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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Embedded mesh solution of the 2-D Euler equations - Evaluation of interface formulations

Solution of the steady 2-D Euler equations using mesh embedding, or local grid refinement, with a cell-centered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.

Allmaras, S. R.↗
NASA NTRS1988

Adaptive p-version based finite element formulations for thermal modeling/analysis of structural configurations

Adaptive p-version based hierarchical finite element formulations in conjunction with a posteriori error estimation concepts are described with emphasis on applicability for thermal modeling/analysis of structural configurations. The basic concepts and formulations of hierarchical p-versiion finite element for thermal analysis are first described. A posteriori error estimation features are utililzed to steer the process of adaptive refinement. Several configurations comprised of one-dimensional structures are evaluated to validate the applicability of the proposed formulations and to demonstrate the potential of the p-version adaptive formulations for thermal modeling/analysis. The methodology offers potential and promises to be an attractive alternative to conventional finite element thermal modeling/analysis approaches.

Tamma, Kumar K.↗
NASA NTRS1988

Development of polyisocyanurate pour foam formulation for space shuttle external tank thermal protection system

Four commercially available polyisocyanurate polyurethane spray-foam insulation formulations are used to coat the external tank of the space shuttle. There are several problems associated with these formulations. For example, some do not perform well as pourable closeout/repair systems. Some do not perform well at cryogenic temperatures (poor adhesion to aluminum at liquid nitrogen temperatures). Their thermal stability at elevated temperatures is not adequate. A major defect in all the systems is the lack of detailed chemical information. The formulations are simply supplied to NASA and Martin Marietta, the primary contractor, as components; Part A (isocyanate) and Part B (poly(s) and additives). Because of the lack of chemical information the performance behavior data for the current system, NASA sought the development of a non-proprietary room temperature curable foam insulation. Requirements for the developed system were that it should exhibit equal or better thermal stability both at elevated and cryogenic temperatures with better adhesion to aluminum as compared to the current system. Several formulations were developed that met these requirements, i.e., thermal stability, good pourability, and good bonding to aluminum.

Harvey, James A.↗
NASA NTRS1989

Evaluation of newly formulated Dow Corning 321 dry film lubricant

An evaluation of the newly formulated Dow Corning 321 dry film lubricant was performed. The purpose of the evaluation was to compare lubricating characteristics of Dow Corning 321 (STW4-2955, SCN No. 3) to those of Molykote 321R (STW4-2955). Ten igniter bolts were installed and torqued on test plates using the old formulation thread lubricant (Molykote 321R), and 10 bolts were installed using the new formulation (Dow Corning 321). After bolt removal, no signs of galling were found on any of the bolts or test plates threaded holes. Average torque-load values for each formulation were very close. Test results showed there are no significant differences in lubrication abilities between Molykote 321R and Dow Corning 321. It is recommended that, once current supplies of Molykote 321R are depleted, Dow Corning 321 dry film lubricant be used in place of Molykote 321R as a thread lubricant on redesigned solid rocket motor assemblies.

Cook, M.↗
NASA NTRS1990

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or drilling degrees of freedom is formulated. The element formulation is based directly on a 4-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 8-node isoparametric element in which the midside degrees of freedom are eliminated in favor of rotational degree of freedom at the corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom including rotational degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element Cartesian-coordinate system is chosen such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9-parameter equilibrating stress field, while the bending part is based on a 13-parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, does not lock, possesses the desirable invariance properties, has no spurious modes, and produces accurate and reliable results.

Aminpour, Mohammad A.↗
NASA NTRS1990

A defect stream function formulation for compressible turbulent boundary layers

Progress to date on the development of a method for turbulent, wall-bounded flow which uses the defect stream function formulation in the outer layer and an analytic law of the wall and wake formulation in the inner region is reviewed. This two-formulation approach avoids the need to computationally resolve the high-gradient inner layer. One of the most appealing recent developments is the transformation of the compressible governing equation for the defect stream function into a linear, second-order differential equation which has analytic solutions for many problems of practical interest. Numerical and analytic results for incompressible and compressible flows are shown to be in excellent agreement with experimental results. In this paper the two-formulation approach is applied to primitive-variable computations. Excellent comparisons with experiment are presented for two compressible flat plate flows.

Barnwell, Richard W.↗
NASA NTRS1992

Boundary formulations for three-dimensional continuum structural shape sensitivity analysis

The direct, singular, boundary element analysis formulation is shown to provide a basis for a computationally efficient and accurate shape design sensitivity analysis approach for the structural response of three-dimensional solid objects. The theoretical formulation for surface displacement and traction component sensitivities, and all components of the stress tensor is presented along with a formulation for the recovery of displacement and stress components in the interior of the object under consideration. Discussion of computational issues related to the overall efficiency of these formulations is given, along with numerical results to demonstrate the accuracy and efficiency of this approach.

Kane, J. H.↗
NASA NTRS1993

Numerical simulation using vorticity-vector potential formulation

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Tokunaga, Hiroshi↗
NASA NTRS1995

Structural design using equilibrium programming formulations

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Scotti, Stephen J.↗
NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.

