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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Effective treatments of the singular line boundary problem for three dimensional grids

The axis singularity problem for 3D blunt body flows is examined. Two techniques of eliminating the axis-singularity difficulty are presented for utilization with finite-difference codes: (1) the 3D Navier-Stokes equations are reformulated utilizing a redefined Jacobian that is nonzero at the singular line, and (2) the 3D Navier-Stokes equations are solved using the Roe flux-difference splitting technique with a finite-volume based method for evaluation of the grid Jacobian and the metrics, and appropriate boundary conditions. Real-gas and viscous computations are also presented, demonstrating the generality of the two methods.

Palmer, Grant↗
NASA NTRS1970

Constant directions of the Riccati equation

A constant direction of the Riccati equation associated with a class of singular discrete-time optimization problems is defined. The set of constant directions is completely characterized using a control viewpoint. Constant directions are used to reduce the computational complexity of the optimal system. Application to optimal filtering in colored noise is given.

Rappaport, D.↗
NASA NTRS1975

Prediction of unsteady aerodynamic loadings caused by leading edge and trailing edge control surface motions in subsonic compressible flow: Analysis and results

A theoretical analysis and computer program was developed for the prediction of unsteady lifting surface loadings caused by motions of leading edge and trailing edge control surfaces having sealed gaps. The final form of the downwash integral equation was formulated by isolating the singularities from the nonsingular terms and using a preferred solution process to remove and evaluate the downwash discontinuities in a systematic manner. Comparisons of theoretical and experimental pressure data are made for several control surface configurations. The comparisons indicate that reasonably accurate theoretical pressure distributions and generalized forces may be obtained for a wide variety of control surface configurations. Spanwise symmetry or antisymmetry of motion, and up to six control surfaces on each half span can be accommodated.

Rowe, W. S.↗
NASA NTRS1976

Viscid-inviscid interaction of incompressible separated flows

A flow model has been devised to deal with the viscid-inviscid interaction of a class of two-dimensional incompressible separated flow problems. It is suggested that the corresponding inviscid flow of these problems is described by the free streamline theory with few unspecified parameters and their values are, in turn, determined by the viscous flow considerations. The problem of a flow past a backward facing step is selected for study in detail. The viscous flow components of turbulent jet mixing, recompression, and reattachment are delineated and studied individually. When they are later combined, it is found that the point of reattachment behaves as a saddle-point-type singularity in the system of differential equations describing the viscous flow process. This feature is employed to the determination of the aforementioned free parameters and thus the establishment of the overall corresponding inviscid flow field. The resulting base pressure coefficient for the specific case agrees reasonably well with the available experimental data.

Chow, W. L.↗
NASA NTRS1984

Thermal ripples in a resistive and radiative instability

The development of the resistive tearing instability in the case of sheared magnetic fields is considered, taking into account also the occurrence of a radiatively driven thermal instability. It is pointed out that thermal conduction has generally been neglected in theories similar to those discussed. The present investigation is concerned with a consideration of both parallel and perpendicular thermal conduction, in addition to finite resistivity and radiative loss. Attention is given to the equations and the model, the spatial singularity which arises with consideration of only the parallel heat conduction, the removal of this singularity and the formation of temperature oscillations (thermal ripples) by inclusion of the perpendicular heat-flux component, and details regarding the numerical procedure. A brief explanation is provided of the conditions required for the oscillations, and potential implications of the results with respect to the solar flare are discussed.

Steinolfson, R. S.↗
NASA NTRS1985

Backward boundary layers in downward flame spread

The gas-phase combustion of a vertical fuel slab pyrolyzing at a finite rate under downward flame spread conditions is investigated theoretically. The backward boundary layer character of the flow is exploited, and a transformation that shifts the singularity associated with boundary-layer equations to a location, upstream of flame lift-off, where the surface temperature is nearly ambient, is employed. The boundary-layer flow is matched asymptotically for large Grashof number to a potential flow that allows the flow induced by the flame and along the upstream surface of the fuel bed to be calculated. Gas-phase temperature and velocity predictions are compared to experiment, and although analysis of the gas phase is emphasized, an approximate spread rate, based on a solid-phase energy balance, is calculated.

Vedha-Nayagam, M.↗
NASA NTRS1992

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Wu, Xuesong↗
NASA NTRS2000

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Ballabrera-Poy, Joaquim↗
NASA NTRS2000

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Ballabrera-Poy, J.↗
NASA NTRS1990

Lower solar chromosphere-corona transition region. I - Theoretical models with small temperature gradients

A study of transition region models including the effects of classical thermal conduction, heating, and radiative cooling is carried out with attention directed toward the problem of understanding the observed emission in the lower transition region. It is found that the observationally inferred emission measure curve implies a near-balance between heating and radiative cooling in the lower transition region, and that the presence of strong hydrogen Ly-alpha cooling leads to the existence of singularities in the solutions of the force balance and energy balance equations when such a near-balance between heating and cooling is assumed. These singularities place strong constraints on the nature of viable models of the lower transition region and must be considered when Ly-alpha cooling is important. Previously suggested explanations of the observed emission from the lower transition region are considered in the context of the results of the present study, and conditions for the applicability of these suggested explanations are discussed.

Woods, D. Tod↗
NASA NTRS1981

Computation of unsteady turbulent boundary layers with flow reversal and evaluation of two separate turbulence models

A procedure which solves the governing boundary layer equations within Keller's box method was developed for calculating unsteady laminar flows with flow reversal. This method is extended to turbulent boundary layers with flow reversal. Test cases are used to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. Turbulent flow calculations are performed. The governing equations for both models are solved. As in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. Predictions of both turbulence models are the same for all practical purposes.

Cebeci, T.↗
NASA NTRS1973

Low-thrust trajectory analysis for the geosynchronous mission

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

Jasper, T. P.↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Condensation modes in magnetized cylindrical plasmas

In order to understand the formation and stability of solar prominences, attention is given to the condensation modes of the thermal instability in a cylindriical plasma whose magnetic field has both potential (longitudinal) and nonpotential (poloidal) components forming helically twisted field lines. It is noted that the field line twist has a significant effect on the stability of condensation modes which are unstable if field lines are straight, but become stable as the twist increases. The problem is treated in a fully self-consistent way, to derive a second-order ordinary differential equation for radiative MHD stability. The approximation made by neglecting inertial terms is valid for coronal loop conditions if there is no singular surface in the plasma, and a simplified differential equation is derived. Attention is given to stability for the m = zero, 1, and 2 modes numerically, for various loop parameters.

An, C.-H.↗
NASA NTRS1985

Kinematic rate control of simulated robot hand at or near wrist singularity

A robot hand should obey movement commands from an operator on a computer program as closely as possible. However, when two of the three rotational axes of the robot wrist are colinear, the wrist loses a degree of freedom, and the usual resolved rate equations (used to move the hand in response to an operator's inputs) are indeterminant. Furthermore, rate limiting occurs in close vicinity to this singularity. An analysis shows that rate limiting occurs not only in the vicinity of this singularity but also substantially away from it, even when the operator commands rotational rates of the robot hand that are only a small percentage of the operational joint rate limits. Therefore, joint angle rates are scaled when they exceed operational limits in a real time simulation of a robot arm. Simulation results show that a small dead band avoids the wrist singularity in the resolved rate equations but can introduce a high frequency oscillation close to the singularity. However, when a coordinated wrist movement is used in conjunction with the resolved rate equations, the high frequency oscillation disappears.

Barker, K.↗