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At least 127 records · Page 7

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NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1988

Venus' superrotation, mixing length theory and eddy diffusion - A parametric study

The concept of the Hadley mechanism is adopted to describe the axisymmetric circulation of the Venus atmosphere. It is shown that, for the atmosphere of a slowly rotating planet such as Venus, a form of the nonliner 'closure' (self-consistent solution) of the fluid dynamics system which constrains the magnitude of the eddy diffusion coefficients can be postulated. A nonlinear one-layer spectral model of the zonally symmetric circulation was then used to establish the relationship between the heat source, the meridional circulation, and the eddy diffusion coefficients, yielding large zonal velocities. Computer experiments indicated that proportional changes in the heat source and eddy diffusion coefficients do not significantly change the zonal velocities. It was also found that, for large eddy diffusion coefficients, the meridional velocity is virtually constant; below a threshold in the diffusion rate, the meridional velocity decreases; and, for large eddy diffusion and small heating rates, the zonal velocities decrease with decreasing planetary rotation rates.

Mayr, H. G.↗

NASA NTRS1991

Computational fluid dynamic analysis of liquid rocket combustion instability

The paper presents a computational analysis of liquid rocket combustion instability. Consideration is given to both a fully nonlinear unsteady calculation as well as a new CFD-based linearized stability analysis. An analytical solution for the linear stability problem in a constant area combustion chamber with uniform mean flow is developed to verify the numerical analyses.

Venkateswaran, Sankaran↗

NASA NTRS1993

Modeling transonic aerodynamic response using nonlinear systems theory for use with modern control theory

The presentation begins with a brief description of the motivation and approach that has been taken for this research. This will be followed by a description of the Volterra Theory of Nonlinear Systems and the CAP-TSD code which is an aeroelastic, transonic CFD (Computational Fluid Dynamics) code. The application of the Volterra theory to a CFD model and, more specifically, to a CAP-TSD model of a rectangular wing with a NACA 0012 airfoil section will be presented.

Silva, Walter A.↗

NASA NTRS2004

Aeroelastic Stability and Response of Rotating Structures

A summary of the work performed under NASA grant is presented. More details can be found in the cited references. This grant led to the development of relatively faster aeroelastic analysis methods for predicting flutter and forced response in fans, compressors, and turbines using computational fluid dynamic (CFD) methods. These methods are based on linearized two- and three-dimensional, unsteady, nonlinear aerodynamic equations. During the period of the grant, aeroelastic analysis that includes the effects of uncertainties in the design variables has also been developed.

Keith, Theo G., Jr.↗

NASA NTRSDate not supplied

Quantification of Numerical Uncertainty via Nonlinear Dynamical Approach

Motivations (Ensure a Higher Level of Confidence in the Predictability & Reliability of Numerical Simulation for Multiscale Complex Nonlinear Fluid Problems) - The last two decades have been an era when computation is ahead of analysis & when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems & non-traditional fields (Especially when computations offer the ONLY way of generating this type of data limited simulations). - At present some of the numerical uncertainties can be explained and minimized by traditional numerical analysis and standard CFD practices. However, such practices, usually based on linearized analysis, MIGHT NOT be sufficient for strongly nonlinear and/or stiff problems. - We need a good understanding of the nonlinear behavior of numerical schemes being used as an integral part of code verification, validation and certification.

HEC↗

NASA NTRS1983

Nonlinear interactions in superfluid dynamics: Nonstationary heat transfer due to second sound shock waves

Second sound techniques were used to study superfluid helium. Second sound shock waves produced relative velocities in the bulk fluid. Maximum counterflow velocities produced in this way are found to follow the Langer-Fischer prediction for the fundamental critical velocity in its functional dependence on temperature and pressure. Comparison of successive shock and rotating experiments provides strong evidence that breakdown results in vorticity production in the flow behind the shock. Schlieren pictures have verified the planar nature of second sound shocks even after multiple reflections. The nonlinear theory of second sound was repeatedly verified in its prediction of double shocks and other nonlinear phenomena.

