5.1. Trufin in Boiling Heat Transfer Boiling is the formation of vapor bubbles at the heating surface. These bubbles form at nucleation sites whose number and location depend upon the surface roughness or cavities, fluid properties, and operating conditions. The boiling heat transfer coefficient is very sensitive to the temperature difference between the surface and the liquid. In addition, the heat transfer coefficient is affected by the local vapor-liquid mixture ratios and velocities, which are a function of the vaporizer design and operating con-ditions. The complex interaction of all these variables makes the accurate prediction of a boiling coefficient virtually impossible, but in large commercial vaporizers the two-phase flow heat transfer becomes controlling and reduces the number of variables. In this section these variables will be discussed and some references given with the aim of providing the engineer an understanding of these factors that affect design of vaporizers. Also some design principles to allow him to produce a vaporizer design will be given. In general, the philosophy of design is that of a designer of process vaporizers. 5.1.1. Pool Boiling Curve If a heating surface is immersed in a pool of liquid that is at the boiling point and the surface temperature is slowly increased, then a plot of the heat flux and the derived heat transfer coefficient versus the temperature difference between the heating surface and the liquid boiling point results in a curve as shown in Fig. 5.1. For the present we are considering a single component liquid; mixtures will be discussed later. Up to the point A or A', heat transfer occurs by natural convection and no bubbles are seen. The liquid pool is superheated and evaporation occurs at the liquid-vapor interface. At point A or A', the local superheat is sufficient to activate nucleation sites on the heating surface and vapor bubbles are formed. The very rapid, almost explosive, formation of the bubbles causes a very strong local velocity within the liquid film and increases heat transfer. In the region from A to B (A' to B') more bub6le nucleation sites are activated and this is the region of nucleate boiling. At point B on the heat flux curve (defined as the critical temperature difference also called the departure from nucleate boiling, DNB, or the bum-out point) the heat flux decreases with a further increase of the surface temperature. Note that point B does not correspond to point B' on the coefficient curve but is at the ΔT where the slope of

240

the h vs. ΔT curve is -1. Several phenomena are occurring as one approaches point B and passes it into the B to C region. The numerous nuclei and the rapid evolution of vapor prevent the liquid from approaching the surface and thus starve the surface of liquid, which was defined by Zuber (1) as a hydrodynamic crisis phenomenon. However, just beyond B after a short transition zone, film boiling oc-curs. Happel and Stephan (2) have also observed and reported the formation of continuous vapor films well before the minimum heat flux, point C. In film boiling a continuous layer of vapor covers the heating surface and keeps the liquid from contacting the surface. The insulating effect of the vapor reduces the rate of heat transfer and the coefficient. As the temperature difference increases, the vapor film becomes thicker and eventually reaches a maximum thickness somewhere near point C' and then the coefficient slowly increases due to the effect of radiation and perhaps further convection effects within the vapor film. The transition from nucleate to film boiling involves a zone where the rapid vapor evolution blankets the tube with a rough vapor-liquid interface that pulsates and occasionally collapses thus wetting the tube. However, as the ΔT is further increased this film becomes smooth and stable but the heat flux is less. The extent of this transition seems to depend upon its definition. Many references define the transition to be between the maximum, B, and the minimum heat flux, C, points as shown by the upper arrows in Figure 5.1. However, some experiments (2,3) have seen stable films well before the minimum flux, C, is reached. Film boiling appears to be closely related to the Leidenfrost effect. This phenomenon was first described by Leidenfrost in 1756 and bears his name. He noted that when liquids were spilled or placed on very hot surfaces, drops were formed which did not contact the surface but floated above the surface and slowly evaporated. However, when the surface temperature was reduced below a certain temperature the drops contacted the surface and rapidly evaporated. The Leidenfrost phenomenon has undergone several periods of intense experimentation and neglect but references to the early literature are found in [references 3 and 4 and more recent work in references 5, 6 and 7]. As noted by Drew and Mueller (3) the temperature differences for the Leidenfrost effect and the boiling critical temperature difference seemed to be closely related. Hence, the actual maximum flux, point B, may be governed by both the hydrodynamic and the film boiling effects. However, film boiling can occur without ever entering the nucleate boiling region as for example in the quenching of metals. From a practical standpoint only the A-B portion of the curve is of interest as operation in the B-C region results in excessive surface temperatures. However, there are occasions when film boiling is unavoidable as in the vaporization of low boiling liquids or in cryogenic vaporizers. The deliberate use of film boiling in attempting to reduce fouling or corrosion has been suggested but is impractical due to variation of operating conditions during start up or shut down and the fluctuations of the film in the transition region. The start up procedure of a vaporizer can affect its subsequent operation whenever the temperature of the heating medium would correspond to a temperature difference greater than the critical ΔT or point B. If the heating source is applied before any liquid is in the vaporizer, then the tube surface temperature, Tw, will reach the medium (steam) temperature, Ts, since no heat transfer is occurring. Then when the liquid is fed to the vaporizer, boiling would begin in the film or B-C region; i.e., (Tw – Tsat,) > ΔTc. However, if the vaporizer is full of liquid when the steam is turned on, then the wall temperature starts at the liquid temperature and rises on the A-B portion of the curve until at equilibrium the wall temperature, Tw, corresponds to a temperature less than point B and the temperature difference, Ts – Tw, results from the heating medium resistance, fouling resistance, and tube wall resistance. Hence, whenever Ts > (Tsat + ΔTc) then the liquid should be in the vaporizer for a cold start up. In normal operation the wall temperature, Tw, would be less than Tsat + ΔTc due to other resistances.

241

5.1.2. Nucleation Nucleation can be either homogenous (occurring within the liquid) or heterogeneous (occurring at a liquid-solid interface). The nucleation phenomenon has been extensively studied both theoretically and experimentally and even a brief review of all the factors involved is beyond the scope of this manual. Cole (8) has an excellent review of nucleation and considerable information is also available in (9, 10, 11). Very briefly, due to the surface tension forces we have across the interface of a spherical bubble

csat rPP /2σ=− l (5.1) where Psat is the saturation pressure of the vapor and the liquid pressure, o the surface tension and rlP c the radius of curvature of the bubble. Through the vapor pressure curve for a fluid, these pressures can be related to a superheat in the liquid in order to maintain a bubble of radius, rc, at equilibrium. The superheat for homogenous nucleation is very large and is difficult to obtain in the presence of surfaces. In thermodynamic equilibrium theory the isotherms on a P-V diagram go through a minimum, (∂P/ ∂V)T = 0, at a liquid superheat which is taken as a homogenous nucleation temperature. In kinetic theory there is a probability that a sufficient number of molecules with greater than average energy can join to form a cluster with an equilibrium radius. The resulting kinetic theory equation for superheat is

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=−

)/(316 3

hJnkTnkTvT

TTv

vsatsat

ll

ll σπρρ

ρλ

(5.2)

n this equation k is the Boltzman constant and h the Plank constant. The heterogeneous nucleation requires less superheat and is in addition a function of the angle of contact between the vapor and solid. Cole (8) has shown the above equation can be modified to

2/13

)/(3)(16

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=−

hJnkTnkTfvT

TTv

vsatsat

ll

ll θσπρρ

ρλ

(5.3)

where the function of f(θ) is a factor involving the bubble contact angle θ. This contact angle is affected by the wettability of the surface, shape of the surfaces (pores etc.) local temperature gradients, etc. Although an excellent understanding of the factors involved in nucleation has been developed it is of little use in the design of vaporizers. This is due to the inability to manufacture and know in advance all the surface characteristics, to control the changes in surface during operation due to corrosion and fouling, and the effect of dissolved gases, mixtures, and solids upon the physical properties of the liquid especially with the local temperature and concentration gradients that will exist around a developing bubble. Further, the effectiveness of nucleation in improving heat transfer decreases as two-phase flow becomes the dominant factor. Figure 5.2 shows how sensitive the boiling flux is to surface conditions and how this surface can change during operation.

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Improving the nucleation characteristics of a surface has the effect of moving the curves of Figure 5.1 to the left but has little effect on the maximum heat flux at point B. The net result is a higher heat transfer at a given temperature difference or for a given heat flux, a lower temperature difference. These results become important when the available temperature differences are small or become very important as in cryogenic services where power consumption is closely related to ΔT. Special proprietary surfaces have been developed and are commercially available (12), as well as mechanically formed surfaces including Trufin. These surfaces can substantially reduce the superheat required for nucleation and increase the heat transfer coefficients by factors of 3 to 10. The relative effectiveness of these surfaces can change for different fluids depending upon how well the specific surface characteristics (pore size and distribution, surface wettability, etc.) can be matched to the fluid characteristics. However, these surfaces must be used with care so that their effectiveness is not destroyed by fouling, corrosion, or accumulation of high boiling residues. 5.1.3. Nucleate Boiling Curve The nucleate boiling curve is considered to start at point A of Figure 5.1 and ends at point B. This portion of the boiling curve has a very steep slope ranging from 2 to 4 and for the heat transfer coefficient, h = a ΔTm. Observations of boiling shows that as the temperature difference, ΔT, is increased more nuclei are activated; however, eventually when the nuclei spacing is less than the bubble diameter the effectiveness of additional nuclei should diminish. So far a theoretical proof of why the exponent, in, should be so high has not been made. Studies of bubble diameters and frequencies, heat transfer under the developing bubble and the pumping action of the bubbles in carrying away the superheated liquid from the film layers (9,10) have only partially explained the heat transfer in nucleate boiling.

