Models flow-through

The treatment of vent flow calculations in most typical relief system configurations involves two classes of computational models flow through nozzles and frictional flow in pipes. 

Two common types of one-dimensional flow regimes examined in interfacial studies Poiseuille and Couette flow [37]. Poiseuille flow is a pressure-driven process commonly used to model flow through pipes. It involves the flow of an incompressible fluid between two infinite stationary plates, where the pressure gradient, Sp/Sx, is constant. At steady state, ignoring gravitational effects, we have... 

This approach has been used in the well-known model HELP (Hydrological Evaluation of Landfill Performance, Schroeder et al. 1994) and a number of complementary models (Nixon et al. 1997). These models mostly assume the landfilled material to be idealized layers with homogenous properties. One such model, HYDRUS, has been used to model flow through Landfill Lostorf, but it was found that it could not fully catch the dynamics of flow, particularly after rain events (Johnson et al. 2001). Water passes through the... 

Bilanin, A.J. Teske, M.E. Modeling flow through spring-loaded safety valves. Proceedings of ASME Pressure Vessels and Piping Conference Pipeline Dynamics Valves, 1990 PVP 190, 29-36. 

Barrier separation efficiency, viscous leak model. In the viscous leak model, flow through the small holes of radius is of the separating, molecular type dealt with in deriving Eqs. 

The flow situation in the porous medium comprising the column of packed resin beads is a complex one. One approach long used to model flow through porous media has been to consider the medium as made up of bundles of straight capillaries or assemblages of randomly oriented straight pores or capillaries in which the flow is of Poiseuille type. 

FIGURE 12.6 Maximum Analytical Model Flow-through-Screen Pressure Drop Divided by the One Dimensional Model Flow-through-Screen Pressure Drop as a Function of Outlet Reynolds Number. 

A number of different approaches are proposed and used in modeling flow through porous media. Some of the most popular approaches include (i) Darcy s law, (ii) Brinkman equation, and (iii) a modified Navier-Stokes equation. In the absence of the bulk fluid motion or advection transport, the reaction gas species can only transport through the GDL and CL by the diffusion mechanisms, which we will discuss in a later section. 

To appreciate the questions raised by Knudsen s results, consider first the relation between molar flow and pressure gradient for a pure gas flowing through a porous plug, rather than a capillary. The form predicted by the dusty gas model can be obtained by setting = 1, grad = 0 in equation... 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

Dispersion Model An impulse input to a stream flowing through a vessel may spread axially because of a combination of molecular diffusion and eddy currents that together are called dispersion. Mathematically, the process can be represented by Fick s equation with a dispersion coefficient replacing the diffusion coefficient. The dispersion coefficient is associated with a linear dimension L and a linear velocity in the Peclet number, Pe = uL/D. In plug flow, = 0 and Pe oq and in a CSTR, oa and Pe = 0. 

A slide surface is a surface where the tangential velocity can be discontinuous as shown in Fig. 9.9. Separate velocities are calculated for each side. Slide lines are useful for modeling phenomena such as sliding friction or flow through pipes. 

Patel, B. R. and Sheikoholeslami, Z., Numerieal modelling of turbulent flow through the orifiee meter. International Symposium on Fluid Flow Measurement, Washington, D.C., November 1986. 

For two-phase flow through pipes, an overall dimensionless dis-eharge eoeffieient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality ehoked flow. Leung [28] indieated that Equation 12-11 be multiplied by a faetor of 0.9 to bring the value in line with the elassie homogeneous equilibrium model (HEM). Equation 12-11 then beeomes... 

In a steady-state situation when gas flows through a porous material at a low velocity (laminar flow), the following empirical formula, Darcy s model, is valid ... 

The exhaust opening is modeled as a finite-sized slot with a uniform velocity distribution. The workbench and the vertical wall below the exhaust slot form a streamline of fluid flow through which the fluid does not cross and, therefore, along this line we have T = 0. Between the slot and the jet, the vertical wall is also a streamline and from the dimensionalization given... 

The ventilation model is a simple flow network with one zone and the different openings modeled as airflow links from the hall to outside Fig. 11.52). For the flow through the roof hood, two additional nodes were considered between the different cross-sections through which the air flows (Fig, 11.53). 

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