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At least 973 records · Page 54

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

Franca, Leopoldo P.↗

Time-dependent Computational Studies of Premixed Flames in Microgravity

This report describes the research performed at the Center for Reactive Flow and Dynamical Systems in the Laboratory for Computational Physics and Fluid Dynamics, at the Naval Research Laboratory, in support of NASA Microgravity Science and Applications Program. The primary focus of this research is on investigating fundamental questions concerning the propagation and extinction of premixed flames in earth gravity and in microgravity environments. Our approach is to use detailed time-dependent, multispecies, numerical models as tools to simulate flames in different gravity environments. The models include a detailed chemical kinetics mechanism consisting of elementary reactions among the eight reactive species involved in hydrogen combustion, coupled to algorithms for convection, thermal conduction, viscosity, molecular and thermal diffusion, and external forces. The external force, gravity, can be put in any direction relative to flame propagation and can have a range of values. Recently more advanced wall boundary conditions such as isothermal and no-slip have been added to the model. This enables the simulation of flames propagating in more practical systems than before. We have used the numerical simulations to investigate the effects of heat losses and buoyancy forces on the structure and stability of flames, to help resolve fundamental questions on the existence of flammability limits when there are no external losses or buoyancy forces in the system, to understand the interaction between the various processes leading to flame instabilities and extinguishment, and to study the dynamics of cell formation and splitting. Our studies have been able to bring out the differences between upward- and downward-propagating flames and predict the zero-gravity behavior of these flames. The simulations have also highlighted the dominant role of wall heat losses in the case of downward-propagating flames. The simulations have been able to qualitatively predict the formation of multiple cells and the cessation of cell-splitting. Our studies have also shown that some flames in a microgravity environment can be extinguished due to a chemical instability and without any external losses. However, further simulations are needed to more completely understand upward-propagating and zero-gravity flames as well as to understand the potential effect of radiative heat losses.

Kailasanath, K.↗

Direct numerical simulation of laminar breakdown in high-speed, axisymmetric boundary layers

The compressible Navier-Stokes equations are solved using spectral collocation and high-order compact-difference techniques to simulate the laminar breakdown in high-speed, axisymmetric boundary-layer flow. Mach 4.5 flow along a hollow cylinder and Mach 6.8 flow along a sharp cone are considered. Data obtained replicate two previously unexplained phenomena, namely, the appearance of so-called 'rope-like waves' and 'the precursor transition effect', in which transitional flow originates near the critical layer well upstream of the transition location at the wall. The numerical data also reveal that neither of these effects can be explained, even qualitatively, by linear stability theory alone. It is shown that rope-like appearance arises from secondary instability. Certain features of the precursor transition effect also emerge from secondary instability but its nature is revealed to be fundamentally nonlinear.

Pruett, C. D.↗

A note on the effects of viscosity on the stability of a trailing-line vortex

The linear stability of the Batchelor (1964) vortex is examined with emphasis on new viscous modes recently found numerically by Khorrami (1991). Unlike the previously reported inviscid modes of instability, these modes are destabilized by viscosity and exhibit small growth rates at large Reynolds numbers. The analysis presented here uses a combination of asymptotic and numerical techniques. The results confirm the existence of the additional modes of instability due to viscosity.

Duck, Peter W.↗

The three-dimensional evolution of a plane mixing layer - Pairing and transition to turbulence

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Moser, Robert D.↗

Boundary Conditions for Jet Flow Computations

Ongoing activities are focused on capturing the sound source in a supersonic jet through careful large eddy simulation (LES). One issue that is addressed is the effect of the boundary conditions, both inflow and outflow, on the predicted flow fluctuations, which represent the sound source. In this study, we examine the accuracy of several boundary conditions to determine their suitability for computations of time-dependent flows. Various boundary conditions are used to compute the flow field of a laminar axisymmetric jet excited at the inflow by a disturbance given by the corresponding eigenfunction of the linearized stability equations. We solve the full time dependent Navier-Stokes equations by a high order numerical scheme. For very small excitations, the computed growth of the modes closely corresponds to that predicted by the linear theory. We then vary the excitation level to see the effect of the boundary conditions in the nonlinear flow regime.