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The position of the A-B section of the boiling curve can be shifted to the left or right by changes in the surface characteristics, surface tension, pressure, dissolved gases or solids, or high boiling components in a mixture. As shown in Figure 5.2 any changes in surfaces affecting the nucleation properties of surfaces, changes the A-B curve, and the effect of pressure on the nucleate curves is shown in Figure 5.3. In binary mixtures where both components can be vaporized, the boiling curves for mixtures usually lie between those of the pure components. With mixtures, the effect of mass diffusion, local concentration gradients caused by the greater evaporation rate of the more volatile component and the resultant effects on the physical properties of the mixture as well as changes in interface saturation temperatures during bubble growth all influence the boiling curves. If one of the components has a very high boiling point so that it is essentially non-volatile, then the effect of increasing its concentration is to shift the curve A-B to the right reducing the coefficient. Further, the accumulation of the high boiler in the nuclei cavities can cause these to become inactive; hence, when certain special surfaces are used their effectiveness can be greatly reduced depending upon the ability of the circulating liquid to wash out the concentrated high boilers from these cavities. 5.1.4. Maximum or Critical Heat Flux In Figure 5.1 point B is the maximum heat flux for the nucleate boiling regime. Theoretically higher fluxes can be obtained by proceeding along the C-D portion, the film boiling regime, of the curve to very high temperature dif-ferences. The above statements apply to single tube pool boiling only as maximum fluxes for boiling inside tubes or bundles are also experienced but are due to hydrodynamic conditions. Several explanations have been made for the maximum heat flux, such as close packed nuclei forcing the liquid away from the surface and the non-wetting of the surface (the Leidenfrost effect). It is possible that both ex-planations may be simultaneously involved. The maximum flux is a function of pressure and also goes through a maximum as was first shown by Cichelli and Bonilla (13) in Figure 5.4. Based on models assuming force balances (14) the following equation for non-metallic liquids was derived with the constant determined empirically:

( )4/1

2max 18.0

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −=

v

cv

v

ggq

ρ

ρρσλρ

l (5.4)

However since many physical properties can be related to the critical pressures, Pc, Mostinski (15) derived the following simple expression

244

9.035.0max )1()(803 rr

cPP

Pq

−= (5.5)

The above equation implies the maximum flux goes to zero at the critical pressure; nevertheless, experiments (16) show there is still a similar effect at supercritical pressures due in part to local density differences as a result of local temperature variations. The maximum flux is somewhat influenced by the heating surface orientation and shape; also some surface effects are seen but in general small changes in surface characteristics do not greatly affect the maximum. Mixtures and the presence of non-volatile liquids can also affect the maximum flux. However, these effects are unpredictable and are neglected in equipment design. 5.1.5. Film Boiling In fully developed film boiling the vapor blankets the heating surface in a smooth continuous film except where the generated vapor escapes from the film in very large bubbles. If the heating surface is vertical and extends through the liquid level, the vapor can escape from the ends of the annular spaces and bubbles may not be generated. There is a transitional region between nucleate and film boiling where the surface is essentially enveloped by the vapor but the interface is rough, tends to fluctuate, and the liquid may occasionally touch the surface for a brief period. This transition occurs in the B-C portion of the curve of Figure 5.1. Depending upon the investigator's definition of film boiling, it can be defined as starting in the B-C portion of the curve or starting at the minimum point C. In fully developed film boiling no effect of surface finish is seen, Figure 5.5. The effect of mixtures, especially those containing non-volatile liquids, does not seem to have been published. In solutions containing dissolved solids, it is difficult to get to the fully developed film region due to rapid fouling of the surface. While film boiling heat transfer is reasonably predictable (18) and it may appear to have some advantages (e.g., corrosion, or fouling by dissolved solids), it is largely avoided because of the high temperature differentials involved. With the high costs of energy, such wastage of temperature potential is uneconomical. Further, the implied advantages are likely to be illusionary. However, there are occasional instances, such as in cryogenic services or certain low boiling chemicals, where film boiling may be unavoidable due to plant constraints on heating sources.

245

5.1.6. Boiling Inside Tubes Although boiling inside tubes may also be in nucleate or film boiling regimes, there are additional factors involved because the vapor and liquid must travel together through the tube. Both heat transfer and pressure drop are, therefore, affected by the pattern of the resulting two phase flow, which because of the evaporation of liquid, changes along the tube. Depending upon the fraction vaporized several different flow regimes are possible, Figure 5.6. For total evaporation in a circulating system the pressure drop through the tube causes an increase in the local boiling point with reference to the pressure existing at the tube outlet; hence, there will be a liquid heating zone at the inlet. When the local tube surface temperature is sufficiently superheated with reference to the local pressure then bubbles will form at the tube surface nuclei and the regimes governed by the nucleate boiling coefficients. As the two-phase mixture accelerates, the two-phase heat transfer can dominate. Depending on tube orientation, a two layer segregated regime (horizontal tubes) or a slug flow (vertical) regime can form which upon further evaporation will develop into an annular flow regime. When the vapor fraction is very large, greater than 60% by weight, a mist flow regime develops and the surface becomes dry and heat transfer is again a convective form but now forced convection to a vapor. The vapor tends to superheat and then evaporate the entrained droplets. If the tube wall temperatures are high enough, a film boiling regime may also occur. Note that in this case an inverted annular flow takes place with an annular vapor film surrounding a liquid core. The overall performance of a tube may also show a maximum heat flux effect similar to the A-B-C portion of the boiling curve in Figure 5.1. However, the maximum flux may be caused by: (a) film boiling, (b) high vapor fractions producing the dry wall regime, or (c) a hydrodynamic instability resulting in surging and unsteady flow through the tube. This latter, (c), effect is a result of the characteristics of the two-phase flow pressure drop curves as a function of the vapor fraction showing maximum and minimum points. Consequentially the instability limit, (c), is a function of the pressure drops in the entire flow circuit loop. 5.1.7. Subcooling and Agitation All of the above discussion for both pool and in-tube boiling was based on the liquid feed being at the vapor saturation temperature.

246

If the liquid pool is subcooled, the heat transfer to the liquid will be a natural convection coefficient if the tube wall temperature is too low to activate the nuclei. Once the nuclei are activated, heat transfer is high as in nucleate boiling but the bubbles rapidly collapse as they penetrate the liquid film on the surface or after the bubbles depart from the surface. This is defined as incipient boiling. Heat transfer coefficients, however, quickly approach those for saturation nucleate boiling.

Agitation in pool boiling (9) effects are shown in Figure 5.7. For in-tube forced convection, heat transfer follows the convective curve until nucleation begins and the nucleate boiling curve is followed, Figure 5.8. This figure also shows that surface finish has very little effect in the coefficients.

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5.2. Vaporizers - Types and Usage 5.2.1. General Vaporizers are constructed in numerous designs and operated in many modes. Depending upon the service application the design, construction, inspection, testing, operation, and maintenance are governed by various specifications, and by codes (national, state, and local government regulatory agencies.) The ultimate objective of all these rules is to insure the safety of the operators and community during the operation of the vaporizer. It is beyond the scope of this manual to discuss all these facets of vaporizers. Instead we will limit our discussion to the types of vaporizers frequently used in the process industries, specifically shell and tube exchangers. These can be broadly classified as those where the vaporization occurs (a) inside the tubes, or (b) outside the tubes. The selection of the vaporizer type depends upon the evaluation of many factors such as; (1) the purpose of vaporization - to generate a vapor or to cool the heating medium, (2) the boiling fluid; single or multicomponent, and does it contain non-volatile liquids or dissolved solids, (3) the type of heating: liquid, gas, radiant, or electric, (4) the fouling characteristics and blow down requirements, (5) the operating pressures; this is especially important under vacuum or near critical pressure. In the following discussion tubes can be plain, finned, or enhanced to improve the nucleation and boiling coefficients, and/or to improve the heating media coefficients. The characteristics and application of Trufin tubes will be discussed later. 5.2.2. Boiling Outside Tubes (a) Kettle Reboilers. A kettle reboiler installation is shown in Figure 5.9 in simple line form. Here a horizontal U-bundle is placed at the bottom of an oversized shell. The liquid level over the bundle is controlled by means of a baffle. Excess liquid (bottoms or blow-down) overflows the baffle into the end section where the level is controlled by means of a level controller. The space above the baffle-liquid level is used to disengage the vapor from the splash and spray above the bundle. The recirculating liquid returns to the bundle in the eccentric annular space between the shell and the tube bundle. One or more (depending upon bundle length) vapor nozzles are used to remove the vapors. A U-tube bundle is frequently used thus eliminating the need for an internal floating head which could have gasket problems; also there are no stresses between tubes and shell. If a high velocity for liquid heating media is required additional passes can be formed. Advantages are: insensitive to hydrodynamics and therefore reliable and easy to size. High heat fluxes are possible, can operate at low,ΔT, can handle high vaporization up to 80%, simple piping, unlimited area. Disadvantages are: all the dirt collects here and non-volatiles accumulate unless an adequate

248

draw-off is maintained; shell side is difficult to clean; difficult to determine the degree of mixing and, thus, determine the correct AT for wide boiling range liquids; the oversize shell is expensive.

Another version of the kettle reboiler, Figure 5.10, is a fixed tube sheet shell and tube exchanger with a full bundle but operated with a liquid level control on the shell side liquid, These types are used in large refrigeration and air conditioning plants. Here the refrigerant is clean, or at most contains traces of oils, and is completely evaporated. The tubes in the vapor space serve to dry and superheat the vapors for use in the compressors. A small draw off is occasionally used to keep the oil content low in the shell. (b) Column Internal Reboiler. Figure 5.11 shows a U-tube bundle inserted into the side of a column. It acts the same as a kettle reboiler but doesn't have the shell and connecting piping. There are fewer hydraulic problems as improper location and improper sizing of the feed and vapor lines in a kettle reboiler can cause operating problems. The disadvantages are the limited amount of surface area that can be installed, requires a large flange and internal supports, tubes are short hence a costly bundle, and the column must be shut down in order to clean as no alternate operation is possible. (c) Horizontal Thermosyphon Reboilers. A regular baffled shell and tube exchanger of the TEMA "X”, “G”, “H", OR "E" type is used as shown in Figure 5.12 with boiling occurring in the shell-side. By piping arrangement, a driving force for circulation is established by the density differences between the liquid in the column and the two-phase mixture in the exit piping. The heating medium flows in the tubes in single or multiple passes. Advantages are: Higher circulation rate can give a better ΔT than a kettle reboiler; column skirt height is less than for a vertical thermosyphon; high velocity and low exit vapor fractions decrease the effect of residual high boilers and reduce fouling, unlimited area, can handle a fouling heating liquid. Disadvantages are: fouling on shell-side; baffling and tube supports may create vapor blankets and localized dryout; multiple nozzles and complicated piping is required; baffles may be needed to prevent

