Mass-conserving Boundary Condition Research Articles

HISTORY MOVING OF CAVITATION FOR DYNAMICALLY LOADED JOURNAL BEARING

On the base of the Elrod algorithm, a generalized equation is derived to describe the lubrication in full film region and in cavitation region of dynamically loaded journal bearing, which is nominated as the incompressible mass-conserving cavitation algorithm. A numerical technique with this algorithm has been solved. By the definition of a switch function g and a variable ξ, which have different meaning in different zone, a generalized equation is derived to integrate the Reynolds equation in full film region with the lubrication equation in cavitation region. This algorithm can predict the moving oil boundary automatically and make the mass conserving boundary condition (JFO theory) more easily and precisely to be applied in actual analysis. It is found that the analysis results with the incompressible mass-conserving cavitation algorithm have good agreement with the existing experiment data. The incompressible cavitation algorithm can predict the history moving of cavitation well. And it is also shown that the pressure value in the cavitation has great effect on the analysis results.

SPECIAL TREATMENT OF PRESSURE CORRECTION BASED ON CONTINUITY CONSERVATION IN A PRESSURE-BASED ALGORITHM

The special features of pressure-correction equations and their effects on the performance of the SIMPLE algorithm have been systematically investigated based on the concept of continuity conservation. Except for use of the same iterative method as for the momentum equations, iterative solution of the pressure-correction equation has special features in three respects: initial values, boundary conditions (BCs), and iterative procedure. First, the initial values in each outer loop are independent and should be reset as zeroes. Second, the BCs are fully reverse to that of velocity: Dirichlet velocity BCs correspond to Neumann BCs of pressure correction, and Neumann velocity BCs lead to pressure-correction Dirichlet BCs. Third, more inner iterations for the pressure-correction equation are required to better satisfy continuity conservation. Dealing properly with these features can greatly improve the efficiency of the SIMPLE algorithm. Computational results and comparisons have shown that global mass conservation BCs are favorable to convergence, but may be slowed down by the local conservation BCs. During the course of convergence, the BCs of the pressure-correction equation are vital: only correct BCs can boost convergence, incorrect BCs cannot. Increasing the inner iterations of the pressure-correction equation will significantly decrease the outer-loop iterations, and therefore effectively improve the performance of the SIMPLE algorithm.

Transient Modeling of Thermal Degradation in Non-Charring Solids

For a more extensive investigation of polymers, a better understanding of its gasification process is extremely essential. Especially compared with the extensive studies in the gas phase, the solid phase received rather little attention. Thus, the purpose of this paper is in its comparison of several modeling approaches for thermal degradation and systematic demonstration of the effects of basic assumptions on the model results, while taking account of in-depth radiation. For this object, this study has examined in more detail the degradation for a horizontally positioned polymer which is exposed to external radiation. After a preliminary study, three different solid degradation models were chosen from the literature, and their corresponding mass and energy conservation equations and boundary conditions were assembled. The in-depth non-gray as well as gray radiation was taken into account by solving relevant radiative transfer equation. In order to concentrate on the fundamental mechanisms of polymer degradation, gas phase reactions and subsequent heat feedback from the gas were neglected. This corresponds to a nitrogen environment. Various other parameters such as the polymer refractive index, polymer absorption coefficient, convective heat loss, solid fuel thickness and external radiative heat flux were changed to discuss their effects on the quantitative as well as qualitative change in the mass loss rate. While the effect of the solid fuel thickness on the mass loss rate was negligible for a thick sample, each parameter among the polymer refractive index, polymer absorption coefficient, convective heat loss, and external radiative heat flux incurred a non-negligible change in the results. Furthermore, the convection term in the energy equation, which is usually neglected in the in-depth pyrolysis by many other works, was shown to account for 29% decrease in the mass loss rate. Finally, depending on the solid degradation model used, the addition of gray radiation to the energy equation was shown to augment or diminish the mass loss rate. It was further enhanced by taking account of the non-gray radiation. This results from the fact that the inner solid is more quickly heated due to the far-reaching effects of radiation from the surface.

DIAGONAL CARTESIAN METHOD FOR NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS OVER COMPLEX BOUNDARIES

A diagonal Cartesian method is proposed for the simulation of incompressible fluid flows over complex boundaries in Cartesian coordinates. A structured grid is utilized for the sake of simplicity. The method approximates complex boundaries using both Cartesian grid lines and diagonal line segments. The grid is generated automatically, and the geometry approximation is shown to be more accurate than the traditional sawtooth method. Mass conservation on complex boundaries is enforced with an appropriate pressure boundary condition. The method, which utilizes cell-centered nodes on a nonstaggered grid, uses boundary velocity information to avoid the specification of pressure values on boundaries, An enlarged control-volume method is introduced for mass conservation and pressure boundary conditions on complex boundaries. The conservation of momentum on complex boundaries is enforced through the finite analytic (FA) method, using nine-point and five-point FA elements. Velocity boundary conditions at moving boundaries are analyzed. The proposed diagonal Cartesian method is verified with the solution of a rotated lid-driven cavity flow. It is shown that this diagonal method predicts the fluid flow very well and improves the accuracy of the numerical simulation compared to the traditional sawtooth method. The application of this method to a grooved channel flow is also presented.

The combustion of a linear droplet array in a convective, coaxial potential flow

An efficient numerical scheme is introduced to describe the effects of forced convection and droplet-droplet interactions on the burning rate of a one-dimensional droplet array. The flow field is described by point sources (or sinks) superimposed on a uniform, coaxial potential flow. The strengths of the sources (or sinks) are found from the mass and heat conservation boundary conditions at the droplet surface. The resulting flow field is then used to solve the energy and species conservation equations, which are first transformed to a generalized coordinate system so that the computations can be carried out in any grid system. In this study, an improved, composite, body-fitted grid was used to solve the equations by an iterative, finite difference method to obtain the temperature (or concentration) field. Droplet pairs of equal sizes with spacings from 4 to 16 radii have been investigated for Peclet numbers from 10 to 120. The temperature distribution around the droplet array, as well as the local Nusselt number around the droplet surfaces, has been calculated. The results show qualitative agreement with analogous heat and mass transfer analyses that have appeared in the literature. Two droplets of unequal sizes and an array of up to six equal sized droplets have also been studied. This simple approach for treating the flow field allows the computation to be extended to a linear array with a large number of droplets. The numerical scheme has excellent convergence behavior, and the composite grid introduced here can also be used for more accurate, viscous flow calculations.

Analytical solutions for convective‐dispersive transport in confined aquifers with different initial and boundary conditions

Analytical solutions of the general one‐ dimensional solute transport model for confined aquifers, applied to specific scenarios, are obtained. The mathematical formulation that is solved includes, in addition to the usual convection/dispersion formulation, (1) distributed first‐order loss, e.g., by metabolism, chemical reaction or irreversible dissolution; (2) linear equilibrium sorption rules; (3) a single, constantly emitting, source of finite length, which can be placed anywhere on the right half line and can be of any reasonable width; (4) mass conserving boundary conditions which include a highly tailorable time distribution of chemical concentration at the inlet boundary; and (5) a highly tailorable initial distribution on [0, ∞). The model constitutes an extension and generalization of the existing literature. Five transport and fate scenarios are presented as follows: (1) a compound initially distributed in stair step fashion, (2) a constant source, (3) a constant rate of entry at the inlet boundary, (4) an inlet boundary concentration that is decaying with time, and (5) conditions 1, 2, 3, and 4 specified at the same time.