Two-phase flow regime considerations in condenser and vaporizer design

INT. COMM. HEAT MASS TRANSFER 0735-1933/88 $3.00 + .00 Vol. 15, pp. 429-448, 1988 ~ergamon Press plc. Printed in the United States

TWO-PHASE FLOW REGIME CONSIDERATIONS IN CONDENSERAND VAPORIZER DESIGN

K. J. Bell School of Chemical Engineering Stillwater, Oklahoma 74078, USA (C~,,L~/nicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT Most design procedures for condensers or vaporizers assume that the two phases are essentially uniformly distributed across the flow cross-section, and well-dispersed in one another to f a c i l i t a t e close approach to thermodynamic equilibrium. Normally, this assumption is tantamount to requiring a vapor shear-controlled flow regime, and i t is important to set the design parameters to provide this. This paper surveys the current state of two-phase flow regime prediction in heat exchangers, and offers suggestions for good design practice. Introduction The two essential requirements for condensation of a vapor are f i r s t , there must be a surface colder than the saturation temperature of the vapor at the pressure existing in the vapor space, and second, that the surface be in contact with the vapor phase.

Of course, there will be a thin film of

condensate on the condensing surface through which heat transfer must take place, but this film should be as thin and/or as turbulent as possible. The requirements for vaporization are that there must be a surface hotter than the saturation temperature of the liquid to be vaporized and that the surface must be wetted.

I f the vaporization is to proceed (at least in part)

by nucleate boiling, the surface needs to be up to 10 K above the saturation temperature unless one of the commercially-available nucleation-promoting surfaces is used.

It is possible for vaporization to occur at lower aT's than 429

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K.J. Bell

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those required to cause nucleation; in this case, the l i q u i d in immediate contact with the surface is superheated and then quiescently vaporizes when i t reaches a vapor-liquid

interface.

The l a t t e r process is used commercially in

such devices as vertical or horizontal tube falling film vaporizers. All of the commonly used design methods for condensers and vaporizers, at least in the process industries, assume that the vapor and liquid phases are in equilibrium with one another at any flow cross-section of the heat exchanger. This is especially true for design procedures for multicomponent mixtures such as Silver's method [ I , 2] and is consistent with the use of socalled condensing curves generated by multicomponent K and H value programs in process simulation and design software.

Even for methods such as the Colburn-

Hougen [3] method for condensation in the presence of a non-condensable gas in which equilibrium is assumed at the vapor-liquid interface for the computation of local heat and mass transfer rates, equilibrium between the bulk phases at any cross-section is assumed for the overall heat and material balances. In order to achieve a near-approach to equilibrium between the vapor and liquid phases in either condensers or vaporizers, there should be at all locations a large interfacial area between the two phases and as much turbulence as possible within each phase in order to minimize the temperature and composition gradients between the interface and the bulk of each phase. Satisfying these conditions requires that the designer carefully consider the two-phase flow regimes that actually exist within the equipment. The theme of this paper is to discuss in broad principle the nature and occurrence of these two-phase flows, to indicate the level of knowledge for two commonly used geometries in heat exchangers, and to describe how this information may be used by the designer in order to achieve the highest probability of operational success of his designs.

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Example of Phase Maldistribution An appreciation of the effect of phase maldistribution in the design of a condenser can be gained from the example of condensing a 0.5 mole fraction mixture of n-butane and n-pentane at 0.345 MPa (50 psia).

This mixture has a

dew point, that is a temperature at which the vapor f i r s t begins to condense, of 63.1°C.

As heat is further removed, the course of the condensation will

depend upon the degree to which the two phases are kept in equilibrium with one another.

The two extreme cases can be identified by the terms "integral

condensation" and "differential condensation".

In integral condensation, i t

is assumed that the two phases are kept in equilibrium with each other at all points during the condensation process.

In differential condensation, i t is

assumed that the liquid phase is removed from the vapor as rapidly as i t is formed and undergoes no further interaction with the vapor. These two processes are diagramed in Fig. 1, showing the temperature profiles as a function of the mole fraction of the original vapor condensed. At f i r s t , the curves are practically identical but the differential condensation temperature soon drops sharply, resulting in a final condensing temperature of approximately 37.8°C, compared to 53.5°C for the integral condensation process. I f the condenser had a single pass coolant, the differential condensation case would result in a substantially lower effective mean temperature difference and therefore a substantially larger heat exchanger. Also the maximum allowable inlet coolant temperature would have to be less than 37.8°C compared to less than 53.5°C for integral condensation; this by i t s e l f would not be a major design constraint for a water-cooled condenser but might be a significant restriction in the possible application of an air-cooled condenser. The problem would be further exacerbated in the more usual case of a multiple pass coolant, for the maximum allowable turnaround temperature in

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the condenser would have to be less than 37.8°C f o r the d i f f e r e n t i a l condensation process compared to 53.5°C for the integral condensation process,

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Since i t is so clearly advantageous to maintain as close as possible the integral condensation process, the question turns to what steps can be taken to insure this.