249

flashing of low boilers near the inlets and concentration of heavies at the exchanger ends; very little design information is available and hydrodynamic problems are not well known or defined; requires large plot area, and high structural costs. (d) Vertical Shell-Side Thermosyphon. The vertical shell-side boiling exchanger is an unusual arrangement not used much in connection with columns but is often encountered in packed catalyst tube reactors. Here, because of the packing and the need for close temperature control, a vertical packed tube reactor of an arrangement shown in Figure 5.13 is used. Sometimes the catalyst bed is on the upper tube sheet when a fast reaction quench is required. Circulation is obtained through the use of an elevated steam drum. Depending upon the temperature conditions at the upper tube sheet, special problems may occur due to the tendency of the steam to form a vapor blanket underneath the tube sheet. 5.2.3. Boiling Inside Tubes (a) Vertical Thermosyphon. A single pass TEMA "E" type shell is used as shown in Figure 5.14. General characteristics of this vaporizer are a large exit pipe with a cross sectional area about equal to the total cross sectional area of the tubes and arranged to minimize the vertical distance between the top tube sheet and the column nozzle. The liquid level in the column is usually kept at the top tube sheet level in order to provide for maximum circulation. Better heat transfer coefficients are obtained if this level is dropped to 1/3 to 1/2 of the tube length; however, circulation is reduced and fouling may increase. For vacuum service where the hydrostatic head can significantly affect the local boil-ing point with a low ΔT, a lower tube submergence is often used. The driving head for circulation is the density difference between the liquid in the column and the two phase mixture in the tubes. These vaporizers frequently are constructed with 3/4 to 1 in. tubes, 8 to 12 ft. long. The exit vapor weight fraction for hydrocarbons ranges from 0.1 to 0.35 and for water about 0.02 to 0.1. Advantages are: circulation is relatively high and

250

tends to minimize fouling; tube-side fouling is easier to clean; the "E" shell and connecting piping is relatively inexpensive, easily supported, and compact. The disadvantages are: requires more head room and column skirt height; maximum heat flux may be lower than kettle reboilers due to instability; the hydrostatic head effect on the boiling point may be a problem at low AT and/or vacuum service, maximum reboiler area is limited, and limited to about 30% vaporization. Experience has shown that the instability encountered at high fluxes is very sensitive to the size, hence, pressure drop in the exit piping. However, stability can be regained by increasing the pressure drop in the liquid recirculation line by means of restrictions or valves. (b) Vertical Long Tube Evaporators. In these evaporators the arrangement is almost the same as in Figure 5.14 except that the recirculation line maybe omitted. Basically they are an once-through evaporator with the feed rate separately controlled. The weight fraction vapor can be very high, approaching 100%, depending upon boiling range and fouling characteristics of the feed. Recirculation, if any, is done by mixing the recir-culated liquid with the fresh feed before pumping the mixture to the evaporator. The effective submergence is very low so that an annular climbing film or mist flow regime exists in the major portion of the tube. These evaporators can operate at relatively low pressures (down to 2 in. Hg abs.) and can handle viscous, wide boiling range mixtures; however, the ΔT used is moderate, about 15 °F. Although smaller tubes have been used many of these evaporators have tube diameters of 2 in. and tube lengths of 20 or more feet. (c) Forced Circulation Evaporators. These may be either vertical or horizontal exchangers and may be of multi-pass construction. Very little vaporization occurs in these tubes especially before the last pass. Essentially these units are treated as a heater and the liquid is flashed after passing through a restriction and then the separated liquid is returned to the pump suction.

251

Advantages are: high velocity and no vaporization reduces fouling; high heat transfer rates; can be used for very low absolute pressures as hydrostatic head effects on boiling points is avoided, mandatory for viscous bottoms, can use standard exchangers, piping is smaller. Disadvantage is the cost of pumps and the power for their operation. 5.2.4. Other Types of Evaporators (a) Fired Vaporizers. In direct fired vaporizers such as steam generators and tube stills the major heat transfer problem is with the heat source and these are specialized designs with proprietary design methods and are beyond the scope of this manual. (b) Film Vaporizers. In falling film vaporizers a thin liquid film flows down the inside of vertical tubes, Figure 5.15, or can fall down across a bank of horizontal tubes. These films are thin so that the heat transfer coefficient is high and bubble formation is very low or non-existent. Since the pressure drops are low and the hydrostatic head is negligible, these vaporizers are well suited to operation at very low pressures as well as having high coefficients at low temperature differences. The hold-up is low and therefore can handle temperature sensitive liquids; also a stripping gas can be used to aid in reducing the temperature level. The disadvantages are: the difficulty of distributing the liquid uniformly on the tubes; the need to maintain an adequate film on all the surfaces; and the possibility to form dry patches when certain physical conditions are exceeded. In Figure 5.15, the tubes are extended above the tube sheet forming a suitable depth pool to aid in uniformly distributing the liquid. A primary overflow weir aids in distributing the feed around the bundle periphery. Each tube may be fabricated as in Figure 5.16 into additional distributing devices. Uniformity of distribution is very essential for vertical tube units. On horizontal tubes the initial uniformity of distribution is not critical and simple overflow or spray devices are used. In horizontal units the bundles are rectangular, with staggered tube pitches, and relatively deep bundles. The major development of horizontal falling film vaporizers was government sponsored research by the Office of Saline Water and the DOE project Ocean Thermal Energy Conversion. Reports of various conferences of these projects contain references and data concerning these vaporizers. In mechanically agitated film vaporizers a film is formed inside a large tube or vessel which has a close fitting agitator, or in some designs a scraper blade, rotating at speeds high enough to keep the liquid on

252

the walls and spread out in a film. Again these vaporizers are suitable for very low pressure (1 mm Hg) operation. The agitator performs several functions: it forms the liquid film; it prevents dry spots, provided sufficient liquid is fed; it agitates the film thus resulting in high heat and mass transfer rates; and fouling is reduced. The disadvantages are: power consumption for mechanical drives; problems with bearings and seals; very expensive design due to close tolerance required; and size and capacity is limited thus necessitating multiple units for large evaporation loads.

253

5.3. Boiling Heat Transfer The prediction of the heat transfer coefficient to boiling liquids is subject to large errors due to the inability to specify, manufacture, and maintain the nucleation characteristics of surfaces, as was illustrated by Figures 5.2 and 5.5. However, the boiling heat transfer coefficient is only part of the overall coefficient and the effect of these large errors is reduced in the overall design but must be considered in selection of safety factors or the selection of operating parameters; e.g., using only a fraction of the available steam pressure. Boiling heat transfer has been studied extensively and good summaries of these researches are found in (9, 10, 21, 22). The design procedures and equations are different for boiling outside of tubes or pool boiling and for boiling inside of tubes. A single tube boiling heat flux curve is a basic starting point and the development of this curve is as follows. A natural convection coefficient equation is used to generate the natural convection heat flux curve by

qnc = hncΔT (5.6) and plotted in Figure 5.17 as line OA. Then a nucleate boiling heat flux curve is calculated and plotted as line AB. The intersection of these lines is point A. A calculation of the maximum flux determines point B on the nucleate curve. Usually these two curves are sufficient but if the critical ΔT at point B can be exceeded, then the minimum flux and the corresponding temperature difference is calculated and establishes point C and the film boiling flux curve CD drawn. No predictive equations exist for the intermediate region (BC) but a straight line is drawn between these points. What we now have is an approximation of the curve in Figure 5.1 by a series of straight lines. The real curve (as in Figure 5.1) has a smooth transition between these straight lines but in design these transition curves are ignored and results in a slight conservatism. 5.3.1. Pool Boiling - Single Tube (a) Natural Convection When the wall temperatures are too low to initiate nucleate boiling the heat transfer coefficient is based on the liquid natural convection coefficient where the ΔT is based on the difference between the wall and the liquid temperatures. For horizontal tubes the following equation is used

254

25.

2

2353.0

ll ⎥

⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ Δ=

k

cTgdk

dh poonc μ

μ

βρ (5.7)

(b) Nucleate Boiling Although several attempts (23, 24) of theoretical type equations utilizing the fluid properties have been proposed, they are impractical because of the required physical property data (often unavailable for the designer's problem), their complicated evaluation, and their inherent uncertainty due to the surface conditions. A simpler approach, widely used by designers, is based on the work of Borishanski (25) who utilized the law of corresponding states and, as modified by Mostinski (15) and Collier (26), is given as

hnb = A* q0.7F(Pr) (5.8) where A* is a constant evaluated at a reference reduced pressure of Pr = 0.0294 and F(Pr) is a function of reduced pressure as shown in Figure 5.18.

A* = 0.00658 69.0cP (5.8a)

F(Pr)1 = 1.8 + 4 + 10 (5.9) 17.0

rP 2.1rP 10

rP However, dropping the last two terms is a safe design (26) for pool boiling hence

255

F(Pr)2 = 1.8 (5.10) 17.0rP

However, for refrigerants (R11, R12, R113, R115, etc.), F(Pr) should be evaluated as

F(Pr)3 = 0.7 + 2 Pr[4 + 1/(1 – Pr)] (5.11) and the values of A* for these refrigerants given in the square brackets in Table 5.1 be used in equation 5.8. (26) It should be emphasized that the above equation was developed for single component liquids and that the system pressure, tube surface condition, presence of non-condensable gases, hystersis of the boiling curve, size and orientation of the surface, subcooling, wettability, and gravitation acceleration are some of the variables that can affect the result. (c) Critical or Maximum Heat Flux. Cichelli and Bonilla (13) found that the maximum flux was a function of reduced pressure, Pr = P/Pc, and that this curve also had a maximum at a reduced pressure of 0.3, Figure 5.4. Based on the assumption that the maximum flux was limited by the hydrodynamic flow pattern at the surface, Zuber (24), developed the following theoretical equation which seems to correlate the data and with a minor adjustment of the theoretical constant, π / 24, is

4/1

2)(

18.0⎥⎥⎦

⎤

⎢⎢⎣

⎡ −=

v

vcvcr

ggq

ρ

ρρσλρ l (5.12)

This equation was for flat plates and some effect of geometry is found which shows the constant ranging from 0.12 to 0.2 (27) depending upon a dimensionless parameter

2/1)(⎥⎦

⎤⎢⎣

⎡ −σρρ

c

vg

gL l

where L is radius or a length of plate. Curves are given for several different shapes, sphere, plates, and cylinders, Figure 5.19. In addition, other factors such as liquid viscosity, subcooling, and surface conditions can affect the values given by equation 5.12. However, equation 5.12 is generally used in commercial design as there are other contributing factors in an actual exchanger that influence the maximum. (d) Minimum Film Boiling Flux. The minimum heat flux, qf, for film boiling, point C in Figure 5.17, occurs when the minimum rate of vapor formation to sustain a stable vapor film is reached. The Zuber theory for the minimum heat flux in film boiling was improved by Berghmans (28) who considered second order perturbations and included the

256

effect of vapor film thickness into the analysis. From an analysis by Berenson (29) for flat plates and the maximum flux equation 5.12, we find that

