Falling-film evaporation on horizontal tubes—a critical review

Review Article

Falling-film evaporation on horizontal tubes—a critical review

Gherhardt Ribatskia,*, Anthony M. Jacobib

aLaboratory of Heat and Mass Transfer, Faculty of Engineering Science, Swiss Federal Institute of Technology, ME G1 465, Station 9,

CH Lausanne 1015, SwitzerlandbDepartment of Mechanical and Industrial Engineering, University of Illinois, 1206 West Green Street, Urbana, IL 61801, USA

Received 12 February 2004; received in revised form 1 December 2004; accepted 14 December 2004

Available online 1 February 2005

Abstract

A state-of-the-art review of horizontal-tube, falling film evaporation is presented; the review is critical, in an attempt to

uncover strengths and weaknesses in prior research, with the overall purpose of clearly identifying gaps in our understanding.

The review covers flow-pattern studies, and the experimental parameters that affect the heat transfer performance on plain

single tubes, enhanced surfaces and tube bundles. In addition, this paper presents a comprehensive review of the significant

efforts to develop mathematical models, and empirical correlations for the heat transfer coefficient. Emphasis is placed on

studies that are related to refrigeration applications.

q 2004 Elsevier Ltd and IIR. All rights reserved.

Keywords: Evaporation; Falling film; Horizontal tube; Finned tube; Bundle; Survey; Heat transfer; Correlation

Evaporation d’un film tombant sur des tubes horizontaux—passage

en revue critique

www.elsevier.com/locate/ijrefrig

Mots cles: Evaporation; Film tombant; Tube horizontal; Tube ailete; Faisceau; Enquete; Transfert de chaleur; Correlation

1. Introduction

Falling-film-type (or spray-film) horizontal-tube evap-

orators have been utilized in the refrigeration, chemical,

petroleum refining, and desalinization industries. Although

the first patent of such an evaporator was registered in 1888

[1], only a few researchers worked in this area prior to the

0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved.

doi:10.1016/j.ijrefrig.2004.12.002

* Corresponding author. Tel.:C41 21 693 5984; fax:C41 21 693

5960.

E-mail addresses: [email protected] (G. Ribatski),

[email protected] (A.M. Jacobi).

1970’s. Since then, this technology has been studied by

many investigators; however, the focus during the 1970’s

was primarily on the use of falling-film evaporators for

ocean thermal energy conversion, (OTEC) systems, with

interest in the early 1980’s driven by the second oil crisis. As

a result of the interest in OTEC applications, most of this

work in the 1970’s and 1980’s used water or ammonia as a

working fluid. Moreover, the heat fluxes and other operating

parameters were constrained to ranges relevant for OTEC

systems.

During the 1990’s, the CFC phase-out began to motivate

wider application of falling-film evaporators. In air-

conditioning and refrigeration applications, the falling film

International Journal of Refrigeration 28 (2005) 635–653

http://www.elsevier.com/locate/ijrefrig

Nomenclature

Ar Archimedes number based on tube diameter

Dext3 g/nl

3, (dimensionless)

Dext surface diameter, (m)

g gravitational acceleration, (m sK2)

Ga modified Galileo number (or Kapitza number)

rs3/m4g, (dimensionless)

H liquid feeder height, (m)

h heat transfer coefficient, (W mK2 KK1)

hlv latent heat of vaporization, (J kgK1)

k thermal conductivity, (W mK1 KK1)

K dimensionless defined by [52], Eq. (4)

n/A active nucleate site density, (mK2)

Nu Nusselt number (h/kl)(nl2/g)1/3, (dimensionless)

p pressure, (N mK2)

Pr Prandtl number n/a, (dimensionless)

Re Reynolds number 4G/m, (dimensionless)

s tube pitch, (m)

T temperature, (K)

Greek letters

a thermal diffusivity, (m2 sK1)

f specific heat flux, (W mK2)

G liquid mass flow rate per unit length of tube

(each side), (kg mK1 sK1)

l instability wavelength given by Eq. (3), (m)

m dynamic viscosity, (kg mK1 sK1)

n kinematics viscosity, (m2 sK1)

q angle along surface perimeter measured from

the tube apex, (8)

r density, (kg mK3)

s surface tension, (kg sK2)

x capillary constant given by [s/(rlg)]1/2, (m)

Subscripts

crit referred to the critical state

l liquid

sat saturation

v vapor

w tube wall

G. Ribatski, A.M. Jacobi / International Journal of Refrigeration 28 (2005) 635–653636

evaporator possesses the following clear advantages over

flooded tube bundles:

High heat transfer coefficient, (1) allowing the evapor-

ation temperature to increase, and thus improving the

cycle efficiency; (2) minimizing the evaporator size,

resulting in reduced initial costs and space requirements.

Low refrigerant charge, (1) lowering the cost of the

refrigeration plant (including the refrigerant inventory);

(2) reducing risks associated with a leak, including the

attendant maintenance costs. This reduced risk allows

wider application of systems using toxic or flammable

fluids, such as ammonia.

These advantages notwithstanding, falling-film evapor-

ators are not widely used in refrigeration and air-

conditioning. In part, reticence to adopt falling-film

technology in these systems is due to difficulties in liquid

distribution and tube alignment, which affect flow uniform-

ity and dryout, especially in deep bundles. Furthermore,

decades of experience with flooded bundles in this industry

has allowed for their heuristic optimization, but heat transfer

surface, bundle geometry, and operating strategies have not

been so refined for falling-film evaporators. At present,

these issues are motivating many researchers.

A prior related review was provided by Thome [2], with

a focus on studies published from 1994 to 1999; to our

knowledge, no other review has appeared in the open

literature. The current article provides a literature review of

horizontal-tube, falling-film-type evaporators, focusing on

the technical difficulties identified above. We focus this

review on falling-film evaporators and exclude vertical tube

arrangements and desalination systems, because our goal is

to assess the state of the art as it is likely to affect air-

conditioning and refrigeration systems. Our goal is to

critically review the literature, for the purpose of clearly

identifying opportunities for application and areas where

further research is needed.

In the present work, by referring to the results of

previous research, we begin with a discussion of the effects

of heat flux, flow rate, film temperature, tube diameter and

liquid feeder configuration on the falling-film evaporation

for single plain tubes. Then, the observed inter-tube flow

patterns are presented as well as proposed methods to

predict inter-tube flow patterns. Following that, experimen-

tal studies concerning falling-film evaporation on enhanced

surfaces and tube bundles are described, and their results

critically discussed. Some interesting prediction methods to

estimate the heat transfer coefficient in subcooled and

saturated conditions are reported in the last part of the

article.

2. Heat transfer aspects on plain surfaces

Generally speaking, prior studies involving smooth tubes

have covered wide ranges of heat flux, flow rates, liquid

feeder height, and tube spacing. The tube diameters have

been similar to those used in heat exchangers. Tests were

conducted for sub-cooling and saturated liquid, and under

both boiling and non-boiling conditions. Except for a few

studies, the experiments were conducted with water and

ammonia, and most of the work focused on how the

Table 1

Description of experimental studies involving falling film on plain single tubes

Fluid Surface

material

Dext (mm) H (mm) G

(!103 kg sK1 mK1)

Tsat or Tl (8C) f (kW mK2)

[3] Water Cu–Ni 25.4, 50.8 – 0–314 49–127 0–63.1

[4] Sea water Cu–Ni 25.4, 50.8 – 0–228 49–127 0–63.1

[5] Water Stainless steel 25.4, 50.8 8–54 144–377 55–100 19–76

[6] Water Brass 25.4, 50.8 3.2 133–373 45–127 15.8–78. 8

[7] Ammonia Stainless steel 50.8 – 4–202 22.2 5–16

[8] Ammonia Low carbon

steel

25.4 25.4 3.7–37.4 12.8–23.9 3.2–25.2

[9] Water Copper 25.4 12.7, 25.4, 50.8 4–40 27, 50 0–83

[10] Ammonia Stainless steel 50.8 50.8 4–350 22.2 5.2–15.8

[11] Water Copper 25.4 3 37–110 99.4 2–100

[12] Water Brass 25.4, 50.8 – 2.78–7.62!

