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Approach using bond-cover coat of unplasticized rubber between soft rubber and adhesive eliminates diffusion problem. Approach is useful in making improved seals in automobile engines, industrial and public plumbing, and in other areas using soft-rubber-to-metal bonds. Seals and gaskets made this way would not have to be replaced very often, reducing cost of maintenance.
A variational principle for time dependent diffusion problems is presented and is demonstrated by applying it to simple seasonal climate models. Two cases are treated. The first, a North-Coakley-type model with constant properties, is used as a tutorial example for the application of the technique. For the second case, heat capacity and thermal conductivity are considered to be latitude dependent in order to treat the effects of land/ocean distribution on the seasonal temperature distribution over the earth. The variational equations are derived and approximate analytical solutions are developed which delineate the influences of the physical asymmetries of the hemispheres in producing an asymmetric annual cycle.
An accurate numerical solution of diffusion problems containing large local gradients can be obtained with a significant reduction in computational time by using a multigrid computational scheme. The spatial domain is covered with sets of uniform square grids of different sizes. The finer grid patterns overlap the coarse grid patterns. The finite-difference expressions for each grid pattern are solved independently by iterative techniques. Two interpolation methods were used to establish the values of the potential function on the fine grid boundaries with information obtained from the coarse grid solution. The accuracy and computational requirements for solving a test problem by a simple multigrid and a multilevel-multigrid method were compared. The multilevel-multigrid method combined with a Taylor series interpolation scheme was found to be best.
A numerical method based on the axisymmetric, incompressible Navier-Stokes equations is combined with a lifting surface code to predict the vortex wake of hovering rotors. The lifting surface code, AMI Hover, is used to obtain the circulation distribution on the blade. This circulation distribution is fed into the Navier-Stokes code to compute the vortex wake under this specified circulation distribution. An iteration approach is used between these two codes to converge the circulation distribution and the shape of the vortex wake. A relaxation scheme is developed to resolve the instability encountered among the tip vortices. A reconcentration scheme is used to solve the diffusion problem due to the strong artificial viscosity. The results from the present method are compared with experimental data obtained by smoke-flow visualization and hot-wire measurements for several rotor blade configurations. The comparisons show that the present method is able to predict the complex wake system shed by a hovering rotor.
A symmetric total variation diminishing (STVD) algorithm has been applied to the solution of the three-dimensional hypersonic flowfield surrounding the Aeroassist Flight Experiment (AFE) vehicle. Both perfect-gas and chemical nonequilibrium models have been used. The perfect-gas flows were computed at two different Reynolds numbers, including a flight trajectory point at maximum dynamic pressure, and on two different grids. Procedures for coupling the solution of the species continuity equations with the Navier-Stokes equations in the presence of chemical nonequilibrium are reviewed and tested on the forebody of the AFE and on the complete flowfield assuming noncatalytic wall and no species diffusion. Problems with the STVD algorithm unique to flows with variable thermodynamic properties (real gas) are identified and algorithm modifications are suggested. A potential heating problem caused by strong flow impingement on the nozzle lip in the near wake at 0-deg angle of attack has been identified.
The performance of five different interface preconditionings for domain-decomposed convection-diffusion problems, including a novel one known as the spectral probe is tested in a three-dimensional parameter space consisting of mesh parameters, Reynolds number, and domain aspect ratio. The preconditioners are representative of the range of practically computable possibilities that have appeared in the literature for the treatment of nonoverlapping subdomains. Numerical examples show that no single preconditioner can be considered uniformly superior or uniformly inferior to the rest, but that knowledge of the particulars of the shape and strength of the convection is important in selecting among them in a given problem.
Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.
The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.
A variable explicit time integration algorithm is developed for unsteady diffusion problems. The algorithm uses nodal partitioning and allows the nodal groups to be updated with different time steps. The stability of the algorithm is analyzed using energy methods and critical time steps are found in terms of element eigenvalues with no restrictions on element types. Several numerical examples are given to illustrate the accuracy of the method.