2/1

09.018.0

⎥⎦

⎤⎢⎣

⎡ +=

v

v

mf

crqq

ρρρl (5.13)

and that the corresponding ΔTmin is

3/12/13/2

min )()()(

127.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

−⎥⎦

⎤⎢⎣

⎡+−

=Δvc

v

v

c

v

v

v

vgg

ggk

Tρρ

μρρ

σρρρρρ λ

lll

l (5.14)

A straight line between points B and C in Figure 5.17 then is used for the so-called transition region. Through point C a film boiling flux curve CD can be drawn using the heat flux calculated from the film boiling coefficients. (e) Film Boiling Heat Flux. At high temperature differences a continuous vapor film covers the surface and analytic analysis has followed an analogy to film condensation. For large horizontal plates

[ ]

4/13

2/

)(425.0

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

Δ

−=

πμ

λρρρ

cv

evvf LT

gkh

l (5.15)

where Lc is the shortest unstable wave length for the Taylor instability given by

[ ]2/1

2 ⎥⎦

⎤⎢⎣

⎡−

=v

cc g

gL

ρρσ

πl

(5.16)

and λe is an effective latent heat including the superheat effect

λe = λ [1 + 0.4(cpv ΔT/λ)] (5.17) For tubes the equations are

4/1'3 )(]/069.59.0[

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

Δ

−+=

cv

evvcf TL

gkdLh

μ

λρρρ l (5.18)

but here

257

λe’ = λ [1 + 0.34(cpv ΔT/λ)]2 (5.19) These equations give the conduction heat transfer but in addition at these temperature levels radiation becomes important. Hence, the total film coefficient as suggested by Bromley (30) is

hft = hf + 0.75 hr (5.20) where hr is the coefficient for radiation transfer assuming the liquid is a black body and radiation is between infinite parallel plates. The flux is then calculated by equation 5.6. 5.3.2. Single Tube in Cross Flow The effect of cross flow on the boiling coefficients is shown in Figure 5.20. Basically the forced convection coefficient may exceed the nucleate boiling coefficient at low temperature differences but at higher ΔT the nucleate boiling coefficient becomes dominant. The simple rule is to use the highest coefficient. The critical or maximum heat flux is also affected by cross flow velocity but the magnitude of this effect is a function of tube size and seems to disappear when ap-proaching industrially used dimensions as shown in Figure 5.21. In the film boiling region equation 5.18 will apply for low cross flow velocities but for higher velocities and for less than 45°C (81°F) subcooling the following equation applies

2/1

7.2 ⎥⎦

⎤⎢⎣

⎡Δ

= ∞

sato

vvc Td

kVh

λρ (5.21)

5.3.3. Boiling on Outside of Tubes in a Bundle In spite of the wide use of horizontal tube bundles there is very little data and only elementary suggestions for predicting its heat transfer. The very early work of Abbot and Comley (31) showed the coefficients for a

258

bundle and a single tube were essentially the same. Other reports by Palen et al., (32) showed that bundles may perform better than single tubes due to the circulation induced through the bundle. Although circulation models are being developed, very little has been published on these models. As shown in Collier (26) and in Figure 5.22 the coefficients vary in a haphazard fashion throughout the bundle but, in general, increase from the bottom to top. Palen (34) recommends using

hb = hnbl Fb Fm + hnc (5.22) where Fb = 1.5, hnc = natural convection coefficient, and hnbl = the single tube nucleate coefficient. Fm is the mixture correction. The 1.5 factor is a conservative approximation as it could range up to 3 depending on a bundle layout, size, and heat flux. There is a maximum flux for a bundle that is different, and lower, than the single tube maximum flux. Based on some plant experience Palen and Small (35) proposed a model assuming a vapor blanketing effect. They developed a correction term, Φb, which is used to multiply the qmax as calculated by equation 5.12 and corrected for mixture effects, eqn. 5.38. Their result can be simplified to

1.1)/(2.2

tpBo

tp

s

Bb

LDd

LK

ALD

=⎟⎟⎠

⎞⎜⎜⎝

⎛=Φ

π (5.23)

where K = 4.12 for square pitch

K = 3.56 for triangular pitch (Φb)min = 0.1

This result is reported to be conservative by Palen et al. (32). 5.3.4. Boiling Inside Tubes As shown in Figure 5.6 vaporization inside tubes involves a number of different flow regimes each of which requires a different evaluation of the coefficient plus a local temperature difference which in turn requires corresponding pressure drop calculations. Since most are of a natural circulation design, only the available liquid head is known thus resulting in a trial and error series of calculations to determine the feed rate per tube. The calculated procedure is, thus, too tedious for hand calculation and computers are utilized. However, the computer programs are also complex and expensive to develop and, therefore, become proprietary. We list below the various equations used for the design of vertical in tube vaporizers. Although horizontal in-tube vaporization is also used, the heat transfer equations and methods are the same but the flow pattern now includes a stratified two-layer region. The major difference between horizontal and vertical in-tube vaporization is the definition of and the flow criteria used to define the limits of each regime. The appropriate heat transfer equation is then used for each regime.

259

(a) Single Phase Liquid Region. In a circulating vaporizer the temperature of the liquid entering the tube is below the local boiling point due to the effect of the hydrostatic head on the saturation temperature. This liquid zone extends to the point where the temperature has increased and the local pressure decreased such that the local saturation point has been reached. Actually some further superheat is required to initiate nucleation. The liquid zone heat transfer coefficients are calculated from

1.

2

2325.43.33.

PrPr

17.0⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ Δ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

l

ll

l

l

ll μ

βρμμ

Tgdk

Gdkdh i

w

iic (5.24)

for L/di > 50 and diG/μ < 2000. For turbulent flow and diG/μ > 10,000 use

3/18.

023.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

l

l

ll k

cGdkdh piic μ

μ (5.25)

and interpolate between these two equations on a Re number basis for 2000 < diG/μ < 10,000. (b) Boiling Region. The boiling region can be further subdivided into a sub cooled boiling, saturated boiling, and two-phase boiling regions with predictive equations for each (9,26). Another approach taken by Chen (36) is to combine the saturated and two-phase regions into one, with an equation combining the convective and nucleate boiling mechanisms

hb = s hnb + hcb (5.26) where hb = the boiling coefficient

hnb = the nucleate boiling coefficient hcb = the convective coefficient s = Chen suppression factor

The convective coefficient is a function of the Martinelli two-phase flow parameter, Xtt, and the Chen correlation using this factor is

chttc

cb Fxfhh

== )( (5.27)

73.0

213.0135.2 ⎥⎦

⎤⎢⎣

⎡+=

ttch x

F (5.28)

( )11.057.0

1⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= −

v

vxx

ttxμμ

ρρ l

l

(5.29)

260

x = weight fraction of vapor hc = liquid phase heat transfer coefficient based on the amount of liquid present, Equation 5.25.

The nucleate boiling coefficient, hnb, is determined as

hnb = hnbl Fm (5.30) where Fm is a correction applied for mixtures (discussed later) and hnbl is the coefficient determined from equation 5.8. The suppression factor, s, is determined as follows:

1. Calculate liquid phase ll μ/Re Gdi= 2. Calculate two-phase Retp = (5.31) 25.1Re chFl

3. Calculate s= 1/[.1 + 2.53(10-6) ] 17.1Re tp

Now equation 5.26 can be solved for hb. The subcooled boiling coefficient can be obtained by again using equation 5.26 but with s = (ΔTb/ΔTo) where ΔTb is the temperature difference between the tube wall and the saturation temperature of the liquid at the given local pressure and ΔTo is the difference between the tube wall and subcooled bulk temperature. Instead of the convective coefficient, hnbl, the liquid coefficient (eqn. 5.24 or 5.25) is used. The nucleate coefficient, hnbl, is obtained from the transformed equation 5.8 as

hnbl = 5.43(10-8)( cP )2.3(ΔT)2.33[F(P)]3.33 (5.32) and equation 5.32 changed to

hnb = hnbl Fm (5.33) where Fm is from equation 5.38. (c) Mist Flow. In mist flow the small amount of remaining liquid is en trained as droplets and the tube wall is essentially dry. The coefficient drops rapidly and approaches that of heat transfer to gas. In this regime sensible heat is transferred to the gas which in turn transfers some of the heat to the droplets until they are completely evaporated after which only sensible heat transfer to gas occurs. The main problem is the determination of the vapor temperature, hence, temperature difference. Two extreme conditions are: (1) no heat is transferred to the droplets hence the vapor temperature rises rapidly; and (2) heat is rapidly transferred to the droplets until they disappear and during this evaporation phase the vapor is at saturation temperature. Condition I is approached at low pressures and velocities and condition 2 at high pressure and velocities. The actual case is somewhere between 1 and 2. Some attempts to develop empirical and theory based equations are reported (26) but the range of data seem too limited. We would recommend to use an equation like 5.25 based on gas properties and then make an engineering judgment guess of the fraction of the sensible heat transferred to the gas that is used up as latent heat for the evaporation of drops. The

261

resulting effect on vapor temperature could be used to calculate an LMTD for the mist region and with the calculated gas coefficient used to determine the heat flux. The mist region can be determined from a Fair (37) map or from the simple equation derived from this map

Gmm = 1.8(106) Xtt lb/hr ft2 (5.34) where Gmm is the maximum mass velocity before mist flow begins. (d) Film Boiling. This type of boiling should be avoided, if possible, due to control problems, possible fouling, and lack of data on pressure drop calculations. But if the temperature difference is high enough over the entire tube length, then the heat transfer coefficient can be calculated by the Glickstein and Whiteside (38) correlation

Nu = 0.106 Re0.64 Pr0.4 (ρb/ρv)0.5 (5.35) where the bulk average density on a no slip basis is

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−= 11

vb x

ρρ

ρρ ll (5.36)

Properties in eqn. 5.35 are based on the liquid. However, the main problem is to determine the mass velocity, G. In film boiling inside a tube we have a core of liquid surrounded by an annular layer of gas which is of very low viscosity. No data in the open literature exist for this case and, thus, determining the circulation rate is a real problem. An alternative estimate of the film coefficient could be made based on pool boiling correlations. (e) Maximum Heat Flux for Stable Operation. In vertical tube thermosyphons there are several limits to operation such as surging, critical heat flux, and mist flow. The surging instability occurs as ΔT is increased beyond a limit but this surging is dependent upon the hydraulic layout and is controllable by the physical arrangement. Blumenkrantz and Taborek (39) discuss the phenomenon. The surging can be controlled by increasing the frictional resistance in the inlet piping. Usual recommended design for thermosyphons has the outlet pipe cross-section area equal to the total cross section area of the tubes. The inlet liquid line is usually smaller and in the range of 25 to 50% of the outlet pipe area. As the temperature difference increases, the evaporation rate of a given tube will increase, pass through a maximum, and then decrease. This was investigated by Lee (40) and confirmed by Palen et.al. (41) and both presented correlations for this effect. The Palen correlation is preferred due to its simplicity

qmax = 16066(di/L)0.35(Pc)0.61 (Pr)0.25( 1 – Pd) (5.37)

