SEARCH · Search NASA

Results for “Finite volume method”

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 487 records · Page 27

All sources NASA NTRS DOE OSTI

DOE OSTI2025

High-Speed and High-Quality Field Welding Repair Based on Advanced Non-Destructive Evaluation and Numerical Modeling

Creep strength-enhanced ferritic (CSEF) steels such as Grade 91 (9Cr-1Mo-V) and Grade 92 (Fe-9Cr-2W-0.5Mo) steels are widely used in the fossil-fuel-fired and nuclear power plants. The weld integrity of these steels is crucial for power plants' safe and reliable operations. Due to harsh service conditions, the steel weld can become susceptible to environmental degradation. Field welding repair is used to restore the degraded weld’s performance where a controlled temper-bead welding technique is commonly used to temper the freshly formed martensite during welding. However, knowledge of weld repairability is limited and experimental trial and error optimization to achieve desired microstructure and joint properties is expensive and time-consuming. Many existing computational models, e.g., finite element models, are limited to solving heat conduction equation and ignoring convective heat transfer due to molten metal flow. These models can result in over-prediction of peak temperatures of weld pool and heat-affected zone (HAZ), which in turn can affect the accuracy of tempering prediction. Moreover, these finite element models require an input of the deposit profiles in advance and thus limits the usability of these models. Here, a molten pool-based, multi-pass multi-layer model has been developed based on computational fluid dynamics (CFD) approach with the Volume of Fluid (VOF) method. The model calculates the bead formation, thereby eliminating the need for pre-determined bead profiles required by finite element models. For computational efficiency, a coordinate system attached to the moving heat source is utilized. A subroutine is developed to convert the temperature profiles in the reference frame stationary to the heat source to that stationary to the workpiece. The converted thermal cycles are then imported into a microstructure model to compute the tempering kinetics and resultant hardness using a Johnson-Mehl-Avrami-Kolmogorov (JMAK), and modified Grange-Baughman parameter. The modeling approach is first developed and validated on single- and multi-pass deposition of stainless steel filler metal onto a SA-533 high strength steel substrate. The models are then applied to a multi-pass V-groove repair weld of Grade 91 steel plate as well as directed energy deposition of Grade 92 steel. Non-destructive characterization of microstructures was performed on Grade 91 and 92 steel welds. Two welding processes, cold metal transfer (CMT) and flux-cored arc welding (FCAW), were investigated for the Grade 91 steel weld samples. For the Grade 92 weld samples, three different heat inputs (low, medium, and high) of gas tungsten arc welding (GTAW) were utilized to replicate traditional field welding processes. The non-destructive evaluation (NDE) method used for this research was immersion ultrasonic testing (UT) using a micro-resolution ultrasonic imaging methodology specifically designed to operate in the through-transmission configuration operating at 20 MHz of frequency. The system used a focused ultrasonic beam spot size diameter between 250-300 μm, and a 6 μm laser vibrometer spot size for detection, to produce highly defined images with longitudinal and mode-converted shear waves. From the micro-resolution ultrasonic C-scan images, three microstructural regions, i.e., weld metal (WM), HAZ, and base metal (BM), were clearly identifiable. Various levels of ultrasonic amplitudes distributed over the three regions were correlated with electron beam backscattered diffraction (EBSD) images using grain size, grain boundaries, and dislocation densities. The results showed that areas with relatively higher ultrasonic amplitude levels were associated with smaller grains and higher dislocation densities, while areas with lower amplitude levels were associated with larger grains and lower dislocation densities. In addition, ultrasonic velocity data obtained across the three different weld microstructural regions of Grade 91 test samples were correlated with optical metallographic images and hardness measurements. The results showed distinctive decreases in ultrasonic velocity and hardness over the HAZ region, where weld failures often occur during service.

36 MATERIALS SCIENCE↗

NASA NTRS1996

Simulation of Two-Fluid Flows by the Least-Squares Finite Element Method Using a Continuum Surface Tension Model

In this paper a numerical procedure for simulating two-fluid flows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols and the continuum surface force (CSF) model developed by Brackbill, et al. In the VOF method fluids of different properties are identified through the use of a continuous field variable (color function). The color function assigns a unique constant (color) to each fluid. The interfaces between different fluids are distinct due to sharp gradients of the color function. The evolution of the interfaces is captured by solving the convective equation of the color function. The CSF model is used as a means to treat surface tension effect at the interfaces. Here a modified version of the CSF model, proposed by Jacqmin, is used to calculate the tension force. In the modified version, the force term is obtained by calculating the divergence of a stress tensor defined by the gradient of the color function. In its analytical form, this stress formulation is equivalent to the original CSF model. Numerically, however, the use of the stress formulation has some advantages over the original CSF model, as it bypasses the difficulty in approximating the curvatures of the interfaces. The least-squares finite element method (LSFEM) is used to discretize the governing equation systems. The LSFEM has proven to be effective in solving incompressible Navier-Stokes equations and pure convection equations, making it an ideal candidate for the present applications. The LSFEM handles all the equations in a unified manner without any additional special treatment such as upwinding or artificial dissipation. Various bench mark tests have been carried out for both two dimensional planar and axisymmetric flows, including a dam breaking, oscillating and stationary bubbles and a conical liquid sheet in a pressure swirl atomizer.

