SEARCH · Engineering Papers

Results for “perturbation analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1988

An asymptotic induced numerical method for the convection-diffusion-reaction equation

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

Scroggs, Jeffrey S.↗

NASA NTRS1988

On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach

The coupling of hyperbolic and parabolic systems is discussed in a domain Omega divided into two distinct subdomains omega(+) and omega(-). The main concern is to find the proper interface conditions to be fulfilled at the surface separating the two domains. Next, they are used in the numerical approximation of the problem. The justification of the interface conditions is based on a singular perturbation analysis, i.e., the hyperbolic system is rendered parabolic by adding a small artifical viscosity. As this goes to zero, the coupled parabolic-parabolic problem degenerates into the original one, yielding some conditions at the interface. These are taken as interface conditions for the hyperbolic-parabolic problem. Actually, two alternative sets of interface conditions are discussed according to whether the regularization procedure is variational or nonvariational. It is shown how these conditions can be used in the frame of a numerical approximation to the given problem. Furthermore, a method of resolution is discussed which alternates the resolution of the hyperbolic problem within omega(-) and of the parabolic one within omega(+). The spectral collocation method is proposed, as an example of space discretization (different methods could be used as well); both explicit and implicit time-advancing schemes are considered. The present study is a preliminary step toward the analysis of the coupling between Euler and Navier-Stokes equations for compressible flows.

Gastaldi, Fabio↗

NASA NTRS1989

Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique

The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.

Nordmann, R.↗

NASA NTRS1989

Fast half-loop maneuvers for a high alpha fighter aircraft using a singular perturbation feedback control law

Singular perturbation analysis is used to derive an outer layer feedback control law for a high alpha fighter aircraft to perform the half-loop maneuver. Pitch rate and angle of attack are treated as fast variables in the derivation. Bang-bang controls are derived to transfer the aircraft state from trim to the outer layer and from the outer layer to specified final half-loop values. The pitch rate is treated as a varibale faster than the angle of attack in the transfer of the state to and from the outer layer. A simulation of the derived control law is conducted at Mach 0.6 and 15,000 feet altitude. The half-loop was performed in 13.12 seconds. It is compared with a NASA pilot simulated half-loop maneuver which took 22.42 seconds for the same initial conditions.

Garrett, Frederick E., Jr.↗

NASA NTRS1989

On the role of ozone in the stability of Rossby normal modes

The role of ozone in the linear stability of Rossby normal modes is examined in a continuously stratified, extratropical baroclinic atmosphere. The flow is described by coupled equations for the quasi-geostraphic potential vorticity and ozone volume mixing ratio. A perturbation analysis is carried out under the assumption of weak diabatic heating, which is generated by Newtonian cooling and dynamics-ozone interaction. An expression for the propagation and growth characteristics is obtained analytically in terms of the vertically averaged wave activity, which depends explicitly on the wave spatial structure, photochemistry, and basic state distributions of wind, temperature, and ozone mixing ratio. Calculations show that stationary internal modes, whose amplitudes are largest in the stratosphre, are destabilized by dynamics-ozone interaction and Newtonian cooling, with e-folding times on the order of 20-40 days.

Nathan, Terrence R.↗

NASA NTRS1990

Flare heating and ionization of the low solar chromosphere. I - Inversion methods for Mg I 4571 and 5173

Various methods of inverting solar Mg I 4571 and 5173 spectral line observations are examined to find the best method of using these lines to calculate the vertical temperature and electron density structure around the temperature minimum region. Following a perturbation analysis by Mein (1971), a Fredholm integral equation of the first kind is obtained which can be inverted to yield these temperature and density structures as a function of time. Several inversion methods are tested and compared. The methods are used to test data as well as to a subset of observations of these absorption lines taken on February 3, 1986 before and during a solar flare. A small but significant increase is found in the temperature and a relatively large increase in the electron density during this flare. The observations are inconsistent with heating and ionization by an intense beam of electrons and with ionization by UV photoionization of Si I.

