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NASA NTRS1987

Inlets, ducts and nozzles

The internal fluid mechanics research program in inlets, ducts, and nozzles is described. The program consists of a balanced effort between the development of computational tools and the conduct of experimental research. The experiments are designed to better understand the fluid flow physics, to develop new or improved flow models, and to provide benchmark quality data sets for validation of the computational methods. The inlet, duct, and nozzle research program is described according to three major classifications of flow phenomena: highly three-dimensional flow fields; shock-boundary layer interactions; and shear layer control. Specific examples of current and future elements of the research program are described for each of these phenomena. In particular, the highly three-dimensional flow field phenomena is highlighted by describing the computational and experiemental research program in transition ducts having a round-to-rectangular area variation. In the case of shock-boundary layer interactions, the specific details of research for normal shock-boundary layer interactions are described. For shear layer control research in vortex generators and the use of aerodynamic excitation for enhancement of the jet mixing process are described. Future research in inlets, ducts, and nozzles will include more emphasis on three-dimensional full Navier-Stokes methods and corresponding experiments designed to concentrate on the appropriate three-dimensional fluid flow physics.

Abbott, John M.↗

NASA NTRS1984

Stress analysis of multilayered plates around circular holes

The elasticity problem for a thick plate consisting of two bonded dissimilar homogeneous layers is considered. It is assumed that the plate is infinite, contains a circular hole, and is subjected to axisymmetric external loads. A technique suitable to the formulation of three-dimensional boundary value problems is introduced and applied to the three-dimensional elasticity solution of an infinite plate with a hole. The effect of Poisson's ratio is studied in some detail, and the axisymmetric problem of a laminated plate is solved. The stresses at the interface are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singularity is presented and the stress intensity factors are computed. Some of the results are compared with those found from the finite element method. The agreement between the two sets with regard to trend and magnitude is found to be very satisfactory.

Delale, F.↗

NASA NTRS1988

Probabilistic structural analysis methods and applications

An advanced algorithm for simulating the probabilistic distribution of structural responses due to statistical uncertainties in loads, geometry, material properties, and boundary conditions is reported. The method effectively combines an advanced algorithm for calculating probability levels for multivariate problems (fast probability integration) together with a general-purpose finite-element code for stress, vibration, and buckling analysis. Application is made to a space propulsion system turbine blade for which the geometry and material properties are treated as random variables.

Cruse, T. A.↗

NASA NTRS1989

Compact finite volume methods for the diffusion equation

An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.

Rose, Milton E.↗

NASA NTRS1990

New developments in adaptive methods for computational fluid dynamics

New developments in a posteriori error estimates, smart algorithms, and h- and h-p adaptive finite element methods are discussed in the context of two- and three-dimensional compressible and incompressible flow simulations. Applications to rotor-stator interaction, rotorcraft aerodynamics, shock and viscous boundary layer interaction and fluid-structure interaction problems are discussed.

Oden, J. T.↗

NASA NTRS1992

A probabilistic approach to the evaluation of fatigue damage in a space propulsion system injector element

The fatigue damage of a space propulsion system component is computed using probabilistic structural analysis methods. The analysis takes into account the variations in static and dynamic loads, the uncertainty in structural damping, and the scatter in material fatigue resistance. The key elements of the probabilistic approach include: (1) a numerical engine model for describing the global component interface loads consistent with engine balance, (2) models for computing the local mode boundary conditions on the component, (3) a static structural analysis model that captures the strains at a damage critical location as a function of engine performance variables, (4) a finite element model for assessment of the random amplitude stress response due to random base and pressure excitations with uncertain power and correlation length, and (5) advanced first order reliability methods for computing the probabilities associated with the fatigue damage.

Rajagopal, K. R.↗

NASA NTRS1979

Improvements in surface singularity analysis and design methods

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Bristow, D. R.↗

NASA NTRS1988

A global-local finite element method suitable for parallel computations

A global-local finite element analysis procedure is developed based on the fast convergent nature of FEM in displacement. A special scheme is used to utilize the global displacement solution as boundary conditions for local regions of interest. In the local region, a refined mesh is used for further stress analysis. This global-local procedure can be easily programmed in parallel on MIMD multi-processor computers for significant time savings. A Sequent Balance 21000 system is used for demonstrating the parallel programming.

Sun, C. T.↗

NASA NTRS1987

Interactive color display of 3-D engineering analysis results

A general approach to three-dimensional postprocessing of engineering analyses is presented. The approach is versatile and may handle the results from a wide range of engineering analysis methods which involve the discretization of continua. To facilitate the understanding of complex three-dimensional numerical models, advanced interactive color postprocessing techniques are introduced. Finite element, finite difference, and boundary element models are evaluated with the prototype postprocessor. The existing color graphics program (POSTPRO3D) was ported to a high-resolution device. Interactive graphic tools were implemented to facilitate qualitative mesh evaluation from a single analysis. A postprocessing environment was design for workstation technology.

