Staggered tubes

The power of a klystron is Hmited to a theoretical 100% of that in the electron beam Py = / , V ,). In some areas, efficiencies of 70 80% have been achieved. Normally, efficiency of 40-60% can be expected. RF power bandwidth, of course, is dependent on the number of cavities and their tuning. Typically, klystrons with multiple cavities can be staggered tuned to provide a flat RF passband at some reduction in efficiency and gain. For example, in four cavity tubes, staggered tuning results in a-l-dB bandwidth of 1% with a gain of 40 dB. 

The following dimensional equations (5-73 to 5-77) are based on flow normal to a bank of staggered tubes without leakage. Multiply the values obtained for h by 0.6 for normal leakage and, in addition, by 0.79 for in-line (not staggered) tube arrangement. 

Example 7 Radiation in Gases Flue gas containing 6 percent carbon dioxide and 11 percent water vapor by volume (wet basis) flows through the convection bank of an oil tube stiU consisting of rows of 0.102-m (4-in) tubes on 0.203-m (8-in) centers, nine 7.62-m (25-ft) tubes in a row, the rows staggered to put the tubes on equilateral triangular centers. The flue gas enters at 871°C (1144 K, 1600°F) and leaves at 538°C (811 K, 1000°F). The oil flows in a countercurrent direction to the gas and rises from 316 to 427°C (600 to 800°F). Tube surface emissivity is 0.8. What is the average heat-input rate, due to gas radiation alone, per square meter of external tube area ... 

Turbulent Flow The correlation by Grimison (Trans. ASME, 59, 583—.594 [1937]) is recommended for predicting pressure drop for turbulent flow (Re > 2,000) across staggered or in-hne tube banks for tube spacings [(a/Dt), (b/Dt)] ranging from 1.25 to 3.0. The pressure drop is given by... 

FK . 6-42 Upp er chart Friction factors for staggered tube banks with minimum fluid flow area in transverse openings. Lower chart Friction factors for staggered tube banks with minimum fluid flow area in diagonal openings. (From Gtimison, Trans. ASME, 59,. 5S3 [1.937],)... 

For banks of staggered tubes, the friction factor for isothermal flow is obtained from Fig. (6-42). Each fence (group of parametric curves) represents a particular Reynolds number defined as... 

Square staggered, often referred to as square rotated—Rotating the square inline pitch 45° no longer gives the shellside fluid clear lanes through the bundle. Tube pitch c is defined as for square inline. 

Nr = Rows of tubes per shell pass (Nr is always equal to the number of minimum clearances through which the fluid flows in series. For square staggered pitch the maximum velocity, Umax, which is required for evaluating Re may occur in the transverse clearances a or the diagonal clearances c. In the latter case Nr is one less than the number of tube rows.)... 

Normally, heat exchanger tubes are arranged in a staggered manner. The continuous plate is considered as being built up of regular hexagons, with a hole in the center for the pipes. This arrangement is shown in Fig. 9.9. 

Value of K for Fluid Flow Perpendicular to a Bank of Staggered Tube "N" Rows Deep... 

Tubes may be arranged in either a horizontal and vertical alignment pattern (which provides for easier cleaning and inspection) or in a staggered layout (which provides for improved heat transfer) because of the more circuitous flow of water around the tubes). 

With liquids the same equation may be used, although for Re less than 2000, there is insufficient published work to justify an equation. McAdams,(27) however, has given a curve for h for a bundle with staggered tubes ten rows deep. 

Typical Condenser. Figure 7-3 illustrates an inlet bathtub used for low vacuums to limit pressure drop at the entrance to the exchanger and across the first rows of tubes. Note staggered baffle spacing with large spacing at inlet, and the side-to-side (40% cut) baffles. Enough baffles must... 

Tamarin, A. I., Zabrodsky, S. S., and Yepanov, G., Heat Transfer Between a Horizontal Staggered Tube Bundle and a Fluidized Bed, Heat Transfer-Soviet Research, 8(5) 51—55 (1976)... 

The coefficients (f)i and (f>0 depend on fluid specific heat c, thermal conductivity k, density p, and viscosity p, as well as the tube diameters. 0 is based on either in-line or staggered tube arrangements. 

Fig. 6-14 Nomenclature for use with Table 6-4 (a) in-line tube rows (/>) staggered tube rows.

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