Hayder, M. E.↗

A Flight Investigation to Determine the Lateral Oscillatory Damping Acceptable for an Airplane in the Landing Approach

An F-86E airplane, in which servo actuation of the ailerons and rudder provides artificial variation of the important lateral and directional aerodynamic stability parameters, has been flown by test pilots of the NASA, U.S. Air Force, and one aircraft manufacturer to determine satisfactory and acceptable levels of lateral oscillatory damping in the landing approach. In addition to normal operational use, particular consideration was given to the emergency condition of failure of stability-augmentation equipment. In this study, the pilots' opinions of the airplane dynamic stability and control characteristics in smooth and simulated rough air have been recorded according to a numerical rating scale. The results are presented in the form of boundaries in terms of cycles to damp to half amplitude, 1/C(sub 1/2), or time to damp to half amplitude, 1/T(1/2) and bank-to-sideslip ratio, and are discussed in relation to existing flying-qualities criteria. Though the present results, which were obtained at 170 knots indicated airspeed and 10,000-feet altitude, indicated that increased damping is required with increased bank-to-sideslip ratio (as found in previous work), consideration of the dampers-failed condition indicated a great reduction in the minimum acceptable damping. At moderate values of bank-to-sideslip ratio, effects of lateral-oscillation period on pilot-opinion variation with damping appeared to be taken into account by use of the parameter 1/T(sub 1/2).

McNeill, Walter E.↗

Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations

The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.

Kennedy, Chistopher A.↗

Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

Svard, Magnus↗

Evolving Design Criteria for Very Large Aperture Space-Based Telescopes and Their Influence on the Need for Integrated Tools in the Optimization Process

NASA's Advanced Mirror Technology Development (AMTD) program has been developing the means to design and build the future generations of space based telescopes. With the nearing completion of the James Webb Space Telescope (JWST), the astrophysics community is already starting to define the requirements for follow on observatories. The restrictions of available launch vehicles and the possibilities of planned future vehicles have fueled the competition between monolithic primaries (with better optical quality) and segmented primaries (with larger apertures, but with diffraction, costs and figure control issues). Regardless of the current shroud sizes and lift capacities, these competing architectures share the need for rapid design tools. As part of the AMTD program a number of tools have been developed and tested to speed up the design process. Starting with the Arnold Mirror Modeler (which creates Finite Element Models (FEM) for structural analysis) and now also feeds these models into thermal stability analyses. They share common file formats and interchangeable results. During the development of the program, numerous trade studies were created for 4 meter and 8 meter monolithic primaries, complete with support systems. Evaluation of these results has led to a better understanding of how the specification drives the results. This paper will show some of the early trade studies for typical specification requirements such as lowest mirror bending frequency and suspension system lowest frequency. The results use representative allowable stress values for each mirror substrate material and construction method and generic material properties. These studies lead to some interesting relationships between feasible designs and the realities of actually trying to build these mirrors. Much of the traditional specifications were developed for much smaller systems, where the mass and volume of the primary where a small portion of the overall satellite. JWST shows us that as the aperture grows, the primary takes up the majority of the mass and volume and the established rules need to be adjusted. For example, a small change in lowest frequency requirement can change the cost by millions of dollars.

