Experimental Investigation of the Influence of Tube Arrangement on Convection Heat Transfer and Flow Resistance in Cross Flow of Gases Over Tube Banks

Abstract

Abstract New measurements of the convection heat-transfer rate between gases and tube banks, with corresponding pressure drop for transverse flow have been made as part of a research program of the Babcock & Wilcox Company to determine the effect of varying the spacing of tubes of identical size. This portion of the program was conducted by the Babcock & Wilcox Company in the mechanical-engineering laboratories of Rensselaer Polytechnic Institute. Thirty-eight arrangements of tubes were tested, differing in center-to-center spacing in the direction of flow and transversely, and these are shown in Fig. 1. The spacing, for both in-line and staggered tube rows varied from the closest practicable to three tube diameters. Each bank with two exceptions comprised ninety tubes, arranged in ten rows transverse to the air stream, each row containing nine tubes. These tubes were 0.31 in. in diameter and uniformly heated electrically throughout the 9⅛-in. length from which heat was transferred to a cool air stream. Heat input to the bank as indicated by wattmeters in the supply line was held constant at 72,000 Btu per hr while the air mass flow was varied. One exception included two tube banks in which the depth of the bank was varied from ten rows to one row with the same heat input per tube. In the other exception the heat input was reduced to 18,000 Btu per hr. Incidentally, the pressure drop was also determined for zero heat input. Heat-transfer rates are reported in terms of the relation of the Nusselt number to the Reynolds number; and the pressure drop is reported in terms of the relation of the Fanning-equation friction factor to the Reynolds number. The Reynolds number was varied from 2000 to 40,000 to include the range of commercial practice, and in view of the small scale of the apparatus, this was accomplished by the use of air under pressure in a closed chamber. These tests have demonstrated that both convection heat transfer and flow resistance of tube banks vary markedly with changes in tube arrangements, no simple statement of the variation being possible. It was also found that the rate of change of these characteristics with changes in the Reynolds number was regularly related to the tube arrangement. The air-boundary convection conductance was found to increase approximately as the two-thirds power of the Reynolds number. The actual exponent ranges from about 0.55 to 0.80, varying in some few cases with Reynolds numbers as well as with the tube arrangement. Friction factors were also found to vary with the Reynolds number. The relation ranges from the 0.2 power to about the −0.3 power when friction factors are expressed as exponential functions of the Reynolds number. The relation between the friction factor and the tube spacing is not the same as that for conductance of the gas boundary, and there is no consistent relation between pressure drop and heat-transfer rate.