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NASA NTRS1994

Evolution of energy-containing turbulent eddies in the solar wind

Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.

Matthaeus, William H.↗

NASA NTRS2004

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Shu, Chi-Wang↗

NASA NTRS2013

Characterization of Swirl-Venturi Lean Direct Injection Designs for Aviation Gas-Turbine Combustion

Injector geometry, physical mixing, chemical processes, and engine cycle conditions together govern performance, operability and emission characteristics of aviation gas-turbine combustion systems. The present investigation explores swirl-venturi lean direct injection combustor fundamentals, characterizing the influence of key geometric injector parameters on reacting flow physics and emission production trends. In this computational study, a design space exploration was performed using a parameterized swirl-venturi lean direct injector model. From the parametric geometry, 20 three-element lean direct injection combustor sectors were produced and simulated using steady-state, Reynolds-averaged Navier-Stokes reacting computations. Species concentrations were solved directly using a reduced 18-step reaction mechanism for Jet-A. Turbulence closure was obtained using a nonlinear κ-ε model. Results demonstrate sensitivities of the geometric perturbations on axially averaged flow field responses. Output variables include axial velocity, turbulent kinetic energy, static temperature, fuel patternation and minor species mass fractions. Significant trends have been reduced to surrogate model approximations, intended to guide future injector design trade studies and advance aviation gas-turbine combustion research.

Combustion Chamber↗

NASA NTRS1976

Journal bearing impedance descriptions for rotordynamic applications

The paper deals with the development of analytic descriptions for plain circumferentially-symmetric fluid journal bearings, which are suitable for use in rotor dynamic analysis. The bearing impedance vector is introduced, which defines the bearing reaction force components as a function of the bearing motion. Impedances are derived directly for the Ocvirk (short) and Sommerfeld (long) bearings, and the relationships between the impedance vector and the more familiar mobility vector are developed and used to derive analytic impedance for finite-length bearings. The static correctness of the finite-length cavitating impedance is verified. Analytic stiffness and damping coefficient definitions are derived in terms of an impedance vector for small motion around an equilibrium position and demonstrated for the finite-length cavitating impedance. Nonlinear transient rotordynamic simulations are presented for the short pi and 2-pi impedances and the finite-length cavitating impedance. It is shown that finite-length impedance yields more accurate results for substantially less computer time than the short-bearing numerical-pressure-integration approach.

Childs, D.↗

NASA NTRS1993

Development of a computational testbed for numerical simulation of combustion instability

A synergistic hierarchy of analytical and computational fluid dynamic techniques is used to analyze three-dimensional combustion instabilities in liquid rocket engines. A mixed finite difference/spectral procedure is employed to study the effects of a distributed vaporization zone on standing and spinning instability modes within the chamber. Droplet atomization and vaporization are treated by a variety of classical models found in the literature. A multi-zone, linearized analytical solution is used to validate the accuracy of the numerical simulations at small amplitudes for a distributed vaporization region. This comparison indicates excellent amplitude and phase agreement under both stable and unstable operating conditions when amplitudes are small and proper grid resolution is used. As amplitudes get larger, expected nonlinearities are observed. The effect of liquid droplet temperature fluctuations was found to be of critical importance in driving the instabilities of the combustion chamber.

Grenda, Jeffrey↗

NASA NTRS1997

[Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems]

The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

Hermann, Robert↗

NASA NTRS2003

Control Law Design in a Computational Aeroelasticity Environment

A methodology for designing active control laws in a computational aeroelasticity environment is given. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this paper solves the transonic small disturbance aerodynamic equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structure. These structural responses are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The Eigensystem Realization Algorithm is then employed to develop an explicit state-space model of the equivalent linear system. The Linear Quadratic Guassian control law design technique is employed to design a control law. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the aeroelastic system is increased through increased angle-of-attack changes.

Newsom, Jerry R.↗

NASA NTRS1989

International Conference on Numerical Methods in Fluid Dynamics, 11th, Williamsburg, VA, June 27-July 1, 1988, Proceedings

Recent advances in computational fluid dynamics (CFD) are discussed in reviews and reports. Topics addressed include CFD models in plasma dynamics, parallel computation for simulation studies, CFD for hypersonic airbreathing aircraft, multigrid methods for the steady incompressible Navier-Stokes equations, upwind differencing techniques, TV stable schemes for shock-interacting flows, Euler models of hypersonic vortex flows, parallel multilevel adaptive methods, and vortex methods for slightly viscous three-dimensional flows. Consideration is given to the accuracy of node-based solutions on irregular meshes, multigrid calculations for cascades, a finite-volume-element method for planar cavity flow, parallel heterogeneous mesh refinement for advection-diffusion equations, the convergence of the spectral-viscosity method for nonlinear conservation laws, and numerical simulations of Taylor vortices in a spherical gap.

