During the observation period, ozone developed a steep gradient near the edge of the polar vortex; deep within the vortex, the average ozone column decreased by about 1.6 percent per day during September.

Mankin, William G.↗

NASA NTRS1991

An experimental study of wall adaptation and interference assessment using Cauchy integral formula

This paper summarizes the results of an experimental study of combined wall adaptation and residual interference assessment using the Cauchy integral formula. The experiments were conducted on a supercritical airfoil model in the Langley 0.3-m Transonic Cryogenic Tunnel solid flexible wall test section. The ratio of model chord to test section height was about 0.7. The method worked satisfactorily in reducing the blockage interference and demonstrated the primary requirement for correcting for the blockage effects at high model incidences to correctly determine high lift characteristics. The studies show that the method has potential for reducing the residual interference to considerably low levels. However, corrections to blockage and upwash velocities gradients may still be required for the final adapted wall shapes.

Murthy, A. V.↗

NASA NTRS1992

Visoelastic relaxation of Venusian coronae and mountain belts: Constraints on global heat flow and tectonism

Venus differs from Earth in that water is essentially absent and its surface temperatures are about 470 K higher. The competing effects of high surface temperature and dry lithologies on the long-term history of surface topography have been studied using the finite-element method. The relaxation history of surface topographic features, such as coronae and mountain belts, is a function of thermal gradient, crustal thickness and lithology, regional stresses, and basal tractions applied to the lithosphere. In this study, we have examined the relative effects of these factors over a period of 500 Ma (presumed to be the mean age of the venusian surface).

Duncan, I.↗

NASA NTRS1993

Conjugate-Gradient Neural Networks in Classification of Multisource and Very-High-Dimensional Remote Sensing Data

Application of neural networks to classification of remote sensing data is discussed. Conventional two-layer backpropagation is found to give good results in classification of remote sensing data but is not efficient in training. A more efficient variant, based on conjugate-gradient optimization, is used for classification of multisource remote sensing and geographic data and very-high-dimensional data. The conjugate-gradient neural networks give excellent performance in classification of multisource data, but do not compare as well with statistical methods in classification of very-high-dimentional data.

Benediktsson, J. A.↗

NASA NTRS2000

Magnetic Susceptibility Effects and Lorentz Damping in Diamagnetic Fluids

A great number of crystals (semi-conductor and protein) grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity and g-jitter. Both static and dynamic (rotating or travelling wave) magnetic fields can be used to reduce the effects of convection in materials processing. In semi-conductor melts, due to their relatively high electrical conductivity, the induced Lorentz force can be effectively used to curtail convective effects. In melts/solutions with reduced electrical conductivity, such as aqueous solutions used in solution crystal growth, protein crystal growth and/or model fluid experiments for simulating melt growth, however, the variation of the magnetic susceptibility with temperature and/or concentration can be utilized to better damp fluid convection than the Lorentz force method. This paper presents a comprehensive, comparative numerical study of the relative damping effects using static magnetic fields and gradients in a simple geometry subjected to a thermal gradient. The governing equations are formulated in general terms and then simplified for the numerical calculations. Operational regimes, based on the best damping technique for different melts/solutions are identified based on fluid properties. Comparisons are provided between the numerical results and available results from experiments in surveyed literature.

Ramachandran, Narayanan↗

NASA NTRS2013

NanoTHOR: Low-Cost Launch of Nanosatellites to Deep Space

The rapid development of high-performance nanosatellite platforms is enabling NASA and commercial ventures to consider performing missions to the asteroids, the Moon, and Mars at lower cost and on shorter timelines than traditional large spacecraft platforms. Currently, however, opportunities to launch secondary payloads to Earth escape are rare, and using chemical rockets to propel secondary payloads from LEO rideshares to escape is problematic due to the risks posed to primary payloads. The NanoTHOR effort has explored the technical feasibility and value proposition for using a simple momentum-exchange tether system to scavenge orbital energy from an upper stage in geostationary transfer orbit in order to boost nanosatellites to Earth escape. A NanoTHOR module will accomplish rapid transfer of a nanosatellite to an escape trajectory by deploying the nanosat at the end of a long, slender, high-strength tether and then using winching in the Earth's gravity!gradient to convert orbital angular momentum into rotational angular momentum. In the Phase I effort, we developed and simulated methods for controlling tether deployment and retraction to spin up a tether system, and these simulations demonstrated the feasibility of providing delta-Vs on the order of 800 m/s with a simple, low-mass tether system. Moreover, the NanoTHOR tether can act as a reusable in-space upper stage, boosting multiple nanosatellites on a single launch and doing so with a mass requirement lower than that of conventional rocket technologies. Serving as an escape-injection stage, NanoTHOR can enable a 6U CubeSat to deliver small payloads to Mars orbit, lunar orbit, and rendezvous with at least 110 of the known near-Earth asteroids. Evaluation of the technology readiness of the component technologies required for NanoTHOR indicate that the hardware required is all mid-TRL, and the lower-TRL controls and integration components can be advanced to mid-TRL with modest investment. By scavenging orbital energy from upper stages without any stored energy or propellant requirements, NanoTHOR permits deep-space nanosat missions to launch on rideshare opportunities, enabling NASA and commercial ventures to conduct affordable and frequent missions to explore deep space destinations.

Hoyt, Robert↗

NASA NTRS1996

Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape

Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.

Canright, David↗

NASA NTRS1988

Finite element substructuring methods for composite mechanics

Finite element substructuring strategies are presented to obtain numerical solutions for three typical problems of interest to the composites community: (1) impact and toughness characterization of composites using Charpy's impact test specimen; (2) free-edge stress analysis of composite laminates; and (3) fracture toughness predictions of composites for individual and combined fracture of modes I, II, and III. The key issue common to these problems is the presence of singular or near singular stress fields. The regions prone to see steep stress gradients are substructured with progressively refined meshes to study the local response simultaneously with the global response. The results from the select examples indicate that finite element substructuring methods are computationally effective for composite singularity mechanics.

Murthy, Pappu L. N.↗

NASA NTRS1988

Finite element substructuring methods for composite mechanics

Murthy, P. L. N.↗