Condensate film flow

In considering the heat that is transferred, the method first put forward by NussELT(%i and later modified by subsequent workers is followed. If the vapour condenses on a vertical surface, the condensate film flows downwards under the influence of gravity, although it is retarded by the viscosity of the liquid. The flow will normally be streamline and the heal flows through the film by conduction. In Nusselt s work it is assumed that the temperature of the film at the cool surface is equal to that of the surface, and at the other side was at the temperature of the vapour. In practice, there must be some small difference in temperature between the vapour and the film, although this may generally be neglected except where non-condensable gas is present in the vapour. 

When the condensing snrface is completely wetted, the condensate film flows under the influence of gravity and vapor shear, and its heat-transfer characteristics can be reasonably predicted from hydrodynamic principles. This is the nsnal design mode for condensation and is developed in detail in the next section. 

If the wall along which the condensate film flows makes an angle 9 with the vertical, then one must replace g by g cos 8 in the original equation of motion (5.7.1) and in all subsequent relations. 

Film condensation on a horizontal tube. For a curvilinear surface, in particular, for a horizontal circular cylinder along which a condensate film flows, the angle 6 is a nonconstant variable. By taking into account the fact that 6(6) d, where d is the diameter of a circular cylinder, and proceeding by analogy with (5.7.7), one can readily obtain the following formula for the heat transfer coefficient averaged over the external surface of the tube provided that the flow in the condensate film is laminar [200] ... 

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 in-tube condensers are often designed for reflux or knock-back application in reactors or distillation columns. In this case, vapor flow is upward, countercurrent to the hquid flow on the tube wall the vapor shear ac4s to tliicken and retard the drainage of the condensate film, reducing the coefficient. Neither the fluid dynamics nor the heat transfer is well understood in this case, but Sohman, Schuster, and Berenson [J. Heat Transfer, 90, 267-276... 

Figure 10-67B. Correlation of McAdams representing the condensing film coefficient on the outside of vertical tubes, integrated for the entire tube length. This represents the streamline transition and turbulent flow conditions for Prandtl numbers 1 and 5. Do not extrapolate Prandtl numbers, Pr beyond 5. (Used by permission Engineering Data Book II 1984, Wolverine Tube, Inc.)...

Figure 10-71. Condensing steam film coefficients for vertical surfaces or horizontal tubes. G 7n,/ restricted to < 1,090. For theoretical h , for horizontal tubes, use and multiply results by 0.8. G = condensate mass flow per unit tube outside circumference, vertical tubes, lb/(hr) (ft). (Used by permission Devore, A. Petroleum Refiner, V. 38, No. 6, 1959. Gulf Publishing Company, Houston, Texas. All rights reserved.)...

Two cases are considered. The first, the laminar flow of a thin film down an inclined surface, is important in the heat transfer from a condensing vapour where the main resistance to transfer lies in the condensate film, as discussed in Chapter 9 (Section 9.6.1). The second is the flow in open channels which are frequently used for transporting liquids down a slope on an industrial site. 

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 ... 

For conditions of turbulent flow the transfer coefficient for the water side, hi = u<>. Ri the scale resistance is constant, and h the coefficient for the condensate film is almost independent of the water velocity. Thus, equation 9.201 reduces to ... 

The schematic diagram of the experimental setup is shown in Fig. 2 and the experimental conditions are shown in Table 2. Each gas was controlled its flow rate by a mass flow controller and supplied to the module at a pressure sli tly higher than the atmospheric pressure. Absorbent solution was suppUed to the module by a circulation pump. A small amount of absorbent solution, which did not permeate the membrane, overflowed and then it was introduced to the upper part of the permeate side. Permeation and returning liquid fell down to the reservoir and it was recycled to the feed side. The dry gas through condenser was discharged from the vacuum pump, and its flow rate was measured by a digital soap-film flow meter. The gas composition was determined by a gas chromatograph (Yanaco, GC-2800, column Porapak Q for CO2 and (N2+O2) analysis, and molecular sieve 5A for N2 and O2 analysis). The performance of the module was calculated by the same procedure reported in our previous paper [1]. 