262

5.3.5. Boiling of Mixtures When a mixture is boiled the heat transfer coefficient predictions are further complicated by the effect of the local changes in composition, which in turn affect physical properties and boiling points. Some understanding of the factors involved result from studies on boiling of binary mixtures. When a binary mixture is boiled, the vapor generated is richer in the lower boiling point component and a plot of the boiling points of the liquid compositions and the dew points of the resulting vapor compositions is shown in Figure 5.23. As the binary mixture, y1 is heated the first vapor bubble forms at the temperature called the bubble point and that vapor has the composition of Y2 as shown in the figure. A plot of these bubble points versus composition gives the lower (liquid) curve. In cooling a binary vapor of composition y, the first drop of condensate forms at the temperature called the dew point and a plot of dew points is the vapor curve. Temperatures between the dew point and bubble point correspond to a mixture of vapor and liquid each of different composition but whose sum total composition is y1. These curves in Figure 5.23 are generated under the special condition of equilibrium between the vapor and liquid. Boiling is a non-equilibrium process; however, the formation of bubbles at the surface depletes the liquid film of the low boiling component and the remaining liquid has a higher local boiling point. Thus the effective ΔT from the surface to the liquid film boiling point is less than the apparent ΔT and the resulting calculated coefficient is lower than the actual coefficient. Further, the bulk liquid temperature is taken as the equilibrium boiling point of the mixture and ignores any superheat in the bulk liquid. (a) Mixture Heat Transfer Coefficients. Early experiments on mixtures showed, as in Figure 5.24, that the heat fluxes lie between the values for the pure components. The heat transfer coefficients, based on the apparent ΔT, are always less than the pure component coefficients and the minimum values occur at the concentrations where there is the greatest separation between the vapor and liquid lines (42) as illustrated in Figures 5.25 and 5.26.

263

While most mixtures follow the curves as in Figure 5.23 where one component is more volatile over the entire concentration range, there are other systems where one component is more volatile over only a portion of the concentration range and less volatile over the remaining portion. These systems form azeotropes where the azeotropic composition is one where the composition of the vapor and liquid are identical. This azeotropic mixture boils as though it were a single component liquid. Examples of such systems (42) are shown in Figures 5.27 and 5.28. These figures show a minimum boiling point azeotropic mixture but maximum boiling point azeotropic mixtures also exist. Recent papers by Stephan (42) and by Thomas (43) give short reviews of some current theories for heat transfer to boiling mixtures. When we have multi-component mixtures the theories become too complicated for design purposes. A simple empirical approach to calculating mixture boiling coefficients is based on the paper of Palen and Small (35) which was later confirmed as suitable for equipment design in (32) and recommended by Palen (34). Here a mixture correction factor, Fm, is used to modify the calculated coefficient of the volatile component, hnbl, determined from equation 5.32 so that the mixture coefficient = hnblFm where

Fm = exp(-0.015 BR) (5.38) where BR = boiling range, dew point-bubble point, °F. with a lower limit of Fm = 0. 1. This relation is shown in Figure 5.29. This equation is recommended (34) as a reasonable approach for multicomponent systems. This empirical equation is based on the boiling range which is the spread between the vapor and liquid curves as shown in Figures 5.23, 5.25, and 5.26 and is close to some of the theoretical methods (42). (b) Mixture Maximum Heat Flux. Although studies of maximum heat flux for mixtures have shown some instances, Figure 5.30, where the maximum flux of a mixture can be greater than the maximum flux of the components, (44) there is some disagreement

264

on the cause for some of the higher values and some question on the adequacy of some theories, see e.g., (44,45,46) for details. For design purposes it is recommended (34) that equation 5.5 be used with the critical pressure of the mixture based on the molar average. This will give maximum fluxes lying between those of the components and will be conservative.

265

5.4. Falling Film Heat Transfer Falling film vaporizers are characterized by having thin films in contact with the heat transfer surfaces; therefore, the heat transfer equations are basically the same as the condensation equations, the only difference being the direction of heat flow. Hence, we give below only a few basic equations and refer you to section 3 for the influence of shear, mass transfer, etc. The above statements assume no nucleate boiling occurs. Due to the high coefficients and low ΔT used in these units, nucleation is normally not experienced; however, the effect of nucleation is to increase the rate of heat transfer, hence, this is a conservative assumption. There is one special characteristic that appears in the vaporizers and that is the dry patch phenomenon. A dry patch can form due to (1) insufficient liquid to wet the surface, and (2) too high a surface temperature and heat flux causing the liquid to form rivulets thus resulting in dry spots. The dry spots have very low heat fluxes and thus reduces capacity and should be avoided. We will discuss the dry spot effects later. 5.4.1. Vertical In-Tube Vaporizer Uniformity of liquid distribution to all tubes is essential for in-tube falling films. The type of distributor, Figure 5.16, used on each tube affects the allowable hydraulic gradient for the flow across the tube sheet; e.g., a simple overflow weir is very sensitive to the hydraulic gradient while a slotted tube is less sensitive. Distributors are not a commercially available item and are engineered for each application. Although the feed to the vaporizers may be at or very close to the saturation temperature, nevertheless, a preheat section is required to establish the temperature gradient within the film. In the laminar region the coefficient is (47)

h = 4.71 k/(3Γ μ/g ρ2)1/3 (5.39) and for the turbulent region the recommended (48) equation is

34.04.03

3/1

23

2 4)10(7.5 ⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ=⎟

⎟⎠

⎞⎜⎜⎝

⎛ −

kc

gkh μ

μρ

μ (5.40)

For surface evaporation the respective equations for local heat transfer coefficients are (48): Laminar flow

22.03/1

23

2 4821.0−−

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ⎟⎟⎠

⎞⎜⎜⎝

⎛=

μρ

μ

gkh (5.41)

Turbulent flow

( ) 65.04.03/1

23

23 4108.3 ⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ⎟⎟⎠

⎞⎜⎜⎝

⎛=

−−

kc

gkh μ

μρ

μ (5.42)

266

The laminar equation 5.41 included the effect of waves and ripples. The transition Reynolds number is just the value from the intersection of these equations, not the transition of flow regimes, and is

06.158004 −

⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ Γk

c

trans

μμ

(5.43)

The above equations provide the local heat transfer coefficients which are used in stepping through the vaporizer. All the fluid properties are evaluated for the liquid phase. This stepping process will also account for the temperature changes and thus give an integrated UΔT value. For mixtures there may be additional mass transfer resistances in the liquid and gas films and techniques of handling these complications are the same as for condensation, therefore, refer to section 3 for further information. 5.4.2. Horizontal Shell-Side Vaporizer Distribution is less critical with horizontal units since drippage between tube rows soon overpowers the initial distribution. While there is still much to be resolved regarding the effect of tube spacing on the effect of drippage and vapor velocities on the motion of drops within the tube bundles, the following equations can be used for approximating the heat transfer, where all the fluid properties are evaluated for the liquid phase. For the preheat zone:

25.12.

2

2336.21.3/1

23

2

PrPr439.0 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ=⎟

⎟⎠

⎞⎜⎜⎝

⎛−

w

ogdk

c

gkh

μ

ρμμρ

μ (5.44)

For the evaporation zone (50):

66.024.03/1

23

2 418.0 ⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛ Γ=⎟

⎟⎠

⎞⎜⎜⎝

⎛

kc

gkh μ

μρ

μ (5.45)

Horizontal units are used with finned tubes or enhancements on both inside and outside of the tubes to improve heat transfer. See the government literature associated with the development of sea water desalinization and ocean thermal energy conversion for further information. 5.4.3. Dry Spots - Film Breakdown Although theories have been developed to explain the dry spot or film breakdown due to either minimum flows or high fluxes, the agreement with experimental data is only fair, see (9, 47) for further references. The best suggestion is to have a minimum flow at the bottom of the tube or bundle, for water, above 150 lb/hr ft and to not exceed a film ΔT of 18°F (10°C) The requirement for minimum wetting rate means a minimum amount of recirculation may be necessary and it is best to assure the recirculation is sufficient for adequate wetting. When handling mixtures this recirculated liquid can affect the concentrations and boiling points of the feed.

267

5.5. Special Surfaces Commercially available special surfaces used to enhance the boiling side heat transfer are finned surfaces, special plated surfaces, and porous surfaces produced by electroplating, sintering, or machining. The Trufin tubes, used for boiling and condensation enhancement, usually have 16 to 40 fins/inch, approximately 1/16 inch high and resemble a screw thread. The basic purpose is to increase the surface per unit length that is exposed to the boiling liquid and an area ratio increase of 2.2 to 6.7 is obtained. The fins are formed by an extrusion process and are available in most metals. The finning process also changes the surface nucleation characteristics and an improved surface factor is reported by Palen et al. (49). Although the heat transfer coefficients are high the fin efficiency is still high because of the very short fin length. For the high conductivity metals, such as copper, the fin efficiency is almost 100% but for low conductivity metals such as stainless steel the efficiency may drop into the 70-80% range. Surface enhancement is not a universally acceptable solution to the improved performance of reboilers. Careful consideration must be given to the particular operating conditions. Some of the factors to be evaluated are as follows. (1) These are expensive surfaces and cost comparisons should be made. (2) These surfaces are available only for a limited number of metals and the corrosion requirements of the system need evaluation. (3) The boiling range and fouling or corrosive characteristics of the liquids could significantly affect the final performance. Implied here is the ability to clean these surfaces. (4) The performance of a tube bundle can be significantly different from the performance of a single tube as described by Palen et al. (49). Here the relative effect of nucleate boiling to two-phase convection heat transfer needs to be determined. Further, apparent comparisons of tube bundle performance vs. single tubes needs a careful consideration of the effect of bundle layout, tube pitch, etc. on the circulation rate, hence two phase heat transfer, about which we are only beginning to understand. (5) The improvement of the boiling coefficient may not improve overall performance if the heating medium, fouling, or tube wall coefficients are limiting. The major application of enhanced surfaces is in boiling clean liquids at low temperature differences. Trufin tubes depend more on surface increase and seem less subject to problems of fouling and wide boiling range liquids. The maximum heat flux appears to equal that of a plain tube based on the projected area. Enhanced surfaces find industrial applications for two reasons: (a) For a given temperature difference the heat duty will be two or three times higher than for plain tubes at low ΔT. This can result in smaller reboilers with savings in space and weight. At high ΔT the relative performance of enhanced vs. plain tubes is less. (b) For a given duty the required temperature difference will be smaller than for plain tubes. This is of great importance when the cost of other equipment, such as compressors, and operating costs are considered. Heat transfer performance for some commercially available enhanced surface tubes are described by Yilmaz (50). 5.5.1. Boiling on Fins One of the problems of boiling from fins is the determination of fin efficiency. As the nucleate boiling coefficient is strongly dependent upon the temperature difference, which in a fin is varying along its length, the calculation of a fin efficiency requires a stepwise computer program. Fin efficiency calculations with a linear variation along the length were derived by Han (51) and Chen (52). A closer approach to