Liepmann, H. W.↗

NASA NTRS2005

Stirling Convertor System Dynamic Model Developed

Free-piston Stirling convertors are being developed for potential use on NASA exploration missions. In support of this effort, the NASA Glenn Research Center has developed the Stirling convertor System Dynamic Model (SDM). The SDM models the Stirling cycle thermodynamics; heat flow; gas, mechanical, and mounting dynamics; the linear alternator; and the controller. The SDM s scope extends from the thermal energy input to thermal, mechanical, and electrical energy output, allowing one to study complex system interactions among subsystems. Thermal, mechanical, fluid, magnetic, and electrical subsystems can be studied in one model. The SDM is a nonlinear time-domain model containing sub-cycle dynamics, which simulates transient and dynamic phenomena that other models cannot. The entire range of convertor operation is modeled, from startup to full-power conditions.

Lewandowski, Edward J.↗

NASA NTRS1992

Lee waves, benign and malignant

The flow of an incompressible, stratified fluid over an obstacle will produce an oscillation in which buoyancy is the restoring force, called a gravity wave. For disturbances of this scale, the atmosphere may be treated as incompressible; and even the linear approximation will explain many of the phenomena observed in the lee of mountains. However, nonlinearities arise in two ways: (1) through the large (scaled) size of the mountain, and (2) from dynamically singular levels in the fluid field. These produce a complicated array of phenomena that present hazards to aircraft and to lee surface areas. If there is no dynamic barrier, these waves can penetrate vertically into the middle atmosphere (30-100 km attitude), where recent observations show them to be of a length scale that must involve the Coriolis force in any modeling. At these altitudes, the amplitude of the waves is very large, and the waves are studied with a view to their potential impact on the projected National Aerospace Plane. This paper presents the results of analyses and state-of-the-art numerical simulations, validated where possible by observational data.

Wurtele, M. G.↗

NASA NTRS1993

Laboratory and theoretical models of planetary-scale instabilities and waves

Research work is proceeding in theoretical, numerical, and experimental geophysical fluid dynamics leading up to a reflight of the GFFC (Geophysical Fluid Flow Cell Experiment) on USML-2. The work is intended not only to generate ideas for future space experiments, but to provide fundamental results concerned with nonlinear and chaotic properties of thermal convection and baroclinic waves in terrestrial and planetary atmospheres. The major efforts are focussed on thermal convection in a rapidly rotating annulus relevant to Jovian atmospheric dynamics, and on the chaotic behavior of baroclinic waves relevant to the Earth's atmosphere. The approach, in preparation for USML-2, is primarily theoretical and numerical. Mechanistic process models are solved numerically in order to identify physical mechanisms that may be observed in the GFFC, and which are important in real geophysical applications. The results from numerical simulations of geophysical fluid flow (subject to rotation and stratification) are compared with previous GFFC experiments on Spacelab-3 and with existing and proposed terrestrial laboratory experiments of various types. Pattern recognition algorithms have been employed to generate low-dimensional descriptions of the highly nonlinear and turbulent numerical simulations. Such empirically truncated descriptions provide for simplified but robust physical interpretations of the dynamics, as well as yielding highly efficient computations of these chaotic flows.

Hart, John E.↗

NASA NTRS2012

Nature's Autonomous Oscillators

Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.

Mayr, H. G.↗

NASA NTRSDate not supplied

Aeroelastic Analysis of Highly Flexible Wings with Linearized Frequency-Domain Aerodynamics

Flutter analysis of configurations with geometric structural nonlinearities typically is done with time-domain analysis. The results from this process are computationally expensive and can yield cumbersome results that may be difficult to manage/interpret. Compared to time-domain methods, frequency-domain flutter analysis can provide additional insight into the characteristics of a flutter stability problem. By linearizing the aeroelastic problem about the nonlinear equilibrium state, this work applies frequency-domain aeroelastic analysis to the Pazy wing, the subject of the Large Deformation Working Group in the Aeroelastic Prediction Workshop. Generalized aerodynamic forces (GAFs) are computed with both a doublet-lattice method and a computational fluid dynamics solver at a range of reduced frequencies as well as a range of dynamic pressures to account for the dependence of the mode shapes on the nonlinear equilibrium state. These GAFs are used in a p-k flutter solver, which is modified to handle the dependence of the stiffness matrix and GAFs on the dynamic pressure.