Metcalf, Thomas R.↗

NASA NTRS1990

Theory of finite disturbances in a centrifugal compression system with a vaneless radial diffuser

A previous small perturbation analysis of circumferential waves in circumferential compression systems, assuming inviscid flow, is shown to be consistent with observations that narrow diffusers are more stable than wide ones, when boundary layer displacement effect is included. The Moore-Greitzer analysis for finite strength transients containing both surge and rotating stall in axial machines is adapted for a centrifugal compression system. Under certain assumptions, and except for a new second order swirl, the diffuser velocity field, including resonant singularities, can be carried over from the previous inviscid linear analysis. Nonlinear transient equations are derived and applied in a simple example to show that throttling through a resonant value of flow coefficient must occur in a sudden surge-like drop, accompanied by a transient rotating wave. This inner solution is superseded by an outer surge response on a longer time scale. Surge may occur purely as result of circumferential wave resonance. Numerical results are shown for various parametric choices relating to throttle schedule and the characteristic slope. A number of circumferential modes considered simultaneously is briefly discussed.

Moore, F. K.↗

NASA NTRS1990

Optimal guidance law development for an advanced launch system

A regular perturbation analysis is presented. Closed-loop simulations were performed with a first order correction including all of the atmospheric terms. In addition, a method was developed for independently checking the accuracy of the analysis and the rather extensive programming required to implement the complete first order correction with all of the aerodynamic effects included. This amounted to developing an equivalent Hamiltonian computed from the first order analysis. A second order correction was also completed for the neglected spherical Earth and back-pressure effects. Finally, an analysis was begun on a method for dealing with control inequality constraints. The results on including higher order corrections do show some improvement for this application; however, it is not known at this stage if significant improvement will result when the aerodynamic forces are included. The weak formulation for solving optimal problems was extended in order to account for state inequality constraints. The formulation was tested on three example problems and numerical results were compared to the exact solutions. Development of a general purpose computational environment for the solution of a large class of optimal control problems is under way. An example, along with the necessary input and the output, is given.

Calise, Anthony J.↗

NASA NTRS1990

Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations

The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. The finite order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects are considered. The spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2 and the binding energies of Be3, Be4, Mg3, and Mg4 were calculated using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as non-dynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical systems under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant both QCI and CC give very similar results.

Taylor, Peter R.↗

NASA NTRS1990

A parallel algorithm for nonlinear convection-diffusion equations

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

Scroggs, Jeffrey S.↗

NASA NTRS1990

Low-frequency ionization-driven instability of a discrete auroral arc model

The low-frequency (time scales of tens of seconds) dynamics of the auroral ionosphere differs from that of the nonauroral ionosphere by the presence of strong, unstable space- and time-dependent ionospheric ionization produced by precipitating auroral electrons. If recombination is relatively unimportant (as at high ionospheric heights), it is shown that, in general, transport processes cannot remove this ionization as fast as it is created, and no equilibrium is possible. These nonequilibrium phenomena are investigated in the context of a nonlinear adiabatic auroral model, which has previously been studied in static situations. A linearized local perturbation analysis is given of what amounts to a current-driven E x B gradient-drift instability with an ionization source, as well as some exact nonlinear solutions valid in a finite but limited spatial region. These solutions show continuing motion of auroral potential and plasma density, as the aurora tries to shift its ionization problems from one place to another. The analysis gives clues to the possibility of generation of chaos and of fine-scale spatial structure.

Cornwall, John M.↗

NASA NTRS1991

A half century historical review of the k-omega model

A brief historical review is presented tracing evolution of the k-omega two-equation turbulence model. The review compares the various k-omega models developed since 1942, and contrasts them to the well-known k-epsilon model. Straight-forward results based on perturbation analysis illustrate advantages offered by k-omega models for flows with adverse pressure gradient and for integration through the sublayer. As part of the historical perspective, the paper shows that Kolmogorov did remarkably well in formulating his model without the aid of a computer.

