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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Efficient numerical treatment of periodic systems with application to stability problems

Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Friedmann, P.↗
NASA NTRS1979

Explicit numerical formulas of improved stability and accuracy for the solution of parabolic equations

A class of explicit numerical formulas which involve next nearest neighbor as well as nearest neighbor points are explored in this paper. These formulas are formal approximations to the linear parabolic partial-differential equation of first order in time and second order in distance. It was found that some of these formulas can employ time steps as much as four times that for the conventional explicit technique without becoming unstable. Others showed improved accuracy for a given time step and spatial grid spacing. One formula achieved a steady-state solution of specified accuracy for an example problem in less than 4 percent of the total computational time required by the conventional explicit technique.

Olstad, W. B.↗
NASA NTRS1985

A simple model for the interaction between vertical eddy heat fluxes and static stability

A numerical model for studying the interaction of vertical eddy heat fluxes and vertical temperature structure in midlatitude regions is described. The temperature profile for the model was derived from calculations of the equilibrium among heating rates in simplified representations of large-scale vertical eddy heat flux, moist convection and radiation. An eddy flux profile is calculated based on the quasi-geostrophic, liner baroclinic instability of a single wave. Model equilibrium states for summer and winter conditions are compared with observations, and the results are discussed in detail.

Gutowski, W. J., Jr.↗
NASA NTRS1995

Unsteady numerical simulations of the stability and dynamics of flames

In this report we describe the research performed at the Naval Research Laboratory in support of the NASA Microgravity Science and Applications Program over the past three years (from Feb. 1992) with emphasis on the work performed since the last microgravity combustion workshop. The primary objective of our research is to develop an understanding of the differences in the structure, stability, dynamics and extinction of flames in earth gravity and in microgravity environments. Numerical simulations, in which the various physical and chemical processes can be independently controlled, can significantly advance our understanding of these differences. Therefore, our approach is to use detailed time-dependent, multi-dimensional, multispecies numerical models to perform carefully designed computational experiments. The basic issues we have addressed, a general description of the numerical approach, and a summary of the results are described in this report. More detailed discussions are available in the papers published which are referenced herein. Some of the basic issues we have addressed recently are (1) the relative importance of wall losses and gravity on the extinguishment of downward-propagating flames; (2) the role of hydrodynamic instabilities in the formation of cellular flames; (3) effects of gravity on burner-stabilized flames, and (4) effects of radiative losses and chemical-kinetics on flames near flammability limits. We have also expanded our efforts to include hydrocarbon flames in addition to hydrogen flames and to perform simulations in support of other on-going efforts in the microgravity combustion sciences program. Modeling hydrocarbon flames typically involves a larger number of species and a much larger number of reactions when compared to hydrogen. In addition, more complex radiation models may also be needed. In order to efficiently compute such complex flames recent developments in parallel computing have been utilized to develop a state-of-the-art parallel flame code. This is discussed below in some detail after a brief discussion of the numerical models.

Kailasanath, K.↗
NASA NTRS2009

Towards an "All Speed" Unstructured Upwind Scheme

In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).

Loh, Ching Y.↗
NASA NTRS1984

A numerical study of the stability of radiative shocks

Attention is given to the oscillatory instability of optically thin radiative shocks in time-dependent numerical calculations of accretion flows onto degenerate dwarfs. The present nonlinear calculations yield good quantitative agreement with the linear results obtained for oscillation frequencies, damping rates, and critical alpha-values. The fundamental mode and the first overtone in the shock radius and luminosity variations can be clearly identified, and evidence is sometimes seen for the second overtone. Time-dependent calculations are also performed which include additional physics relevant to degenerate dwarf accretion, such as electron thermal conduction, unequal electron and ion temperatures, Compton cooling, and relativistic corrections to the bremsstrahlung cooling law. All oscillatory modes are found to be damped, and hence stable, in the case of a 1-solar mass white dwarf accreting in spherical symmetry.