10K4m3 sK1 mK1

49–127 16–79

[13–15] Water Copper 25.4 3–63.5 21.3–156 99.4 2–208

[16] Water, ethyl

alcohol

Copper 25.4 12.7, 25.4, 50.8 2.5–50 57 0–80

[17] Water, isopro-

pyl alcohol

Copper 18 4.5–87 38–130 25, 21.5 18.4, 9.4

[18] R-113 – – – – 47 7–80

[19] Water – 38 – 40–400 40–100 15–75

[20] Water Aluminum 132 – – – –

[21] R-11 Copper 18.0 20 8–91 23.5 1–43

[22] Water Brass 25.4, 50.8 6.3 135–366 49–127 30–80

[23] R-113 Copper 22.0 – 32.1–96.3 47.2 7.3–72.7

[24,25] R-11 Copper 25.0 25.0 1–180 44.6 0.5–2.5

[26] R-134a Copper 12.7, 19.1 38–65!10K3 kg sK1 2.0 5–40

[27] R-134a Copper 19.1, 12.7 – 38–65!10K3 kg sK1 K14, 2 5–40

[28] Water, isopro-

pyl alcohol

Copper 19.5 7.8–48.8 5–150 9–50 0–150

[29] Water, ethylene

glicol, mixture

of water and

ethylene glycol

and ethyl alco-

hol

Brass 9.52, 12.7,

15.87, 19.

05, 22.22

0–100 0–360 25–40 0–115

[30] R-134a with a

polyol-ester

32 cs/40 8C

uZ0, 1, 2 and

3.0%

Copper 19.1 – 13 2 5–40

[31] Water Aluminum 132 – – 17–50 71–158

[32] Ammonia Stainless steel 19.1 102, 51 7–39 K23.3–10 8–60

[33] Water, ethylene

glicol, mixture

of water and

ethylene glycol

Brass 15.9,

19.01,

22.22

5–50 0–360 25–40 0–115

[34] Water Surface cov-

ered with a

constant foil

38 10–20 40–400 42–100 15–75

[35] Water Copper 19.5 7.8, 2.3, 48.8 10–150 20, 35, 50 0

[36] Wateri, R-11ii Copper 18 6 15–354 99.4i, 23.5ii 2–500

G. Ribatski, A.M. Jacobi / International Journal of Refrigeration 28 (2005) 635–653 637


experimental parameters affect the heat transfer. Table 1

describes the experimental data bank of studies concerning

falling film evaporation on single plain tubes.

2.1. Heat flux effect

For completely wetted surfaces in strictly convective

conditions, the heat flux, f, does not affect the heat transfer

coefficient, h, [6,7,12,22,25,33]. On the other hand, under

boiling-dominated conditions, the heat transfer coefficient

increases with the heat flux [3,4,6,22,27,32]. Apparently,

this behavior is due to increased nucleation site density, n/A,

and increased boiling area. For a low heat flux, bubbles

nucleate near the bottom of the tube. As f increases,

nucleation occurs nearer to the top of the tube [6,22]. With

an increase in heat flux, a temperature profile in the film

sufficient for nucleation closer to the film impingement

region is possible. A strong dependence of Nusselt number,

Nu, on f, with high rates of increase in h with heat flux has

been noted at low temperatures [3]. This finding seems to

agree with pool boiling experiments of Ribatski and Saiz

Jabardo [37], according to whom the variation of h with f is

comparatively high at low reduced pressure. Thus, one

expects parameters such as the contact angle, surface

material and roughness to affect the increase in h with

heat flux for falling film evaporators. However, no work

concerning the possible effects of these parameters on

falling film has been reported.

2.2. Flow rate effect

In convection-dominated conditions, as the flow rate, G,

increases the heat transfer coefficient decreases first, but

increases after a minimum value [7,14,25,38]. This

minimum might represent a transition from laminar to

turbulent film flow [25,38]. However, according to Rogers et

al. [31], this assertion is a flawed, arbitrary assumption.

Even modeling that does not consider the flow regime

transition exhibits similar behavior [14,39,40]. According to

Brumfield and Theofanous [41], the film can be fully

turbulent only for Reynolds numbers, Re, higher than 6000.

They suggest that the film is controlled by wave structures

imposed on the base film flow. At low Reynolds numbers,

the waves and the base flow are laminar; at intermediate

Reynolds numbers the base flow is laminar while the waves

are turbulent, and at high Reynolds numbers, both regions

are turbulent. Carey [42] proposed a transitional Reynolds

number of 1500. For falling film condensation, a similar

process, values of 1200, 1800 and 2000 also have been

proposed for the Reynolds number at which the flow

becomes turbulent (see Thome [43]).

The following behaviors are also noted under convec-

tion-dominated conditions: the heat transfer coefficient is

almost independent of the flow rate [5,8,11,32], and the heat

transfer coefficient increases with G [6,9,12,17,22,28,32,

34]. Under boiling conditions and when Re falls between

1000 and 8000, Parken [6] and Parken et al. [22] also

observed an increase in h with G. Chyu and Bergles [14], for

high heat flux, and Moeykens and Pate [27], independent of

f, did not note flow rate effects on h. According to both

studies, h is independent of G due to the predominance of

boiling effects.

Changes in the inter-tube flow mode (droplet, jet and

sheet), and partial surface dryout can affect the effects of

flow rate on the heat transfer coefficient. Hu and Jacobi [33]

noted an increase in h with G for the droplet and jet modes.

For the sheet mode, this behavior was noted solely for water.

It can be related to wave effects on the film surface [33],

which are high for water as the result of the larger Re

achieved in the experiments with this fluid.

2.3. Temperature effect

For convective heat transfer, h increases with the liquid

temperature. It seems that this temperature effect is closely

related to the decrease of viscosity and consequent decrease

in the film thickness [5,6,12,22,28]. The increase in h occurs

around the overall surface perimeter and can be correlated

by the following equation [6]:

hðTAÞ

hðTBÞZ

nlðTAÞ

nlðTBÞ

� �n

(1)

It should be noted that Ganic and Roppo [9] found that the

fluid temperature does not affect the heat transfer coefficient.

For boiling conditions, temperature gradients near the

surface are increased as the film thickness decreases, and a

decreased film thickness can be caused by viscosity

reductions associated with bulk temperature increases. A

steeper temperature profile can inhibit bubble growth (see

Cerza and Sernas [44]), and change the position along the

surface perimeter at which active nucleation sites appear.

On the other hand, in pool boiling the heat transfer

coefficient increases with temperature, because of the

increase in n/A. In the context of falling-film evaporators,

these two competing effects can either increase or decrease

h. These opposing effects might be responsible for

disagreement in prior work, ostensibly conducted under

similar conditions. Refs. [3,4,6,32] point out an increase in h

with film temperature for boiling conditions. Fletcher et al.

[3,4] noted this behavior for a tube diameter of 25.4 mm,

while for an external diameter of 50.8 mm the effect of film

temperature seemed to be marginal. Parken et al. [22] noted

an increase in h with the film temperature for a tube with

DextZ50.8 mm and a liquid temperature up to 100 8C. An

opposite behavior was observed for higher temperatures; i.e.

for DextZ25.4 mm, and Tl!100 8C, they observed a weak

effect of film temperature on h; while for temperatures

higher than 100 8C, h increased with liquid temperature.

These behaviors seem to be related to the effects of the

diameter and the liquid temperature in the relative weight of

convective and boiling mechanisms, as previously discussed.

Fig. 1. The effect of the liquid feeder height on the heat transfer

coefficient distribution along the external perimeter of a horizontal

cylindrical surface submitted to falling film evaporation under non-

boiling conditions (based on experimental results of Liu [5]).


2.4. Tube diameter effect

Tube diameter affects the heat transfer coefficient

because it changes the thermal boundary layer development

length and the length of liquid impingement region, relative

to the overall flow length of pDext/2. Under non-boiling

conditions, these regions are characterized by higher local h,

resulting in an increase in the heat transfer coefficient with a

decreasing tube diameter [6,12,22,33], because a larger frac-

tion of the surface area is subject to impingement and deve-

lopment effects. Liu [5] did not note effects of diameter on h.