This requires that we consider further the nature of two-

phase (vapor/liquid) flow patterns and the parameters that govern these patterns.

Two-Phase Flow Patterns in Horizontal Tubes Fig. 2 shows one version of the commonly recognized flow patterns for two-phase flow inside horizontal tubes.

Description of these patterns is of

course highly subjective and there is some variation among workers in the field concerning the definition and nomenclature of the various patterns. However, the essential situation is this:

For ordinary fluids under ordinary

process conditions, two forces control the behavior and distribution of the phases.

These forces are gravity, always acting towards the center of the

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earth, and vapor shear forces, acting on the vapor-liquid interface in the direction of motion of the vapor. When gravity forces dominate (usually under conditions of low vapor and liquid flow rates), one obtains the stratified and wavy flow patterns shown on the l e f t side of the figure.

When vapor shear

forces dominate (usually at high vapor flow rates), one obtains the annular flow pattern (with or without entrained liquid in the core) shown on the right side of the diagram. When the flow rates are very high and the liquid mass fraction predominates, one can obtain the dispersed bubble flow pattern which is a shear-controlled flow of some importance in reboiler design but of very limited interest in condensers. Intermediate flow rates correspond to patterns in which both gravitational and vapor shear forces are important. Clearly, inside horizontal tubes, the gravity-controlled flow regimes are more likely to lead to phase non-equilibrium compared to the vapor shearcontrolled flows.

While phase non-equilibrium

is not an absolutely essential

consequence of a gravity-controlled flow for all geometries, i t is very often the case.

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Having decided, at least in the present instance, that one desires a vapor shear-controlled flow in order to minimize non-equilibrium between the phases, the designer needs a quantitative set of c r i t e r i a by which he may predict a priori what set of conditions will result in a given flow regime. Such representations in graphical form are usually called flow pattern maps, and Fig. 3 shows the most generally accepted flow pattern map for two-phase flow inside tubes, the Taitel-Dukler map [5].

The parameters defining the map

are given below: 1/2

PL PG JG2 JL K = [ (pL - PG) g ~L cos~ ]

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There are several points that need to be emphasized concerning the use of any flow pattern map:

1.

The definition of any two-phase flow pattern is highly subjective and different observers may disagree upon exactly what they are looking at, a confusion that is confounded by the various means of measuring two-phase flows and the resulting different c r i t e r i a that are used to characterize two-phase flows.

.

Corollary to (1), the boundaries drawn on a map as lines might better be viewed as very broad transition regions from one relatively welldefined flow pattern to another.

3.

Few flow pattern maps are represented in non-dimensional form; those that are in dimensional form (such as the Grant maps to be discussed later) must be regarded as representative of only the fluid and geometrical data base for which they were obtained, and extension or extrapolation to other flow properties and geometries done only with the greatest caution and because there is no viable alternative.

.

Most flow pattern maps are based on air-water flows, i . e . , cases in which the ratio of the vapor to liquid mass flow does not change from one part of the conduit to another.

On the other hand, condensing and

vaporizing flows are always in a state of change from one quality to another.

While we make the assumption out of necessity that we can

treat condensing and vaporizing flows as i f the local parameters are characterized by fully-developed adiabatic flows, this is at best only a reasonable approximation.

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In fact, even the question of what constitutes a fully-developed adiabatic flow is open to severe question.

Collier [6] cites work by

Gill and Hewitt in which two different methods of producing an airwater flow (a jet injector and a p~rous wall injector) gave quite different entrained liquid mass velocities even after ~/d = 150. The porous wall injector, which might be presumed to approximate most closely a process heat exchanger situation, does not appear to have attained an equilibrium value at that distance.

All of the above warnings not withstanding, i t is s t i l l

better to use

whatever limited information one can find and to use i t with f u l l

recognition

of i t s limitations than to t o t a l l y ignore these considerations in the design of equipment.

Two-Phase Flow Across Tube Banks The shell and tube heat exchanger is frequently approximated in design calculations as a series of ideal tube banks in crossflow, connected by window or turnaround regions.

Grant and co-workers [7] studied air-water two-phase

flows across tube banks in both horizontal crossflow and vertical up-flow. The characteristic flow patterns that they observed are shown in Fig. 4, and the corresponding flow pattern maps they developed in Figs. 5 and 6.

