Area ratio

The area ratio is defined as the ratio of downcomer-to-riser cross-sectional area, but can also be represented by a downcomer-to-riser hydraulic diameter ratio. It is a simple representation of the flow restriction that exists in the bioreactor design since wall friction is of little importance unless viscosity is significantly increased (Chisti, 1989). 

An excessive reduction in the downcomer diameter (very low area ratio) would be too restrictive and reduce the liquid velocity such that the gas phase could 

Valves are occasionally used to adjust the area ratio for experimentation, such as the research by BendjabaUah et al. (1999). They closed the valve from fully to 40% open without major effects on gas holdup. This would lead to the conclusion that an optimum area ratio exists, which does not impact gas holdup and also minimizes cost. The optimum ratio may not be easily determined since it depends on the scale and operating range, and the installation of a restrictive valve in the downcomer (assuming the optimum area ratio is below the valve-free area ratio) would provide the necessary flexibiUty and means to get there (Weiland, 1984). Additional losses and dynamics would be introduced by the valve and must also be addressed. 

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Drop dispersions are hardly ever uniform, and size distribution must be allowed for in calculating a. This can be done by means of the Sauter mean drop diameter, based on the average volume-to-area ratio for N drops. 

It has become quite popular to optimize the manifold design using computational fluid dynamic codes, ie, FID AP, Phoenix, Fluent, etc, which solve the full Navier-Stokes equations for Newtonian fluids. The effect of the area ratio, on the flow distribution has been studied numerically and the flow distribution was reported to improve with decreasing yiR. 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

The quahtative flow distribution in a manifold can be estimated by examining a streamline plot. Figure 13 shows the streamline plot for the manifold having AR = 4. Note that the same amount of fluid flows between two consecutive streamlines. The area ratio is an important parameter affecting the flow distribution in a manifold, as shown in Figure 14a, which shows the percent flow rate in each channel for three cases. As the area ratio increases, the percent flow rate increases in channels no. 1 and no. 8, whereas the percent flow rate decreases in the middle channels. 

Fig. 14. Flow rates for (a) area ratios of (--) 4, ( ) 8, and (---) 16, each having the same flow rate and Re = 50 and (b) Reynolds numbers of...

In thermoelectric cooling appHcations, extensive use has been made of cascaded systems to attain very low temperatures, but because the final stage is so small compared to the others, the thermal flux is limited (Eig. 3). The relative sizes of the stages ate adjusted to obtain the maximum AT. Thus, for higher cooling capacity, the size of each stage is increased while the area ratios ate maintained. 

Cathode-anode area ratio and spacing Current density... 

For laminar flow the losses in sudden contraction may be estimated for area ratios Ao A < 0.2 by an equivalent additional pipe length Lc given by... 

Ejector Performance The performance of any ejec tor is a function of the area of the motive-gas nozzle and venturi throat, pressure of the motive gas, suction and discharge pressures, and ratios of specific heats, molecular weights, and temperatures. Figure 10-102, based on the assumption of constant-area mixing, is useful in evaluating single-stage-ejector performance for compression ratios up to 10 and area ratios up to 100 (see Fig. 10-103 for notation). 

FIG. 14-43 Overall (Murphree) efficiencies of sieve plates with hole/active area ratios of 0.08 and 0.14. Efficiency values greater than 1.0 (100%) result from crossflow effects (Figs. 14-38, 14-39). [Yanagi and Sakata, Ind. Eng. Chem., Proc. Des. Devel., 2i, 712 (J.9S2).] Reproduced with permission, copyright 1982 American Chemical Society. 

TABLE 17-4 Required Cyclone Length as a Function of Area Ratio... 

Full-Bore and Punctured Pipe Discharge With a pipe puncture, the mass flux at the discharge point is larger than the mass flux in the pipe G,p, by the puncdure-to-pipe area ratio A j/Ap, or (D/Dp) , denned as C. Specifically ... 

