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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 577 records · Page 32
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NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗
NASA NTRS1996

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Zheng, Xiaoqing↗
NASA NTRS1976

A method for generating numerical pilot opinion ratings using the optimal pilot model

A method for generating numerical pilot opinion ratings using the optimal pilot model is introduced. The method is contained in a rating hypothesis which states that the numerical rating which a human pilot assigns to a specific vehicle and task can be directly related to the numerical value of the index of performance resulting from the optimal pilot modeling procedure as applied to that vehicle and task. The hypothesis is tested using the data from four piloted simulations. The results indicate that the hypothesis is reasonable, but that the predictive capability of the method is a strong function of the accuracy of the pilot model itself. This accuracy is, in turn, dependent upon the parameters which define the optimal modeling problem. A procedure for specifying the parameters for the optimal pilot model in the absence of experimental data is suggested.

Hess, R. A.↗
NASA NTRS1990

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

Wahls, Richard A.↗
NASA NTRS1974

The numerical calculation of inviscid plume flow fields

A numerical method is presented for the computation of inviscid, axisymmetric, underexpanded plumes. The numerical techniques developed by Moretti (1969, 1971, 1972) are used in conjunction with Abbett's (1970) theory for locating the Mach disk. Abbett's theory and three other prediction methods are compared to experimental results. Results are presented for jets exhausting into static ambients and supersonic free stream. Detailed results from a flow field with multiple Mach disks are also presented. Finally, some problems associated with the computation of very small Mach disks are discussed.

Salas, M. D.↗
NASA NTRS1998

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws: The Two Dimensional Time Marching Schemes - 1

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Chang, Sin-Chung↗
NASA NTRS1990

Unsteady transonic Navier-Stokes computations for an oscillating wing using single and multiple zones

Modern jet transports and maneuvering tactical fighters operating in the transonic regime often give rise to time-dependent fluid physics that interact with flexible structural components, e.g., vortical flow, shocks, and separation. Efficient computational fluid dynamic (CFD) methods are required to study such computationally intensive problems. In this work a numerical method is presented to address this problem. Time-dependent, compressible, Navier-Stokes equations are used to simulate unsteady transonic flow about a three-dimensional rigid wing undergoing a forced periodic motion in angle of attack. An efficient, implicit, diagonal algorithm is utilized because of its low operation count per time step compared to other methods that solve systems of block matrix equations. The formal time accuracy is addressed theoretically and demonstrated numerically by comparison of computational results with experimental data. A zonal grid approach, capable of treating complex geometries, is presented and its time accuracy is demonstrated by comparing a zonal computation with a single grid computation and experimental data.

Chaderjian, Neal M.↗
NASA NTRS1980

Normal and shear impact of layered composite with a crack - Dynamic stress intensification

The dynamic response of a layered composite under normal and shear impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. One of the objectives was to develop an analytical method for determining dynamic stress solutions which should lead to a numerical method which utilizes Fourier transform for the space variable and Laplace transform for the time variable. The time-dependent angle loading is separated into two parts: a symmetric and a skew-symmetric with reference to the crack plane. By superposition, the transient boundary conditions consist of applying normal and shear tractions to a crack embedded in a layered composite; one phase of the composite could represent the fiber while the other could be the matrix. Mathematically, these conditions reduce the problem to a system of dual integral equations solved in the transform plane for the transform of the dynamic stress-intensity factor.

Sih, G. C.↗
NASA NTRS1984

Research in applied mathematics, numerical analysis, and computer science

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

Source record↗
NASA NTRS1996

Fluid Stochastic Petri Nets: Theory, Applications, and Solution

In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

Horton, Graham↗
NASA NTRS1994

Accurate Evaluation of Quantum Integrals

Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schr\"{o}dinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.

Galant, David C.↗
NASA NTRS1995

Accurate Evaluation of Quantum Integrals

Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.

Galant, D. C.↗
NASA NTRS2001

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Chang, Sin-Chung↗
NASA NTRS1992

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Soh, Woo Y.↗
NASA NTRS1994

Atomization simulations using an Eulerian-VOF-Lagrangian method

This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservations are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present innovative approach by simulating benchmark problems including the coaxial jet atomization.

Chen, Yen-Sen↗
NASA NTRS1988

Euler solution of multiblade rotor flow

A numerical method for solving the Euler equations for multiblade rotors has been developed and some preliminary results reported. The numerical scheme is a combination of several recent methods and algorithm improvements, adapted to the particular requirements of rotor-body interactions. A cylindrical basic grid has been used to study conventional multiblade helicopter rotors. Test calculations have been made for two- and six-blade rotors in hover and for a two-blade rotor in forward flight, under transonic tip conditions but without lift. The results show good agreement with experimental data.

Chen, C. L.↗