All of

their experiments were done with adiabatic air-water flows near atmospheric pressure, the range of geometric variables was very limited, and the flow pattern maps are dimensional.

Thus the precautions of the preceding section

need to be applied very carefully in this case. Even so, certain important points evolve from a comparison of the flow regime maps.

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If i t is agreed that, from the standpoint of maintaining close contact between the phases, we wish to avoid the stratified flow pattern we see that there is greater opportunity to get into the desirable spray flow regime at lower vapor and liquid velocities in vertical crossflow than in horizontal crossflow.

There is an even larger indicated area of chugging flow, which is

probably satisfactory from a heat transfer standpoint but may cause problems in s t a b i l i t y of operation and/or mechanical damage to the exchanger. This means that we should consider using vertically-cut baffles rather than horizontally-cut baffles, yet this has not been standard practice among heat exchanger designers.

Standard practice has been to cut the baffles vertically

as shown in Fig. 7 (with a notch at the bottom of the baffle to f a c i l i t a t e drainage of liquid at shutdown).

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DIRECTION OF

~ - - VAPOR FLOW

I I

"CONVENTIONAL" VERTICALLY-CUT BAFFLES FOR HORIZONTAL SHELLSIDE CONDENSER

HORIZONTALLY-CUT BAFFLES FOR SHELLSIDE CONDENSATION, TO AVOID STRATIFICATION

FIG. 7 Comparison of Horizontal Shell-Side Condenser Baffle Configurations

From the author's personal experience there have been several instances in which i t has been possible to improve the performance of a horizontal shell-side condenser by rotating the bundle and therefore the baffle cut 90° in order to move the baffles from a vertically-cut orientation to a horizontally-cut orientation.

(Because of impingement plate orientation and

other mechanical details, most horizontal condenser bundles cannot be rotated 90° without structural modification.)

Not unexpectedly, vertical upflow

modestly increases the shell-side pressure drop, and this factor needs to be taken into account before any such action is taken. I t seems probable, at least to the author, that Fig. 8 more f a i r l y represents what is happening with horizontally-cut baffles as long as the flow rates are kept high enough that the bulk of the flow must go across the tube f i e l d , rather than leaking between the baffle and the shell and between the baffles and the tubes in the upper part of the bundle.

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K.J. Bell

COOLANT VAPOR OUT IN

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FIG. 8 Schematic of Flow Patterns in a Horizontal Shell-Side Condenser With Horizontally Cut Baffles

Some adiabatic air-water studies done by Kikagi et al. [8] and supported in a videotape [9] indicate that s t r a t i f i e d flow exists to higher vapor and liquid superficial velocities than indicated by the Grant flow regime maps. Since there were significant clearances between the baffle and the shell and between the tubes and baffles in the experiment (and of course in commercial heat exchangers as well), i t appears that these leakage streams must be subtracted from the gross flow before one attempts to predict the flow regime for the crossflow sections.

However, this is only part of a much broader

question of the whole structure of two-phase flow on the shell side.

More

complete studies are required of two-phase flow over the entire range of geometrical parameters of interest in commercial heat exchanger configurations.

Example of a Horizontal Shell-Side Vaporizer Horizontal shell-side vaporizers are used in a nu~,~&r of applications including large scale refrigeration systems where they are commonly referred to as flooded c h i l l e r s .

In a vaporizer or reboiler, of course, the concern is

to insure that all of the surface is kept wet; otherwise, the heat transfer

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process consists of simply superheating a vapor phase with a usually very low heat transfer coefficient.

Again, i t seems l i k e l y that the wetted surface

requirement can be most readily met by insuring that the shell-side flow stays in the spray flow regime, though the heat transfer requirements would probably be satisfied by a chugging flow.

However, chugging flow might result in

undesirable pressure fluctuations or mechanical vibration and consequent damage to the heat exchanger. There are two aspects of keeping the surface wet that need to be separately considered.

First is to insure that there is liquid in the

immediate v i c i n i t y of the surface, whether this is provided by the existence of a gravity-dominated

pool or by a liquid-laden vapor phase flowing past the

surface at an essentially steady rate.

In the l a t t e r case, a fraction of the

liquid will be deposited upon the surface; i f the rate of deposition is equal to or greater than the rate of vaporization, the surface will stay wet. However, i t is also necessary to insure that the surface cannot dry out, followed by an irreversible rise in the surface temperature.

This suggests

that one must be very careful in designing heat exchangers in which the temperature of the heat source exceeds the wall temperature at which a stable liquid film can be re-established (the "re-wetting" problem always of concern to nuclear reactor designers).

