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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.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Evolution of disturbances in stagnation point flow

The evolution of three-dimensional disturbances in an incompressible three-dimensional stagnation-point flow in an inviscid fluid is investigated. Since it is not possible to apply classical normal mode analysis to the disturbance equations for the fully three-dimensional stagnation-point flow to obtain solutions, an initial-value problem is solved instead. The evolution of the disturbances provide the necessary information to determine stability and indeed the complete transient as well. It is found that when considering the disturbance energy, the planar stagnation-point flow, which is independent of one of the transverse coordinates, represents a neutrally stable flow whereas the fully three-dimensional flow is either stable or unstable, depending on whether the flow is away from or towards the stagnation point in the transverse direction that is neglected in the planar stagnation point.

Criminale, William O.↗
NASA NTRS1993

Finite difference time domain analysis of chirped dielectric gratings

The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.

Hochmuth, Diane H.↗
NASA NTRS1993

Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

Radhakrishnan, Krishnan↗
NASA NTRS1994

Towards enhancing and delaying disturbances in free shear flows

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Criminale, W. O.↗
NASA NTRS1995

Acoustic field in unsteady moving media

In the interaction of an acoustic field with a moving airframe the authors encounter a canonical initial value problem for an acoustic field induced by an unsteady source distribution, q(t,x) with q equivalent to 0 for t less than or equal to 0, in a medium moving with a uniform unsteady velocity U(t)i in the coordinate system x fixed on the airframe. Signals issued from a source point S in the domain of dependence D of an observation point P at time t will arrive at point P more than once corresponding to different retarded times, Tau in the interval (0, t). The number of arrivals is called the multiplicity of the point S. The multiplicity equals 1 if the velocity U remains subsonic and can be greater when U becomes supersonic. For an unsteady uniform flow U(t)i, rules are formulated for defining the smallest number of I subdomains V(sub i) of D with the union of V(sub i) equal to D. Each subdomain has multiplicity 1 and a formula for the corresponding retarded time. The number of subdomains V(sub i) with nonempty intersection is the multiplicity m of the intersection. The multiplicity is at most I. Examples demonstrating these rules are presented for media at accelerating and/or decelerating supersonic speed.

Bauer, F.↗
NASA NTRS1995

Experimental confirmation of a PDE-based approach to design of feedback controls

Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

Banks, H. T.↗
NASA NTRS1995

qSmoothed particle interpolation

Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of a nonhydrodynamical nature. Under this approach, SPH is viewed as strickly as interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogenous sound speed and (2) Burger's equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite-difference methods. It is shown that the power of SPI arises when the smoothing particles are free to move.

Laguna, Pablo↗
NASA NTRS1996

Designing ROW Methods

There are many aspects to consider when designing a Rosenbrock-Wanner-Wolfbrandt (ROW) method for the numerical integration of ordinary differential equations (ODE's) solving initial value problems (IVP's). The process can be simplified by constructing ROW methods around good Runge-Kutta (RK) methods. The formulation of a new, simple, embedded, third-order, ROW method demonstrates this design approach.

Freed, Alan D.↗
NASA NTRS1999

Generalized Functions for the Fractional Calculus

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Lorenzo, Carl F.↗
NASA NTRS1999

Mid-Field Sonic Boom Extrapolation Methodology

In the design cycle of low-boom airplanes, sonic boom prediction must be accurate and efficient. The classical linear method, Whitham's F-function theory, has been widely applied to predict sonic boom signatures. However, linear theory fails to capture the nonlinear effects created by large civil transport. Computational fluid dynamics (CFD) has been used successfully to predict sonic boom signals at the near and mid fields. Nevertheless, it is computationally expansive in airplane design runs. In the present study, the method of characteristics is used to predict sonic boom signals in an efficient fashion. The governing equations are the axisymmetric Euler's equations with constant enthalpy. Since the method solves Euler's equations, it captures more nonlinear effects than the classical Whitham's F-function technique. Furthermore, the method of characteristics is an efficient marching scheme for initial value problems. In this study, we will first review the current CFD extrapolation technique and the work previously done in sonic boom extrapolation. Then, we will introduce the governing equations and the method of characteristics. Finally, we will show that the present method yields the same accurate results as previous CFD techniques, but with higher efficiency.

Cheung, Samson↗
NASA NTRS2001

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Barth, Timothy↗
NASA NTRS2005

Simulation of Blast Waves with Headwind

The blast wave resulting from an explosion was simulated to provide guidance for models estimating risks for human spacecraft flight. Simulations included effects of headwind on blast propagation, Blasts were modelled as an initial value problem with a uniform high energy sphere expanding into an ambient field. Both still air and cases with headwind were calculated.

Olsen, Michael E.↗
NASA NTRS2007

The Attenuation of a Detonation Wave by an Aircraft Engine Axial Turbine Stage

A Constant Volume Combustion Cycle Engine concept consisting of a Pulse Detonation Combustor (PDC) followed by a conventional axial turbine was simulated numerically to determine the attenuation and reflection of a notional PDC pulse by the turbine. The multi-stage, time-accurate, turbomachinery solver TURBO was used to perform the calculation. The solution domain consisted of one notional detonation tube coupled to 5 vane passages and 8 rotor passages representing 1/8th of the annulus. The detonation tube was implemented as an initial value problem with the thermodynamic state of the tube contents, when the detonation wave is about to exit, provided by a 1D code. Pressure time history data from the numerical simulation was compared to experimental data from a similar configuration to verify that the simulation is giving reasonable results. Analysis of the pressure data showed a spectrally averaged attenuation of about 15 dB across the turbine stage. An evaluation of turbine performance is also presented.

VanZante, Dale↗
NASA NTRS2017

Reachability Subspace Exploration Using Continuation Methods

Reachability manifold computation suffers from the curse of dimensionality and for large state spaces is computationally intractable. This paper examines the use of continuation methods to address this issue by formulating the reachability sub-space manifold calculation into a number of initial valued problems. As a result of computing the reachability manifold for a subspace of interest, an exponential improvement in computational cost occurs. This concept is applied to a position subspace reachability problem of a spacecraft in a Keplerian orbit under maximum thrust constraints. Future work includes a comparison of the proposed method with computing reachability manifolds using viscosity solutions of the Hamilton Jacobi Bellman partial differential equation.

orbital mechanics↗
NASA NTRSDate not supplied

Robust Trajectory Optimization Techniques Using a Sweeping Gradient Method and Linear Covariance Analysis

We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.

Benjamin W L Margolis↗
NASA NTRSDate not supplied

Co-Optimization of Navigation System Requirements and Trajectory Design Using a Sweeping Gradient Method and Linear Covariance Analysis

We describe the application of a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov) to the co-optimization of navigation system requirement generation and robust trajectory design. SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve a combined robust optimal trajectory and navigation system design problem. In this paper, we formulate the required models to apply the combined SGM and LinCov techniques to a Near-Rectilinear Halo Orbit rendezvous approach scenario and show results for several intermediate problems.

Benjamin W L Margolis↗
NASA NTRS1971

On some problems in a theory of thermally and mechanically interacting continuous media

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Lee, Y. M.↗