Conversely, under boiling conditions the relative area of

active boiling increases with the surface diameter, because

development of the thermal profile allows bubble growth.

Thus, the overall behavior of h with Dext depends on the

local h in the boiling region relative to the values on other

surface regions. These effects can explain differing trends

observed under similar conditions. In the presence of bubble

nucleation, Parken [6] and Parken et al. [22] observed an

increase in h with the tube diameter, but Fletcher et al. [3],

Moeykens [26], and Moeykens and Pate [27] noted an

opposite behavior.

2.5. The effect of liquid feeder configuration

The device used for liquid feeding can affect the

evaporator performance. In general, feeder misalignment

and designs that fail to provide axial uniformity can increase

refrigerant maldistribution in the bundle and thus influence

the heat transfer rate. For convective heat transfer, the liquid

feeder configuration may increase the heat transfer coeffi-

cient by increasing convective effects related to the liquid

impingement on the tube surface. Parken [6] and Parken and

Fletcher [12] for a feeder with wedge shape, and Fletcher et

al. [3] using a perforated plate noted axial temperature

variations along the tube apex due to the flow non-uniformity.

This effect is more pronounced for smaller tubes [6,12]. It has

been reported that film imperfections affect only the liquid

impact region [6,24]; however, Liu [5] observed that a small

misalignment produced an asymmetrical temperature distri-

bution all the way around the surface perimeter.

Fujita and Tsutsui [24,25] found that a cylindrical feeder

with holes along the bottom produced a heat transfer

coefficient 20% lower than that produced by a porous

sintered tube, a tube with holes along the top, and a

perforated plate with one, two, or three dummy tubes.

Moeykens and Pate [27] reported results under boiling

conditions for wide-angle, low-pressure-drop type and

wide-angle, high-pressure-drop type commercial spray

nozzles. The high-pressure-drop nozzles had the best

performance, according to the authors mainly because of

the impingement effect. However, using this nozzle might

not lead to an increase in overall evaporator performance,

because the impingement effect is confined to the top tubes,

and in a deep bundle impingement on the top few tubes

becomes less important than other factors, such as flow

uniformity. For ammonia, at saturation temperatures greater

than K1.1 8C, and commercial low-pressure-drop nozzles,

Zeng et al. [32] observed higher heat transfer coefficients for

spray nozzles with a cone angle greater than 908.

2.6. The effect of the liquid feeder height

The liquid feeder height can affect the heat transfer coef-

ficient by modifying the flow mode, or through an increased

impingement velocity. An increased feeder height,H, can also

allow better spray distribution and thereby mitigate misalign-

ment effects.

Under non-boiling conditions, the heat transfer coeffi-

cient increases with H [5,6,13,14,17,28]. This effect is less

pronounced for fluids with a high liquid viscosity [5].

Parken [6] reported h increased with H solely in the liquid

impact region, while according to other Refs. [5,17], and as

shown in Fig. 1 the heat transfer coefficient increased with H

along the whole surface perimeter. For the jet flow mode Hu

and Jacobi [33] noted that the heat transfer coefficient

increased with H. In the case of droplet-and-film modes they

observed a weak effect of H. Ganic and Roppo [9] carried

out experiments for droplet-and-jet modes. Although they

noted the increase in h with H at some flow rates, they did

not relate this behavior to flow modes. In boiling conditions,

Zeng et al. [32] for film temperatures lower than K1.1 8C,

Chyu [13], and Chyu and Bergles [14] pointed out a weak

effect of the feeder height on h.

2.7. Effects of a vapor flow

A vapor flow can affect the evaporator performance in

the following ways: it can change the flow mode and

promote the deflection of the liquid flow, droplet atomiz-

ation and droplet drag; it can affect the film velocity profile

and promote waves on the film surface [45]. The fluid


maldistribution caused by the gas flow can lead to partial

surface dryout. On the other hand, the enhancement of

convective effects on the film surface can increase h. The

vapor flow direction (countercurrent, concurrent or cross-

current) can influence these effects.

Under boiling conditions, Parken [6] noted a heat

transfer enhancement and the suppression of bubble

nucleation with an increase in vapor velocity from 9 to

18 m sK1. These effects were insignificant for velocities up

to 9 m sK1. According to Parken, this behavior seems to be

related to a reduction in the film thickness and an increase in

the liquid velocity. For concurrent vapor flow and based on

the results from a numeric model, Liu [5] pointed out

that the degree to which h increases with the vapor velocity

is higher in thin films. In addition, he concluded that its

effect is insignificant for typical gas velocities of evapor-

ators. According to the same study, in countercurrent flow,

vapor effects can reduce the heat transfer coefficient due to

an increase in the film thickness resulting from an adverse

velocity profile in the film.

For sub-cooled water with a countercurrent air flow,

Armbruster and Mitrovic [28] noted an increase in h with air

velocity. This effect was more pronounced at low partial

vapor pressure, and was insignificant at high relative

humidity. The effects of air velocity and relative humidity

were small at high heat fluxes. According to them, the air

temperature seemed not to affect h. Experimental results of

Armbruster and Mitrovic [35] for water and an adiabatic

surface showed the effects of air velocity and relative

humidity on the temperature of the liquid to be small. These

results clearly suggest that the main effects of air velocity

and relative humidity on h are imparted during the liquid

free fall. For concurrent air velocity up to 15 m sK1, Hu and

Jacobi [33] noted an increase in h with air velocity, but the

effect was within the uncertainty in their experimental results.

3. Flow patterns studies

When a liquid film flows from one horizontal tube to

another below it, according to an increasing flow rate order,

the flow may take the form of droplets, circular jets, or a

continuous sheet, as shown in Fig. 2. The pattern is referred

to as falling-film mode and may play an important role in the

heat transfer process. Yung et al. [46] correlated the flow

rate for a transition from the droplet mode to the jet mode

with the droplet production frequency set equal to the

capillary wave oscillation frequency. Yung and his

co-workers based their studies on results from a single

tube with a single liquid detachment site in quiescent vapor.

The flow rate on one-side per unit length of the tube at the

transition was given by

2GZ 0:81rl

l

pd3p

6

2ps

rll3

� �1=2

(2)

where

lZ xffiffiffiffiffiffiffiffiffiffiffi4p2n

p(3)

In Eqs. (2) and (3), nZ2, x is the capillary constant given byffiffiffiffiffiffiffiffiffiffiffis=rlg

p, and dp is the diameter of primary drops, experi-

mentally determined for water and alcohol to be equal to 3x.

Experimental observations by Ganic and Roppo [9]

indicated that the transition from the droplet to the jet mode

occurred over a relatively large range of Reynolds number

around 180, and it was affected by the tube spacing. When

studying film condensation, Kutateladze et al. [47]

suggested that the modified Archimedes number based on

the capillary constant controlled the transition of flow mode.

Mitrovic [17] pointed out that the transition of flow modes

was dependent on the flow rate, fluid thermophysical

properties and the tube spacing.

Armbruster and Mitrovic [48] modeled the mode

transitions among the droplet, jet and sheet modes,

according to ReZAGa1/4, where A is an empirical constant.

For sufficiently high stagnation pressure, they observed that

the radial flows from adjacent jets collide and the film

surface is raised between the jets. The crests created at the

top of the tube remain nearly unchanged around the tube,

and form the departure sites for jets leaving the tube. This

flow mode is called the staggered jet mode. On the other

hand, for low pressure at the stagnation point, the liquid

stagnation region does not cause crests to form, and the in-

line jet mode is observed. Like Dhir et al. [49], Armbruster

and Mitrovic noted mode transition hysteresis (mode

transition at distinct G for increasing and reducing flow

rate) solely for the transition from the jet to the sheet mode.

In addition, Armbruster and Mitrovic found the transition

solely dependent on the liquid flow rate.

Fujita and Tsutsui [24,25] defined the two flow modes as

follows: a distinct droplet mode—liquid initially falls as jet

and then disintegrates into droplets as the falling velocity

increases; a disturbed jets mode—characterized by the

collapse of neighbor jets, resulting in a sheet, followed by its

rupture. They noted that the transition between the droplet

and the proposed new droplet mode occurred at Reynolds

number around 100 independent of feeding method. In

contrast, the other mode transitions were affected by the

feeder configuration with a decrease in the effects with the

increase in the dummy tube number.

