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At least 127 records · Page 7

Optimal Design of Grid-Stiffened Panels and Shells With Variable Curvature

A design strategy for optimal design of composite grid-stiffened structures with variable curvature subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. Stiffening configuration is herein defined as a design variable that indicates the combination of axial, transverse and diagonal stiffeners in the stiffened panel. The design optimization process is adapted to identify the lightest-weight stiffening configuration and stiffener spacing for grid-stiffened composite panels given the overall panel dimensions. in-plane design loads, material properties. and boundary conditions of the grid-stiffened panel or shell.

Ambur, Damodar R.↗

Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis

A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.

Ambur, Damodar R.↗

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗

Uncertainty Analysis of Decomposing Polyurethane Foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.

Hobbs, Michael L.↗

Automated Approach to Very High-Order Aeroacoustic Computations

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗

Stochastic Models of Tropical Rain-Rate Fields

Because of the extreme variability of rain rate in space and time and the difficulties with remote sensing methods of measuring rain rates, accurate determination of rainfall over large areas and time periods has long been a problem for hydrologists, meteorogists, and climatologists. A number of statistical models of rain have been developed in order to investigate the impact of rain variability on satellite remote sensing methods, validation of satellite rain products, and generation of rain maps with accompanying error estimates. These models may be useful in examining 'sub-grid scale' issues in representing precipitation in numerical mdoels. A stochastic model will first be described which can generate time-dependent high-resolution spatial rain fields with space and time correlations similar to those seen in rain data, as well as representing the presence of areas with zero rain rate and log-normally distributed rain rates where there is rain. A simpler model derived from this, formulated in the spectral domain, seems to imply fractal-like rain statistics at small scales when fit to rain data.

Bell, Thomas L.↗

A grid spacing control technique for algebraic grid generation methods

A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.

Smith, R. E.↗

Multigrid solution of the Euler equations on unstructured and adaptive meshes

A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structured multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

Mavriplis, Dimitri↗

Analyzing Carbon Dioxide and Methane Emissions in California Using Airborne Measurements and Model Simulations

Greenhouse gas (GHG) concentrations have increased over the past decades and are linked to global temperature increases and climate change. These changes in climate have been suggested to have varying effects, and uncertain consequences, on agriculture, water supply, weather, sea-level rise, the economy, and energy. To counteract the trend of increasing atmospheric concentrations of GHGs, the state of California has passed the California Global Warming Act of 2006 (AB-32). This requires that by the year 2020, GHG (e.g., carbon dioxide (CO2) and methane (CH4)) emissions will be reduced to 1990 levels. To quantify GHG fluxes, emission inventories are routinely compiled for the State of California (e.g., CH4 emissions from the California Greenhouse Gas Emissions Measurement (CALGEM) Project). The major sources of CO2 and CH4 in the state of California are: transportation, electricity production, oil and gas extraction, cement plants, agriculture, landfills/waste, livestock, and wetlands. However, uncertainties remain in these emission inventories because many factors contributing to these processes are poorly quantified. To alleviate these uncertainties, a synergistic approach of applying air-borne measurements and chemical transport modeling (CTM) efforts to provide a method of quantifying local and regional GHG emissions will be performed during this study. Additionally, in order to further understand the temporal and spatial distributions of GHG fluxes in California and the impact these species have on regional climate, CTM simulations of daily variations and seasonality of total column CO2 and CH4 will be analyzed. To assess the magnitude and spatial variation of GHG emissions and to identify local “hot spots”, airborne measurements of CH4 and CO2 were made by the Alpha Jet Atmospheric eXperiment (AJAX) over the San Francisco Bay Area (SFBA) and San Joaquin Valley (SJV) in January and February 2013 during the Discover-AQ-CA study. High mixing ratios of GHGs were observed in-flight with a high degree of spatial variability. To provide an additional method to quantify GHG emissions, and analyze AJAX measurement data, the GEOS-Chem CTM is used to simulate SFBA/SJV GHG measurements. A nested-grid version of GEOS-Chem will be applied and utilizes varying emission inventories and model parameterizations to simulate GHG fluxes/emissions. The model considers CO2 fluxes from fossil fuel use, biomass/biofuel burning, terrestrial and oceanic biosphere exchanges, shipping and aviation, and production from the oxidation of carbon monoxide, CH4, and non-methane volatile organic carbons. The major sources of CH4 simulated in GEOS-Chem are domesticated animals, rice fields, natural gas leakage, natural gas venting/flaring (oil production), coal mining, wetlands, and biomass burning. Preliminary results from the comparison between available observations (e.g., AJAX and CALGEM CH4 emission maps) and GEOS-Chem results will be presented, along with a discussion of CO2 and CH4 source apportionment and the use of the GEOS-Chem-adjoint to perform inverse GHG modeling.

