# Basics of condensation

(Difference between revisions)
 Revision as of 18:24, 25 May 2010 (view source)← Older edit Revision as of 17:53, 6 June 2010 (view source)Newer edit → Line 37: Line 37: Section 7.2 presents the mechanisms of dropwise condensation, starting with the surface tension and capillary pressure, followed by a detailed discussion on thermal resistance in the condensation process, and heat transfer coefficient for dropwise condensation. Section 7.3 begins with an introduction to the filmwise condensation problem, which is followed by the generalized governing equations for laminar film condensation of a binary vapor. The classical Nusselt analysis of laminar film condensation on a vertical wall is discussed, and the generalized condensation process for a flowing vapor reservoir for both laminar and turbulent film condensation will be addressed. Turbulent film condensation in a tube with both cocurrent and countercurrent vapor flow is also presented, as are empirical correlations for filmwise condensation configurations. Section 7.3 closes with a discussion of the effect of noncondensable gases. This chapter is closed by discussion on evaporation from a vertical falling film on a heated surface and spray cooling in Section 7.4. Section 7.2 presents the mechanisms of dropwise condensation, starting with the surface tension and capillary pressure, followed by a detailed discussion on thermal resistance in the condensation process, and heat transfer coefficient for dropwise condensation. Section 7.3 begins with an introduction to the filmwise condensation problem, which is followed by the generalized governing equations for laminar film condensation of a binary vapor. The classical Nusselt analysis of laminar film condensation on a vertical wall is discussed, and the generalized condensation process for a flowing vapor reservoir for both laminar and turbulent film condensation will be addressed. Turbulent film condensation in a tube with both cocurrent and countercurrent vapor flow is also presented, as are empirical correlations for filmwise condensation configurations. Section 7.3 closes with a discussion of the effect of noncondensable gases. This chapter is closed by discussion on evaporation from a vertical falling film on a heated surface and spray cooling in Section 7.4. + + ==Heterogeneous and Homogeneous Condensation== + ''See Main Article'' [[Heterogeneous and Homogeneous Condensation]]
+ ==Phase Diagrams for Condensation of Binary Vapor== + ''See Main Article'' [[Phase Diagrams for Condensation of Binary Vapor]]
==References== ==References==

## Introduction

Condensation occurs when a saturated or superheated vapor – pure or multi-component – comes into contact with an object, such as a wall or other contaminant, that has a temperature below the saturation temperature. In most applications involving the condensation of a vapor, heat is transferred to a solid wall adjacent to the vapor. If the solid wall temperature is below the equilibrium saturation temperature at the system pressure, a liquid droplet embryo may form at this solid-vapor interface. This condensation is referred to as heterogeneous nucleation of a liquid droplet embryo. Heterogeneous liquid droplet nucleation is nucleation of a vapor droplet embryo at the interface of a metastable vapor phase and another phase; this second phase is usually solid and is naturally held at a lower temperature than the vapor. A metastable vapor is one that is supercooled below its equilibrium saturation temperature at the system pressure (see Chapter 2). Figure 7.1 is a flowchart schematic showing the different modes by which a liquid droplet embryo can form. It can be seen from this figure that the embryos can also be formed homogeneously. Homogeneous nucleation of a liquid droplet occurs entirely within a supercooled vapor. The liquid droplet is completely surrounded by supercooled vapor and is not attached to a lower temperature wall, as is the case in the heterogeneous process.

The heterogeneous condensation occurs when vapor condenses on the cooled surface as a thin film or as droplets, depending on whether the surface is wettable or nonwettable with the condensate. If the surface is wettable with the condensate, a continuous condensate film forms on the surface and filmwise condensation occurs [see Fig. 7.2(a)]. Conversely, if the surface is not wettable with the condensate, a series of condensate droplets form on the surface (i.e., dropwise condensation occurs) [see Fig. 7.2(b)]. Dropwise condensation is preferred over filmwise condensation, because its resulting overall heat transfer coefficient is higher by as much as an order of magnitude. This difference occurs because the cooler wall surface always has an area that is not covered by condensate. The resistances encountered at the liquid-vapor interface, along with the conduction through the liquid itself, are removed and the heat transfer is increased significantly. Therefore, in industrial applications it is wise to
Figure 7.1 Flow charts of the different condensation
Figure 7.2 Heterogeneous Condensation
introduce conditions that promote dropwise condensation. The dropwise condensation can be promoted by taking one or more of the following steps:

1.Introduce a nonwetting agent into the vapor that will eventually deposit on the cooling surface to break up wetting conditions.