Based on extensive observations of flow mode tran-

sitions, Hu and Jacobi [50] suggested the following flow

modes: the droplet mode, the droplet-jet mode, an unsteady-

jet mode—characterized by a steadiness in the location of

the jet departure site—the inline jet mode, the staggered jet

mode, the jet-sheet mode, and the sheet mode. The flow

modes proposed by Hu and Jacobi are shown in Fig. 3. In

contrast to earlier reports, Hu and Jacobi observed hysteresis

for all transitions. The flow mode was found to be relatively

independent of geometric effects over the range of their

experiments. The effects of gravitational, inertial, viscous

Fig. 2. The idealized inter-tube falling-film modes (Mitrovic [17]): (a) the droplet mode-liquid leaving the tube intermittently; (b) the jet mode-

liquid leaving the tube as a continuous column; (c) the sheet mode-liquid fil forms an unbroken sheet between the tubes.


and surface tension forces are captured by correlating the

transitional Reynolds number to a modified Galileo number,

using a power-law fit, ReZAGab, where A and b are

empirical constants. Data obtained with a concurrent air

flow and velocities up to 15 m sK1 indicated that a flow in

the surrounding vapor affects the transitions involving

droplet modes only. Recently, based on experimental results

with a countercurrent air flow, Wei and Jacobi [51] pointed

out that for low Galileo numbers an air flow destabilizes the

jet and sheet mode, and reduces transition hysteresis.

Few studies concerning the investigation of the mode

Fig. 3. Intertube flow modes for ethylene glycol according to Hu and Jacob

jet-sheet; (f ) sheet mode.

flow on heat transfer enhanced surfaces have been

reported. For R-113, normal propanol, and methanol on

an adiabatic finned surface (1064 fins mK1), Honda

et al. [52] related the mode transitions to the following

dimensionless parameter:

K ZG

s3=4g

rl

� �1=4

(4)

From the droplet mode to the jet mode the transition K

ranged from 0.06 for normal propanol to 0.13 for R-113.

i [50]: (a) droplet; (b) droplet-jet; (c) in-line jet; (d) staggered jet; (e)


For the three test fluids, the jet-sheet mode began at KZ0.32,

and a complete sheet was observedwhenK reached from 0.37

to 0.47. In a similar report for R-113 on finned tubes, Honda

et al. [53] found a significant increase in Re for transition from

the jet mode to the sheet mode with a downward-flowing

vapor. However, for three-dimensional fins this effect was

dramatically reduced due to the promotion of the liquid

distribution by the surface structure.

More recently, Roques et al. [54] investigated adiabatic

flow modes on plain and enhanced surfaces. They proposed

correlations similar to those of Hu and Jacobi [50]. Flow

mode hysteresis effects were not observed. Plain and Turbo-

BII surfaces presented a lower Re at the transition from the

jet to the jet-sheet mode. Lower Reynolds numbers at

transitions concerning droplet and jet modes were noted for

the surface Thermoexcel-C. This behavior was related to the

effects of small fins that enabled the jet mode to remain

stable at low Re. For the Thermoexcel-C and Turbo-Chil the

complete sheet mode began at a relatively high Re when

compared to the others structures.

Fig. 4 shows the mode transitions as given by different

investigators. The figure reflects a significant scatter in tran-

sition data; however, such results are reasonable given the

subjective nature of interpreting two-phase flow regimes.

4. Heat transfer on enhanced surfaces

The use of enhanced (structured) surfaces can provide

heat transfer coefficients approximately 10 times higher than

those obtained on plain surfaces. Furthermore, they can also

improve the liquid refrigerant distribution. The mechanisms

causing the enhanced behavior can be divided into the

following categories: enhanced boiling, achieved by surface

structures that promote bubble nucleation; enhanced con-

vection, due to the effect of surface structures on surface

area, film velocity profile and turbulence, and interfacial

temperature variation and the attendant Marangoni effects.

Summarized in Table 2 are several studies from the

Fig. 4. Comparison of correlations for flow mode transitions on

plain tubes; it neglects transition hysteresis.

literature related to falling films on horizontal, enhanced

surfaces and a summary of the experimental conditions.

Commercial surfaces developed for flooded evaporators

(Turbo-B, Turbo-BII, High Flux and Thermoexcel-E),

condensers (Turbo-CII, GEWA-SE, GEWA-SC, Turbo-

Chil and Thermoexcel-C) and finned tubes are listed in

Table 2. According to this table, no research has been

carried out for new refrigerants (zeotropic blends) or

hydrocarbons. Although not listed in this table, the liquid

feeder devices used in the experiments are similar to the

ones used on plain surfaces research.

In general, convection-enhancing surfaces present higher

heat transfer enhancements at low heat fluxes. According to

Chyu and Bergles [15], the heat transfer enhancement

provided by GEWA-T surface is a consequence of the

increase in the surface area by the fins. Their conclusion was

based on observations according to which h enhancement is

proportional to the increase in the overall surface area. For

an increase of 100% in the surface area provided by helical

grooves, Conti [7] noted an increase of 3.5 times in h

compared to a plain tube. For finned surfaces under

convectively dominated conditions, Liu and Yi [36] found

an increase in h due to surface tension effects and an

increase in the surface area. For a surface with conical

cavities and water as refrigerant, they noted a similar

behavior, in this case due to the increase in the surface area

[36]. For surfaces with longitudinal grooves, Putilin et al.

[34] and Rifert et al. [19] noted an increase between 30 and

90% in h compared to plain tubes. Both studies report higher

heat transfer coefficients in the region close to the end of the

grooves, due to boundary layer disruption [19,34]. On the

contrary, according to Sabin and Poppendiex [8], longitudi-

nal grooves have no effects on the heat transfer coefficient.

This apparent contradiction is related to the groove dimen-

sions, because on the surfaces of Refs. [19,34] grooves

present a depth about 10 times higher than those of [8].

Shallow grooves behave as a simple surface roughness, and

will not affect h for laminar flow. For the experimental

results of Sabin and Poppendiex [8], a diamond-knurled

surface gives the best performance.

At high heat flux, boiling effects dominate and surface

structures that promote bubble nucleation tend to provide

higher heat transfer coefficients. Therefore, at high heat

fluxes Thermoexcel-E and High Flux surfaces give higher

performance than does GEWA-T [13,15,56]. At reduced f,

although bubble nucleation was not observed, Sabin and

Poppendiex [8] used the High Flux surface and noted a heat

transfer coefficient three times that of plain tubes, but Chyu

et al. [11] reported a similar h for these surfaces. According

to Liu and Yi [36], at high heat flux, the surface with conical

cavities presents a better performance than the finned

surface and the Gewa-T surfaces studied by Chyu and

Bergles [15]. Wang et al. [18] optimized the dimensions of

JK-1 surfaces under boiling-dominated conditions. Accord-

ing to Tan et al. [23], the surfaces type JK-2, an evolution of

JK-1 obtained by machining grooves in the surface tunnels,

Table 2

Description of experimental studies involving falling film on enhanced surfaces

Fluid Surface characteristics Dext

(mm)

G (x103 kg

sK1 mK1)

Tsat or Tl

(8C)

f (kWmK2)

[4] Sea water Knurled 50.8 0–228 49–127 0–63.1

[7] Ammonia High flux and helically grooved tubes

with 1100 and 315 groovesmK1

50 3.7–204 22.2 5–16

[8] Ammonia High flux and the following surface

preparations: turned and stripe-

burnished, diamond knurled, straight

knurled and covered with rough nickel

25.4 3.7–37.1 12.8–23.9 3.2–25.2

[11] Water GEWA-T19C, GEWA-T26B, high flux 25.4 37–110 99.4 2–208

[13] Water High flux, GEWA-T19C, GEWA-T26B

and thermoexcel-E

25.4 21–210 99.4 0.6–208

[15] Water GEWA-T19C, GEWA-T26B,

thermoexcel-E, high flux

25.4 28–212 99.4 1–130

[16] Water and ethyl alcohol High flux 25.4 2.5–50 45, 57 0–80

[18] R-113 15 Distinct configurations of JK-1 tube

that presents a porous structure

– 32–86 47 7–80

[19] Water Longitudinally-profiled tubes 38.0 40–400 40–100 15–75

[21] R-11 Similar to JK-1 with addition of a

protuberance. Tubes with distinct

protuberance configurations.

