Pressure drop factor

Fluid Temperature, °C Minimum velocity, m/s Pumping rate factor Pressure drop factor Outside tubes Inside tubes... 

APa = Static pressure drop, inches of water Fp = Static pressure drop factor, see Table 1 N = Number of tube rows Actual density at average air temperature... 

These ratios are useful in dealing with small towers, and serve as guides for the borderline cases of others. There are no guides to the smallest sized packing to place in a tower. However, /4-in. is about the smallest ceramic used with %-in. and 1-in. being the most popular. Operating and pressure drop factors will usually control this selection. 

Read pressure drop factor, Fp, from Figure 10-142. 

Fp = static pressure drop factor from Reference 3 (see Table 7-6)... 

For G/S particle systems, enhancement in convective heat transfer is achieved at the expense of increased pressure drop in moving the gas at higher velocities. A measure of the relative benefit of enhanced heat transfer to added expenditure for fluid movement can be approximated by an effectiveness factor, E, defined as the ratio of the heat transfer coefficient to some kind of a pressure drop factor. For G/S systems in which particles are buoyed by the flowing gas stream, this pressure drop factor is expressed by the Archimedes number Ar, and E can be written... 

Important Note Bubble cap HHD factor is equivalent to the DPntAYi dry pressure drop of valve trays. The bubble cap tray total pressure drop factor DPTRay is equivalent to the HDC2 factor of valve-type trays. You may therefore substitute these bubble cap values in the ETF efficiency equations as given for valve trays to determine bubble cap tray efficiency. 

Haldor Topspe s ammonia synthesis technology is based on the S-200 ammonia converter. This is a two-bed radial flow converter with indirect cooling between the beds. Features of the S-200 include efficient use of converter volume and low pressure drop (factors related to the use of small catalyst particles 1.5 to 3.0 mm), and high conversion per pass due to indirect cooling85. 

A discussion of the derivation and limits on the use of the Heat Mass Transfer and Pressure Drop Factors has been pubhshed previously (1). A summary of the derivations is contained in the next paragraphs. 

The Pressure Drop Factor represents the cellxdar structural contribution to the pressure loss down the length of the flow path and can be thought of as the cellular contribution to the core pressure drop coefficient (8). The Pressure Drop Factor is defined as ... 

The Heat Mass Transfer and Pressure Drop Factors will be used to evaluate the relative performance of various channel shapes that might be used for catalyst supports. In these applications it is desirable to maximize the heat and mass transfer and to minimize the pressure drop. As their derivations show, these factors represent the cellular contributions to these phenomena. Therefore, if the outer dimensions (length, cross-sectional area, and volume) and the characteristics of the environment (temperature, fluid viscosity and density) are held constant, these two factors determine the heat transfer, mass transfer, and pressure drop behavior of the system. 

The following sections will discuss the Heat Mass Transfer and Pressure Drop Factors of catalyst supports of various channel shapes through the identification of the open frontal area, the geometric surface area, and the channel shape-related quantities of Friction Factor and Nusselt Number. 

The Heat Mass Transfer and Pressure Drop Factors for the regular polygons are given by combining Equations 5 and 6 with the definitions in Equations 2 and 4. The expressions are ... 

Note that the Heat Mass Transfer Factor is dependent on the shape of the channel and the ceU density but independent of the open frontal area while the Pressure Drop Factor is dependent on the open frontal area of the cellular structure as weU. Figure 2 shows the Heat Mass Transfer and Pressure Drop Factors at 100% open frontal area for 400 cpsi regular polygons as functions of the shape. 

These graphs show that both the Pressure Drop Factor and the Heat Mass TrEinsfer Factor decrease as the number of sides of the regular polygon increases. At a given ceU density and open firontal area, the triangle has the best heat and mass transfer unfortunately, the triangle also has the highest pressure drop. 

These relationships are shown in Figure 4. It is notable that both the Heat Mass and Pressure Drop Factors reach minimum values at the equilateral triangle (shape = 0.464), which represents the poorest of the isosceles triangles for heat and mass transfer but also the isosceles triangle lowest in pressure drop. 

Figure 4 The Heat Mass Transfer and Pressure Drop Factors for Several Isosceles Triangles.

Combining the information in Figure 5 with the calculated open frontal area and geometric surface area values and through the use of Equations 2 and 4, the Heat Mass Transfer and Pressure Drop Factors can be calculated for the sine ducts. These results are shown in Figure 6. 

In order to achieve the best possible catalyst conversion efficiency at a constant volume, while minimizing the power drain due to excessive pressure drop through the converter, one would maximize the heat and mass transfer with respect to the pressure drop. In other words, in the graph shown in Figure 7 for 100% open frontal area, where the Heat Mass Transfer Factor is on the x-axis and the Pressure Drop Factor is on the y-axis, the slope of the curve should to be as shallow as possible. All of the channel shapes evaluated here tend to fall close to the same hne. However, as the open frontal area decreases from 100%, the Pressure Drop Factor increases while the Heat Mass Transfer Factor remains constant so that the relative attractiveness of some channel structures will be improved as the OFA is taken into account. 

Using the Heat Mass Transfer and Pressure Drop Factors, comparisons can be made among different shapes and descriptions of cell structures in order to optimize the heat transfer and catalyst performance with respect to the pressure drop. 

The three sets of structures evaluated here have similar relationships between the Pressure Drop Factor and the Heat Mass Transfer Factor. However, the extent of the regular polygons is very limited and even more so because only three of them can be packed efficiently. 

X Factor Fp is a pressure-drop factor and a relative mass-transfer coefficient. Based on NH -HjO data other factors based on COi-NaOH data. 

Figure 1. Normalized pressure drop factor variation with Remfor a single fluid flow in a porous medium.

Multidimensional Effects. In the previous section, we studied the wall effect on the shear factor. To give a full account of the wall effects, we now look at the no-slip flow effect posed by the containing wall (multidimensional effect) on the total pressure drop. For simplicity, let us rewrite the normalized pressure drop factor, fv, based on the permeability of the medium rather than the particle diameter,... 

Figure 12 shows the multidimensional effect on the normalized pressure drop factor from both the exact solution, equation 121, and its approximation, equation 123. It can be observed that equation 123 gives a fairly good approximation to the exact solution. The multidimensional effect is significant when the normalized bed radius is small, say, F1/2D/2 < 100. When the normalized bed radius is large, Crrul - 1. 

Figures 14 and 15 show the normalized pressure drop factor for a densely packed bed of monosized spherical particles. For Rem < 7,fv is fairly independent of Rern, and at high Rem values, it increases fairly linearly with Rem. The data points are the experimental results taken from Fand et al. (110), where the bed diameter is D = 86.6 mm and the particle diameter is ds = 3.072 mm. One can observe that the 2-dimen-sional model of Liu et al. (32), referred to as equation 107, agrees with the experimental data fairly well in the whole range of the modified Reynolds number. From Figure 14, one observes a smooth transition from the Darcy s flow to Forchheirner flow regime. The one-dimensional model of Liu et al. (32) (i.e., equation 106) showed only slightly smaller fv value. Hence, the no-slip effect or two-dimensional effect for this bed is small. As shown in Figures 14 and 15, the Ergun equation consistently underpredicts the pressure drop. The deviation becomes larger when flow rate is increased.

Figure 14. Variation of pressure drop factor with modified Reynolds number for a densely packed bed of monosized spherical particles at low flow rates. The symbols are experimental data taken from reference 110.

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