2.Apply grease or waxy products that are poor wetting agents to the cool wall surface in order to promote nonwetting conditions.

3.Permanently coat the wall surface with a low surface energy or noble metal.

Figure 7.3 Homogeneous condensation: (a) condensation on small contaminant particles in the vapor mixture, (b) condensation on liquid droplets, and (c) condensation of vapor bubbles.

If a tiny, sufficiently supercooled contaminant, is introduced to the vapor, condensate will form on the contamination in the middle of the vapor. This is an example of homogeneous condensation that is different from the heterogeneous condensation mentioned above, in that it relies on a solid, liquid, or even vapor contaminant to initiate condensation. This type of condensation produces a mist-like quality and is depicted in Fig. 7.3 (a). Two more examples of homogeneous condensation are shown in Figs. 7.3 (b) and (c). When liquid is introduced into vapor through a nozzle, liquid droplets are formed; vapor condenses on the surface of these droplets suspended in a vapor phase [see Fig. 7.3 (b)]. When vapor bubbles are introduced into the bulk liquid, as shown in Fig. 7.3 (c), the vapor bubbles surrounded by the cold liquid shrink and eventually collapse due to condensation.

In many industrial applications the saturated vapor to be condensed is in fact a miscible binary vapor mixture. In a multicomponent vapor, the saturation temperature is referred to as the dew point. As will be described below, this binary mixture does condense differently than a pure vapor and has lower heat transfer and condensation rates (Fujii, 1991). Fig. 7.4 (a) shows the transverse distributions of temperature T and mass fractions ω1v and ω2v in the condensate film, vapor boundary layer, and bulk vapor of a steady condensation process consisting of a binary miscible vapor mixture in contact with a vertical cooled wall; the phase equilibrium diagram of this condensation process is shown in Fig. 7.4 (b). Dew point line refects the point at which the binary vapor/gas begins to condense. When there is less ω1 and more ω2, this occurs at a higher temperature. The boiling point line reflects the point at which the binary liquid begins to boil or when the binary vapor is completely condensed. When a binary vapor mixture is cooled below its saturation temperature by contact with a cold wall, the less volatile component 2 (with higher saturation temperature) condenses more than the volatile component 1. In other words, as the vapor mixture cools, the component with the higher saturation temperature at the system saturation pressure will condense first. If it is assumed that the bulk vapor mixture is kept at a constant density, the volatile component (with lower saturation temperature) must become very dense (while remaining in its vapor form) at the liquid-vapor interface. Meanwhile, the less volatile component condenses into the liquid phase
Figure 7.4 Temperature and mass fraction in the condensation of a binary miscible vaport mixture: (a) T and ω distribution in the condensate film and vapor boundary layer; (b) variation of T and ω on a diagram of phase equilibrium
first. This can be seen in Fig. 7.4 (a), where the volatile component increases in mass at the interface, while the less volatile component is at its lowest mass at the interface. Gravity or drag forces constantly flush the surface of the wall, so the dense mass of the volatile component is removed by convection forces. However, due to this buildup of the volatile component at the interface, a larger resistance to heat flow is produced in a multicomponent system than in a pure vapor condensation process. Due to the difference in saturation properties of the binary mixture components, the temperature drop across the interface is larger than for a pure vapor condensation process. Therefore, the interfacial resistance for the condensation of a binary vapor mixture usually cannot be neglected, as is sometimes the case for the condensation of pure vapors. This interfacial resistance will, however, be developed below for a pure vapor. Figure 7.4(b) illustrates condensation of a binary mixture of miscible vapors on a phase equilibrium chart. Initially the vapor is at T and it is placed in contact with a cooler wall. The vapor temperature decreases until it reaches Tsat, at which point the condensation process begins. The dew point line on the diagram is the saturation temperature for various concentrations of the two components in the mixture. The less volatile component in the mixture (component 2 in this case) will condense faster than the other. At the temperature of the interface between the liquid and the vapor phases, the mass fraction of each phase can be read off the tie line between the dew point and boiling point lines. As can be seen, the condensate film will be much heavier with the less volatile component, and the vapor will have a higher concentration of the more volatile component.
Figure 7.5 Condensation of immiscible fluids.
Other applications involve the condensation of vapors of partially or completely immiscible liquids such as water or organic compounds. During condensation of vapors of some immiscible liquids, the condensate will form in a combination of dropwise and filmwise liquid. One component will condense as a liquid film with droplets of the other component floating within or on top of it. This mixture can be seen in Fig. 7.5 and is caused by the different surface tension forces of the two components in relation to the vapor and solid wall. Figures 7.6 and 7.7 show the phase diagrams for binary mixtures with a miscibility gap and with completely immiscible liquids, respectively. The point where the dew point lines meet the immiscible liquid regions is the eutectic point, which occurs at the
Figure 7.6 Phase diagram of liquids with a miscibility gap.
Figure 7.7 Phase diagram of completely immiscible pure liquid.
eutectic temperature for a given pressure. Condensation may occur in several forms for these cases. If the wall temperature is greater than the eutectic temperature or if the condensate film is sufficiently thick, the interface temperature must also be above the eutectic temperature. This case is similar to the condensation of miscible liquids: a homogenous condensate film will form, and the concentrations of each component in the vapor and liquid phases can be read off the tie line corresponding to the interface temperature. When the wall temperature is less than the eutectic temperature and the condensate film is thin, the interface temperature will be equal to the eutectic temperature. As condensation occurs, two immiscible liquid phases form. These liquid phases are in equilibrium with the remaining vapor, which will have the eutectic composition.

