Reynolds number film condensation

The Reynolds number for condensation on the outer surfaces of vertical tube or plates increases in the flow direction due to the increase of the liquid filn thickness S. The flow of liquid film exhibits different regimes, depending 01 the value of the Reynolds number. It is observed that the outer surface of th liquid film remains smooth and wave-free for about Re < 30, as shown ii Fig. 10 -23, and thus the flow is clearly laminar. Ripples or waves appear 01 the free surface of the condensate flow as the Reynolds number increases, anr the conden.sale flow becomes fully turbulent at about Re 1800. The con densate flow is called wavy-laminar in the range of 450 < Re < 1800 an turbulent for Re > 1800. However, some disagreement exists about the valu of Re at which the flow becomes wavy-laminar or turbulent. 

Reynolds number of condensate film, AT/fij-, dimensionless Pressure, atm or Ib /in. p, critical pressure... 

The Reynolds number of the condensate film (falling film) is 4r/ I, where F is the weight rate of flow (loading rate) of condensate per unit perimeter kg/(s m) [lb/(h ft)]. The thickness of the condensate film for Reynolds number less than 2100 is (SflF/p g). ... 

Vertical Tubes For the following cases Reynolds number < 2100 and is calculated by using F = Wp/ KD. The Nusselt equation for the heat-transfer coefficient for condensate films may be written in the following ways (using liquid physical properties and where L is the cooled lengm and At is — t,) ... 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

For condensing vapor in vertical downflow, in which the hquid flows as a thin annular film, the frictional contribution to the pressure drop may be estimated based on the gas flow alone, using the friction factor plotted in Fig. 6-31, where Re is the Reynolds number for the gas flowing alone (Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASME, June 22-24, 1949, pp. 19-28). 

If G is the mass rate of flow of condensate, the mass rate of flow per unit area G is G/S and the Reynolds number for the condensate film is then given by ... 

The presence of waves will increase the heat-transfer coefficient, so the use of equation 12.51 above a Reynolds number of 30 will give conservative (safe) estimates. The effect of waves on condensate film on heat transfer is discussed by Kutateladze (1963). 

Above a Reynolds number of around 2000, the condensate film becomes turbulent. The effect of turbulence in the condensate film was investigated by Colburn (1934) and Colburn s results are generally used for condenser design, Figure 12.43. Equation 12.51 is also shown on Figure 12.43. The Prandtl number for the condensate film is given by ... 

Transition from laminar to turbulent flow within the condensed film can occur when the vapor is condensed on a tall surface or on a tall vertical bank of horizontal tubes [45] to [47]. It has been found that the film Reynolds number, based on the mean velocity in the film, um, and the hydraulic diameter, D, can be used to characterize the conditions under which transition from laminar flow occurs. The mean velocity in the film is given by definition as ... 

When a plate on which condensation occurs is sufficiently large or there is a sufficient amount of condensate flow, turbulence may appear in the condensate film. This turbulence results in higher heat-transfer rates. As in forced-convection flow problems, the criterion for determining whether the flow is laminar or turbulent is the Reynolds number, and for the condensation system it is defined as... 

Because the film Reynolds number is so important in determining condensation behavior, it is convenient to express the heat-transfer coefficient directly in terms of Re. We include the effect of inclination and write the heat-transfer equations in the form... 

The Reynolds number must be checked to determine if the condensate film is laminar or turbulent. Properties are evaluated at the film temperature ... 

In trying to calculate the Reynolds number we find that it is dependent on the mass flow of condensate. But this is dependent on the heat-transfer coefficient, which is dependent on the Reynolds number. To solve the problem we assume either laminar or turbulent flow, calculate the heat-transfer coefficient, and then check the Reynolds number to see if our assumption was correct. Let us assume laminar film condensation. At atmospheric pressure we have... 

FIG. 5-8 Dukler plot showing average condensing-film coefficient as a function of physical properties of the condensate film and the terminal Reynolds number. (Dotted line indicates Nusselt theory for Reynolds number < 2100.) [Reproduced hy permission from Chem. Eng. Prog., 55, 64 (1959).]... 

At Reynolds numbers greater than about 30, it is observed that waves form at the liquid-vapor interface although the flow in liquid film remains laminar. I he flow in this case is said to be wavy laminar. The waves at the liquid-vapor interface tend to increase heat transfer. But the waves also complicate the analysis and make it very difficult to obtain analytical solutions. Therefore, we have to rely on experimental studies. The increase in heat transfer due to the wave effect is, on average, about 20 percent, but it can exceed 50 percent. The exact amount of enhancement depends on the Reynolds number. Rased on his experimental studies, Kutateladze (1963) recommended the following relation for the average heat transfer coefficient in wavy laminar condensate flow for p p, and 30 < Re < 1800,... 

Equation 12.51 will apply up to a Reynolds number of 30 above this value waves on the condensate film become important. The Reynolds number for the condensate film is given by... 

Cooling water, for example, will be placed on the tube side because of its tendency to form a scale. Water usually contains dissolved salts, like calcium carbonate, which may deposit on the tube wall. A condensing fluid will be placed in the shell side to prevent the liquid film from growing too large, reducing the heat-transfer coefficient, or in the tube side if subcooling of the liquid is desirable. In the shell side, turbulence occurs at a lower Reynolds number than in the tube side because of the baffles. Thus, the shell side is the best location for very viscous fluids. 

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