ALBERT

Description: A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. High pressure, water pumps, industrial chemical pumps, and cryogenic pumps are mentioned as a few of many applications. The initial motivation was the LOX-GOX seals for the space shuttle main engine, but the study was expanded to include any face or annular seal where boiling occurs. Some of the distinctive behavior characteristics of two-phase seals were discussed, particularly their axial stability. While two-phase seals probably exhibit instability to disturbances of other degrees of freedom such as wobble, etc., under certain conditions, such analyses are too complex to be treated at present. Since an all liquid seal (with parallel faces) has a neutral axial stiffness curve, and is stabilized axially by convergent coning, other degrees of freedom stability analyses are necessary. However, the axial stability behavior of the two-phase seal is always a consideration no matter how well the seal is aligned and regardless of the speed. Hence, axial stability is thought of as the primary design consideration for two-phase seals and indeed the stability behavior under sub-cooling variations probably overshadows other concerns. The main thrust was the dynamic analysis of axial motion of two-phase face seals, principally the determination of axial stiffness, and the steady behavior of two-phase annular seals. The main conclusions are that seals with two-phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two-phase seal is described and documented. The analyses, results, and computer codes are summarized.

Description: The present investigation is concerned with a fully discrete accuracy and stability analysis of the one-dimensional heat equation, taking into account the evaluation of two-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices. Schemes of the considered characteristics are not amenable to uncoupled semidiscrete and ordinary differential equation analyses. The obtained results illustrate that superior behavior may be achieved by schemes of the employed type when compared with the performance of the standard one-pass explicit schemes. The key idea in the considered approach is related to the utilization of a reduced-quadrature capacity matrix in the evaluation of the right-hand-side residual.

Description: A solution procedure for solving nonlinear time-marching problems is presented. The nonsymmetric systems of equations arising from a Newton-type linearization of these time-marching problems are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms.

Description: The current status of streamline-upwind/Petrov-Galerkin (SUPG) methods for the analysis of flow problems is surveyed in an analytical review. Problem areas addressed include classical Galerkin, upwind, artificial-diffusion, SUPG, discontinuous Galerkin, space-time FEM, and discontinuity-capturing approaches to the scalar advection-diffusion equation; incompressible flows; advective-diffusive systems; and the compressible Euler and Navier-Stokes equations. Graphs and diagrams are provided, and the good stability properties of state-of-the-art SUPG methods are pointed out.

Description: Galerkin/least-squares finite-element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of streamline-upwind Petrov-Galerkin methods, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. Some numerical results for compressible Navier-Stokes flows are presented.

Description: Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

Description: Symmetric finite-element formulations are presented for the primitive-variables form of the Stokes equations. These formulations are convergent for any combination of pressure and velocity interpolations. Various boundary conditions, such as pressure, are accommodated.

Description: The application of Galerkin/least-squares methodology to computational fluid dynamics is reviewed. Applications to advective-diffusive systems of equations and incompressible and compressible Euler and Navier-Stokes equations are described. Space-time finite-element methodology for time-dependent problems is emphasized and the status and role of so-called 'discontinuity-capturing operators' is reviewed.

Description: The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.