Turbulent flow entrance region

The research conducted by Hogg [213] has indicated that turbulent flow entrance length in coils with circular cross sections is much shorter than that for laminar flow. Turbulent flow can become fully developed within the first half-turn of the coil. Therefore, most of the turbulent flow and heat transfer analyses concentrate on the fully developed region. 

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

Equations (6-4) and (6-5) apply to fully developed turbulent flow in tubes. In the entrance region the flow is not developed, and Nusselt [3] recommended the following equation ... 

Developing Turbulent Flov/ in the Entrance Region 4/6 Turbulent Flo. v in N oncircular Tubes 476 Flow through Tube Annulus 477 Heat Transler Enhancement 477... 

The entry lengths for turbulent flow are typically short, often just 10 tube diameters long, and thus the Nusselt number determined for fully developed turbulent flow can be used approximately for the entire tube. This simple approach gives reasonable results for pressure drop and heat transfer for long tubes and conservative re.sults for short ones. Correlations for the friction and heat transfer coefficients for the entrance regions are available in the literature for better accuracy. 

Prediction of the heat-transfer coefficient in the transition flow regime is uncertain due to the strong effects of entrance conditions and instability of the flow pattern. Gnielinski [18] modified the Petukhov-Popov equation to accommodate the transition region and extend it into the turbulent flow range ... 

Additional observations have shown that the transition from laminar to turbulent flow actually may occur over a wide range of Reynolds numbers. In a pipe, flow is always laminar at Reynolds numbers below 2100, but laminar flow can persist up to Reynolds numbers of several thousand under special conditions of well-rounded tube entrance and very quiet liquid in the tank. Under ordinary conditions, the flow in a pipe or tube is turbulent at Reynolds numbers above about 4000. Between 2100 and 4000 a transition region is found where the flow may be either laminar or turbulent, depending upon conditions at the entrance of the tube and on the distance from the entrance. 

Transition length for laminar and turbulent flow. The length of the entrance region of the tube necessary for the boundary layer to reach the center of the tube and for fully developed flow to be established is called the transition length. Since the velocity varies not only with length of tube but with radial distance from the center of the tube, flow in the entrance region is two dimensional. 

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]. 

FIGURE 5.24 Turbulent flow apparent friction factors in the hydrodynamic entrance region of a parallel plate duct with uniform inlet velocity [45]. 

R. G. Deissler, Analysis of Turbulent Heat Transfer and Flow in the Entrance Regions of Smooth Passages, NACA TN 3016,1953. 

J. A. Malina, and E. M. Sparrow, Variable-Property, Constant-Property, and Entrance Region Heat Transfer Results for Turbulent Flow of Water and Oil in a Circular Tube, Chem. Eng. Sci., (19) 953-962,1964. 

M. Sakakibara, Analysis of Heat Transfer in the Entrance Region with Fully Developed Turbulent Flow between Parallel Plates—The Case of Uniform Wall Heat Flux, Mem. Fac. of Eng. Fukui Univ., (30/2) 107-120,1982. 

Values of the asymptotic heat transfer factors jH in the thermal entrance region are reported for concentrated aqueous solutions of polyacrylamide and polyethylene oxide. The results are shown in Fig. 10.30, as a function of the Reynolds number Re . These values were measured in tubes of 0.98,1.30, and 2.25 cm (0.386,0.512, and 0.886 in) inside diameter in a recirculating-flow loop. The asymptotic turbulent heat transfer data in the thermal entrance region are seen to be a function of the Reynolds number Re and of the axial position xld. The following empirical correlation is derived from the data [35,37] ... 

The behavior of a viscoelastic fluid in turbulent flow in the hydrodynamic entrance region of a rectangular channel can be estimated by assuming that the circular tube results are applicable provided that the hydraulic diameter replaces the tube diameter. 

Cell Size Effect. - The mass transfer coefficient is inversely proportional to width of a cell for fully developed laminar region, and surface area is proportional to cell width. This means conversion through a cell is constant. However, as flow is proportional to the square of cell width as velocity is held constant, the conversion efficiency decreases as cell width increases. This tendency is shown in Figure 10. A large cell size may offer a moderate conversion rate and a longer hydrodynamic entrance region. These are favorable characteristics for a catalyst. On the other hand, for fully developed turbulent flow, the mass transfer coefficient increases with cell width to the 0.2 power, and the surface area is proportional to the width. This means conversion increases as the cell width increases to the 0.8 power. Therefore, the cell size effect for turbulent flow is rather small compared with laminar flow. However, the conversion efficiency decreases as cell width increases as is for laminar flow. 

The type of flow— laminar, turbulent, well-developed, or hydrodynamic entrance region—should be considered. 

For turbulent flow, the thermal entrance region is shorter than for laminar flow (with the exception of liquid metals which have a very low Prandtl number), and thus the fully developed values of the Nusselt number are frequently used directly in heat transfer design without reference to the thermal entrance effects. The turbulent fully developed Nusselt number in a smooth channel can be expressed as a function of the Reynolds number and of the Prandtl number. 

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