268

boiling conditions was made by Cumo (53) who made a numerical solution for the case where the heat flux was proportional to the third power of the local wall to liquid temperature difference. Haley and Westwater (54) solved a one dimensional general conduction equation. The effect of fin clearances was studied by Westwater (55) who found that bubble size was a factor but a 1/16-in clearance at atmospheric pressure was sufficient to avoid interference. 5.5.2. Mean Temperature Difference In all boiling processes the liquid is superheated with reference to the vapor saturation temperature but the effect of superheat on the temperature difference calculation is neglected. The amount of superheat cannot be predicted and is usually small compared to the ΔTsat; thus this effect is ignored. For in-tube boiling the heat transfer coefficient calculational procedure requires the division of the tube into zones for each flow regime which in turn requires calculating the heat transferred zone by zone and thus the temperature difference is also included in the calculations. The net result is no separate calculation of a mean temperature difference is made for in-tube vaporization. For boiling outside of tubes the determination of a mean temperature difference is an arbitrary choice based on the amount of subcooling, the boiling range, and to some extent the geometry of the reboiler. The problem is the degree of mixing that occurs in the shell which depends on the circulation rate. Very little is presently known about shell-side circulation and methods for estimating the circulation rates are only in early stages of development. As shown by Palen et al. (32) in Figure 5.31 the bulk temperature within the tube bundle varies with length and the effective ΔT differs substantially from the assumed ΔT or the ΔT based on exit temperatures; thus depending upon the assumptions made, several methods of calculating the mean temperature difference can be used. Some of these choices are: (1) For a pure component or a narrow boiling range mixture, the vapor saturation temperature is used, and if a single component condensing vapor is the heating medium, the temperature difference is this difference. If the heating medium is transferring sensible heat, then a log mean of the vapor saturation temperature and the heating medium terminal temperatures is used. (2) For a wide boiling range mixture or where the sensible heat load is a substantial fraction of the total heat load, a counterflow log mean ΔT gives optimistic results (32, 34) and an LMTD based on exit vapor temperature is recommended. (3) When the effect of static head on the boiling point is significant; e.g., in large bundles and/or in vacuum service, then the boiling temperature should be based on the mean pressure in the bundle including the imposed static head. (4) When a horizontal thermosyphon reboiler is used, a counterflow LMTD is very optimistic and use of a cocurrent flow LMTD is suggested. Since experimentally measured boiling coefficients, and any resulting correlations, are dependent on the temperature differences used to calculate these coefficients from the basic data, then the same LMTD method should be used in the design of reboilers when using these data or correlations. However, the

269

generalized correlations given above have such a spread of data that the temperature difference determination is a minor factor in the data spread and the MTD suggestions in the above paragraph should be followed.

270

282

5.9. Special Considerations As the boil up rate is very sensitive to the ∆T it is necessary to determine the range of the ∆T to provide for the anticipated boil up range under both clean and fouled conditions. This ∆T range should be within the controllable limits of the heating media. The boil up is basically controlled by varying the heating medium temperatures. For a condensing media a pressure control is used and for a sensible heat source media a by-pass control is used but here both temperature difference and heat transfer coefficient of the heating medium changes. For a condensing media, a problem arises when boiling at low loads with a clean vaporizer that the required pressure may be so low (or a vacuum) that condensate removal becomes difficult. For a sensible heat source, the amount of by-pass may so reduce the flow in the vaporizer that problems in distribution or accelerated fouling may occur. The vaporizer should have liquid in it and be started up at the lowest ∆T possible. It is possible in those cases of large fouling allowances, excessive conservatism in design, or underestimated coefficients that the design ∆T can be large enough for a clean reboiler to get into the film boiling regime. The design flux may also be low enough so that it can be met in the transition or film boiling modes. Under these conditions the effect of ∆T is reversed from that of nucleate boiling thus the controls will be ineffective and the rate of fouling may be increased. If a condensing medium pressure becomes too low at low loads or clean condition, then a partial flooding of the surface should allow increasing the pressure into a controllable range. The surface should be flooded a fixed amount. Trying to control the boil up by varying the amount of flooding is difficult due to the slow response. With partial flooding consider the effect of stresses especially in horizontal units where the stresses are different in the flooded and unflooded tubes. Wide boiling range mixtures, where the boiling point of the heavy component exceeds the heating medium temperature, require reboilers in which circulation occurs even in the convective heat transfer region otherwise the light component will be stripped out and stagnation will occur. Operation near the critical pressure have several problems. The density difference between vapor and liquid is low so the driving head for circulation is low. The maximum heat flux and the critical ∆T are also low. Operating under film boiling conditions might be considered as a possible solution. Low pressure (vacuum) operation requires careful analysis of the effect of static head on the boiling point and the possible temperature pinch thus caused at the top of the liquid zone. This boiling point elevation also results in much greater liquid preheat lengths and also reduces the available head for circulation. The large density differences cause higher acceleration pressure losses which result in reduced circulation. Low pressures require larger cavities for nucleation thus suppressing nucleate boiling coefficients, but the use of enhanced surfaces can be effective. Low ∆T operation (8°F) may sometimes be necessary because of process economics. Here the problem is nucleation and the use of enhanced surfaces is required. However, prediction of heat transfer coefficients is very uncertain and experimental tests on the specific surface liquid combination are recommended. Boiling curves developed from a small single tube pool boiling apparatus will provide a guide to the basic heat transfer coefficients which can be modified as necessary from the above discussed methods.

283

Very high ∆T is often encountered when vaporizing a low boiling point liquid; e.g., ammonia, with low pressure steam and here another problem of potential freezing of the heating medium must be considered. An available high temperature medium is another cause for high ∆T. At high ∆T the three limitations of film boiling, mist flow, and instability must be evaluated by the methods given above. Instability can be controlled within limits by throttling of the recirculation line or can be avoided by a shellside reboiler. Mist flow only represents a low heat transfer coefficient. Film boiling is a possible mode of operation if the potential for transition boiling is avoided where the control criteria are reversed. A possible solution to transition and fihn boiling is the use of medium- to high-finned tubes where the temperature drop along the fins is such that nucleate boiling occurs near the fin tips. Boiling on fins has been tested in the laboratory but no publication of a commercial application has been found. 5.9.1. Examples of Design Problems To design a heat exchanger requires that one first specify essentially all the dimensions of an exchanger and then one can proceed with the heat transfer calculations to determine whether the assumed design will give the desired performance and, if not, then the initial design is modified and the calculations repeated until an acceptable match of design and performance is obtained. A design problem is, therefore, a series of rating problems. In the rating of an exchanger its dimensions are known and only the heat transfer calculations are required; however, for vaporizers these calculations still involve considerable iterative trials to converge on an answer. It is obvious that the better the initial guess matches the final design the less the amount of calculation; hence, here is where experience is beneficial to the designer. In an attempt to aid a novice designer each of the examples below show in the initial steps one way of getting an initial design. In the second example, 5 steps are also used, however, in step 4 the guess of fraction vaporized is based on experience or as in this case prior knowledge of the experimental value.

5.10. Example of Design Problems for Trufin in Boiling Heat Transfer

5.10.1. Design Example - Kettle Reboiler Size a kettle reboiler to transfer 43.3(106) Btu/hr to vaporize a hydrocarbon mixture at 170 psia using steam available at 395°F. The critical pressure of this liquid is 434 psia and it has a boiling range of 60°F. The boiling temperature is 330°F. Design the reboiler using 3/4-in. OD tubes on 1.125-in square pitch. We will estimate the latent heat as 144 Btu/Ibm and liquid density as 41 lbm/ft3. Step 1. Calculate or estimate heating medium, tube wall, and fouling coefficients. For this example (and in order to compare to a test unit) the steam coefficient is 2000 and the tube wall is 4800. This reboiler was claimed to be clean; hence,

fwo

o Rhh

R ++=11

Ro = 1/2000 + 1/4800 = 0.000708

Step 2. Calculate the mixture correction factor, Fm from eq. 5.38.

Fm = exp(– 00.015 x 60) = 0.41 Step 3. Calculate B and RoB and find q. From eqns. 5.8a, 5.10 and 5.62.