Wilcox, David C.↗

NASA NTRS1991

Fossil fuel and biomass burning effect on climate - Heating or cooling?

The basic theory of the effect of pollution on cloud microphysics and its global implications is applied to compare the relative effect of a small increase in the consumption rate of oil, coal, or biomass burning on cooling and heating of the atmosphere. The characteristics of and evidence for the SO2 induced cooling effect are reviewed. This perturbation analysis approach permits linearization, therefore simplifying the analysis and reducing the number of uncertain parameters. For biomass burning the analysis is restricted to burning associated with deforestation. Predictions of the effect of an increase in oil or coal burning show that within the present conditions the cooling effect from oil and coal burning may range from 0.4 to 8 times the heating effect.

Kaufman, Yoram J.↗

NASA NTRS1991

Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils

A Lanczos procedure is presently applied to a Navier-Stokes (N-S) solver for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S solvers.

Mahajan, Aparajit J.↗

NASA NTRS1991

A geometric approach to regulator and tracker design for an aerospace plane

The paper presents a nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control, that leads to regulators with automatic gain scheduling which exhibit similar dynamic behavior over the entire flight envelope of the aerospace plane. Additionally, design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. The unifying feature of the three nonlinear feedback control methodologies is that they all have a geometric interpretation. First, the translational dynamics are decomposed into reduced-order slow and fast dynamics by way of a formal singular perturbation analysis. After feedback linearization the fast dynamics are robustly stabilized via a variable structure control approach. The slow dynamics are stabilized using conventional proportional-integral compensation based on the nominal slow dynamics. A number of sample command and disturbance responses at opposite ends of the flight envelope are presented for a nonlinear aerospace plane model.

Van Buren, Mark A.↗

NASA NTRS1992

A hybrid approach to near-optimal launch vehicle guidance

This paper evaluates a proposed hybrid analytical/numerical approach to launch-vehicle guidance for ascent to orbit injection. The feedback-guidance approach is based on a piecewise nearly analytic zero-order solution evaluated using a collocation method. The zero-order solution is then improved through a regular perturbation analysis, wherein the neglected dynamics are corrected in the first-order term. For real-time implementation, the guidance approach requires solving a set of small dimension nonlinear algebraic equations and performing quadrature. Assessment of performance and reliability are carried out through closed-loop simulation for a vertically launched 2-stage heavy-lift capacity vehicle to a low earth orbit. The solutions are compared with optimal solutions generated from a multiple shooting code. In the example the guidance approach delivers over 99.9 percent of optimal performance and terminal constraint accuracy.

Leung, Martin S. K.↗

NASA NTRS1993

Parametric instabilities of finite-amplitude, circularly polarized Alfven waves in an anisotropic plasma

A class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in a plasma with pressure anisotropy is studied by application of the CGL equations. A linear perturbation analysis is used to find the dispersion relation governing the instabilities, which is a fifth-order polynomial and is solved numerically. A large-amplitude, circularly polarized wave is unstable with respect to decay into three waves: one sound-like wave and two side-band Alfven-like waves. It is found that, in addition to the decay instability, two new instabilities that are absent in the framework of the MHD equations can occur, depending on the plasma parameters.

Hamabata, Hiromitsu↗

NASA NTRS1994

Calculation and measurement of the influence of flow parameters on rotordynamic coefficients in labyrinth seals

First experimental investigations performed on a new test rig are presented. For a staggered labyrinth seal with fourteen cavities the stiffness coefficient and the leakage flow are measured. The experimental results are compared to calculated results which are obtained by a one-volume bulk-flow theory. A perturbation analysis is made for seven terms. It is found out that the friction factors have great impact on the dynamic coefficients. They are obtained by turbulent flow computation by a finite-volume model with the Reynolds equations used as basic equations.

Kwanka, K.↗