Condensation wavy film

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. 

WAVY AND TURBULENT FILM CONDENSATION ON A VERTICAL SURFACE... 

Stagnant saturated steam at 100°C condenses onto a vertical plate with a surface temperature of 70°C. Approximately how far down the plate does the film become wavy ... 

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. 

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,... 

Nusselt s film condensation theory presumes a laminar film flow. As the amount of condensate increases downstream, the Reynolds number formed with the film thickness increases. The initially flat film becomes wavy and is eventually transformed from a laminar to a turbulent film the heat transfer is significantly better than in the laminar film. The heat transfer in turbulent film condensation was first calculated approximately by Grigull [4.14], who applied the Prandtl analogy for pipe flow to the turbulent condensate film. In addition to the quantities for laminar film condensation the Prandtl number appears as a new parameter. The results can not be represented explicitly. In order to obtain a clear representation, we will now define the Reynolds number of the condensate film... 

In the transition region between laminar and turbulent condensation, the condensate film is wavy. In Fig. 4.12 this transition region is represented by the dotted lines, according to results from Henstock and Hanratti [4.16]. 

The factor / takes into account here the waviness of the laminar condensate film, / 1.15 QlalII is the heat transfer coefficient for laminar film condensation from Nusselt s film condensation theory and aturb is that for a turbulent condensate film, which is found, for example from (4.41) together with (4.42). 

As the film thickens further, turbulence will develop in the condensate film, and the heat transfer mechanism then undergoes a significant change, since the heat is transferred across the condensate film by turbulent mixing as well as by molecular conduction. For gravity-dominated flow (i.e., natural convection), the transition from laminar-wavy flow to turbulent flow occurs at film Reynolds numbers of about 1600 [18]. 

Vertical Surfaces. Condensation heat transfer coefficients for external condensation on vertical surfaces depend on whether the vapor is saturated or supersaturated the condensate film is laminar or turbulent and the condensate film surface is wave-free or wavy. Most correlations assume a constant condensation surface temperature, but variable surface temperature conditions are correlated as well as summarized in Table 17.23. All coefficients represent mean values (over a total surface length), that is, h = (1/L) 10 hloc dx. 

A presence of interfacial waves increases the heat transfer coefficient predicted by Nusselt theory by a factor up to 1.1. An underprediction of a heat transfer coefficient by the Nusselt theory is more pronounced for larger condensate flow rates. For laminar condensation having both a wave-free and wavy portion of the condensate film, the correlation based on the work of Kutateladze as reported in [81] (the fourth correlation from the top of Table 17.23) can be used as long as the flow is laminar. 

However, even at relatively low film Reynolds numbers, the assumption that the condensate layer is in laminar flow is open to some question. Experiments have shown that the surface of the film exhibits considerable waviness (turbulence). This waviness causes increased heat transfer rates. Better heat transfer correlations for vertical condensation were presented by Dukler in 1960. He obtained velocity distributions in the liquid film as a function of the interfacial shear (due to the vapor velocity) and film thickness. From the integration of the velocity and temperature profiles, liquid film thickness and point heat-transfer coefficients were computed. According to the Dukler development, there is no... 

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