Imamura, J. N.↗
NASA NTRS1981

Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. This paper presents the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. It is found that a disk as massive as 1 solar mass, surrounding a 1 solar mass protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300 K or greater. Stability of a cooler disk requires that it be less massive, but even at 100 K a stable disk can have an appreciable fraction (about 1/3) of a solar mass.

Cassen, P. M.↗
NASA NTRS1978

Numerical experiments on the stability of disklike galaxies

It is noted that the stability properties of available galactic models are not consistent with presumptions based on observation and that axisymmetric disk systems with velocity dispersions like those of the Galaxy display major changes in form on a dynamical time scale. A report is given on a series of numerical experiments carried out as part of a systematic search for purely self-consistent disk galaxy models that might undergo little change over the time of several galactic rotations. The stability problem is reviewed, the method and calculations used are described, and initial conditions are outlined. The problem of estimating growth rates is discussed, and growth rates are evaluated for various disturbances. Experimental results are presented concerning growths of axisymmetric disturbances in 'cold' systems as well as disturbances with m = 1, 2, and 3. It is found that m = 2 disturbances are the most virulent and should dominate when all m values are allowed, but that the most rapidly growing disturbances are inhibited when several m values are allowed.

Miller, R. H.↗
NASA NTRS1947

Fundamental Aerodynamic Investigations for Development of Arrow-Stabilized Projectiles

The numerous patent applications on arrow-stabilized projectiles indicate that the idea of projectiles without spin is not new, but has appeared in various proposals throughout the last decades. As far as projectiles for subsonic speeds are concerned, suitable shapes have been developed for sometime, for example, numerous grenades. Most of the patent applications, though, are not practicable particularly for projectiles with supersonic speed. This is because the inventor usually does not have any knowledge of aerodynamic flow around the projectile nor any particular understanding of the practical solution. The lack of wind tunnels for the development of projectiles made it necessary to use firing tests for development. These are obviously extremely tedious or expensive and lead almost always to failures. The often expressed opinion that arrow-stabilized projectiles cannot fly supersonically can be traced to this condition. That this is not the case has been shown for the first time by Roechling on long projectiles with foldable fins. Since no aerodynamic investigations were made for the development of these projectiles, only tedious series of firing tests with systematic variation of the fins could lead to satisfactory results. These particular projectiles though have a disadvantage which lies in the nature cf foldable fins. They occasionally do not open uniformly in flight, thus causing unsymmetry in flow and greater scatter. The junctions of fins and body are very bad aerodynamically and increase the drag. It must be possible to develop high-performance arrow-stabilized projectiles based on the aerodynamic research conducted during the last few years at Peenemuende and new construction ideas. Thus the final shape, ready for operational use, could be developed in the wind tunnel without loss of expensive time in firing tests. The principle of arrow-stabilized performance has been applied to a large number of caliburs which were stabilized by various means Most promising was the development of a subcaliber wing-stabilized projectile with driving disc (Treibspiegel) where rigid control surfaces extend beyond the caliber of the projectile into the free stream. The stabilized projectiles of full-caliber, wing-stabilized projectiles with fins within the caliber is considerably more difficult. A completely satisfactory solution for the latter has not been found yet.

Kurzweg, Hermann↗
NASA NTRS2017

A new concept of stability in orbit propagation, useful for quantifying numerical errors

We present the concept of topological stability in the numerical propagation of orbits, and show how it results in a useful new method for measuring the global numerical error of an orbit propagation. The concept applies to any problem in orbital dynamics. Moreover, it can be extended to any three-dimensional system of di erential equations of second order. In order to assess the topological stability of a given integration a special metric is introduced, which can be used to estimate the numerical errors robustly. The method is particularly well suited for dealing with strongly perturbed and chaotic systems. The construction is based on the constraint imposed by the Hopf map that supports the Kustaanheimo-Stiefel transformation. Generic concepts of stability are translated to KS space.

Pelaez, Jesus↗
NASA NTRS1973

Numerical experiments in climate stability.