I f the surface overheats so that i t cannot be

re-wet in normal operation, not only is the thermal capacity of the heat exchanger markedly reduced, but mechanical damage can result. Fig. 9 shows a horizontal shell side vaporizer that was installed in a gas processing plant.

The tube side fluid was a hot gas which was to be the

thermal source for vaporizing a liquid on the shell side.

After the heat

exchanger was placed in operation, the upper tubes in the bundle evidently were not wetted so that they rapidly attained a temperature intermediate to that of the h6t gas on the tube side add the vapor on the shell side.

The

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resulting thermal expansion of the upper tubes compared to the lower tubes (which were immersed in the pool of liquid)

resulted in bowing the heat

exchanger into the banana shape shown. The heat exchanger had to be scrapped and a new heat exchanger c o n f i g u r a t i o n i n s t a l l e d .

There seems to be the

possibility that, had the heat exchanger been constructed with horizontallycut b a f f l e s and that the liquid to be vaporized was introduced on the shell side before the hot gas was admitted to the tubes, the heat exchanger might well have continued to operate s a t i s f a c t o r i l y because of the entrained liquid in the vapor maintaining a continuous liquid supply on the upper tubes. VAPOR OUT

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! ~0.25m

SAME EXCHANGER. ~ PUT IN SERVICE.

BEING

FIG. 9 Example of Mechanical Damage Arising from Failure to Maintain Correct Flow Patterns

However, i t should be pointed out that this is at best a rather delicate balancing act:

I f there were any momentary reduction of the liquid supply

such that droplets could no longer be delivered to the upper tubes, in all probability exactly the same process would have occurred as with the presumed s t r a t i f i e d pool that actually did exist.

In this case, i t would seem that

prudent design would call for a rethinking of the entire operational

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philosophy, perhaps requiring that the bundle be t o t a l l y flooded and the liquid level maintained by a control device, i . e . , a conventional flooded chiller or kettle reboiler.

Limitations to the Use of Vapor Shear-Controlled Flows The examples above have emphasized the use of vapor shear-controlled flows in condensers and vaporizers in order to obtain at least rough thermodynamic equilibrium between the vapor and liquid phases, and also to maintain the thermal-hydraulic requirements for the heat transfer processes. Several limitations to this practice have been pointed out along the way including the uncertainty in our present design methods for predicting whether or not a given set of conditions will result in a vapor shear-controlled flow and the possibility that the i n i t i a l surface wetting process may be irreversibly destroyed by operational changes in flow rate or operating conditions. Another problem is that achieving a vapor shear-controlled flow will almost always require more pressure drop than a stratified flow.

This problem

is obviously more serious under vacuum conditions than at high pressure, and i t is inherently more serious for condensers than for vaporizers since any loss of pressure in a condenser will reduce the condensing temperature and therefore the temperature difference against the coolant.

Alternatively, in a

reboiler, reduction of the boiling temperature due to pressure drop can result in the possibility of exceeding the critical heat flux.

The allowable

pressure drop problem problem is substantially exacerbated by the fact that we are not yet very good at predicting two-phase pressure drops with any accuracy at a l l . One answer to those situations where a vapor shear-controlled flow is either not feasible within allowable pressure drops or not sufficiently

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dependable for the designer's and operator's requirements is to use a configuration in which gravity will achieve the desired results and vapor shear will at least not work against the gravitational mechanisms. The idea of using gravitational forces to control the flows leads the designer in the direction of vertical upflow vaporization and vertical downflow condensation.

Vertical upflow vaporization is widely practiced in industry in

vertical intube thermosiphon reboilers, for which there is a large body of data and design methods available.

(Vertical shell-side thermosiphon

operation is also occasionally carried out, but there are d i f f i c u l t i e s in insuring that the vapor phase does not accumulate in contact with the upper tubesheet, allowing the tubesheet to overheat with resulting thermal stress problems in the heat exchanger.) Condensation in vertical downflow, whether on the shell side or on the tube side, is a way of using gravity to drive the liquid flow while s t i l l maintaining good contact between the liquid and vapor phases. Vertical intube condensation is relatively straightforward as long as care is taken to insure that the tubes are of sufficiently large diameter to avoid bridging and backfilling, which would prevent non-condensable gases from escaping to the vent system. Venting for tube-side condensation is best accomplished by providing a deep head into which the condensate and any non-condensable gases can flow and separate by gravity; the non-condensable gases are then removed through a shrouded vent. Vertical in-shell condensation provides the opportunity for the liquid condensed early in the process to rain through the remaining vapor phase in each crossflow path.

