Average flow model

The statistic models consider surface roughness as a stochastic process, and concern the averaged or statistic behavior of lubrication and contact. For instance, the average flow model, proposed by Patir and Cheng [2], combined with the Greenwood and Williamsons statistic model of asperity contact [3] has been one of widely accepted models for mixed lubrication in early times. 

As a result of asperity contact, the nominal contact zone is split into a number of discrete areas that can be cataloged either to the lubrication region or asperity contact area (Fig. 2). The mean hydrodynamic pressure in the lubrication regions, pi, can be calculated by the average flow model, while contact pressure is estimated via Eq (7). Consequently, the film thickness is determined through numerical iterations to... 

Patir, N. and Cheng, H. S., "Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication, ASME J. Lubr. Technol., Vol. lOO.No. 1,1978,pp. 12-17. 

Patir, N., Effects of Surface Roughness on Partial Film Lubrication Using an Average Flow Model Based on Numerical Simulation. Ph.D. Thesis, Northwestern University, 1978. 

PATIR, N. and CHENG, H.S., An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, Trans ASME, J. Lub Tech, 100 (1), p 12, 1978. 

Reply bv the Authors Patir and Cheng s average flow model was applied point by point in the entire computation domain. The film thickness at each node includes the elastic deformation caused by the hydrodynamic and contact pressures. It is then applied to calculate the flow factors to be used in the average Reynolds equation. Such process is repeated until the results converge. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

In the fluid flow model, simulation is based on Darcy s law for the steady flow of Newtonian fluids through porous media. This law states that the average... 

In choosing a model, the user can optimize fate assessment efforts by delineating first, the source release patterns and second, the dominant dynamical processes. Taking the intramedia processes first, one can address model criteria by considering the ratio of characteristic times. The advection time is the principal length scale of the domain L divided by the average flow speed u i.e. 

The basic premise of the segregated flow model is that the various fluid elements move through the reactor at different speeds without mixing with one another. Consequently, each little fluid element will behave as if it were a batch reactor operating at constant pressure. The conversions attained within the various fluid elements will be equal to those in batch reactors with holding times equal to the residence times of the different fluid elements. The average conversion level in the effluent is then given by... 

RANS simulations usually exploiting some k-e turbulence model, intended for global information on the average flow field and the global transport phenomena in full-scale process equipment, with additional output (of limited confidence level) on spatial distributions of k and e ... 

The approaches adopted in the homogeneous model and the separated flow model are opposites in the former it is assumed that the two-phase flow can be treated as a hypothetical single-phase flow having some kind of average properties, while in the separated flow model it is assumed that distinct parts of the flow cross section can be assigned to the two phases, reflecting what occurs to a large extent in annular flow. 

Some early spray models were based on the combination of a discrete droplet model with a multidimensional gas flow model for the prediction of turbulent combustion of liquid fuels in steady flow combustors and in direct injection engines. In an improved spray model,[438] the full Reynolds-averaged Navier-Stokes equations were... 

This chapter is devoted to methods for describing the turbulent transport of passive scalars. The basic transport equations resulting from Reynolds averaging have been derived in earlier chapters and contain unclosed terms that must be modeled. Thus the available models for these terms are the primary focus of this chapter. However, to begin the discussion, we first review transport models based on the direct numerical simulation of the Navier-Stokes equation, and other models that do not require one-point closures. The presentation of turbulent transport models in this chapter is not intended to be comprehensive. Instead, the emphasis is on the differences between particular classes of models, and how they relate to models for turbulent reacting flow. A more detailed discussion of turbulent-flow models can be found in Pope (2000). For practical advice on choosing appropriate models for particular flows, the reader may wish to consult Wilcox (1993). 

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