Concentric annular ducts turbulent flow

Presented in this section are the friction factor and Nusselt number for turbulent flow and heat transfer in concentric annular ducts. The effects of eccentricity on the friction factor and Nusselt number are also discussed. 

Critical Reynolds Number For concentric annular ducts, the critical Reynolds number at which turbulent flow occurs varies with the radius ratio. Hanks [109] has determined the lower limit of Recrit for concentric annular ducts from a theoretical perspective for the case of a uniform flow at the duct inlet. This is shown in Fig. 5.16. The critical Reynolds number is within 3 percent of the selected measurements for air and water [109]. 

Fully Developed Flow. Knudsen and Katz [110] obtained the following velocity distributions for fully developed turbulent flow in a smooth concentric annular duct in terms of wall coordinates u+ and y+ ... 

TABLE 5.27 Nusselt Numbers and Influence Coefficients for Fully Developed Turbulent Flow in a Concentric Annular Duct with Uniform Heat Flux at One Wall and the Other Wall Insulated [111]... 

Hydrodynamically Developing Flow. Hydrodynamically developing turbulent flow in concentric annular ducts has been investigated by Rothfus et al. [114], Olson and Sparrow [115], and Okiishi and Serouy [116]. The measured apparent friction factors at the inner wall of two concentric annuli (r = 0.3367 and r = 0.5618) with a square entrance are shown in Fig. 5.17 (r = 0.5618), where / is the fully developed friction factor at the inner wall. The values of/ equal 0.01,0.008, and 0.0066 for Re = 6000,1.5 x 104, and 3 x 104, respectively [114]. 

FIGURE 5.17 Normalized apparent friction factors for turbulent flow in the hydro-dynamic entrance region of a smooth concentric annular duct (r = 0.5168) [114]. 

Thermally Developing Flow. Kays and Leung [111] present experimental results for thermally developing turbulent flow in four concentric annular ducts, r = 0.192,0.255,0.376, and 0.500, with the boundary condition of one wall at uniform heat flux and the other insulated, that is, the fundamental solution of the second kind. In accordance with this solution, the local Nusselt numbers Nu and Nu at the outer and inner walls are expressed as... 

Simultaneously Developing Flow. Little information is available on simultaneously developing turbulent flow in concentric annular ducts. However, the theoretical and experimental studies by Roberts and Barrow [118] indicate that the Nusselt numbers for simultaneously developing flow are not significantly different from those for thermally developing flow. 

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