Space-based telescopes↗

Impacts of the Angular Dependence of the Solar Diffuser BRDF Degradation Factor on the SNPP VIIRS Reflective Solar Band On-Orbit Radiometric Calibration

Using an onboard sunlit solar diffuser (SD) as the primary radiance source, the visible infrared imaging radiometer suite (VIIRS) on the Suomi National Polar-orbiting Partnership satellite regularly performs radiometric calibration of its reflective solar bands (RSBs). The SD bidirectional reflectance distribution function (BRDF) value decreases over time. A numerical degradation factor is used to quantify the degradation and is determined by an onboard SD stability monitor (SDSM), which observes the sun and the sunlit SD at almost the same time. We had shown previously that the BRDF degradation factor was angle-dependent. Consequently, due to that the SDSM and the RSB view the SD at very different angles relative to both the solar and the SD surface normal vectors, directly applying the BRDF degradation factor determined by the SDSM to the VIIRS RSB calibration can result in large systematic errors. We develop a phenomenological model to calculate the BRDF degradation factor for the RSB SD view from the degradation factor for the SDSM SD view. Using the yearly undulations observed in the VIIRS detector gains for the M1-M4 bands calculated with the SD BRDF degradation factor for the SDSM SD view and the difference between the VIIRS detector gains calculated from the SD and the lunar observations, we obtain the model parameter values and thus establish the relation between the BRDF degradation factors for the RSB and the SDSM SD view directions.

Lei, Ning↗

Dynamic response and stability analysis of flexible, multibody systems

A general version of Lagrange's equations, including auxiliary nonholonomic, rheonomic conditions of constraint, is used in the dynamic simulation and stability analysis of interconnected flexible bodies. Modeling of the nonlinear flexible/rigid dynamic coupling effects, the interaction forces/torques, and the elastic deformation effects is discussed. A digital computer program is developed to obtain time-domain solution for the nonlinear response of systems represented as a collection of individual bodies, numerical linearization of system-governing equations, time-domain solution for the perturbation response about a nominal state, and a frequency-domain stability analysis corresponding to the linearization. The digital simulation code is employed to study the dynamic behavior of a typical satellite and a spacecraft with deployable experiment booms.

Bodley, C. S.↗

Modelling of jet- and swirl-stabilized reacting flows in axisymmetric combustors

Turbulent nonreactive and reactive flows with and without swirl are analyzed, with particular attention given to the flow fields of a gas-fueled nonpremixed swirl-stabilized combustor and a premixed opposed-jet combustor. Local mean flow properties, including velocity, temperature, and major species concentrations, are calculated by solving numerically the governing partial differential equations with associated submodels for turbulence and combustion. The results of the study indicate that the constant-density k-epsilon turbulence model provides a satisfactory representation of the aerodynamics in most practical combustor flows. The exception is the case of jet-stabilized combustor flow, due to the fact that the k-epsilon model cannot replicate the highly dissipative phenomenon found in such flows.

Nikjooy, M.↗

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Shortis, Trudi A.↗

Stability derivatives for bodies of revolution at subsonic speeds

The paper considers a rigid pointed body of revolution in a steady uniform subsonic flow. The body performs harmonic small-amplitude pitching oscillations around its zero angle of attack position. The body is assumed to be smooth and sufficiently slender so that the small perturbation concept can be applied. The basis of the method used, following Revell (1960), is the relation of a body-fixed perturbation potential to the general velocity potential. Normal force distributions as well as total force and moment coefficients are calculated for parabolic spindles and the numerical results show good agreement between Revell's second-order slender body theory and the present theory for the static stability derivatives of the parabolic spindles.

Liu, D. D.↗

A new approach to mixed H2/H infinity controller synthesis using gradient-based parameter optimization methods

In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.

Ly, Uy-Loi↗

Stability of outer planetary orbits around binary stars - A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and coworkers and the general, numerically integrated results of Laplace's method by Graziani and Black (1981) are compared for varying values of the mass parameter mu. For mu = 0 to 0.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For mu greater than 0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of mu.

Kubala, A.↗

Stability of the Halley Cometo-Sheath with Resistivity and Plasma Motion

The MHD stability of the cometary inner shealth determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is investigated by numerically solving the wave equations which include resistivity, plasma motion and plasma pressure with the help of two-point boundary value method.

Comets Cometosheath MHD Stability↗