Evaporation processes generally occur from liquid films, drops, and jets. Films may flow on a heated or adiabatic surface as a result of gravity or vapor shear. Drops may evaporate from a heated substrate, or they may be suspended in a gas mixture or immiscible fluid. Jets may be cylindrical in shape or elongated (ribbon-like).

In film evaporators, a liquid film is evaporated in order to: (1) cool the surface on which it flows, (2) cool the liquid itself, or (3) increase the concentration of some component(s) in the liquid. Heat may be transferred to the film surface by conduction or convection. The design of film evaporators is most frequently constrained by the extent of the liquid superheat, since nucleate boiling must be prevented. Nucleate boiling can lead to product deterioration because elevated temperatures increase chemical reaction rates. Also, the accumulation of deposits on walls (fouling) as a result of nucleate boiling hinders heat transfer. To avoid nucleate boiling, liquid superheating should not exceed 3 to 40 K, depending on the liquid. This chapter deals with evaporation with no nucleate boiling.

In addition to the capability for low liquid superheating, film evaporators may be designed to achieve short residence time (that is, contact time between the liquid and the evaporator wall), which further reduces the tendency for chemical reactions to occur. The tendency for fouling is also reduced in more rapidly flowing films. These features are ideal for heat-sensitive fluids such as those in food processing and polymer devolatilization (Alhusseini et al., 1998).

A thin liquid film in an evaporator can be produced by several arrangements, two of which are falling and climbing films (See Fig. 7.8). In falling film evaporators, the liquid is evenly distributed around the opening of a vertical channel – usually a tube – and falls under gravitational force as its surface evaporates to a vapor or gas mixture. If the vapor is drawn to the bottom, the flow is cocurrent as shown in Fig. 7.8(a) and the shear stress of the vapor on the liquid film increases its speed downward. When the vapor is drawn to the top, the flow is countercurrent as shown in Fig. 7.8(b). A climbing film evaporator Fig. 7.8(c) is designed so that liquid is fed into the bottom, and vapor shear pushes the liquid film along the wall to the top. In all of these cases, the lack of a hydrostatic pressure drop eliminates the corresponding temperature drop along the evaporator length, thereby increasing the uniformity in temperature. A more complicated example, shown in Fig. 7.8 (d), is a two-phase closed thermosyphon where evaporation takes place in the evaporator section and liquid and vapor flow in opposite directions.

