Advanced Heat and Mass Transfer

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1 Advanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell Chapter 7 Condensation and Evaporation All rights are reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, without the written permission of the authors. 1

2 Condensation occurs when a saturated 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 a multi-component vapor, the saturation temperature is referred to as the dew point. 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 will 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 subcooled below its equilibrium saturation temperature at the system pressure (see Chapter 2). Advanced Heat and Mass Transfer by Amir Faghri, 2

3 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 homogenously. 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. 3

4 Condensation Liquid droplet nucleation Homogeneous Heterogeneous Liquid droplet nucleation entirely within a superheated vapor Liquid droplet nucleation occurring at the interface of a metastable vapor and another phase (usually solid) at a lower temperature Figure 7.1 Flowchart of the different modes of condensation. 4

5 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 surface with a low surface energy or noble metal. 5

6 (a) Filmwise condensation Figure 7.2 Heterogeneous condensation. (b) Dropwise condensation 6

7 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. 7

8 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). 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. 8

9 Fig. 7.4 (a) shows the transverse distributions of temperature T and mass fractions ω 1v and ω 2v 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 reflects the point at which the binary vapor/gas begins to condense. When there is less ω 1 and more ω 2, 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. 9

10 T Liquid film Concentration boundary layer Thermal boundary layer in vapor Bulk flow of binary vapor mixture T T T T sat Variation of ω and T in the concentration boundary layer Dew point line T w T δ T δ Tw ω v ω 1v + ω 2v =1 ω 2v ω 1v Boiling point line y 0 ω 1v 1 (a) (b) Figure 7.5 Condensation of immiscible fluids. Figure 7.4 Temperature and mass fraction in the condensation of a binary miscible vapor 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 (Fujii, 1991; Reproduced with kind permission of Springer Science and Business Media). ω 1vδ ω 1v 10

11 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 first. 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. 11

12 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 eutectic temperature for a given pressure. 12

13 Temperature Pure comp. 2 Miscible liquid region heavy w/ comp. 2 Dew point line Liquid-vapor region heavy w/ comp. 2 Boiling point line Vapor region Immiscible liquid region 0 mass fraction of component 1 (ω 1 ) Dew point line Liquid-vapor region heavy w/ comp. 1 Figure 7.6 Phase diagram of liquids with a miscibility gap. Miscible liquid region heavy w/ comp. 1 Pure comp. 1 Pure comp. 2 Dew point line Vapor region Dew point line Pure comp. 1 Temperature Liquid-vapor region heavy with component 2 Boiling point line Liquid-vapor region heavy with component 1 Immiscible liquid region 0 mass fraction of component 1 (ω 1 ) Figure 7.7 Phase diagram of completely immiscible pure liquid. 13

14 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. 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). 14

15 Figure 7.8 Examples of film evaporators. 15

16 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 size of the liquid drop and the temperature distribution at two different times (t 2 > t 1 ) are shown in Fig 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 Such processes are used in bulk cooling as well as spray fuel injection in diesel engines. 16

17 r r θ r I θ r I ω v ω v ω v,i ω v,i ω v, ω v, T w T t 2 > t 1 t 2 > t 1 t 2 t 1 T I t 2 t 1 T T I T Figure 7.9 Evaporation from a liquid droplet on a heated wall. r I Figure 7.10 Evaporation from a liquid droplet suspended in vaporgas mixture. r I 17

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