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At least 55 records · Page 3

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗

Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum

This paper describes the eight-day August 2013 test campaign designed to investigate and demonstrate viability of using classical magnetoplasmadynamics to obtain a propulsive momentum transfer via the quantum vacuum virtual plasma. This paper will not address the physics of the quantum vacuum plasma thruster, but instead will describe the test integration, test operations, and the results obtained from the test campaign. Approximately 30-50 micro-Newtons of thrust were recorded from an electric propulsion test article consisting primarily of a radio frequency (RF) resonant cavity excited at approximately 935 megahertz. Testing was performed on a low-thrust torsion pendulum that is capable of detecting force at a single-digit micronewton level, within a stainless steel vacuum chamber with the door closed but at ambient atmospheric pressure. Several different test configurations were used, including two different test articles as well as a reversal of the test article orientation. In addition, the test article was replaced by an RF load to verify that the force was not being generated by effects not associated with the test article. The two test articles were designed by Cannae LLC of Doylestown, Pennsylvania. The torsion pendulum was designed, built, and operated by Eagleworks Laboratories at the NASA Johnson Space Center of Houston, Texas. Approximately six days of test integration were required, followed by two days of test operations, during which, technical issues were discovered and resolved. Integration of the two test articles and their supporting equipment was performed in an iterative fashion between the test bench and the vacuum chamber. In other words, the test article was tested on the bench, then moved to the chamber, then moved back as needed to resolve issues. Manual frequency control was required throughout the test. Thrust was observed on both test articles, even though one of the test articles was designed with the expectation that it would not produce thrust. Specifically, one test article contained internal physical modifications that were designed to produce thrust, while the other did not (with the latter being referred to as the "null" test article). Test data gathered includes torsion pendulum displacement measurements which are used to calculate generated force, still imagery in the visible spectrum to document the physical configuration, still imagery in the infrared spectrum to characterize the thermal environment, and video imagery. Post-test data includes static and animated graphics produced during RF resonant cavity characterization using the COMSOL Multiphysics® software application. Excerpts from all of the above are included and discussed in this paper. Lessons learned from test integration and operations include identification of the need to replace manual control of the resonant cavity target frequency with an automated frequency control capability. Future test plans include the development of an automatic frequency control circuit. Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma. Future test plans include independent verification and validation at other test facilities.

Brady, David↗

Preliminary design of composite wings for buckling, strength and displacement constraints

An unstiffened panel buckling constraint for balanced, symmetric laminated composites is included on the global design level in a mathematical programming structural optimization procedure for designing wing structures. Constraints are introduced by penalty functions, and Newton's method based on approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. Constraint approximations used during the optimization process contribute to the computational efficiency of the procedure. A criterion is developed that identifies the appropriate conservative form of the constraint approximations that are used with the optimization procedure. Minimum-mass design results are obtained for a multispar high-aspect-ratio wing subjected to material strength, minimum-gage, displacement, panel buckling and twist constraints. The material systems considered for the examples are all graphite-epoxy, graphite-epoxy with boron-epoxy spar caps, and all aluminum. The composite material designs are shown to have an advantage over the aluminum designs since they can often satisfy additional constraints with only small mass increases.

Starnes, J. H., Jr.↗

Fast simulation techniques for switching converters

Techniques for simulating a switching converter are examined. The state equations for the equivalent circuits, which represent the switching converter, are presented and explained. The uses of the Newton-Raphson iteration, low ripple approximation, half-cycle symmetry, and discrete time equations to compute the interval durations are described. An example is presented in which these methods are illustrated by applying them to a parallel-loaded resonant inverter with three equivalent circuits for its continuous mode of operation.

King, Roger J.↗

An upwind approach to unsteady flowfield simulation

A numerical method to determine unsteady solutions of the laminar, perfect gas Navier-Stokes equations has been developed. The structured finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the interaction of blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the viscous terms are computed by central differencing. Comparisons of numerical, analytical, and experimental results are made in two and three dimensions. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing.

Atwood, Christopher A.↗

Computation of viscous blast wave flowfields

A method to determine unsteady solutions of the Navier-Stokes equations was developed and applied. The structural finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the interaction of blast-waves with stationary targets. The inviscid flux is evaluated using MacCormack's modified Steger-Warming flux or Roe flux difference splittings with total variation diminishing limiters, while the viscous flux is computed using central differences. The use of implicit boundary conditions in conjunction with a telescoping in time and space method permitted solutions to this strongly unsteady class of problems. Comparisons of numerical, analytical, and experimental results were made in two and three dimensions. These comparisons revealed accurate wave speed resolution with nonoscillatory discontinuity capturing. The purpose of this effort was to address the three-dimensional, viscous blast-wave problem. Test cases were undertaken to reveal these methods' weaknesses in three regimes: (1) viscous-dominated flow; (2) complex unsteady flow; and (3) three-dimensional flow. Comparisons of these computations to analytic and experimental results provided initial validation of the resultant code. Addition details on the numerical method and on the validation can be found in the appendix. Presently, the code is capable of single zone computations with selection of any permutation of solid wall or flow-through boundaries.