18 8–91 23.5 1–43

[23] R-113 JK-1 and JK-2 (a second generation of

JK-1 tubes)

22.0 32–96 47.2 7.3–72.7

[26,30] Mixtures of R-134a and the

polyol-ester oils: 32 cs/40 8C

and 68 cs/40 8C u up to 5%

GEWA-SE, GEWA-SC, Turbo-B,

Turbo-CII, finned tubes 1024 fins mK1,

1575 fins mK1

19 6.5 2 5–40

[34] Water 20 Distinct configurations of

longitudinally profiled tubes

30, 38 40–200 42–100 15–75

[36] Water and R-11 Surface with conical cavities, and a

helically finned tube 1429 fins mK1

18 15–354 23.5, 99.4 2–500

[54] Water, glycol, and

water glycol mixtures

Turbo-BIIi, Turbo-Chili, thermoexcel-Cii 12.7ii,

19.1i0–210 15–35 0

[55] Ammonia Finned 1575 fins mK1 and corrugated

tubes

19 6.95–39.4 K23.3–10 10–80


achieves a heat transfer coefficient that is 50–190% higher

than that of JK-1, as can be noted in Fig. 5. The experimental

points shown in this figure were digitized from the

publication. This improvement results from greater rough-

ness in the tunnels of the JK-2 than in the JK-1. The

roughness increases the number of nucleation sites. In

addition, at high heat flux the internal grooves in JK-2

improve the liquid distribution on the surface through

capillary effects [23]. Moeykens et al. [30] observed that

enhanced boiling surfaces gave a higher performance than

finned tubes and a lower performance than the surfaces

developed for condensers. Fig. 6 summarizes these results

and also shows the experimental data of Webb and Pais [57].

According to Fig. 6, the pool boiling on the Turbo-B surface

gives the highest performance.

Liu and Yi [36] defined the convective and boiling

regimes for falling films. In the convective regime, h is

constant, while in the boiling regime h increases with f.

They observed both regimes independent of the surface

configuration. Wang et al. [18] using boiling-enhanced

surfaces, and Zeng et al. [55] using finned and corrugated

surfaces, observed the boiling regime only. On the other

hand, Kuwahara et al. [21] pointed out a marginal effect off

on a boiling-enhanced surface despite the occurrence of

bubble nucleation. Moeykens et al. [30] noted that the heat

transfer performance increased with f, reached a maximum,

and then declined with a further increase in heat flux. The

decrease in h is most likely due to the partial dryout. A

distinct behavior is observed for GEWA-SC whose

performance is weakly dependent on f. These behaviors

are also displayed in Fig. 6. The surfaces Thermoexcel-E,

JK-1 and JK-2 use superficial structures characterized by

minute parallel tunnels with tiny holes (porous) to connect

to the outside surface. The heat transfer enhancement

achieved by these surfaces is associated with the heat flux

level and is related to liquid suction and bubble ejection

through the pores in a manner similar to the mechanism

proposed by Nakayama et al. [58] for pool boiling [15,18].

On the basis of this understanding, Wang et al. [18]

suggested increasing the pore diameter with f.

Fig. 5. Falling film heat transfer results of the JK-1 and JK-2

enhanced surfaces from digitized data of Tan et al. [23]. R-113,

TsatZ47.2 8C, GZ0.0963 kg mK1 sK1.


In general, at low heat fluxes, the falling film provides a

higher heat transfer rate than does pool boiling. This differ-

ence increases for convective-enhanced surfaces [15,18,

21,36,56], and it is related to increased convective effects for

falling film relative to free convection, the main heat transfer

mechanism in incipient pool boiling. At high heat fluxes, this

effect diminishes due to the dominance of boiling effects. The

heat flux at which these mechanisms compete depends on the

surface structure [15,21,36,56]. Hysteresis effects (distinct f

vs. (TwKTsat) curves depending upon whether the surface has

been going through a heating or cooling process) were noted

for boiling-enhancing surfaces in the following Refs. [11,13,

15,23,56]. In contrast, Kurahara et al. [21] noted small

hysteresis effects, though they obtained experimental results

for boiling-enhanced surfaces.

Without partial dryout on the surface, the flow rate

affects h solely through its impact on convection [15,21,36,56].

Wang et al. [18] noted an increase in h with G for boiling-

Fig. 6. A comparison between the results of R-134a fromMoeykens

[26] for falling film evaporation on single plain, and enhanced

surfaces at TsatZ2 8C, and the data from Webb and Pais [57] for

pool boiling on enhanced surfaces at 4.4 8C.

enhanced surfaces. For finned surfaces and standard nozzles,

Zeng et al. [55] observed that at high Tsat the effects of G are

related to the heat flux level. At high f, h increases with G as

a result of the decrease in the dry area on the tube. An

opposite trend is observed at low f due to the increase in the

film thickness on fin tips in the absence of partial dryout.

Using finned surfaces and R-11, Liu and Yi [36] noted a

maximum h value for a Reynolds number of 250 and a

constant heat transfer coefficient at ReO1000. For a surface

with longitudinal grooves, Rifert et al. [19] observed an

increase in h with G, independent of f the magnitude of this

effect was related to the groove dimensions. For a similar

surface structure, Putilin et al. [34] noted that the degree of

heat transfer enhancement in relation to the plain surface

increases with G.

At high saturation temperatures, Zeng et al. [55] noted an

increase in h with an increase in the nozzle height and a

reduction in the nozzle angle. According to Chyu and

Bergles [15,56], the liquid feeder height does not affect the

heat transfer coefficient for boiling-enhanced surfaces, due

to boiling dominance effects, or for convective-enhancing

surfaces, due to the reduction in the effect of the impact of

the liquid by the fins. In the case of a High Flux surface at a

low heat flux they noted that the nozzle height affected h in a

similar manner as for plain surfaces.

According to Moeykens et al. [30], small concentrations

of a lubricant can considerably increase the heat transfer

performance. The oil concentration at which the optimal

performance was observed decreased with an increase in f.

This behavior was related to the foaming effect of the oil and

was noted for the Turbo-CII and a finned surface

(1575 fins mK1).

5. Falling film on bundles of horizontal tubes

In contrast to the studies of a single tube, for which the

surface is generally heated by an electric current, the heating

effect was usually provided by the flow of a heated fluid in

the tube bundle studies. Table 3 describes the experimental

data bank of studies directed at falling-film tube bundles.

The principal conclusions of these studies are discussed in

the following paragraphs.

In the ideal case, the falling film would be uniformly

distributed on the evaporator surface; however, maldistribu-

tion effects and even partial dryout occur in applications

where a uniform distribution is not achieved. When dryout

occurs, the heat transfer coefficients are higher for the upper

tubes due to partial dryout on the lower surfaces [38,58].

When all surfaces are wet, the upper tubes still exhibit a

higher h, due to the impact of the liquid from the feeder [70],

and the local increase in G from row to row because of the

irrigation caused by interstitial drizzles [65]. In a square-

pitch arrangement, Moeykens et al. [67,68] using R-134a

noted a higher performance in the first row, while for R-123

they found an increase in h from row to row. A similar

Table 3

Description of experimental studies involving falling film on tube bundles

Fluid Liquid feeder characteristics Tube bundle layout/tube characteris-

ticsa/tube diameter/tube material

[23] R-123, water, glycol, water–glycol

mixtures, alcohol, and hydraulic oil

A reservoir with the low region pre-

senting a form of a semi-cylinder with

regularly spaced holes in its lower

generatrix.

5 Horizontal plain tubes vertically

aligned 1%H%80 mm/1%Dext%80 -

mm/stainless steel

[26] R-134a, R-22, R-123 and mixtures of

these refrigerants with oil lubricant.