The residence time of a liquid in a falling film evaporator may be increased with a countercurrent configuration. If this configuration is chosen, however, the likelihood of entrainment, flooding, or liquid blocking should be considered. Unlike the cocurrent configuration, countercurrent flow is more prone to
Figure 7.8 Evaporation from a liquid droplet on a heated wall.
Figure 7.9 Examples of film evaporators.
entrainment, which occurs when liquid is carried upward by the vapor (see Section 7.3.8). Liquid blocking – when liquid bridges the channel and blocks the vapor path – can also be more likely in a countercurrent configuration.

In addition to the film evaporation described above, evaporations from liquid droplets attached to a heated wall or surrounded by hot gas can also find their application in irrigation of crops, firefighting, and combustion. Figure 7.9 shows evaporation from a liquid droplet attached to a heated wall; its application can be found in surface spray cooling, where liquid droplets are sprayed onto a hot surface. Heat is conducted through the droplet to the interface, where an abrupt temperature drop takes place due to evaporation. The mass fraction of the vapor component in the gas mixture, ωv, is greatest next to the interface, and by diffusion the mass fraction decreases to its bulk level with increasing distance from the wall. The size of the liquid drop and the temperature distribution at two different times (t2>t1) are shown in Fig. 7.9. As time goes on, the liquid droplet becomes smaller (as indicated by the dashed-line), while the temperature at the heated wall and interface remain unchanged.

When a liquid droplet is surrounded by a hot gas mixture, evaporation takes place on the surface of the droplet, as shown in Figure 7.10. Such processes are used in bulk cooling as well as spray fuel injection in diesel engines. The time
Figure 7.10 Evaporation from a liquid droplet suspended in a vapor-gas mixture.
required for such a droplet to completely evaporate as a member of a dispersed phase will determine the overall heat transfer (cooling effect). The partial pressure, pv, and the mass fraction, ωv, of the vapor in the gas mixture are the greatest adjacent to the surface of the droplet, and diffusion causes the partial pressure and mass fraction to decrease with increasing distance from the interface. The temperature profile in the drop is dominated by transient conduction, but convection takes place outside the drop. Since the evaporating liquid is directly supplied by the liquid droplet, evaporation on the drop surface is dominated by heat transfer, not by mass diffusion.

Section 7.2 presents the mechanisms of dropwise condensation, starting with the surface tension and capillary pressure, followed by a detailed discussion on thermal resistance in the condensation process, and heat transfer coefficient for dropwise condensation. Section 7.3 begins with an introduction to the filmwise condensation problem, which is followed by the generalized governing equations for laminar film condensation of a binary vapor. The classical Nusselt analysis of laminar film condensation on a vertical wall is discussed, and the generalized condensation process for a flowing vapor reservoir for both laminar and turbulent film condensation will be addressed. Turbulent film condensation in a tube with both cocurrent and countercurrent vapor flow is also presented, as are empirical correlations for filmwise condensation configurations. Section 7.3 closes with a discussion of the effect of noncondensable gases. This chapter is closed by discussion on evaporation from a vertical falling film on a heated surface and spray cooling in Section 7.4.

## Heterogeneous and Homogeneous Condensation

See Main Article Heterogeneous and Homogeneous Condensation

## Phase Diagrams for Condensation of Binary Vapor

See Main Article Phase Diagrams for Condensation of Binary Vapor

## References

Fujii, T., 1991, Theory of Laminar Film Condensation, Springer-Verlag, New York, New York.

Alhusseini, K.A., Tuzla, K., and Chen, J.C., 1998, “Falling Film Evaporation of Single Component Liquids,” ASME Journal of Heat Transfer, Vol. 41, pp. 1623-1632.