Bret K Stanford↗

NASA NTRS1991

Effects of varying subatmospheric pressure on stationary plasma arc welds

An experimental study was performed examining the variation of penetration, fluid behavior, heat-affected zone and arc in plasma arc welding (PAW) with respect to subatmospheric ambient pressure. The results reveal nonlinear variation of keyhole size, time of penetration, and size of the heat-affected zone with pressure. In a restricted range of pressure, dynamic components of fluid flow directed out of the molten pool appear and have a profound effect on keyhole formation. The generated plasma arc is observed to decrease in intensity with decreasing pressure, resulting in a reduction of penetration at lower pressures.

Chin, J. J.↗

NASA NTRS1994

Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2

The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.

Lyell, M. J.↗

NASA NTRS2015

Characterizing Droplet Formation from Non-Linear Slosh in a Propellant Tank

The Fluid Dynamics Branch (ER42) at the Marshall Space Flight Center (MSFC) was tasked with characterizing the formation and evolution of liquid droplets resulting from nonlinear propellant slosh in a storage tank. Lateral excitation of propellant tanks can produce high amplitude nonlinear slosh waves through large amplitude excitations and or excitation frequencies near a resonance frequency of the tank. The high amplitude slosh waves become breaking waves upon attaining a certain amplitude or encountering a contracting geometry such as the upper dome section of a spherical tank. Inherent perturbations in the thinning regions of breaking waves result in alternating regions of high and low pressure within the fluid. Droplets form once the force from the local pressure differential becomes larger than the force maintaining the fluid interface shape due to surface tension. Droplets released from breaking waves in a pressurized tank may lead to ullage collapse given the appropriate conditions due to the increased liquid surface area and thus heat transfer between the fluids. The goal of this project is to create an engineering model that describes droplet formation as a function of propellant slosh for use in the evaluation of ullage collapse during a sloshing event. The Volume of Fluid (VOF) model in the production level Computational Fluid Dynamics (CFD) code Loci-Stream was used to predict droplet formation from breaking waves with realistic surface tension characteristics. Various excitation frequencies and amplitudes were investigated at multiple fill levels for a single storage tank to create the engineering model of droplet formation from lateral propellant slosh.

Brodnick, Jacob↗

NASA NTRS1993

Basic studies of baroclinic flows

A fully nonlinear 3-dimensional numerical model (GEOSIM), previously developed and validated for several cases of geophysical fluid flow, has been used to investigate the dynamical behavior of laboratory experiments of fluid flows similar to those of the Earth's atmosphere. The phenomena investigated are amplitude vacillation, and the response of the fluid system to uneven heating and cooling. The previous year's work included hysteresis in the transition between axisymmetric and wave flow. Investigation is also continuing of the flows in the Geophysical Fluid Flow Cell (GFFC), a low-gravity Spacelab experiment. Much of the effort in the past year has been spent in validation of the model under a wide range of external parameters including nonlinear flow regimes. With the implementation of a 3-dimensional upwind differencing scheme, higher spectral resolution, and a shorter time step, the model has been found capable of predicting the majority of flow regimes observed in one complete series of baroclinic annulus experiments of Pfeffer and co-workers. Detailed analysis of amplitude vacillation has revealed that the phase splitting described in the laboratory experiments occurs in some but not all cases. Through the use of animation of the models output, a vivid 3-dimensional view of the phase splitting was shown to the audience of the Southeastern Geophysical Fluid Dynamics Conference in March of this year. A study on interannual variability was made using GEOSIM with periodic variations in the thermal forcing. Thus far, the model has not predicted a chaotic behavior as observed in the experiments, although there is a sensitivity in the wavenumber selection to the initial conditions. Work on this subject, and on annulus experiments with non-axisymmetric thermal heating, will continue. The comparison of GEOSIM's predictions will result from the Spacelab 3 GFFC experiments continued over the past year, on a 'back-burner' basis. At this point, the study (in the form of a draft of a journal article) is nearly completed. The results from GEOSIM compared very well with the experiments, and the use of the model allows the demonstration of flow mechanics that were not possible with the experimental data. For example, animation of the model output shows that the forking of the spiral bands is a transient phenomenon, due to the differential east-west propagation of convection bands from different latitudes.

Miller, Timothy L.↗

NASA NTRS1990

A mathematical model of the structure and evolution of small scale discrete auroral arcs

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Seyler, C. E.↗