Wide-angle low-pressure-drop com-

mercial nozzles; solid pattern, circular

and square plum type; orifices diameter

of 3.97, 4.76 and 5.56 mm nozzle height

of 41.3 and 66.7 mm

20 Tubes in 4 vertical rows; triangular-

and square-pitch/finned tube

(1575 fins mK1), GEWA-SC, Turbo-B,

Turbo-CII and plain tube/Dextz19 mm/

copper

[36] Water and R-11 Feeder with wedge shape and nozzle

width of 1 mm

3 Tubes in a vertical row/plain tube,

surface with conical cavities, and a

helically finned tube 1429 fins mK1/

DextZ18 mm/copper

[38] R-11 Porous sintered tube; tube with holes

along its bottom; and a plate with a row

of holes in its center line

5 Horizontal plain tubes vertically

aligned/DextZ25 mm/copper.

[59] R-22, R-12 and R-113 A perforated tube inside another tube

with drilled holes in its upper generatrix

1 and 3 horizontal rows with 5 vertical

rows, 22 horizontal rows vertically

aligned. Distinct triangular layouts

including 60 tubes/18 mm/stainless

steel

[60] Sea water – /16, 24 and 32 mm/copper

[61] Water A tray with 3 rows of 3 mm holes,

drilled 20 mm apart

3 Horizontal rows with 5 vertical rows/

elliptical and circular/19 mm/aluminum

[62] R-12, R-22 Similar to [59] 5 Horizontal tubes vertically aligned/9

types of porous tubes with coating by

deposition, spraying, and sintering; and

4 types of jacketing tubes/20 mm/

stainless steel and copper

[63] Ammonia Spray nozzles 100 Columns each with 30 plain tubes;

308 triangular layouts/25.4 mm/tita-

nium

[64] Water Distance between the nozzles and tubes

of 76 mm

3 Tubes in a vertical row; 3–2–3

triangular-pitch; and 3 by 3 square

pitch/plain tube, finned tube (1575 fins/

m) and longitudinally groove surface;/

19 mm/stainless steel

[65] Ammonia Standard- and wide-angle commercial

round full-cone nozzles; distance

between nozzles and tubes of 150 mm.

3!3 square-pitch and a 3–2–3 triangu-

lar-pitch/DextZ19 mm/stainless steel

[66] R-134a Wide-angle commercial nozzles that

promote circular and square plumes

(orifices DZ4 mm DZ4.76 mm and

DZ5.56 mm) distances between noz-

zles and tubes of 41.3 and 66.7 mm


pitch/finned tubes 1575 fins mK1/

DextZ19 mm/copper

[67] R-134a Wide-angle commercial round full-

cone nozzles (orifice DZ5.56 mm),

distance between nozzles and tubes of

66.7 mm


and square-pitch/finned tube

(1575 fins mK1), GEWA-SC, Turbo-B,

Turbo-CII and plain tube/DextZ19 mm/

copper.

[68] Mixtures of R-123 and a 305 SUS

naphthenic mineral oil; u up to 2.5%

Wide-angle commercial round full-

cone nozzles (orifice DZ4.76 mm and

DZ5.56 mm), distance between noz-

zles and tubes of 44.3 mm

20 Tubes in 4 vertical rows triangular-

and square-pitch/plain; Turbo-B and

Turbo-CII/DextZ19 mm/copper


Table 3 (continued)

Fluid Liquid feeder characteristics Tube bundle layout/tube characteris-

ticsa/tube diameter/tube material

[69] Mixtures of R-134a and oil 340-SUS

polyol-ester ; R-22 and oil 300-SUS

alkyl-benzene; u up to 2.5%

Similar to [67] 20 Tubes in 4 vertical rows; triangular-

pitch/plain tube, GEWA-SC, Turbo-B,

finned tube (1575 fins/m)/DextZ19 mm/copper

[70] Ammonia Standard- and wide-angle commercial

round full-cone nozzles; distances

between nozzles and tubes of 50.8 and

102 mm

3 by 3 square pitch/DextZ19.1 mm/

stainless steel

[71] R-141b Full cone circular spray nozzles with an

orifice diameter of 2 mm

5 Tubes in a triangular-pitch arrange-

ment with 2 horizontal rows/plain tubes

with and without a peripheral liquid

collector/DextZ19 mm/copper

[72] R-11 A tube with holes at its bottom above

each column, and two tubes with holes

on their surfaces positioned in the third

horizontal row

36 Tubes (1024 fins/m) in 5 horizontal

rows; triangular-pitch arrangement/

DextZ19.1 mm/R-11 vapor in counter-

current flow

[73,74] Ammonia Standard- (orifice DZ4.76 mm/spray

angle 908) and wide-angle (orifice DZ3.99 mm/spray angle 1108) commercial

round full-cone nozzles; distance

between nozzles and tubes up to

150 mm

3–2–3 triangular-pitch/DextZ19 mm/

stainless steel

[75] Water Similar to [36] 3 Horizontal tubes vertically aligned/

DextZ13, 20, and 30 mm/copper

a When not specified, consider the experiments as conducted solely for plain tubes.


behavior was measured by Fujita and Tsutsui [38], Liu and

Yi [36] and Liu et al. [75]. Danilova et al. [59] and Bukin

et al. [62] did not note substantial variations along the tube

bundle depth.

In a triangular-pitch arrangement, the flow rate distri-

bution tends to be less uniform than in a square-pitch

arrangement and thus row-to-row variation is larger [26].

Plain surfaces in a triangular-pitch bundle exhibit a decrease

of h from row to row [63,69]. This behavior is noted for low

flow rates [63] and high heat fluxes [69]. Finned tubes such

as GEWA-SC can exhibit maldistribution effects, because

the surface structure inhibits the longitudinal movement of

liquid [64,67]. For the surfaces Turbo-CII and Turbo-B,

Moeykens and co-workers found that the relative perform-

ance among rows varied with the refrigerant, heat flux, and

film flow rate [67–69]. For R-123 and low heat fluxes, the

surface Turbo-B gives the highest performance at the lowest

row [68]. Some methods have been proposed to avoid partial

dryout on the lower rows [71,72]. By adding spray tubes at

the center of the bundle, Tatara and Payvar [72] found an

increase in the thermal performance, relative to a configur-

ation that used only liquid drip tubes above the tube bundle;

they also found, a reduction in the overfeed rate for a similar

global h. Chang and Chiou [71] added liquid collectors to

the bottom of the tubes and thus reduced the difference in the

local h along the bundle depth.

The results of Moeykens et al. [67] for R-134a and

Turbo-B surface reveal that the triangular-pitch bundle

gives higher bundle-averaged heat transfer coefficients than

does the square-pitch bundle at high heat fluxes. An opposite

behavior occurs at low heat fluxes. In the square-pitch

bundle, the effects of f and G are less prominent. On the

other hand, for R-123 and the same surface structure,

Moeykens et al. [68] found that a square-pitch bundle gave a

higher performance. A less uniform flow distribution on

triangular-pitch bundles [64] seems related to higher f

effects for this arrangement. Zeng et al. [73,74] pointed out

that square-pitch bundle tends to provide a higher

performance than a triangular-pitch bundle at low saturation

temperatures, and the triangular-pitch bundle is more likely

to provide a better performance at high saturation tempera-

tures, as shown in Fig. 7. The experimental points shown in

this figure were digitized from the publication. Fig. 7 also

reveals an increase in the heat transfer performance with the

saturation temperature. In this figure, contrary to Moeykens

[26], by comparing heat transfer performance of the distinct

tubes in the bundle, a less uniform flow rate distribution can

be noted for triangular-pitch arrangement. Two distinct

arrangements of the triangular-pitch bundle were compared

by Danilova et al. [59]. A comparison shows that the per-

formance increases with a reduction in the horizontal

distance between vertical rows.

Moeykens et al. [26], using R-134a on tube bundles,

reported the following order of performance as shown

Fig. 7. Falling film heat transfer results of individual tubes on square (filled symbols) and triangular-pitch (blank symbols) plain-tube bundles

from Zeng et al. [73]. Ammonia at (a) TsatZK23.3 8C and (b) TsatZ10 8C, DextZ19.1 mm, Gz0.075 kg mK1 sK1, nozzle height of 50.8 mm,

pitch ratio of 1.25, and standard-angle nozzles.