Johnson, Matthew S.↗

Soil Sampling Techniques For Alabama Grain Fields

Characterizing the spatial variability of nutrients facilitates precision soil sampling. Questions exist regarding the best technique for directed soil sampling based on a priori knowledge of soil and crop patterns. The objective of this study was to evaluate zone delineation techniques for Alabama grain fields to determine which method best minimized the soil test variability. Site one (25.8 ha) and site three (20.0 ha) were located in the Tennessee Valley region, and site two (24.2 ha) was located in the Coastal Plain region of Alabama. Tennessee Valley soils ranged from well drained Rhodic and Typic Paleudults to somewhat poorly drained Aquic Paleudults and Fluventic Dystrudepts. Coastal Plain s o i l s ranged from coarse-loamy Rhodic Kandiudults to loamy Arenic Kandiudults. Soils were sampled by grid soil sampling methods (grid sizes of 0.40 ha and 1 ha) consisting of: 1) twenty composited cores collected randomly throughout each grid (grid-cell sampling) and, 2) six composited cores collected randomly from a -3x3 m area at the center of each grid (grid-point sampling). Zones were established from 1) an Order 1 Soil Survey, 2) corn (Zea mays L.) yield maps, and 3) airborne remote sensing images. All soil properties were moderately to strongly spatially dependent as per semivariogram analyses. Differences in grid-point and grid-cell soil test values suggested grid-point sampling does not accurately represent grid values. Zones created by soil survey, yield data, and remote sensing images displayed lower coefficient of variations (8CV) for soil test values than overall field values, suggesting these techniques group soil test variability. However, few differences were observed between the three zone delineation techniques. Results suggest directed sampling using zone delineation techniques outlined in this paper would result in more efficient soil sampling for these Alabama grain fields.

Thompson, A. N.↗

Large-Eddy Simulation of Variable Speed Power Turbine Cascade with Inflow Turbulence

Numerical results are presented from theNASAGlenn Research Center’sin-house turbomachinery code, Glenn-HT applied to the Variable Speed Power Turbine (VSPT) experiment at the NASA Transonic Turbine Blade Cascade Facility.The main goal of this paper is to implement a digital filtering method to generate turbulence upstream and a sub-grid model (Localized dynamic k-equation model (LDKM)) in the framework of LES in order to investigate the effect of inflow turbulence on the transition seen in the VSPT experimental data at the cruise condition (incidence angle of 40oand Tu = 0.5%, 5%,10%, and 15%). Although the boundary layer on thesuction side and pressure side of the blades is initially laminar due to favorable pressure gradient, the laminar flow can transition to turbulent flow past a separation zoneon the suction sideor by natural or by-pass transition. This process determinesthe total-pressure lossesin the wake. Therefore, it is desirable to develop a reliable prediction tool to accurately capture the transition mechanism in blade rows operated under the conditions of low Reynolds number andat a variety offree stream turbulence conditions. Our numerical studies reveal that the location of separationis rather insensitive to the level of Tu, however the effect ofincreasingTu seems to be in reducing the size and ultimately suppressing the separation bubble. In addition, we performedspectral analysis to identify the peak frequencies in the region where the separation bubble is formed, which provides valuable insights into the transition/separation mechanism.

CFD↗

A comparison of high resolution upwind solvers on 3-D inviscid hypersonic flows

A detailed comparison of numerical results obtained by solving the Euler equations for the inviscid flow over delta wings in reentry configurations is presented. The investigation involves a side-by-side comparison between independently developed upwind Euler solvers at VKI (M3D) and NASA Johnson Space Center (E3D) using identical grids. In both solvers the governing equations are integrated by means of time marching finite volume shock capturing methods, based on a cell centered upwind evaluation of the cell face fluxes and nonlinear limiters. High resolution schemes are obtained via MUSCL characteristic variable extrapolation to ensure total variation diminishing (TVD) properties and therefore monotonic discontinuity capturing. Further comparisons are made with several published results by other authors based on both upwind and central discretizations. The present results contribute in asserting the high resolution upwind TVD schemes as the most reliable numerical technique to handle the strong discontinuities typical of high speed flows. The performances of the two upwind solvers are satisfactory and the numerical results in good agreement. However, the important issue of reaching a grid converged solution for the present complex three-dimensional inviscid flow problems was not achieved.

Manna, M.↗

Flow aerodynamics modeling of an MHD swirl combustor - Calculations and experimental verification

The paper describes a computer code for calculating the flow dynamics of a constant-density flow in the second-stage trumpet shaped nozzle section of a two-stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite-difference computer code has been developed for the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for the efficient solution of the equations. The code produces as output the flow field map of the nondimensional stream function, axial and swirl velocity. It was found that the best location for seed injection to obtain a uniform distribution at the combustor exit is in the central location for seed injected at the entrance to the second stage combustor.

Gupta, A. K.↗

Flow aerodynamics modeling of an MHD swirl combustor - Calculations and experimental verification

This paper describes a computer code for calculating the flow dynamics of constant density flow in the second stage trumpet shaped nozzle section of a two stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite difference computer code has been developed to allow the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for efficient solution of the equations. Turbulence simulation is by way of a two-equation Kappa-epsilon model. The code produces as output the flowfield map of the nondimensional stream function, axial, and swirl velocity. Good agreement was obtained between the theoretical predictions and the qualitative experimental results. The best seed injector location for uniform seed distribution at combustor exit is with injector located centrally on the combustor axis at entrance to the second stage combustor.

Gupta, A. K.↗

Flow structure capturing on overset patched meshes

The present paper describes the application of a simple, robust stable implicit approach to solutions of the conservative equations of gasdynamics on either composite or overset meshes to capture flow structures such as shocks with high resolution in complex geometric domains. Without requiring special flux conservative operators, but rather, interpolating conservative variable data at mesh boundaries, the well posed upwind method provides accurate and oscillation free solutions, even when shocks cross the interior patch boundaries. In three problems with flow complexities that require grid refinement, the paper demonstrates the capability to conveniently carry out for gasdynamics the adaptive refined meshing strategy in overset patches proposed by Berger and Oliger (1984), and it extends this technique to rapidly convergent implicit methods for the Euler and Navier-Stokes equations. The numerical experiments show concretely, in a realistic aerodynamic problem, the savings in mesh points (about an order of magnitude here in two dimensions) for similar accuracy that flow structure aligned adaptive patched meshing affords compared to uniform grid refinement.

Venkatapathy, E.↗

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗

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↗

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Jorgenson, Philip C. E.↗