The basic equations for filmwise condensation were derived by Nusselt (1916), and his equations form the basis for practical condenser design. The basic Nusselt equations are derived in Volume 1, Chapter 9. In the Nusselt model of condensation laminar flow is assumed in the film, and heat transfer is assumed to take place entirely by conduction through the film. In practical condensers the Nusselt model will strictly only apply at low liquid and vapour rates, and where the flowing condensate film is undisturbed. Turbulence can be induced in the liquid film at high liquid rates, and by shear at high vapour rates. This will generally increase the rate of heat transfer over that predicted using the Nusselt model. The effect of vapour shear and film turbulence are discussed in Volume 1, Chapter 9, see also Butterworth (1978) and Taborek (1974). 

Figure 12.43 can be used to estimate condensate film coefficients in the absence of appreciable vapour shear. Horizontal and downward vertical vapour flow will increase the rate of heat transfer, and the use of Figure 12.43 will give conservative values for most practical condenser designs. 

Two flow models are used to estimate the mean condensation coefficient in horizontal tubes stratified flow, Figure 12.45a, and annular flow, Figure 12.45. The stratified flow model represents the limiting condition at low condensate and vapour rates, and the annular model the condition at high vapour and low condensate rates. For the stratified flow model, the condensate film coefficient can be estimated from the Nusselt equation, applying a suitable correction for the reduction in the coefficient caused by... 

The Nusselt Equations apply to laminar flow of the condensing film. For horizontal condensation the equations... 

A knowledge of the thicknesses of flowing liquid films is of importance in a wide range of practical problems involving film flow. Such problems include the calculation of heat transfer in evaporators and condensers, mass transfer in film-type equipment, the design of overflows and downcomers, etc. 

Grigull (G8), 1942 Treatment of heat transfer in condensate film on vertical surface, assuming applicability of Prandtl pipe-flow relationships. Comparison with experimental data,... 

Brauer (B17), 1958 Application of results on film flow (B14) to case of heat flow in filmwise condensation of pure vapors on vertical walls. Nomograms for practical use. 

While the fluid dynamics of the actual film-flow process across the disc is daunt-ingly complex, a very approximate interim how model may be based upon Nusselt s treatment of the how of a condensate him. This assumes that the how is stable (i.e., ripple free), that there is no circumferential slip at the disc/liquid surface, and that there is no shear at the gas/liquid interface. The treatment is based... 

AirCIri). This is an executable program for any air-cooler condenser. The inputted Q will be the heat duty transferred. Data inputs for condenser tube-side transport property values of viscosity, thermal conductivity, and specific heat should be determined as for two-phase flow values calculated in Chap. 6. Use the average tube-side temperature for these condensing film transport property values. Weighted average values between gas and liquid should also be determined and applied like that used in the two-phase flow equations in Chap. 6. 

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 ... 

Flow regimes in a condensed film on a vertical fiat plate. 

In many practical applications, condensation occurs on a column of vertically aligned horizontal tubes. In such a case, as illustrated in Fig. 11.16, the condensate cascades from tube to tube down the column of tubes. If the flow remains laminar, the heat transfer rate from lower tubes will decrease because of the thickening condensate film. 

Vapor can condense on a cooled surface in two ways. Attention has mainly been given in this chapter to one of these modes of condensation, i.e.. to him condensation. The classical Nusselt-type analysis for film condensation with laminar film flow has been presented hnd the extension of this analysis to account for effects such as subcooling in the film and vapor shear stress at the outer edge of the film has been discussed. The conditions under which the flow in the film becomes turbulent have also been discussed. More advanced analysis of laminar film condensation based on the use of the boundary layer-type equations have been reviewed. 

If the plate described in Problem 11.12 was 3 m high instead of 30 mm high, would the flow in the condensed film on the surface become turbulent If it does become turbulent, find the distance from the top of the plate at which transition occurs. 

Hirshburg, R.l. and Florschuetz, L.W., Laminar Wavy-Film Flow Part I, Hydrodynamics Analysis, Part II, Condensation and Evaporation, J. Heat Transfer, Vol. 104, pp. 452-464, 1982. 

Stuhltrager. E., Naridomi, Y., Miyara. A., and Uehara, H.. "Flow Dynamics and Heat Transfer of a Condensate Film on a Vertical Wall. I. Numerical Analysis and Flow Dynamics/ Int. J. Heat Mass Transfer, Vol. 36. pp. 1677-1686, 1993. 

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