Wu, Jie↗

NASA NTRS1973

Studies in tilt rotor VTOL aircraft aeroelasticity, volume 2

Two methods for natural mode vibration analysis are discussed. The first consists of a direct approach based on a finite element representation of the complete structure as an entity. The mass and stiffness matrices for the complete structure are assembled by properly combining the mass and stiffness matrices of the individual elements into which the structure has been divided. The second approach is that of component mode synthesis. This method is based on the concept of synthesizing the natural modes of the complete structure from modes of conveniently difined substructures, or components, into which the structure has been partitioned. In this way the expedient of reducing the system degrees of freedom, and thus the size of the eigenvalue problem, can be introduced by partial modal synthesis.

Kvaternik, R. G.↗

NASA NTRS2011

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Mishchenko, Michael I.↗

NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗

NASA NTRS1997

Hypersonic Flow Computations on Unstructured Meshes

A method for computing inviscid hypersonic flow over complex configurations using unstructured meshes is presented. The unstructured grid solver uses an edge{based finite{volume formulation. Fluxes are computed using a flux vector splitting scheme that is capable of representing constant enthalpy solutions. Second{order accuracy in smooth flow regions is obtained by linearly reconstructing the solution, and stability near discontinuities is maintained by locally forcing the scheme to reduce to first-order accuracy. The implementation of the algorithm to parallel computers is described. Computations using the proposed method are presented for a sphere-cone configuration at Mach numbers of 5.25 and 10.6, and a complex hypersonic re-entry vehicle at Mach numbers of 4.5 and 9.8. Results are compared to experimental data and computations made with established structured grid methods. The use of the solver as a screening tool for rapid aerodynamic assessment of proposed vehicles is described.

Bibb, K. L.↗

NASA NTRS1989

Development of direct-inverse 3-D methods for applied transonic aerodynamic wing design and analysis

An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.

Carlson, Leland A.↗

NASA NTRS1987

Inviscid transonic wing design using inverse methods in curvilinear coordinates

An inverse wing design method has been developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.

Gally, Thomas A.↗

NASA NTRS1985

A comparison of finite volume flux vector splittings for the Euler equations

A comparison is made between the computational results of the Steger-Warming (1981) and van Leer (1982) flux splitting methods, which have been applied in generalized coordinates to quasi-one-dimensional transonic flow in a nozzle and two-dimensional subsonic, transonic, and supersonic flow over airfoils. The latter splitting method leads to higher convergence rates and a sharper representation of shocks in the transition region. The second-order accurate, one-sided-difference model is extended to a third-order, upwind-biased model with only small additional computational effort.

Anderson, W. K.↗

NASA NTRS1990

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

Barth, Timothy J.↗

NASA NTRS1992

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Fan, Mark S.↗

NASA NTRS1993

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Steinthorsson, Erlendur↗

NASA NTRS2002

Heat Transfer in High-Temperature Fibrous Insulation

The combined radiation/conduction heat transfer in high-porosity, high-temperature fibrous insulations was investigated experimentally and numerically. The effective thermal conductivity of fibrous insulation samples was measured over the temperature range of 300-1300 K and environmental pressure range of 1.33 x 10(exp -5)-101.32 kPa. The fibrous insulation samples tested had nominal densities of 24, 48, and 72 kilograms per cubic meter and thicknesses of 13.3, 26.6 and 39.9 millimeters. Seven samples were tested such that the applied heat flux vector was aligned with local gravity vector to eliminate natural convection as a mode of heat transfer. Two samples were tested with reverse orientation to investigate natural convection effects. It was determined that for the fibrous insulation densities and thicknesses investigated no heat transfer takes place through natural convection. A finite volume numerical model was developed to solve the governing combined radiation and conduction heat transfer equations. Various methods of modeling the gas/solid conduction interaction in fibrous insulations were investigated. The radiation heat transfer was modeled using the modified two-flux approximation assuming anisotropic scattering and gray medium. A genetic-algorithm based parameter estimation technique was utilized with this model to determine the relevant radiative properties of the fibrous insulation over the temperature range of 300-1300 K. The parameter estimation was performed by least square minimization of the difference between measured and predicted values of effective thermal conductivity at a density of 24 kilograms per cubic meters and at nominal pressures of 1.33 x 10(exp -4) and 99.98 kPa. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements at other densities and pressures. The numerical model was also validated by comparison with a transient thermal test simulating reentry aerodynamic heating conditions.

Daryabeigi, Kamran↗

NASA NTRS1999

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗

NASA NTRS1995

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

Pindera, Marek-Jerzy↗

NASA NTRS1992

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Rosenfeld, Moshe↗

NASA NTRS1989

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

Moitra, Anutosh↗

NASA NTRS1996

Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows

A method is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered finite-volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.

Frink, Neal T.↗