Schuler, James J.↗
NASA NTRS1994

Theoretical investigation of wave-vector-dependent analytical and numerical formulations of the interband impact-ionization transition rate for electrons in bulk silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E. Scholl, and M. Rudan (1993), and a more exact, numerical method of Y. Wang and K. F. Brennan (1994). Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formular, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with the completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to the overlap intergrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such the transition rate may be overestimated at those points for which 'near vertical,' small change in k, transitions occur.

Kolnik, Jan↗
NASA NTRS1995

Practical aspects of variable reduction formulations and reduced basis algorithms in multidisciplinary design optimization

This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step.

Lewis, Robert Michael↗
NASA NTRS1997

Implementation of Free-Formulation-Based Flat Shell Elements into NASA Comet Code and Development of Nonlinear Shallow Shell Element

This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.

Barut, A.↗
NASA NTRS1994

Theoretical Investigation of Wave-Vector-Dependent Analytical and Numerical Formulations of the Interband Impact-Ionization Transition Rate for Electron in Bulk Silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E Scholl, and M. Rudan, and a more exact, numerical method of Y. Wang and K. F. Brennan. Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formula, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with (he completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to (he overlap integrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such [he transition rate may be overestimated at those points for which "near vertical," small change in k, transitions occur.

Kolnik, Jan↗
NASA NTRS2001

DAO's Next Generation Physical-Space/Finite-Volume Data Assimilation System: Formulation and Initial Evaluation

The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will describe the general system formulation, the adaptive quality control and general aspects of the error covariance modeling. The NASA-NCAR GCM is a completely new model which replaces the CEOs GCM used in the previous GEOS-1/2/3 Data Assimilation systems. A particular configuration of adaptive Statistical Quality Control and the Physical-space Statistical Analysis System (PSAS) are currently implemented in DAO's operational Data Assimilation System. However, the unique finite-volume formulation of the NASA-NCAR GCM, combined with the generality of the observation-space formulation of PSAS, provides for a very simple and accurate model-analysis interface. The system assimilates a variety of conventional and satellite observations. In particular, TOVS Level 1B radiances are assimilated using a 1-D variational scheme, both in clear sky and cloudy conditions. Computationally, the fvDAS runs approximately 10 times faster than the operational GEOS-Terra system. We will show that the next-generation fvDAS has much improved observation-minus-6hr forecast (O-F) statistics, as well as 5-day forecast skills. Top of the atmosphere radiation fields are in closer agreement with CERES measurements, with realistic precipitation and moisture fields. We will also show that the finite-volume formulation of the fvDAS produce assimilated fields which are more suitable for driving constituent transport models.

daSilva, A.↗
NASA NTRS2002

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation: Constant Stress Rate Experiments - Part 2

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress rate and preload testing at ambient and elevated temperatures. The data fit to the relation of strength versus the log of the stress rate was very reasonable for most of the materials. Also, the preloading technique was determined equally applicable to the case of slow-crack-growth (SCG) parameter n greater than 30 for both the power-law and exponential formulations. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important SCG parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

Choi, Sung R.↗
NASA NTRS2002

Trailing Edge Noise Prediction Based on a New Acoustic Formulation

A new analytic result in acoustics called 'Formulation 1B,' proposed by Farassat, is used to compute broadband trailing edge noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams-Hawkings equation with the loading source term, and has been shown in previous research to provide time domain predictions of broadband noise that are in excellent agreement with experiment. Furthermore, this formulation lends itself readily to rotating reference frames and statistical analysis of broadband trailing edge noise. Formulation 1B is used to calculate the far field noise radiated from the trailing edge of a NACA 0012 airfoil in low Mach number flows, using both analytical and experimental data on the airfoil surface. The results are compared to analytical results and experimental measurements that are available in the literature. Good agreement between predictions and measurements is obtained.

Casper, J.↗
NASA NTRS2003

A Generalized Fluid Formulation for Turbomachinery Computations

A generalized formulation of the equations of motion of an arbitrary fluid are developed for the purpose of defining a common iterative algorithm for computational procedures. The method makes use of the equations of motion in conservation form with separate pseudo-time derivatives used for defining the numerical flux for a Riemann solver and the convergence algorithm. The partial differential equations are complemented by an thermodynamic and caloric equations of state of a complexity necessary for describing the fluid. Representative solutions with a new code based on this general equation formulation are provided for three turbomachinery problems. The first uses air as a working fluid while the second uses gaseous oxygen in a regime in which real gas effects are of little importance. These nearly perfect gas computations provide a basis for comparing with existing perfect gas code computations. The third case is for the flow of liquid oxygen through a turbine where real gas effects are significant. Vortex shedding predictions with the LOX formulations reduce the discrepancy between perfect gas computations and experiment by approximately an order of magnitude, thereby verifying the real gas formulation as well as providing an effective case where its capabilities are necessary.

Merkle, Charles L.↗