Atwood, Christopher A.↗

Navier-Stokes simulations of unsteady transonic flow phenomena

Numerical simulations of two classes of unsteady flows are obtained via the Navier-Stokes equations: a blast-wave/target interaction problem class and a transonic cavity flow problem class. The method developed for the viscous blast-wave/target interaction problem assumes a laminar, perfect gas implemented in a structured finite-volume framework. The approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the blast-waves with stationary targets. The inviscid flux is evaluated using either of two upwind techniques, while the full viscous terms are computed by central differencing. Comparisons of unsteady numerical, analytical, and experimental results are made in two- and three-dimensions for Couette flows, a starting shock-tunnel, and a shock-tube blockage study. The results show accurate wave speed resolution and nonoscillatory discontinuity capturing of the predominantly inviscid flows. Viscous effects were increasingly significant at large post-interaction times. While the blast-wave/target interaction problem benefits from high-resolution methods applied to the Euler terms, the transonic cavity flow problem requires the use of an efficient scheme implemented in a geometrically flexible overset mesh environment. Hence, the Reynolds averaged Navier-Stokes equations implemented in a diagonal form are applied to the cavity flow class of problems. Comparisons between numerical and experimental results are made in two-dimensions for free shear layers and both rectangular and quieted cavities, and in three-dimensions for Stratospheric Observatory For Infrared Astronomy (SOFIA) geometries. The acoustic behavior of the rectangular and three-dimensional cavity flows compare well with experiment in terms of frequency, magnitude, and quieting trends. However, there is a more rapid decrease in computed acoustic energy with frequency than observed experimentally owing to numerical dissipation. In addition, optical phase distortion due to the time-varying density field is modelled using geometrical constructs. The computed optical distortion trends compare with the experimentally inferred result, but underpredicts the fluctuating phase difference magnitude.

Atwood, C. A.↗

Computational analysis of methods for reduction of induced drag

The purpose of this effort was to perform a computational flow analysis of a design concept centered around induced drag reduction and tip-vortex energy recovery. The flow model solves the unsteady three-dimensional Euler equations, discretized as a finite-volume method, utilizing a high-resolution approximate Riemann solver for cell interface flux definitions. The numerical scheme is an approximately-factored block LU implicit Newton iterative-refinement method. Multiblock domain decomposition is used to partition the field into an ordered arrangement of blocks. Three configurations are analyzed: a baseline fuselage-wing, a fuselage-wing-nacelle, and a fuselage-wing-nacelle-propfan. Aerodynamic force coefficients, propfan performance coefficients, and flowfield maps are used to qualitatively access design efficacy. Where appropriate, comparisons are made with available experimental data.

Janus, J. M.↗

Computation of Steady and Unsteady Laminar Flames: Theory

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Hagstrom, Thomas↗

Solar Wind Change Exchange from the Magnetosheath

We report the results of a long (approximately 100 ks) XMM-Newton observation designed to observe solar wind charge exchange emission (SWCX) from Earth's magnetosheath. By luck, the observation took place during a period of minimal solar wind flux so the SWCX emission was also minimal. Never-the-less, there is a significant if not stunning correlation between the observed O VIII count rate and our model for magnetosheath emission. We also report on the observed O VII and O VII emission.

Snowden, Steve↗

Application of Newton's method to the postbuckling of rings under pressure loadings

The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.

Thurston, Gaylen A.↗

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

Baker, A. J.↗

Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.

Erickson, W. D.↗

Advances in upwind relaxation methods

Numerical techniques for solving the compressible Euler and Navier-Stokes equations are discussed with an emphasis on characteristic-based schemes. Two popular approaches, flux difference splitting and flux vector splitting, are described in one-dimensional Cartesian coordinates and then extended to three-dimensional generalized coordinates. A technique for increasing the spatial accuracy is presented, followed by a discussion of numerical dissipation mechanisms. An introduction to the use of implicit time integration schemes for accelerating the convergence rate to steady-state solutions including Newton's method, relaxation strategies, and approximate factorization techniques and their implementation on a vector processor concludes the chapter.

Walters, R. W.↗

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗

The Newton Modified Barrier Method for QP Problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.

Melman, A.↗