Dwoyer, D. L.↗

NASA NTRS1998

Numerical Stability and Control Analysis Towards Falling-Leaf Prediction Capabilities of Splitflow for Two Generic High-Performance Aircraft Models

Aerodynamic analysis are performed using the Lockheed-Martin Tactical Aircraft Systems (LMTAS) Splitflow computational fluid dynamics code to investigate the computational prediction capabilities for vortex-dominated flow fields of two different tailless aircraft models at large angles of attack and sideslip. These computations are performed with the goal of providing useful stability and control data to designers of high performance aircraft. Appropriate metrics for accuracy, time, and ease of use are determined in consultations with both the LMTAS Advanced Design and Stability and Control groups. Results are obtained and compared to wind-tunnel data for all six components of forces and moments. Moment data is combined to form a "falling leaf" stability analysis. Finally, a handful of viscous simulations were also performed to further investigate nonlinearities and possible viscous effects in the differences between the accumulated inviscid computational and experimental data.

Charlton, Eric F.↗

NASA NTRS1985

Minimal norm constrained interpolation

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Irvine, L. D.↗

NASA NTRS2008

Shear Thinning Near the Critical Point of Xenon

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: 10(exp -3) < gamma-dot tau < 700, where gamma-dot tau is the shear rate scaled by the relaxation time tau of critical fluctuations. The measurements had a temperature resolution of 0.01 mK and were conducted in microgravity aboard the Space Shuttle Columbia to avoid the density stratification caused by Earth's gravity. The viscometer measured the drag on a delicate nickel screen as it oscillated in the xenon at amplitudes 3 mu,m < chi (sub 0) >430 mu, and frequencies 1 Hz < omega/2 pi < 5 Hz. To separate shear thinning from other nonlinearities, we computed the ratio of the viscous force on the screen at gamma-dot tau to the force at gamma-dot tau approximates 0: C(sub gamma) is identical with F(chi(sub 0), omega tau, gamma-dot tau )/F)(chi(sub 0, omega tau, 0). At low frequencies, (omega tau)(exp 2) < gamma-dot tau, C(sub gamma) depends only on gamma-dot tau, as predicted by dynamic critical scaling. At high frequencies, (omega tau)(exp 2) > gamma-dot tau, C(sub gamma) depends also on both x(sub 0) and omega. The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: eta(gamma-dot)/eta(0)=[1+A(sub gamma)|gamma-dot tau|](exp - chi(sub eta)/3+chi(sub eta)), where chi(sub eta) =0.069 is the critical exponent for viscosity and mode-coupling theory predicts A(sub gamma) =0.121. For xenon we find A(sub gamma) =0.137 +/- 0.029, in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature T(sub c) were independent of the cooling rate (both above and below T(sub c) and these data were symmetric about T(sub c) to within a temperature scale factor. The scale factors for the magnitude of the oscillator s response differed from those for the oscillator's phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below T(sub c).

Zimmerli, Gregory A.↗

NASA NTRS1991

Fluid management technology: Liquid slosh dynamics and control

Flight experiments were defined for the Cryogenic On-Orbit Liquid Depot Storage, Acquisition and Transfer Satellite (COLD-SAT) test bed satellite and the Shuttle middeck to help establish the influence of the gravitational environment on liquid slosh dynamics and control. Several analytical and experimental studies were also conducted to support the experiments and to help understand the anticipated results. Both FLOW-3D and NASA-VOF3D computer codes were utilized to simulate low Bond number, small amplitude sloshing, for which the motions are dominated by surface forces; it was found that neither code provided a satisfactory simulation. Thus, a new analysis of low Bond number sloshing was formulated, using an integral minimization technique that will allow the assumptions made about surface physics phenomena to be modified easily when better knowledge becomes available from flight experiments. Several examples were computed by the innovative use of a finite-element structural code. An existing spherical-pendulum analogy of nonlinear, rotary sloshing was also modified for easier use and extended to low-gravity conditions. Laboratory experiments were conducted to determine the requirements for liquid-vapor interface sensors as a method of resolving liquid surface motions in flight experiments. The feasibility of measuring the small slosh forces anticipated in flight experiments was also investigated.

Dodge, Franklin T.↗

NASA NTRS2018

kL-based Linear and Nonlinear Two-Equation Turbulence Models

The development and implementation of kL-based Reynolds Average Navier-Stokes (RANS) two-equation turbulence models are reported herein. The kL is based on Abdol-Hamid's closure and Menter's modification to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's kL equation is well suited for term-by-term modeling and displays useful features compared to other scale formulation. One of the important differences is the inclusion of higher order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady flows in URANS mode. The present report documents the formulation of two model levels of turbulence models as implemented in the computational fluid dynamics FUN3D code. The levels are the two-equation linear k-kL and the two-equation algebraic Reynolds stress model (ARSM). Free shear, separated and corner flow cases are documented and compared with experimental, and other turbulence model data. The results show generally very good comparisons with experimental data. The results from this formulation are similar or better than results using the SST two-equation turbulence model. ARSM shows great promise with similar level of computational resources as basic two-equation turbulence models.