A* = 0.00658(434).69 = 0.435

F(P)2 = 1.8 ( ) 17.434170 = 1.535

B = [(0.435)(1.535)]3.33 = 0.26

Correcting B for the mixture, use fig. 5.29 at BR of 60°F,

B = 0.26 x 0.41 = 0.1066 hence

RoB = 0. 1066 x 0.000708 = 7.5(10-5) At ΔT=65 Figure 5.33 gives q/B=280,000 hence

q = 0.1066 x 280,000 = 29,848 Btu/hr ft2

Step 4. Calculate single tube maximum q1, eq. 5.5

284

q1max = 803(434)(170/434).35 (1 – 170/434).9 = 160,488 Btu/hr ft2

Step 5. Preliminary estimate of bundle size For a bundle

qb = q1max Φb where

Φb = 2.2(πDBL/AB s). If we approximate

Φ = 2.2Ψ by letting Ψ be (for square pitch)

oB

t

pdLD

B

s

BdD

pLDA

LD

t

oB πππ

ππ

2

4

4

2

2=

×=

Now let

max1

242.2

qq

dDp b

oB

tb =

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=Φ

π

ftdq

qPD

ob

tB 118.2

)12/75.0)()(848,29()488.160()12/125.1)(4)(2.2()4)(2.2( 2

max12

===∴ππ

As the above approximation ignores the additional effect of circulation on the boiling coefficient, DB = 2 ft. B

Step 6. Calculate bundle maximum flux, eqn, 5.23 For U-tube on this pitch a total of 180 U-tubes or 360 ends will form a 2 foot diameter. For one foot of bundle length

0889.0)12/75(.)360(

)1)(2(===Ψ

πππ

s

BA

LD

Φb = 2.2Ψ = (2.2)(0.0889) = .1956

maximum bundle flux

q = Φbq1max

285

q = 0. 1956 x 160,488 = 31,392 Btu/hr ft2

Step 7 Calculate the bundle heat transfer For a 2 ft bundle assume q = 28,600 Btu/hr ft2 and calculate heat transfer coefficients based on this flux and the values obtained in steps 3 and 5. From eqn. 5.8 calculate hnbl

hnbl = (0.435)(1.535)(28,600)0.7 = 878.3 Btu/hr ft2°F Step 8. Calculate natural convection coefficient, eqn 5.7 We have insufficient information to calculate this coefficient but we will assume it is 40 Btu/hr ft2°F. Step 9. Calculate bundle coefficient, eqn. 5.22

hb = 878.3 x 0.41 x 1.5 + 40 = 580.1 Btu/hr ft2°F

U = 1/(115 80.1 + 0.000708) = 411.2 Btu/hr ft2°F

q=UΔT

q = 411.2 x 65 = 26,730 Btu/hr ft2°F The measured coefficient for this reboiler (72) was 440 Btu/hr ft2°F or 7% higher. Step 10. Check bundle design. Step 9 heat flux (26,730) is less than the maximum allowed bundle flux of step 6 (31,392) hence OK. Since Φb in step 6 is greater than 0. 1 no vapor lanes or larger pitches are required; therefore, bundle is OK. Step 11. Size the bundle.

Required length = 1963.360730,2661043××

× = 22.8 ft

This length checks with the test unit length of 23 ft. Step 12. Check for entrainment. Number of vapor nozzles per eqn. 5.64

Nn = 2523× = 2.3 round up to 3

Vapor per nozzle

286

Wn = 3144000,300,43× = 100,231 lbm/hr

Entrainment limit, eq. 5.63

VL = 2290 X 1.7255.

725.1415

⎥⎦⎤

⎢⎣⎡

− = 1409 lbm/hr ft3

(Note dynes/cm = [Ibf/ft] / 6.86 x 10-5) Therefore the vapor volume/nozzle = 100,231/1409 = 71.1 ft3. If the shell is 25 ft long then the cross section area for vapor above the liquid level is 71.1/8.33 = 8.537 ft2. The shell diameter is then determined from tables of segmental areas; however, for first approximation assume a liquid level at the center line then

Ds = (2 x 8.537 x 4/π)0.5 = 4.66 ft This is a large shell compared to the bundle diameter; therefore, consider the use of entrainment separation devices. 5.10.2. In-Tube Thermosyphon - Example Problem Size a vertical thermosyphon vaporizer to transfer 1,483,000 Btu/hr to an organic liquid with the following properties: boiling point @ 17 psia = 185.5°F, = 0.45, latent heat= 154.8 Btu/lb, lpc lμ = 0.96 lb/ft. hr, μ v

= 0.0208 lb/ft. hr, k = 0.086 Btu/hr ft. °F, and densities lb/ft3 liquid = 44.8, vapor = 0. 18 1, cP = 593.9 psia. Heating medium is steam at 217.4°F. Use 1-in. 12 BWG carbon steel tubes 8 ft. long. For this problem assumes no other fouling is present. This example is based on a test by Johnson (73). Boiling point elevation for 8 ft static head is 9°F. The heat source is steam condensing on the outside of the tubes with a coefficient of 1000. Step 1. Calculate Ro

Rw = )891)(.30()1)(12/109.0( = 0.00035

Ro = 1000

1 + 0.00034 = 0.00135

Step 2 Calculate the maximum limiting flux using eqn. 5.37

qmax = 16066 ( )35.2

812/782.

⎥⎥⎦

⎤

⎢⎢⎣

⎡(593.9).61

25.

9.59317

⎟⎠⎞

⎜⎝⎛

(1 – .0286) = 22,548 Btu/hr ft2

287

288

This is a high flux and would require a 22548 x.00135 = 30.4 temperature drop across the steam tube wall. As only 217.4 – 185.5 = 31.9°F is available it is obvious the operation is well below the maximum. Step 3. Determining a boiling flux Calculate a nucleate boiling flux using Figure 5.33 Here

B = [0.00658(593.9).69(1.8)(17 / 593.9).17]3.33 = 0.1214 (5.62) hence

RoB = 0.00135 x 0.1214 = 0.00016 For ΔT = 31.9° from the figure we should calculate

q = 44,000 x 0.1214 = 5342 Btu/hr ft2

This flux represents only the nucleate boiling coefficient and this is a lower limit. To include a two-phase convective effect assume a 50% increase in the boiling side. Hence, from the above flux and ΔT get U (167.4), subtract the Ro (.00135) resistances to get the boiling coefficient (216.4) increase the nucleate coefficient by the assumed ratio (= 324.6), then recalculate the new overall coefficient (225.7) and heat flux (7200). Step 4. Determining the recirculation rate.

Vapor per tube = 8 x 0.2618 x 7200 / 154.8 = 97.4 lb/hr Now one has to assume the fraction vaporized. We will short cut this trial and error by assuming the experimental value of 9%. Therefore, the feed rate/tube = 97.4/.09 = 1082 lb/hr. Step 5. Calculate basic values needed to check pressure drop, circulation rate, and preheat zone.

Gt = 1082 / (π x (.782)2 / [4 x 1441) = 324,404 lb/ft2 hr

V = 324,404 / (3600 x 44.8) = 2.01 ft/sec

Re = .782 x 324,404 / (12 x .96) = 22,021 From friction factor charts f = 0.0075 Hence in the liquid zone the head loss per foot of tube is by eqn. 5.51

ΔH = (4 x .0075 x 12 / .782) x 2.012 / 64.4 = 0.029 ft/ft Using an average vaporization of 9/2 = 4.5% we can calculate Xtt, (eqn. 5.29)

398.10208.096.0

8.44181.0

045.0045.1X

11.057.0

tt =⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛ −

=

289

Next get (eqn. 5.55) 2

ttΦl

2ttΦl = 1 + 20 / 1.398 + (1 / 1.398)2 = 15.82

The two-phase AH based on average liquid content of 0.955 is

ΔH = 15.82 x .029 (0.955)2 = 0.42 ft/ft The two-phase density due to slip is (eqn. 5.48 and 5.49)

Rv = 82.15/11− = 0. 749

ρtp = (.749 x .181) + [(1 – .749) x 44.8] = 11.38 lb/ft3

The boiling zone static head loss is

ΔH = 11.38/44.8 = 0.254 ft/ft Using eqn. 5.50 for PΔm

Gt = 324,404/3600 = 90.11 lb/ft2 sec

( ) ( ) ( ) ft751.0lb/ft64.33749.181.

09.251.8.44

09.12.32

11.90ΔP 2222

m ==⎟⎟⎠

⎞⎜⎜⎝

⎛

×+

×−

=

Heat transfer in preheat zone; eqn. 5.25

( ) ⎟⎠⎞

⎜⎝⎛ ××

⎟⎠⎞

⎜⎝⎛ ×

=782.

782.12086.086.

96.45.22021023.0h3/1

8. = 121.1 Btu/hr ft2 °F on outside area

Therefore

U = 1 / (1 / 121.1 + .00135) = 104. 1 Btu/hr ft2 °F Using a ΔT = 31°F the temperature rise in preheat zone is

45.1012312618.1.104

×××

= 1.86 °F/ft

Step 6. Estimating preheat and boiling lengths. Assume preheat zone = 3 ft Friction loss in preheat zone = 3 x .029 = 0.087 ft

290

Effective submergence at this point = total head (8) – friction loss (.087) – preheat zone (3) = 4.91 ft liquid which is equivalent to a boiling point elevation of

(4.91/8) x 9 = 5.53 °F Length required for this temperature rise is 5.53/1.74 = 3.18 ft. Close enough. Check on circulation and pressure drops Available head = 8 ft liquid neglecting liquid line losses Overall momentum loss = .751 ft Friction losses

boiling zone 5 x .42 2.100 preheat zone .087

Static heads

boiling zone 5 x .254 1.270 preheat zone 3.000

7.21ft Considering there is some losses in the liquid recirculating line the above agreement is close enough. Step 7. Calculate heat transfer in boiling zone From eqn. 5.8

hnbl = 0.00658(593.9).69(7200).7[1.8(17 / 593.9).17 = 266.2 x .782 / 1 = 208. 1 Btu/hr ft2 °F on OD area

From eqn. 5.28

226.2213.0398.1135.2F

73.0

ch =⎟⎠⎞

⎜⎝⎛ +=

Determines from eqn. 5.31

Retp = 22,021 x 2.2261.25 = 59,874

s = 1 / {1 + [2.53(10-6) x (59,874)1.17]} = 0.504 From eqn. 5.27

hcb = 121.1 x 2.226 = 269.6 Btu/hr ft2 °F on an outside area basis From eqn. 5.26

291

hb = (.504)(208.1) + 268.6 = 374.5

Adding the steam and wall resistance to obtain U for the boiling section

U = 1 / [(1 / 374.5) + 0.00135] = 249 Step 8. Calculate average coefficient for tube and area An average coefficient for the preheat and boiling zone is

Uav = (3 x 104.1 + 5 x 249.0)/8 = 194.5 Btu/hr ft2 °F Required area = 1,483,000/194.5 x 31.9 = 239 ft2 vs. 201 ft2 in the test vaporizer. Thus, this simplified calculation came within 19% of predicting the test results which is acceptable. In design case after calculating the required area (239 ft2) a safety factor should be added to allow for the error spread in all the involved equations. Also fouling should be considered and should be included in the term Ro term. We did not include fouling in this example since we were trying to compare the calculation method with data obtained in a clean vaporizer. 5.10.3. Boiling Outside Trufin Tubes - Example Problem To illustrate the value of and methods of calculation for Trufin tubes in boiling, a comparison of the performance of a plain surface and finned surface tube will be made. The plain tube is 0.75 and o.d., 18 B.W.G. wall and 90/10 Cu-Ni. The Trufin is Wolverine Cat. No. 65-265049-53. This tube has a surface area of 0.640 ft2/ft with an Ao/Ai ratio of 4.61, a fin height of 0.057 and width of 0.012 inches. There are 26 fins per inch. The tubes are heated with steam having a coefficient of 2000. A pure hydrocarbon having a critical pressure of 489 psia will be boiled at 100 psia with an overall temperature difference of 10'F. The bundle factor, Fb, is 1.5 and the surface factor, Fs, for this temperature is 1.0 for the plain tube and 1.5 for the Trufin tube. Evaluation of the Plain Tube Performance 1. Calculate Ro.

