Reynolds number for 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. 

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 ... 

Show that the condensation Reynolds number for laminar condensation on a vertical plate may be expressed as... 

It can be seen from Fig. 7.17 that the condensing heat-transfer coefficient for a fluid with a Prandtl number of approximately 2 (for instance, steam) is not strongly dependent on flow rate or Reynolds number. For this reason, heat-transfer coefficients for steam condensing on vertical tubes are frequently not calculated, but are assigned a value of 1500 to 2000Btu/(h)(ft2)(°F) [8500 to 11,340 W/(m2)(K)]. 

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... 

FIGURE 6.22 Condensation number versus Reynolds number for gravity-driven condensation on a vertical surface. 

There are two types of correlations for estimating the heat transfer coefficient for condensation inside vertical tube. In the first type of correlations, the local heat transfer coefficient is expressed in the form of a degradation factor defined as the ratio of the experimental heat transfer coefficient (when noncondensable gas is present) and pure steam heat transfer coefficient (Kuhn et al. [1997]). The correlations in general are the functions of local noncondensable gas mass fraction and mixture Reynolds number (or condensate Reynolds number). In the other type of correlations, the local heat transfer coefficient is expressed in the form of dimensionless numbers. In these correlations, local Nusselt number is expressed as a function of mixed Re5molds number, Jakob number, noncondensable gas mass fraction, condensate Reynolds number, and so on. 

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 ... 

The preceding equation automatically allows for the effect of the number of vertical rows of horizontal tubes as proposed by Kem and cited later in this discussion. The flow should be streamlined (laminar) flow, with a Reynolds Number of 1,800- 2,100 for the condensation, see Figures 10-67Aand 10-67B. 

Under conditions of high vapour velocity Carpenter and Colburn 9 have shown that turbulence may occur with low values of the Reynolds number, in the range 200-400. When the vapour velocity is high, there will be an appreciable drag on the condensate him and the expression obtained for the heat transfer coefficient is difficult to manage. 

Comparing equation 9.176 for streamline flow of condensate and equation 9.179 for turbulent flow, it is seen that, with increasing Reynolds number, hm decreases with streamline flow but increases with turbulent flow. These results are shown in Figure 9.49. 

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 ... 

Eqs. (11.42) and (11.43) are very convenient for design calculations when the mass flow rate of condensate is specified and the required temperature difference is to be determined. However, when the condensation rate is not specified, the solution of Eq. (11.42) requires an iterative procedure since the Reynolds number cannot be calculated a priori. A simple iterative approach is described in Example 11.3. In the laminar regime, if the condensation rate is not known and the temperature difference is specified, iteration can be avoided by using Eq. (11.21) instead of Eq. (11.43). 

The Reynolds number can then be recalculated using this value of the heat transfer coefficient which then allows a new value of the condensation rate and therefore a new value of die Reynolds number to be found and so on. Repeating this iterative procedure gives converged values for the Reynolds number and heat transfer coefficient of 162 and 10,590 W/m2K respectively. Using these values, the total heat transfer rate is,... 

For problems in which the temperature difference is unknown, it is useful to cast Eq. (11.55) in terms of the condensation Reynolds number. It will be recalled that the Reynolds number is defined as Re = 417/utf, where T is the total condensation rate from the entire tube. Using this definition and noting that T = 2Ti/2.t0ui Eq. (11.54) can be written as ... 

Eqs. (11.55) and (11.57) are valid for laminar flow. If flat plate flow is used as a rough guide, it will be seen that these equations can be expected to yield accurate results for about Re < 60. This Reynolds number is twice the value for a flat plate because condensation occurs on both sides of the tube. 

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... 

Using Eq. (9-28) as a starting point, develop an expression for the average heat-transfer coefficient in turbulent condensation as a function of only the fluid properties, length of the plate, and temperature difference i.e., eliminate the Reynolds number from Eq. (9-28) to obtain a relation similar to Eq. (9-10) for laminar condensation. 

Related Calculations. For low values of Reynolds number (4T//x), the Nusselt equation can be used to predict condensing heat-transfer coefficients for vertical tubes ... 

This approach can be used for condensing on the outside of vertical tubes. The equivalent diameter should be used in evaluating the value of Ad, and the outside tube diameter should be used in calculating the terminal Reynolds number. 

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