Turbulent flow noncircular tubes

Perhaps the simplest classification of flow regimes is on the basis of the superficial Reynolds number of each phase. Such a Reynolds number is expressed on the basis of the tube diameter (or an apparent hydraulic radius for noncircular channels), the gas or liquid superficial mass-velocity, and the gas or liquid viscosity. At least four types of flow are then possible, namely liquid in apparent viscous or turbulent flow combined with gas in apparent viscous or turbulent flow. The critical Reynolds number would seem to be a rather uncertain quantity with this definition. In usage, a value of 2000 has been suggested (L6) and widely adopted for this purpose. Other workers (N4, S5) have found that superficial liquid Reynolds numbers of 8000 are required to give turbulent behavior in horizontal or vertical bubble, plug, slug or froth flow. Therefore, although this classification based on superficial Reynolds number is widely used... 

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... 

Flow in Noncircular Ducts The length scale in the Nusselt and Reynolds numbers for noncircular ducts is the hydraulic diameter, D), = 4AJp, where A, is the cross-sectional area for flow and p is the wetted perimeter. Nusselt numbers for fully developed laminar flow in a variety of noncircular ducts are given by Mills (Heat Transfer, 2d ed., Prentice-Hall, 1999, p. 307). For turbulent flows, correlations for round tubes can be used with D replaced by l. ... 

FIGURE 8-19 The relation for pressure loss (and head loss) is one of the most general relations in fluid mechanics, and it is valid for laminar or turbulent flows, circular or noncircular tubes, and pipes with smooth or rough surfaces. 

The head loss /i(, represents the additional height that the fluid needs to be raised by a pump in order to overcome the frictional losses in the pipe. The head loss is caused by viscosity, and it is directly related to the wall shear stress. Equation 8—45 is valid for both laminar and turbulent flows in both circular and noncircular tubes, but Eq. 8-46 is valid only for fully developed laminar flow in circular pipes. 

For fully developed turbulent flow, the inner and outer convection coefficients are approximately equal to each other, and the tube annulus can be treated as a noncircular duct with a hydrauLc diameter of - 77, . The Nusselt num-... 

The drag coefficient A for turbulent flows in rectilinear tubes of noncircular cross-section can also be computed using relations (1.6.12) and (1.6.13), where the equivalent diameter... 

More detailed information about the structure of turbulent flows in a circular (noncircular) tube and a plane channel, as well as various relations for determining the average velocity profile and the drag coefficient, can be found in the books [138, 198, 268, 276, 289], which contain extensive literature surveys. Systematic data for rough tubes and results of studying fluctuating parameters of turbulent flow can also be found in the cited references. 

It is generally accepted that the hydraulic diameter correlates Nu and /for fully developed turbulent flow in circular and noncircular ducts. This is true for the results accurate to within 15 percent for most noncircular ducts. Exceptions are for those having sharp-angled corners in the flow passage or concentric annuli with inner wall heating. In these cases, Nu and /could be lower than 15 percent compared to the circular tube values. Table 17.16 can be used for more accurate correlations of Nu and /for noncircular ducts. 

A careful observation of accurate experimental friction factors for all noncircular smooth ducts reveals that ducts with laminar/Re < 16 have turbulent/factors lower than those for the circular tube, whereas ducts with laminar/Re > 16 have turbulent/factors higher than those for the circular tube [48], Similar trends are observed for the Nusselt numbers. If one is satisfied within 15 percent accuracy, Eqs. 17.87 and 17.88 for/and Nu can be used for noncircular passages with the hydraulic diameter as the characteristic length in / Nu, and Re otherwise, refer to Table 17.16 for more accurate results for turbulent flow. 

Table 17.18 summarizes the dependence of Ap and h on V for developed and developing laminar and turbulent flows. Although these results are for the circular tube, the general functional relationship should be valid for noncircular ducts as a first approximation. 

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