Computation of Pressure Drop

We discussed the issue of pressure drop over a cyclone with tangential inlet in Chap. 4. The infiuence of solids loading on the pressure drop will be discussed qualitatively in Chap. 9. The effect can be explained simply as the consequence of increased wall friction caused by the solids on the wall. 

According to the MM, pressure loss across a cyclone occurs, primarily, as a result of friction with the walls and irreversible losses within the vortex core, the latter often dominating the overall pressure loss. Inlet acceleration losses may also occur. 

The wall loss, or the loss in the cyclone body, is given by. 

These two equations can be compared with Eqs. (4.3.3) and (4.3.4) from the model of Barth. 

In some installations, the incoming gas-solid mixture must be accelerated from a region of low velocity to that which exists at the entrance of the cyclone. Such a condition would exist at the inlet to a highly-loaded primary cyclone above a fiuidized bed, for example. If we apply the mechanical energy balance between a point located in the low velocity region (ahead of an inlet horn, for example) and a point in the high velocity region (within the horn) we obtain for the acceleration pressure loss. 

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TABLE 6.3. Approximate Computation of Pressure Drop of Liquids and Gases in Highly Turbulent Flow in Steel Pipes ... 

The main value of data describing turbulent energy requirements is in the computation of pressure drop-flow rate characteristics for installed plant but there are also examples of performance evaluation using energy data -. As with laminar flow characteristics, although different, those for turbulent flow are relatively simple and easily described in terms of the friction factor-Reynolds number relationship used to describe empty tube. 

Because of the low gas and liquid mass velocities in pilot plant reactors, pressure drop is low and generally difficult to measure. In commercial reactors, however, it is usually important and computations of pressure drop are usually needed to set pump and compressor designs. Several pressure drop correlations are available in the literature. One poDular one is that by Larkins, White and Jeffrey [39] modified by Reiss [58] which applies to both the trickle gas continuous regime and the pulse flow regime. The correlation is represented below. 

The best approach is to have a computer program check a series of pressure drops and see how energy requirements decrease as surface increases. If this Option is not available, the following simple method can be used to obtain specification sheet values. Start with a pressure drop of 6.9 kPa (1 psi), and anolv three correction factors, F and F, as follows. 

By computing the pressure drop in the static mixer and the pressure drop in the granulating head and adding this to the exergy requirements of the compressor, it is possible to compute the exergy input of the alternative scheme, and compare this with the regular extruder (Figure 11.7). 

Evaluating the Flow Curve from Experimental Data The flow rate of 3% CMC solution in water was measured in a long capillary as a function of pressure drop. Based on the results given in the following table, compute the non-Newtonian viscosity versus the shear-rate curve. 

Fig. 9.5 Computed average velocities (proportional to volumetric flow rate) as a function of pressure drop. Length, 50 in Vi,z 5.66 in/s. Curve A, steady state curve B, adiabatic high inlet temperature curve C, adiabatic low inlet temperature. Note the double-valued flow rates at a given pressure rise in the adiabatic operation and the maximum pressure rise at finite flow-rate values. [Reprinted by permission from R. E. Colwell and K. R. Nicholls, The Screw Extroder, Ind. Eng. Chem., 51, 841-843 (1959).]...

This is the most commonly used model for natural gas nets, and most algorithms for incompressible networks may be used for gas networks as well, simply by replacing eqn (3) by eqn (4) in the library of pressure drop correlations. There are several commercially available computer programs for gas networks, among which the ones from the British Gas Corporation (6) and Intercomp (7) are found. 

Care is needed when modeling compressible gas flows, flows of vapor-liquid mixtures, slurry flows, and flows of non-Newtonian liquids. Some simulators use different pipe models for compressible flow. The prediction of pressure drop in multiphase flow is inexact at best and can be subject to very large errors if the extent of vaporization is unknown. In most of these cases, the simulation model should be replaced by a computational fluid dynamics (CFD) model of the important parts of the plant. 

Suitable computational models for each of the layers discussed above were developed on the basis of available information and a time scale analysis of flow in OXY reactors (see Ranade, 1999b for more details). Because of the magnitude of pressure drop across the grid, it was found necessary to employ compressible flow equations. An ideal gas assumption was used to calculate the density of gas at any point (as a... 

The same calculated results are plotted in terms of defined using Eq. (14) and the computed excess pressure drop (Fig. 8.7). Now the values approach an asymptote at small Reynolds number, which is more useful for microfluidic flows. 

Now compute the pressure drop on each fluid side, after correcting /factors for variable property effects, in a manner similar to step 8 of the rating problem for the crossflow exchanger. 

Melt rheometers either impose a fixed flow rate and measure the pressure drop across a die, or, as in the melt flow indexer, impose a fixed pressure and measure the flow rate. Equation (B.5) gives the shear stress, but Eq. (B.IO) requires knowledge of n to calculate the shear strain rate. It is conventional to plot shear stress data against the apparent shear rate y, calculated using n = 1 (assuming Newtonian behaviour). If the data is used subsequently to compute the pressure drop in a cylindrical die, there will be no error. However, if a flow curve determined with a cylindrical die is used to predict... 

Larrain and Bonilla conducted theoretical analysis of pressure drop in laminar flow of fluid in a coiled pipe [97]. They extended the series to 14th order and solved by means of computer. Austin and Seader came up with a comprehensive review of previous work and gave a detailed numerical solution in the whole laminar range [98]. Their solution, based on the vorticity field, gave excellent agreement with experiments but it did not yield any understanding of the complex interactions between the different forces. 

The derived correlation can be used for supercritical fluid heat transfer calculations, in circular and other flow geometries, for heat exchangers, steam generators, nuclear reactors and other heat transfer equipment, for future comparison with other datasets, and for verification of computer codes and scaling parameters between water and modeling fluids. This correlation can be also used for supercritical carbon dioxide and other fluids. However, its accuracy might be less in these cases. Some specifics of pressure-drop calculations were also listed in the paper. 

Compute the pressure drops on both sides of a shell-and-tube heat exchanger. 

Two methods to predict the pressure drop threshold APthreshoid) to initiate bubble nucleation in polymer foaming processes are developed. One method uses the modified nucleation theory developed in our previous work, while the other utilizes computer simulations to model the growth profiles of the first observable bubbles in batch foaming experiments. Both approaches have shown good agreement in their AP,hreshoid predictions. Moreover, the effects of pressure drop rate, gas content, and temperature on APthreshoid Q demonstrated. 

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