This constant exposure of the already-condensed liquid

falling in thin films or dispersed liquid masses should keep the condensing process reasonably close to the integral condensation case.

If shell-side

condensation is used (Fig. 10), i t is important to insure that there is a good

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vent provided near the end of the condensation process, but above any liquid level established on the shell side of the exchanger.

If the outlet piping is

sufficiently oversized (and the horizontal intube two-phase flow regime map will be useful in this regard) such that the effluent two-phase flow is stratified, venting may be done either off of the top of the exit piping or from the receiver vessel (assuming that the vessel has adequately-designed internals to assure good vapor-liquid separation.)

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FIG. 10 Schematic of a Vertical Shell-side Condenser, Showing Proper Vent Location

The usual objection to vertical condensation is that the condensate cannot ordinarily drain directly back into the column but must be pumped back.

A vertically-mounted condenser may also offer some servicing

difficulties since i t generally must be lifted upwards and then laid horizontally before i t can be serviced. However, both of these considerations are more matters of convenience, rather than imposing unacceptable penalties upon the configuration.

When one balances these inconveniences against the

possible failure of a condenser to operate in a thermal-hydraulically

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satisfactory fashion, the real engineering choices are f a i r l y evidently displayed.

In a closely related situation, the reader will perhaps recall

that I - i vertical effluent heat exchangers with tube-side expansion joints came into popular use once one looked at the economic cost of f a i l i n g to recover the energy in the reactor effluent stream. The argument that "We have never done i t that way before" rarely will stand up against a strong counterargument of energy savings and as long as designability and operability are not compromised.

SUMMARY The intent of this paper is to demonstrate the importance of considering two-phase flow patterns in the design of vaporizers and condensers. While the arguments have been primarily developed for the shell and tube exchanger (both sides), i t is not hard to extend the essential ideas to other geometries. The major d i f f i c u l t y with using this design tool is the lack of generally applicable two-phase flow pattern correlations, especially those having some internal evidence of fundamental v a l i d i t y .

Certainly much more research -

especially, but not entirely, experimental at this point - must be devoted to developing flow pattern maps applicable to other geometries and for a wider range of conditions than simply adiabatic air-water flows.

However, even

existing information wisely used by the designer can at least put him in a generally safe area. As a general rule, maintaining flows in the vapor shear-controlled flow patterns is highly desirable.

However, this usually entails higher pressure

drops than in s t r a t i f i e d flow, and perhaps greater than can be allowed in a given situation.

In this case, the designer will be well advised to think in

terms of condensation in vertical downward flows and vaporization in vertical upward flows.

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Acknowledgment The ideas in this paper have been developed over a period of many years as a result of association with many of the outstanding figures in the fields of two-phase flow and heat transfer and heat exchanger design and application.

The l i s t must certainly include - though i t is not limited to -

Duncan Chisholm, Allan Colburn, Geoff Hewitt, Al Mueller, Joe Palen, Warren Rohsenow, B i l l Small, Jerry Taborek, and Jim Westwater. Nomenclature F

Taitel-Dukler parameter

g

Gravitational acceleration

J

Superficial phase velocity, m/s

K

Taitel-Dukler parameter

(dp/dz) Frictional pressure gradient for the given phase flowing alone in the tube, (N/m2)/m Taitel-Dukler parameter Taitel-Dukler parameter Tube inclination angle, = 0 for horizontal flow, > 0 for downward flow. Absolute viscosity, Ns/m2 p

Density, kg/m3

Subscripts G

Gas or vapor phase

L

Liquid phase References

1.

Silver, L., Trans. Inst. Chem. Engrs., Vol. 25, 30 (1947).

2.

Bell, K. J., and M. A. Ghaly, AIChE Symp. Series No. 131, Vol. 69, 72

3.

Colburn, A. P., and O. A. Hougen, Ind. Eng. Chem., Vol. 26, No. 11, 1178

4.

Alves, G. E., Chem. Eng. Prog., Vol. 50, No. 9, 449 (1954).

(1973).

(1934).

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5.

Taite], Y., and A. E. Dukler, AIChE J., Vo]. 22, 47 (1976).

6.

Collier, J. G., Convective Boi]in~ and Condensation 2nd Ed., p. 86, McGraw-Hill, New York (1981).

7.

Grant, I. D. R., Nat'] Eng. Lab. Report 590, East Kilbride, Scotland, UK (1975),

8.

Kikagi, M.., K. Ogata, and A. Kawada, Proc. 2nd ASME - JSME Thermal Engineering Joint Conference, 65 (1987).

9.

Ishihara, K., Private Communication (1987).