Area effects in galvanic corrosion are very important. An unfavorable area ratio is a large cathode and a small anode. Corrosion of the anode may be 100 to 1,000 times greater than if the two areas were the same. This is the reason why stainless steels are susceptible to rapid pitting in some environments. Steel rivets in a copper plate will corrode much more severely than a steel plate with copper rivets. 

A suitable volume-to-area ratio is 20 mL (125 mL) of solution/cm" (in ) of specimen surface. This corresponds to the recommendation of ASTM Standard A262 for the Huey test. The preferred vohime-to-... 

Liquid chromatography was performed on symmetry 5 p.m (100 X 4.6 mm i.d) column at 40°C. The mobile phase consisted of acetronitrile 0.043 M H PO (36 63, v/v) adjusted to pH 6.7 with 5 M NaOH and pumped at a flow rate of 1.2 ml/min. Detection of clarithromycin and azithromycin as an internal standard (I.S) was monitored on an electrochemical detector operated at a potential of 0.85 Volt. Each analysis required no longer than 14 min. Quantitation over the range of 0.05 - 5.0 p.g/ml was made by correlating peak area ratio of the dmg to that of the I.S versus concentration. A linear relationship was verified as indicated by a correlation coefficient, r, better than 0.999. 

Most galvanic corrosion processes are sensitive to the relatively exposed areas of the noble (cathode) and active (anode) metals. The corrosion rate of the active metal is proportional to the area of exposed noble metal divided by the area of exposed active metal. A favorable area ratio (large anode, small cathode) can permit the coupling of dissimilar metals. An unfavorable area ratio (large cathode, small anode) of the same two metals in the same environment can be costly. 

Correct application of this principle can lead to what would appear to he peculiar recommendations. For example, if just one member of a couple is to be coated, it should be the noble member. Most coating systems leave holidays or tiny openings where the metal is exposed. If the active metal is coated, the area of exposure at the holidays can be quite small compared to the area of the noble metal, resulting in an unfavorable area ratio. On the other hand, if the noble metal is coated, the holidays provide a small cathodic area and hence a highly favorable area ratio with respect to the active metal. Similarly, if dissimilar metal fasteners must be used, they should be noble relative to the metals being fastened (see Case History 16.1). 

When possible, avoid coupling materials having widely dissimilar galvanic potentials. If this cannot he avoided, make use of favorable area ratios by giving the active metal a large exposed area relative to the noble metal. For example, copper or copper-based alloy tubes may be joined to a steel tube sheet. Because of the favorable area ratio in this case, a relatively inexpensive steel tube sheet may be intentionally substituted for a bronze or a brass tube sheet if thickness specifications allow for a small amount of galvanic corrosion of the steel. 

Corrosion of the fasteners occurred due to their galvanic interaction with passive stainless steel. Deterioration was rapid because of the unfavorable area ratio formed by the large areas of stainless steel and the small area of the fasteners, which was further reduced by the incomplete plastic covering overexposed fastener surfaces. 

However, if part of the reinforcing steel is aerated, a cell is formed as in Section 2.2.4.2. With a high surface area ratio SJS and with well-aerated cathodes, very high corrosion rates can occur at anodic regions. 

Liner holes. Liner area to casing area and liner hold area to casing area are important to the performance of combustors. For example, the pressure loss coefficient has a minimum value in the range of 0.6 of the liner area/ casing area ratio with a temperature ratio of 4 1. 

As one can see, the larger-diameter wires suffer a much more rapid degradation in ac resistance with increasing frequency than do smaller-diameter wires. So it is advantageous to use multiple strands of smaller wires instead of one large diameter wire. The ac current density of the smaller wires (>30 AWG) can actually be pushed to two to three times the assumed current density used in the charts because their surface area to cross-sectional area ratio is much greater. 

Air free area ratio (A p) The ratio of free area to the core area. 

Free area ratio The ratio of an actual opening to the obstructed portion of that opening. 

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