Fig. 8. Falling film heat transfer results on tube bundles from

Moeykens [26]. R-134a, TsatZ2 8C, triangular-pitch, a nozzle

height of 66.7 mm, and wide-angle nozzles.


in Fig. 8: Turbo-CII, Turbo-B, GEWA-SC, finned

(1575 fins mK1) and plain tubes. Contrary to what is

shown for single surfaces in Fig. 6, in which the

enhanced-condensation tubes give similar performances,

bundles using Turbo-CII provided a performance up to

100% higher than those using GEWA-SC. This behavior can

be related to the restriction of the longitudinal liquid

movement on GEWA-SC by the fins, resulting in a large

variation in the local flow rate that increases in the lower

rows, and promotes the formation of dry patches [63,66].

For R-123, the Turbo-B tube provides a better performance

than does the Turbo-CII [68]. Thome [2] suggested that the

reason why the Turbo-CII outperformed the Turbo-B for R-

134a but the opposite occurred for R-123 could be the large

surface tension difference between these refrigerants and the

distinct mechanisms of the liquid retention provided by

these surfaces.

How much the bundle-averaged heat transfer coefficient

is affected by the flow rate depends on the surface structure

and the bundle layout [67,68]. When the surfaces are wet, a

flow rate increase seems to reduce the global h due to an

increased film thickness [67]. On the other hand, when dry


patches are present, the global h increases with G due to the

decrease in the dry areas [9,28,38,62,71]. These behaviors

are noted in Fig. 8 for Turbo-CII. At low f, the performance

at the lowest flow rate is high; at high f, the performance at

the lowest flow rate is low. For the square-pitch bundle and

at Tsat higher than K23,3 8C, Zeng et al. [70] observed a

slight increase in global h with G, while for the triangular-

pitch bundle Zeng et al. [74] found an insignificant effect of

G, independent of Tsat. No effect of G on global h was noted

in the following Refs. [36,62,75]. Danilova et al. [59] found

that the behaviors for global h with G on tube bundles were

similar to those of a single tube, due to the dominance of

boiling effects, and as pointed out by Fujita and Tsutsui [38],

to the flow regime on the surfaces (laminar, turbulent).

Danilova et al. [59] also suggested that the flow rate be

as high as possible in order to obtain the maximum

evaporation-zone heat-transfer.

The following has been noted for the global h with

increasing f: h decreases due to increased dry areas within

the bundle [38,68,71]; h increases when boiling effects are

dominant [59,62,68,70,74]; h is almost constant under

strictly convective conditions [36,38,59]. An increase in the

vapor flow with f, promoted by the higher evaporation rate,

can also increase the global h, due to the enhancement of the

convective effects (caused by vapor shear), principally on

the upper rows. The behavior of global h with f depends

upon, among other factors, the heat flux itself, G (as shown

in Fig. 8), the refrigerant, the surface structure and the layout

of the bundle [66–69].

Vapor flow in the bundle can promote either an increase

in the film thickness [72] or a reduction in it due to the drag

of liquid [45]. It can also promote either the formation of dry

patches or better liquid distribution [46]. Thus, the effects

of a vapor flow can either increase or decrease the bundle

average heat transfer coefficient. A majority of the studies

listed in Table 3 were carried out on limited rows and do not

include vapor-shear effects. Therefore, when vapor-shear

effects are relevant to the bundle performance, care must

be exercised in trying to extrapolate these results to full

evaporator performance.

Zeng et al. [70,74] observed a decrease in the global h

with an increase in the nozzle height, which was enhanced at

high temperatures. This behavior seems to be related to an

increase in maldistribution effects. For strictly convective

heat transfer, Liu and Yi [36] pointed out that the global h

was not affected by the tube spacing. For square-pitch

bundles and high temperatures, Zeng et al. [70,74] observed

that a wide-angle nozzle provided a higher performance

than did a standard-angle nozzle; however, for a triangular-

pitch bundle the bundle performance was not affected by the

nozzle angle. Chyu et al. [65] developed an analytical

method to predict the liquid flow distribution on the first row

of a bundle. In the same paper, they indicated that, in order

to cover the same area, more square nozzles than round

nozzles are needed. However, they also suggested that the

square nozzles provided an advantage in the uniformity of

the spray flow. The results of Moeykens and Pate [66] can be

related to both of these statements, since they noted that the

square nozzle presented a higher global h than the round

nozzle, and an increase in the nozzle spacing reduced

differences in performance.

Moeykens and his co-workers [68,69] also investigated

the performance of the bundles with refrigerant/oil mixtures.

For refrigerants R-134a and R-22, the addition of oil pro-

moted foaming, which is suggested to enhance the heat

transfer because it helps maintain wetting of the bundle [68].

On the other hand, for R-123, the heat transfer performance

decreased with the addition of oil on the Turbo-B bundle. In

the case of Turbo-CII and plain tube bundles, the oil addi-

tion to R-123 improves the bundle performance at low f.

For this refrigerant, foaming is observed solely with plain

tubes [69]. Apparently, foaming heat transfer enhancement

with the addition of oil cannot be due to foaming alone.

6. Methods to predict the heat transfer rate

6.1. Empirically based correlations

In general, most efforts that involve the development of

heat transfer correlations for falling films on horizontal

cylindrical surfaces are intended for direct application;

therefore, such correlations provide reasonable results in

their range of applicability and can be implemented without

much difficulty. However, because their development is

usually based on a restricted set of data, care must be taken

to apply them within the parameter space of their

development—extrapolation of such correlations may not

yield good predictions. Although existing correlations are

limited in applicability, they are usually cast in terms of

dimensionless parameters such as the Nusselt, Prandtl,

Reynolds, and Archimedes numbers, along with dimension-

less geometric variables, with the hope that such an

approach will elucidate the physical mechanisms or

relationships more clearly than a dimensional approach.

Results from simulations using numerical models have also

been used to develop correlations [76,77].

Proposed heat transfer correlations are summarized in

Table 4, where the experimental data bank used to fit these

correlations is also partially described. The selection of a

correlation should include an assessment of the flow regime

(laminar or turbulent) [10], and the falling-film flow mode

[33]. Furthermore, the prevailing heat transfer mechanisms

should be considered, e.g. for boiling conditions, different

correlations are proposed [10,22,59]. Correlations deve-

loped from experimental results with water are widely

available [17,22,28,31,33,75], as are correlations from

experiments with ammonia [10,55,70,74]. Danilova and

co-workers [59] proposed correlations based on experi-

mental results with the refrigerants of R-22, R-12 and R-113

in a tube bank. The correlations proposed by Fujita and

Tsutsui [25,38] are based on experimental data using R-11.

Table 4

Heat transfer correlations for for falling film evaporation on horizontal cylindrical surfaces

Equ-

ation

Correlation Data bank Comments

[10] (5) NuZ2.2(H/Dext)0.1ReK1/3 Ammonia, single plain tubes Laminar flow Re!1.680PrK3/2

(6) NuZ0:185ðH=DextÞ0:1Prl Turbulent flow ReR1.680PrK3/2

[17] (7) NuZ0:0137ðReÞ0:349Prlððs=DextÞ0:158=

ð1CexpðK0:0032Re1:32ÞÞ

Water, single plain tubes ReO320

[22] (8) NuZ0:042Re0:15Prl Water, single plain tubes Strictily convective DextZ25.4 mm

(9) NuZ0:038Re0:15Prl Strictily convective DextZ50.8 mm

(10) NuZ0:00082Re0:10Prlf0:4 Boiling conditions DextZ25.4 mm

(11) NuZ0:00094Re0:10Prlf0:4 Boiling conditions DextZ50.8 mm

[31] (12) NuZ0:2071Re0:24PrlArK0:111 Water, single plain tubes diameter

effect according to [78]

Properties evaluated at film average

temperature

[33] (13) NuZ0:113Re0:85PrlArK0:27

ð1Cs=DextÞ0:04

Water, ethylene glicol, mixture of water

and ethylene glycol, single plain tubes

Droplet mode

(14) NuZ1:378Re0:42PrlArK0:23

ð1Cs=DextÞ0:08

Jet mode

(15) NuZ2:194Re0:28PrlArK0:20

ð1Cs=DextÞ0:07

Sheet mode

[38] (16) NuZ ½ReK2=3CaRe0:3Prl�1=2 R-11, vertical row of horizontal tubes Top tube aZ0.008 other tubes, aZ0.