Some examples of profiles of PBL quantities retrieved from Doppler radar and lidar observations are shown, and the extent to which the deduced quantities agree with the traditional eddy viscosity concept is examined. It is found in one case that the concept of 'top down bottom up' diffusion introduced by Wyngaard (1983) is more pertinent than that of the eddy viscosity. In another case it is found that, in stable layers with sufficiently large Richardson number, the momentum fluxes could be counter-gradient. In this latter case the use of a negative turbulence diffusion coefficient would result in an ill-posed differential equation, thus confusing the 'diffusion problem'.
Scalar fields undergoing random advection have attracted much attention from researchers in both the theoretical and practical sectors. Research interest spans from the study of the small scale structures of turbulent scalar fields to the modeling and simulations of turbulent reacting flows. The probability density function (PDF) method is an effective tool in the study of turbulent scalar fields, especially for those which involve chemical reactions. It has been argued that a one-point, joint PDF approach is the one to choose from among many simulation and closure methods for turbulent combustion and chemically reacting flows based on its practical feasibility in the foreseeable future for multiple reactants. Instead of the multi-point PDF, the joint PDF of a scalar and its gradient which represents the roles of both scalar and scalar diffusion is introduced. A proper closure model for the molecular diffusion term in the PDF equation is investigated. Another direction in this research is to study the mapping closure method that has been recently proposed to deal with the PDF's in turbulent fields. This method seems to have captured the physics correctly when applied to diffusion problems. However, if the turbulent stretching is included, the amplitude mapping has to be supplemented by either adjusting the parameters representing turbulent stretching at each time step or by introducing the coordinate mapping. This technique is still under development and seems to be quite promising. The final objective of this project is to understand some fundamental properties of the turbulent scalar fields and to develop practical numerical schemes that are capable of handling turbulent reacting flows.
Fundamental studies of fluid mechanics and transport in partially saturated soils are presented. Solution of transient diffusion problems in support of the development of probes for the in-situ measurement of moisture content is given. Numerical and analytical methods are used to study the fundamental problem of meniscus and saturation front propagation in geometric models of porous media.
A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to turbulent channel flow at low Reynolds number, where it is found to successfully predict low-order statistics with fewer degrees of freedom than traditional numerical methods. This reduction is achieved by utilizing local hp-refinement such that the computational grid is refined simultaneously in all three spatial coordinates with decreasing distance from the wall. Another advantage of DG is that Dirichlet boundary conditions can be enforced weakly through integrals of the numerical fluxes. Both for a model advection-diffusion problem and for turbulent channel flow, weak enforcement of wall boundaries is found to improve results at low resolution. Such weak boundary conditions may play a pivotal role in wall modeling for large-eddy simulation.
Pulse Phase Thermography (PPT) has been reported as a novel powerful technique of the thermal NDE. It employs application of the Discrete Fourier Transform (DFT) to thermal images obtained following flash heating of the front surface of a specimen. The computed phasegrams are excellent for defect visualization in a wide range of materials. This is in part due to their low sensitivity to uneven heating. This work is an attempt to analyze advantages and limitations of PPT. Results of application of the DFT to simulated temperature decays are presented. The temperature evolution on a surface has been simulated based on an analytical solution of the one-dimensional heat diffusion problem. A more sophisticated study has been done for different sizes of defects using numerical solution of the three-dimensional mathematical model. Capabilities of PPT for in-depth scanning and for monitoring of the material loss are discussed. The recommendations for the practical application of the PPT are presented. Experimental results obtained following these recommendations are reported.
Multistage, explicit time stepping can be tailored to accelerate convergence for scalar advection-diffusion problems by using optimized multistage coefficients that vary with the local cell Reynolds number. And, when combined with local preconditioning, variable-coefficient multistage schemes for computational fluid dynamics codes can also provide an order of magnitude faster convergence, relative to standard, fixed-coefficient schemes, for the Navier-Stokes system of equations.
We report progress in the development of agglomerated multigrid techniques for fully un- structured grids in three dimensions, building upon two previous studies focused on efficiently solving a model diffusion equation. We demonstrate a robust fully-coarsened agglomerated multigrid technique for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A signi cant speed-up in computer time is demonstrated for a model diffusion problem, the Euler equations, and the Reynolds-averaged Navier-Stokes equations for 3D realistic complex geometries.
We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.
Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.