Abdol-Hamid, K. S.↗

NASA NTRS1985

Some recent advances in computational aerodynamics for helicopter applications

The growing application of computational aerodynamics to nonlinear helicopter problems is outlined, with particular emphasis on several recent quasi-two-dimensional examples that used the thin-layer Navier-Stokes equations and an eddy-viscosity model to approximate turbulence. Rotor blade section characteristics can now be calculated accurately over a wide range of transonic flow conditions. However, a finite-difference simulation of the complete flow field about a helicopter in forward flight is not currently feasible, despite the impressive progress that is being made in both two and three dimensions. The principal limitations are today's computer speeds and memories, algorithm and solution methods, grid generation, vortex modeling, structural and aerodynamic coupling, and a shortage of engineers who are skilled in both computational fluid dynamics and helicopter aerodynamics and dynamics.

Mccroskey, W. J.↗

NASA NTRS2006

Experimental and Computational Analysis of Unidirectional Flow Through Stirling Engine Heater Head

A high efficiency Stirling Radioisotope Generator (SRG) is being developed for possible use in long-duration space science missions. NASA s advanced technology goals for next generation Stirling convertors include increasing the Carnot efficiency and percent of Carnot efficiency. To help achieve these goals, a multi-dimensional Computational Fluid Dynamics (CFD) code is being developed to numerically model unsteady fluid flow and heat transfer phenomena of the oscillating working gas inside Stirling convertors. In the absence of transient pressure drop data for the zero mean oscillating multi-dimensional flows present in the Technology Demonstration Convertors on test at NASA Glenn Research Center, unidirectional flow pressure drop test data is used to compare against 2D and 3D computational solutions. This study focuses on tracking pressure drop and mass flow rate data for unidirectional flow though a Stirling heater head using a commercial CFD code (CFD-ACE). The commercial CFD code uses a porous-media model which is dependent on permeability and the inertial coefficient present in the linear and nonlinear terms of the Darcy-Forchheimer equation. Permeability and inertial coefficient were calculated from unidirectional flow test data. CFD simulations of the unidirectional flow test were validated using the porous-media model input parameters which increased simulation accuracy by 14 percent on average.

Wilson, Scott D.↗

NASA NTRS2016

Development of Semi-Empirical Damping Equation for Baffled Tank with Oblate Spheroidal Dome

Propellant slosh is a potential source of disturbance that can significantly impact the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the slosh, slosh mass, slosh mass center location, and the critical damping ratio. A fundamental study has been undertaken at NASA MSFC to understand the fluid damping physics from a ring baffle in the barrel section of a propellant tank. An asymptotic damping equation and CFD blended equation have been derived by NASA MSFC team to complement the popularly used Miles equation at different flow regimes. The new development has found success in providing a nonlinear damping model for the Space Launch System. The purpose of this study is to further extend the semi-empirical damping equations into the oblate spheroidal dome section of the propellant tanks. First, previous experimental data from the spherical baffled tank are collected and analyzed. Several methods of taking the dome curvature effect, including a generalized Miles equation, area projection method, and equalized fill height method, are assessed. CFD simulation is used to shed light on the interaction of vorticity around the baffle with the locally curved wall and liquid-gas interface. The final damping equation will be validated by a recent subscale test with an oblate spheroidal dome conducted at NASA MSFC.

Yang, H. Q.↗

NASA NTRS1995

Galactic cosmic-ray mediation of a spherical solar wind flow. 1: The steady state cold gas hydrodynamical approximation

Realistic models of the outer heliosphere should consider that the interstellar cosmic-ray pressure becomes comparable to pressures in the solar wind at distances more than 100 AU from the Sun. The cosmic-ray pressure dynamically affects solar wind flow through deceleration. This effect, which occurs over a scale length of the order of the effective diffusion length at large radial distances, has important implications for cosmic-ray modulation and acceleration. As a first step toward solution of this nonlinear problem, a steady state numerical model was developed for a relatively cold spherical solar wind flow which encounters the confining isotropic pressure of the surrounding Galactic medium. This pressure is assumed to be dominated by energetic particles (Galactic cosmic rays). The system of equations, which are solved self-consistently, includes the relevant hydrodynamical equations for the solar wind flow and the spherical cosmic-ray transport equation. To avoid the closure parameter problem of the two-fluid model, the latter equation is solved for the energy-dependent cosmic-ray distribution function.

Le Roux, J. A.↗

NASA NTRS1996

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Hewitt, R. E.↗