Film condensation turbulent flow

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 10-77. Turbulent film condensation of light hydrocarbons and their mixtures—up-flow, (used by permission Clements, L. D., and Colver, C. P. AlChE Heat Transfer Symposium V. 131, No. 69, 1973. American Institute of Chemical Engineers. All rights reserved.)...

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 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). 

Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces free or forced convection laminar or turbulent flow liquids, gases, liquid metals, non-Newtonian fluids pure substances or mixtures completely or partially condensable air, water, refrigerants, or other specific substances fluidized or fixed particles combined convection and radiation and others. In spite of such qualifications, it should be... 

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 ... 

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. 

Consider laminar film condensation on a vertical plate when the vapor is flow ing parallel to the surface in a downward direction at velocity, V. Assume that a turbulent boundary layer is formed in the vapor along the outer surface of the laminar liquid film. Determine a criterion that will indicate when the effect of the shear stress at the outer edge of the condensed liquid film on the heat transfer rate is less than 59c. Assume that pv [Pg.602]

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... 

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... 

Actual condensation can take place in many different ways. If the condensate forms a continuous film, Fig. 4.1, we speak of film condensation. The condensate film can be quiescent, or be in laminar or turbulent flow. The thermal resistance is decisive for the condensation rate, if the molecular kinetic resistance can be neglected. In calculations it is sufficient to just investigate this resistance, as Nusselt [4.2] first did for a flowing laminar film. 

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... 

Turbulent film condensation of vapour flowing in tubes. 

For definiteness, we consider the transfer processes between a cylindrical wall and a turbulently flowing n-component fluid mixture. For condensation of vapor mixtures flowing inside a vertical tube, for example, the wall can be considered to be the surface of the liquid condensate film. We examine the phenomena occurring at any axial position in the tube, assuming that fully developed flow conditions are attained. For steady-state conditions, the equations of continuity of mass of component i (assuming no chemical reactions), Eqs. 1.3.7 take the form... 

Seat-transfer coefficients in film condensation line A A, theoretical relation for laminar flow, horizontal and vertical tubes also, recommended relation for horizontal tubes line BB, recommended relation for laminar flow, vertical tubes line CC, approximate relation for turbulent flow, vertical tubes. 

There are several types of situations covered by Eq, (21.16). The simplest case is zero convective flow and equimolal counterdiffusion of A and B, as occurs in the diffusive mixing of two gases. This is also the case for the diffusion of A and B in the vapor phase for distillations that have constant molal overflow. The second common case is the diffusion of only one component of the mixture, where the convective flow is caused by the diffusion of that component. Examples include evaporation of a liquid with diffusion of the vapor from the interface into a gas stream and condensation of a vapor in the presence of a noncondensable gas. Many examples of gas absorption also involve diffusion of only one component, which creates a convective flow toward the interface. These two types of mass transfer in gases are treated in the following sections for the simple case of steady-state mass transfer through a stagnant gas layer or film of known thickness. The effects of transient diffusion and laminar or turbulent flow are taken up later. 

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]. 

Rohsenow et al. [21] extended the analysis into the turbulent film regime using the heat transfer-momentum analogy. The results for a downward flowing vapor are shown in Fig. 14.7 for Prf = 1.0 and 10.0. At high vapor velocities, as the dimensionless shear stress x increases, the transition to turbulence occurs at smaller values of the film Reynolds number (Eq. 14.31) as represented by the dashed lines. The influence of x on both laminar and turbulent film condensation is evident. 

R. A. Seban, Remarks on Film Condensation with Turbulent Flow, Trans. ASME, 76, pp. 299-303, 1954. 

Heat transfer coefficients for condensation processes depend on the condensation models involved, condensation rate, flow pattern, heat transfer surface geometry, and surface orientation. The behavior of condensate is controlled by inertia, gravity, vapor-liquid film interfacial shear, and surface tension forces. Two major condensation mechanisms in film condensation are gravity-controlled and shear-controlled (forced convective) condensation in passages where the surface tension effect is negligible. At high vapor shear, the condensate film may became turbulent. 

Repairing the condenser by plugging leaking tubes was unsuccessful as seen by the corrosion of plugs, top tube sheet, and seal welds. Plugging the tubes caused turbulent flow, which eroded the passive film on the steel plugs and caused severe corrosion of the plugs, top tube sheet, and steel welds. 

The following equations are of fundamental importance for film condensation in laminar and turbulent flow on vertical and horizontal devices. 

---