Abel, John F.↗

NASA NTRS1997

Computational Study of Electron-Molecule Collisions Related to Low-Temperature Plasmas

Computational study of electron-molecule collisions not only complements experimental measurements, but can also be used to investigate processes not readily accessible experimentally. A number of ab initio computational methods are available for these types of calculations. Here we describe a recently developed technique, the finite element Z-matrix method, Analogous to the R-matrix, method, it partitions the space into regions and employs real matrix elements. However, unlike the implementation of the R-matrix method commonly used in atomic and molecular physics, the Z-matrix method is fully variational. In the present implementation, a mixed basis of finite elements and Gaussians is used to represent the continuum electron, thus offering full flexibility without imposing fixed boundary conditions. Numerical examples include the electron-impact dissociation of N2 via the metastable A3Su+ state, a process which may be important in the lower thermosphere, and the dissociation of the CF radical, a process of interest to plasma etching. To understand the dissociation pathways, large scale quantum chemical calculations have been carried out for all target states which dissociate to the lowest five limits in the case of N2, and to the lowest two limits in the case of CF. For N2, the structural calculations clearly show the preference for predissociation if the initial state is the ground X1 Sg+ state, but direct dissociation appears to be preferable if the initial state is the A3Su+ state. Multi-configuration SCF target functions are used in the collisional calculation.

Huo, Winifred M.↗

NASA NTRS2008

Integrated Force Method for Indeterminate Structures

Two methods of solving indeterminate structural-mechanics problems have been developed as products of research on the theory of strain compatibility. In these methods, stresses are considered to be the primary unknowns (in contrast to strains and displacements being considered as the primary unknowns in some prior methods). One of these methods, denoted the integrated force method (IFM), makes it possible to compute stresses, strains, and displacements with high fidelity by use of modest finite-element models that entail relatively small amounts of computation. The other method, denoted the completed Beltrami Mitchell formulation (CBMF), enables direct determination of stresses in an elastic continuum with general boundary conditions, without the need to first calculate displacements as in traditional methods. The equilibrium equation, the compatibility condition, and the material law are the three fundamental concepts of the theory of structures. For almost 150 years, it has been commonly supposed that the theory is complete. However, until now, the understanding of the compatibility condition remained incomplete, and the compatibility condition was confused with the continuity condition. Furthermore, the compatibility condition as applied to structures in its previous incomplete form was inconsistent with the strain formulation in elasticity.

Hopkins, Dale A.↗

NASA NTRS1990

Effects of grain size and grain boundary on critical current density of high T(sub c) superconducting oxides

By means of adding impurity elements in high T sub c oxides, the effects were studied of grain size and grain boundary on the critical current density of the following systems: YBa2Cu3O(7-y) and Bi-Pr-Sr-Ca-Cu-O. In order to only change the microstructure instead of the superconductivity of the grains in the samples, the impurity elements were added into the systems in terms of the methods like this: (1) substituting Y with the lanthanide except Pr, Ce, and Tb in YBa2Cu3O(7-y) system to finning down grains in the samples, therefore, the effect can be investigated of the grain size on the critical current density of 1:2:3 compounds; (2) mixing the high T sub c oxides with the metal elements, such as Ag, according to the composition of (high T sub c oxide)1-xAgx to metallize the grain boundaries in the samples, studying the effect of the electric conductivity of the grain boundaries on the critical current density; (3) adding SiO2, PbO2, and SnO2 into the high T sub c oxide to form impurity phases in the grain boundaries, trying to find out the effects of the impurity phases or metalloid grain boundaries on the critical current density of the high T sub c superconductors. The experimental results indicate that in the case of of the presence of the metalloid grain boundaries finning down grains fails to enhance the j sub c, but restrains it strongly, the granular high T sub c superconductors with the small size grains coupled weakly is always the low j sub c system.

Zhao, Y.↗

NASA NTRS1977

A numerical study of the temperature field in a cooled radial turbine rotor

The three dimensional temperature distribution in the cooled rotor of a radial inflow turbine is determined numerically using the finite element method. Through this approach, the complicated geometries of the hot rotor and coolant passage surfaces are handled easily, and the temperatures are determined without loss of accuracy at these convective boundaries. Different cooling techniques with given coolant to primary flow ratios are investigated, and the corresponding rotor temperature fields are presented for comparison.

Hamed, A.↗

NASA NTRS1992

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest.

Taylor, Arthur C., III↗

NASA NTRS1993

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Bibel, G. D.↗

NASA NTRS1993

A displacement gradient BEM for accurate stress computation near boundaries in 2-D anisotropic problems

A displacement gradient method for 2D anisotropic elasticity problems is presented, which effectively minimizes the boundary layer effect through a two-step procedure. First, the boundary integral equations are solved for the unknown boundary displacements and tractions. Second, a direct integral equation for displacement gradients is developed in terms of boundary tractions. Three methods based on different evaluation procedures and locations for determining the displacement gradients are proposed. In the first method the displacement gradients are averaged at nodes common to adjacent elements. The second method stores the gradients element-wise. In the third method, the gradients are evaluated at the nodes of discontinuous elements. The three methods are applied to near-isotropic plates with circular and elliptic cutouts. It is concluded that all three methods can yield accurate stress distributions.

Sistla, R.↗

NASA NTRS1993

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

Bibel, G. D.↗

NASA NTRS2000

A Finite-Element Approach for Modeling Inviscid and Viscous Compressible Flows using Prismatic Grids

The Galerkin finite-element method is used to solve the Euler and Navier-Stokes equations on prismatic meshes. It is shown that the prismatic grid is advantageous for correctly and efficiently capturing the boundary layers in high Reynolds number flows. It can be captured accurately because of the ability to cluster grid points normal to the body. The efficiency derives from the implicit treatment of the normal direction. To treat the normal direction implicitly, a semi-implicit Runge-Kutta time stepping scheme is developed. The semi-implicit algorithm is validated on simple geometries for inviscid and viscous flows and its convergence history is compared to that of the explicit Runge-Kutta scheme. The semi-implicit scheme is shown to be a factor of 3 to 4 faster in terms of CPU time to convergence.

Pandya, S. A.↗