The Single Pipe Model

The results from the single pipe model under laminar flow conditions matched fairly well the results from actual surveys at two sites. At a third site, the match was better under plug flow conditions. It should be borne in mind that the flow conditions at an individual property will be somewhere in between the idealised plug and laminar conditions that have been reported. 

The models, which are described in more detail elsewhere (Van der Leer et al, 2002), enable the most relevant features of a water supply zone to be incorporated in the prediction of zonal compliance with lead standards, as a function of boA plumbosolvency (corrosivity of the water to lead) and the zone s physical characteristics. A zonal model simulates the emissions of lead at individual simulated houses, through time, across an entire water supply zone or area of supply. It uses a single pipe model to determine the lead emission profile at each simulated house, the characteristics of each simulated house being the outcome of the random ascription of variables, which follows the Monte Carlo method for establishing a probabilistic firame-work. 

This diffusive flow must be taken into account in the derivation of the material-balance or continuity equation in terms of A. The result is the axial dispersion or dispersed plug flow (DPF) model for nonideal flow. It is a single-parameter model, the parameter being DL or its equivalent as a dimensionless parameter. It was originally developed to describe relatively small departures from PF in pipes and packed beds, that is, for relatively small amounts of backmixing, but, in principle, can be used for any degree of backmixing. 

Simpler optimization problems exist in which the process models represent flow through a single pipe, flow in parallel pipes, compressors, heat exchangers, and so on. Other flow optimization problems occur in chemical reactors, for which various types of process models have been proposed for the flow behavior, including well-mixed tanks, tanks with dead space and bypassing, plug flow vessels, dispersion models, and so on. This subject is treated in Chapter 14. 

Heat losses from the exhaust gas, as it travels down the exhaust pipe from the engine to the catalyst, result in slower catalyst warm-up and reduced conversion. These heat losses can be reduced by moving the catalyst closer to the engine or by using a dual skin (insulated) exhaust pipe rather than a standard single skin pipe. The diameter of the exhaust pipe will also have an effect. By using a model for heat losses from the exhaust pipe, such as that published by Ansell et al. (1996), such effects can be quantified. 

This structure assures correct pressure-flow solutions and, thus keeps the model consistent. Software packages, such as ASPEN Dynamics , will ensure this correct coupling. In general, two flow calculating devices cannot be connected directly, but must have a pressure (typically a volume) element in between. Two flow devices can be connected if a single equation can be written that describes the pressure drop over the connected section. For instance, some programs allow two pipe models to be connected. 

In [132] the second moment of the variance coefficient M = (a/c) was calculated for a single phase (air) turbulent flow in a pipe with a Tee mixer with the CFD code (Phoenix, version 1.6) for two distances x/D = 3 and 5 from the addition point and different values of momentum length/pipe diameter ud/ yD The K-e model utilized contained two additional laws of conservation for the mean kinetic energy K and the dissipation s. The parameter range extended over 0.026 model used reproduces well the existing experimental data and only a few adjustments are necessary to the already existing process relationship, whose constant is ca. 70% lower than the newly acquired one. 

To proceed the limiting forms of the Leibnitz and the Gauss theorems , appropriate for two phase flow, are applied. These theorems are considered direct extensions of the single phase theorems examined in sect 1.2.6 so no further derivation is given here. In most reactor model formulations the pipe walls are supposed to be fixed and impermeable. In the limit z —> 0, the limiting form of the Leibnitz theorem for volume reduces to the following relation for area [43, 47] ... 

Assumed the established model use single U-tube heat exchanger, because of the small pitch in two pipes, will interfere each other, could cause heat change different of the outside pipe and concrete. To simplify the calculation, instead the two pipe of U-tube of an equivalence pipe. Its equivalent diameter D =->j2D (Bose JE,1993), D is the diameter of one of the U-tube. Consider that the heat change of equivalence pipe wall and concrete is uniform ... 

They measured a magnitude of m = -1 for one single type of coal in different pipe sizes. They measured different vaiues of K for different coals. The in-situ concentration C, remained constant with speed, but the volumetric concentration of solids that could be moved increased with V. This concept will be reexamined in Section 4.10 as part of the two-layer models. 

By considering all systems as a single one while estimating the model parameters it is assumed that the degradation process model is the same for all systems. In most cases, the degradation process depends also on operating conditions that may be partially unknown. In the pipe corrosion example, the evolution of the pipe thickness depends on the used metal but it also depends on the characteristics of the fluid carried by the pipe (liquid/gaz, temperature, pressure. ..) and on the location (air/ground/underwater. ..) and on the environmental conditions of the pipe (temperature, humidity. ..). 

For more dilute multiphase systems, the correlations developed by Bamea and Mizrahi (1973) are to be preferred because of the underlying physical arguments. Not only did they present a detailed review of the many multiparticle models available at the time, but they also distinguished between three independent effects, viz., (a) a hydrostatic effect, taken into account by using an apparent suspension density rather than the fluid density (b) a momentum transfer hindrance effect due to increased momentum transfer within the fluid due to the presence and motion of adjacent particles taken into account by an apparent viscosity and (c) a wall effect as the adjacent particles have a similar restraining effect on the flow field as the pipe wall for a single particle setding in a pipe. 

The SNPP reactor model, shown in Figure 12-124, utilizes a single pass design where flow is piped to the aft of the reactor vessel (relative to the spaceship direction of travel), is directed to the front of the reactor by an internal downcomer annulus, travels aft through the heated portion of the reactor, is collected in the outlet plenum, and exits near the aft of the reactor vessel Except where noted, alt data used is from gas cooled reactor concept OSO-470 (Reference 12-14), which uses UOj fuel and has an annulus between each fuel pin and the core blodt for coolant flow. Table 12-8 lists pertinent parameters from this core concept. There are 354 fuel pins which are divided into five channels (three 72-pin channels, one 71-pin channel, and one 66-pin channel) plus one single channel hot pin for modeling purposes. 

The reactor inlet and outlet plenum is modeled using a REI.AP5-3D branch component to allow multiple connections to a single hydraulic component in a condensed input form. Form loss coefficients for the plenum connections are tuned to create a reactor pressure drop of approximately 2.5% of the inlet pressure as dictated by Reference 12-1. No exit flow losses are applied at the fuel pin exits however, forward and reverse loss factors of 0.408 and 0.665 are applied between the outlet plenum and the outlet pipe. 

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