where Ro = wall resistance + tube-side resistance

( )( )( ) 000162.652.29

75.12/049.R wall ==

hwall = 6174

( ) 00074.652.2000

75.6174

1R ο =+=

2. Calculate the single tube boiling coefficient using eq. 5.32

hnbl = (5.43)(10-8)(489)2.3[1.8(100 / 489)0.17]3.33 ΔT2.3 = 0.24 ΔT2.3

292

assuming the maximum possible ΔT of 10°F

hnbl = (0.24)(10)2.3 = 47.9

3. Calculate the bundle boiling coefficient, overall U, and the heat flux then check the assumed ΔT. Assume a natural convection coefficient, hnv = 40, and using the bundle factor of 1.5 in eq. 5.22.

hb = (47.9)(1.5) + 40 = 111. 8

U0 = 1 / (1 / 111.8 + .00074) = 103.2

the available boiling ΔT is then

ΔTb = 10 – (10)(.00074)(103.2) = 9.2°F

This is not close enough to the assumed value of 10 so repeat steps 2 and 3. 2’ Assume ΔTb = 9.2

hnbI = (0.24)(9.2)2.33 = 42.25 3' hb = (42.25)(1.5) + 40 = 103.4

U0 = 1 / [(1 / 103.4) + .00074] = 96 4. Calculate available boiling ΔT.

ΔTb = 10 – (10)(.00074)(96) = 9.29°F

q = UΔT = (96)(10) = 960 Btu/hr ft2 (outside area) Evaluation of the Trufin Tube Performance 1. Calculate Ro

The inside area basis will be used

( )( )( )( ) 0.00013

579.2953.12/049.R wall ==

Ro (wall + steam resistance) = 0.00013 + 1/2000 = 0.00063

2. Calculate the boiling coefficient using eq. 5.32 with a surface factor of 1.5

hnbl = (1.5)(0.24) ΔT2.33 = 0.36 ΔT2.33

assume a boiling ΔT of 8°F

hnbl = (0.36)(8)2.33 = 45.8

293

using eq. 5.22 with Fb = 1.5 and hc =30

hb = (45.8)(1.5) + 30 = 98.7 3. Adjust for fin efficiency.

Figure 5.37 is used. This was derived for the case boiling liquids on fins where h = bΔT2.

using the assumed ΔT of 8 and hb = 98.7

b = 98.7 / (8)2 = 1.542

the abscissa for fig 5.37 is then

( )( )( )( ) 320.812/018.029

542.1212057. =×

an efficiency of 87% is read and

hb = (98.7)(.87) = 85.9 on an outside area basis

On an inside area basis;

hb (85.9)(4.61) = 396

U = 1/ (1/396 + .00063) = 317

q = UΔT = (317)(10) = 3170 Btu/hr ft2 (inside basis)

Check assumed value of boiling ΔT of 8°F.

ΔT (wall + steam) = (0.00063)(3170) = 2.0

ΔTboiling = 10 – 2 = 8°F

This checks with assumed value. If not then, repeat steps 2 and 3 with a new value.

Comparison of Performance Since the area per foot of the two tubes are different, comparison will be made on a per foot of length basis. 1. For plain tube

q/foot = (960)(.1963) = 188.5 Btu/hr-foot length 2. For Trufin

q/foot =(3170)(.640/4.61) = 440.1 Btu/hr-foot length

Therefore the performance ratio of Trufin to plain is: 440.1 / 188.5 = 2.3

294

Table 5.1

Simple dimensional equation for nucleate pooling boiling heat transfer (after Borishanski)

Liquid Pressure

range atm. A*

from exp A*

Eqn 5.9 Critical

pressure atm. No. in

Fig 5.18

Water Water Water Water Water Water

Pentane

Heptane (80%) n-heptane Benzene Benzene Diphenyl

Methanol Ethanol Ethanol Butanol

R11 R12 R12 R13

R13B1 R22 R113 R115

RC318

Methylene chloride

Ammonia Methane

1 – 70

1 – 196 0.09 – 1 1 – 72.5 1 – 170 1 – 5.25

1 – 28.6

0.45 – 14.8 0.45 – 14.8

1 – 44.4 0.9 – 20.7

0.9 – 8

0.08 – 1.39 1 – 20.7 1 – 59

0.17 – 1.38

1 – 3 1 – 4.9

6 – 40.5 2.8 – 10.5 17 – 39

0.4 – 2.15 1 – 3 8 – 31

3.6 – 27

1 – 4.5 1 – 8 1 – 42

1.61 1.58 2.28 1.76 1.75 2.26

.429 .464 .642 .417 .520 .441

(.272) .720 1.019 (.173)

.768 [.681]

.956 1.37 [1.01]

.705 1.744 [.976] [.941]

.488 1.49 [.934]

1.23 [.984]

(.752) 1.54 1.06

1.66 1.66 1.66 1.66 1.66 1.66

.449 .381 .381 .588 .583 .425

.815 .701 .701 .547

.539 .516 .516 .496 .508 .586 .453 .425

.394

.677 1.039 .563

216.9 216.9 216.9 216.9 216.9 216.9

32.8 25.9 25.9 48.1 48.1 30.4

78.0 62.6 62.6 43.8

42.9 40.3 40.3 37.9 39.1 48.4 33.4 30.6

27.3

59.6 110.8 45.6

1 2 3 4 5 6

7 8 9 11 -- --

13 10 12 14

-- 15 -- -- -- -- -- --

--

-- -- --

Values shown in round brackets ( ) are uncertain. Values shown in brackets [ ] relate to the use of Equations 5.11 for F(P).

295

NOMENCLATURE A* Constant defined in equation 5.9. dimensionless As Surface area. ft2 B Constant defined in equation 5.62. dimensionless BR Boiling range, dew point-bubble point. °F cp Specific heat, for liquid and clpc pv, for vapor Btu/lbm °F

d Tube diameter, do for outside and di for inside. ft. Dp Diameter of tube bundle. ft. Ds Shell diameter. ft. Fb Tube bundle correction factor. dimensionless Fcb Chen Factor. dimensionless Fm Mixture correction factor. dimensionless f Friction factor. dimensionless G Mass velocity. Ibm/ft2 hr Gt Mass velocity based on total flow. Ibm/ft2 hr Gtmax Total mass velocity based on minimum cross flow area. Ibm/ft2 hr Gmm Mass velocity at beginning of mist flow. Ibm/ft2 hr g Gravitational constant. ft/hr2

gc Conversion constant. Ibm ft/lbf hr2

H Height. ft Hl

Height of liquid zone. ft ΔH Head loss per foot of tube. ft/ft h Film heat transfer coefficient; hb = boiling, hc = convective, hf film, =

liquid, hlh

r = radiation, hcb = convective boiling, hft = film total, hnb = nucleate boiling, hnbl = single tube nucleate boiling.

Btu/hr ft2 °F

296

K Constant in equation 5.23. dimensionless k Thermal conductivity. Btu/hr ft2 °F L Length. ft Lc Minimum unstable wave length. ft m Exponent. dimensionless N Number of tube rows. dimensionless Nn Number of vapor nozzles. dimensionless Nu Nusselt number. dimensionless P Pressure. lbf/ft2

cP Critical pressure. lbf/in2

Pr Reduced pressure = P/PC. dimensionless Pr Prandtl number. dimensionless Psat Saturation pressure at plane interface. lbf/ft2 pt Transverse tube pitch. ft ΔP Pressure drop; ΔPT = total, ΔPs =static, ΔPm = momcntum, ΔPf = friction. lbf/ft2

q Heat flux; qmax = maximum, qmf = minimum film, qnc = natural convection, qcr

= critical. Btu/hr ft2

Re Reynolds number. dimensionless Rl, Rv Volume fraction of liquid, vapor. dimensionless Ro Sum of thermal resistances other than the boiling resistance. hr ft2 °F/Btu rc Radius of bubble. ft s Chen suppression factor. T Temperature; Ts = steam, Tw = wall, Tsat = saturation. °F ΔT Temperature difference; ΔTb = tube wall-saturation, ΔTc = critical, ΔTO = tube

waIl-bulk liquid, ΔTmin = difference at minimum film boiling coefficient. °F

V Velocity. ft/hr

297

V∞ Velocity approaching tube. ft/hr VL Vapor load. lbm/hr ft3 Xtt Martinelli parameter, equation 5.29. x Weight fraction of vapor. y Mole fraction low boiling component in liquid. GREEK β Coefficient of thermal expansion. 1/°R Γ Flow rate per unit length. Ibm/hr ft λ Latent heat; λe, λ’ = effective latent heats see eqn. 5.17, 5.19. Btu/Ibm

μ Dynamic viscosity; lμ = liquid, vμ = vapor lb./ft hr

ρ Density; ρl = liquid, ρv = vapor, ρb = bulk average, ρtp = two-phase. σ Surface tension. lbf/ft v Specific volume change liquid-vapor. ft3/lbm Φb Bundle maximum flux correction factor. dimensionless

2vtt

2tt Φ,Φl Martinelli two phase factors. dimensionless

298

BIBLIOGRAPHY 1. Zuber, N., Hydrodynamic Aspects of Boiling Heat Transfer, doctoral dissertation, Univ. of California at

Los Angeles, (1959). 2. Happel, O. and K. Stephan, Heat transfer from nucleate to the beginning of film boiling in binary

mixtures. Paper B7.8 Heat Transfer 1974. Proc. 5th Int. Heat Transfer Conf., Vol. IV, pp. 340-344. 3. Drew, T. B. and A.C. Mueller, Boiling, Trans. Am. Inst. Chem. Engrs. 33, (1937) 4. Bell, K.J., The Leidenfrost phenomenon: a survey, Chem. Eng. Prog. Sym. Series Vol. 63, No. 79, pp.

73-82, (1967). 5. Rhodes, T.R. and K.J. Bell, The Leidenfrost phenomenon at pressures up to the critical., Heat

Transfer-Toronto 1978, Proc. 6th. Int. Heat Transfer Conf., Vol. 1, pp. 251-255. 6. Hall, W.B., The stability of Leidenfrost drops., Heat Transfer-1974, Proc. 5th Int. Heat Transfer Conf.,

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