Two semiempirical climate models are formulated as time-dependent problems in order to study the stability of their asymptotic steady state equilibrium solutions to perturbations in internal (in this case, initial) conditions. For fixed external conditions the time-dependent versions of these models exhibit fully transitive behavior to positive perturbations in initial conditions, slight intransivity to negative perturbations up to -18 K, and an ice-covered earth regime is obtained for extremely large negative perturbations in initial temperatures (below -18 K). The parametrization found to be most critical in these models is the albedo-temperature coupling, especially in tropical regions. The temperature albedo parametrization from an intransitive climate model used in a time-dependent form of one of the preceding models is found to be highly sensitive to negative perturbations in both internal and external conditions. Numerical experimentation with these semiempirical models shows the important role of the tropics in maintaining the equilibrium climate and suggests that the radiation balance in equatorial latitudes might have a controlling influence on the equatorward extent of the polar ice cap.

Schneider, S. H.↗
NASA NTRS1976

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗
NASA NTRS1978

A numerical study of capillary stability in a circular cylindrical container with a concave spheroidal bottom

The paper describes a theoretical investigation of the stability under gravitational and surface forces of a liquid in a circular cylindrical container with a concave spheroidal bottom for the case in which the volume of the liquid is sufficiently small so that the bottom is not covered completely. The gravitational field is assumed to be directed along the symmetry axis of the container, and for a specific container shape the critical Bond number is calculated as a function of liquid volume for contact angles of gamma = 0, 1, 2, and 4 deg. For gamma = 0 deg, some critical equilibrium configurations and corresponding perturbation modes are presented.

Concus, P.↗
NASA NTRS1985

Numerical experiments on the stability of controlled shear flows

Three-dimensional, nonlinear simulations are presented for the parallel water boundary layer subjected to pressure gradient, suction, or heating control. The focus is on the secondary instability responsible for the K-type transition. Heating control is found to be the least effective in delaying the secondary instability. Flow-field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer.

Zang, T. A.↗
NASA NTRS1987

A numerical study of flare stabilized projectiles at Mach 7.0

The effect of nose shape on two flare stabilized projectiles was studied using a Parabolized Navier-Stokes code. Pressure coefficients, forces and moments, skin friction coefficients, and Stanton number calculations are presented for the hemisphere-cylinder-flare and the cone-cylinder-flare configurations. Pitching moment and static margin plots versus flare angles and flare lengths are presented in a parametric study to show aerodynamic stability effects. Distinctly different flow field values of pressure, local Mach number, and dynamic pressure were generated by the two different nose configurations. These flow field values just upstream of the flare will be examined. The code demonstrated its value as a design tool by making a clear distinction between aerodynamically stable characteristics for this variety of nose shapes, flare angles, and flare lengths.

Hughson, Montgomery C.↗
NASA NTRS1986

CONDIF - A modified central-difference scheme with unconditional stability and very low numerical diffusion

This paper describes a method, called CONDIF, which retains the essential nature of the central difference scheme (CDS) but eliminates the over- and under-shoots. It modifies the CDS by introducing a controlled amount of numerical diffusion based on local gradients. The results obtained for a number of test problems show that the CONDIF is significantly more accurate than the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid. In the worst case, it yields results similar to those of the hybrid scheme. Though the CONDIF is unconditionally stable, under some conditions the rate of convergence deteriorates as the grid Peclet number is increased. Efforts are currently underway to develop a faster converging variation of CONDIF.

Runchal, Akshai K.↗
NASA NTRS1988

Numerical experiments on the stability of controlled boundary layers

Nonlinear simulations are presented for instability and transition in parallel water boundary layers subjected to pressure gradient, suction, or heating control. In the nonlinear regime, finite amplitude, 2-D Tollmein-Schlichting waves grow faster than is predicted by linear theory. Moreover, this discrepancy is greatest in the case of heating control. Likewise, heating control is found to be the least effective in delaying secondary instabilities of both the fundamental and subharmonic type. Flow field details (including temperature profiles) are presented for both the uncontrolled boundary layer and the heated boundary layer.

Zang, Thomas A.↗