010

[55] (17) NuZ0:0568ReK0:0058Prlðpsat=pcritÞ0:323

ðfDext=ðTcritKTsatÞklÞ1:034

Ammonia, single 1575 fins mK1 tube

[59] (18) NuZ0:03Re0:22ðf=hlvrvnlðnl=gÞ1=3Þ0:04

Prlðs=DextÞ0:48

R-22, R-12 and R-113 on tubes

vertically aligned

Strictily convective

(19) h=klðs=gðrlKrvÞÞ1=2Z1:32!

10K3ðf=hlvrvnlðs=gðrlKrvÞÞ1=2Þ0:63!

ðpsat=sðs=gðrlKrvÞÞ1=2Þ0:72Prl

Boiling conditions

[70] (20) NuZ0:0495ReK0:00399Prlðpsat=pcritÞ0:261

ðfDext=ðTcritKTsatÞklÞ0:722

Ammonia, 3 by 3 square pitch

[74] (21) NuZ0:0678Re0:049Prlp0:456r ðfDext=

ðTcritKTsatÞklÞ0:704

Ammonia, 3–2–3 triangular-pitch

[78] (22) NuZ0:041Re0:30PrlArK0:04 Water on a vertical row of horizontal

tubes


Recently, Zeng and his co-workers [70,74] developed

correlations based on triangular- and square-pitch bundle

spray evaporation with ammonia.

6.2. Analytically based models

In addition to the empirical correlations cited above, a

number of models have been proposed. Typically, these

models classify the flow and heat transfer as shown in Fig. 9: a

free fall, jet impingement, thermal developing, and fully

developed region.LocalNusselt numbers are obtained through

the application of continuity, momentum and the energy

equations for each of these regions. Such modeling can either

result in simple correlations involving dimensionless para-

meters, or a solution obtained through numerical methods.

In general, differences between the models are due to

how the flow is classified (i.e., the above mentioned

regions), the model used for the jet impingement region,

initial and boundary conditions, the falling film modes, and

the flow regime, either laminar [6,8,13,14,40,75,79] or

turbulent [5,75,76,80]. A range of turbulence models has

been considered by those developing falling-film models.

Assuming the effects of waviness at the liquid–vapor

interface are similar to those for vertical falling films,

Kocamustafaogullari and Chen [40] and Rogers [79] applied

corrections for such effects to the empirical correlations that

were proposed by Zazuli [40] and Kutateladze and Gogonin

[81], respectively. It is interesting to note that Marangoni

effect is not typically included, but some cases it might be

important (such as for a subcooled film [79]). In most

models, heat transfer is considered to result in sensible

heating or thin-film evaporation; however, Lorenz and

Young [39] suggested a model based on the assumption that

evaporation on the heating surface was due to the bubble

nucleation. These effects are modeled through a correlation

for pool boiling [82] considering a uniform nucleation along

the heating surface perimeter. Their approach does not agree

with experimental behaviors described earlier, according to

Fig. 9. Illustration of falling film regions adopted in the models, and the heat transfer coefficient distribution along the surface perimeter

according to experimental results, and models from distinct authors.

Fig. 10. Effects of film Reynolds number on the falling film Nusselt

number of a plain tube according to distinct models. R-22, TsatZ0 8C, a feeder height of 0.003 and a tube diameter of 25.4 mm.


which high intensity in bubble nucleation was noted on the

tube bottom. Parken [6] and Saiz Jabardo [83] suggested a

study of the nucleation criteria for thin films, related to the

one proposed by Bergles and Rohsenow [84]. Finally, only

the model developed by Liu [5] includes the effects of a

concurrent vapor flow.

Fig. 9 also shows the local h along the surface perimeter

according to the experimental results of Liu [5] and Parken

[6], and the models by Chyu and Bergles [14], Sabin and

Popendiex [8], and Fujita and Tsutsui [80]. Generally

speaking, the models by Chyu and Bergles [14] and Fujita

and Tsutsui [80] deviate significantly from the experimental

results of Liu [5]. Distinct differences can be noted near the

tube bottom, due to the fact that the effects of heat transfer

enhancement in this region are not modeled. The model of

Chyu and Bergles does not predict the decrease in h near the

tube bottom, related to the fact that the fully developed

region is not present. In the case of the Sabin and

Popendiex’s model, lower heat transfer coefficients can be

noted near top of the tube, because they considered only a

thermal developed region. Fig. 10 shows the flow rate

effects on the overall Nusselt, as predicted by the models of

Chyu and Bergles [14], Sabin and Popendiex [8], and Fujita

and Tsutsui [80]. The models of Sabin and Popendiex [8]

and Fujita and Tsutsui [80] for laminar film flow exhibit a

decrease in Nu with Re, independent of the Reynolds

number range. This behavior is simply due to an increase in

the film thickness with liquid flow rate. For Reynolds

numbers lower than 100, all the model results are similar.

Distinct trends can be noted at higher Reynolds numbers,

where the models proposed by Chyu and Bergles [14] and

Fujita and Tsutsui [80] for the turbulent flow predict the

Nusselt number to increase with Re. In the model of Fujita

and Tsutsui, the trend is caused by an increase in the film

temperature gradients near the heating surface, because

turbulence effects increase with the flow rate. The observed

trend at high Re for the model of Chyu and Bergles is related

to the changes in area associated to the development region

that occur with changes in flow rate. It is interesting to note

that in the case of a sufficiently high flow rate, the fully

developed region is not present. Therefore, according to this

model, the minimum in Nu with Re is not related to a

transition in the film flow regime from laminar to turbulent,

but rather it is due to development effects.

7. Conclusions

From this review, the following conclusions can be drawn:

The parameter space relevant to falling-film evaporator

performance is large and complex; despite numerous

studies, even some of the basic mechanisms responsible


for heat transfer behavior remain unclear. In particular,

the conditions for incipient nucleate boiling need to be

investigated, because the occurrence of nucleate boiling

and its impact is obfuscated by the effects of flow rate,

fluid properties, temperature and heat flux.

In general, enhanced surfaces provide higher heat

transfer performance than do plain tubes; however,

confidence in the predicted enhancement is undermined

by complexity in the heat transfer dependence on

geometry, tube layout, and operating conditions. Special

attention must be directed not only to the optimization of

enhanced tube geometry but also to the definition of the

conditions in which enhancements can be clearly

identified and quantified.

Bundle depth effects related to liquid maldistribution and

partial dryout remain unclear. Liquid distribution has a

dramatic impact on evaporator performance. Because

they are important and not well understood, additional

experiments on bundle-depth effects should be under-

taken. The results of such studies can be used in the

development of methods to avoid dry regions and to

quantify flow non-uniformity effects on performance.

Apparently, the presence of oil can enhance the heat

transfer coefficient by 100% under certain conditions,

but it can have a deleterious effect under other conditions.

Systematic experiments with different refrigerant-oil

mixtures, surface structures, and geometric parameters

are necessary to understand this behavior and develop

reliable design tools.

Several models focusing on the prediction of h have been

proposed. However, in general, they do not include

Marangoni effect, vapor-shear effects, interfacial wavi-

ness, or nucleate boiling effects. Empirical correlations

are strongly dependent on specific operating conditions

under which they were developed, and great care must be

exercised in trying to generalize such relations. Further

experimental work is needed before generalized corre-

lations can be developed; carefully considered experi-

ments should be undertaken to broaden the current

parametric space for which data are available and to

resolve contradictions in the extant data.

The falling-film evaporator meets many of the needs of

the air-conditioning and refrigeration industry. The

thermal performance of falling-film heat exchangers is

excellent—it is thermally superior to flooded evaporators

and competitive with plate heat exchangers. Falling-film

heat exchangers are tolerant of contaminating gases and

can probably operate with a lower refrigerant charge

than plate heat exchangers.

Acknowledgements

The first author gratefully acknowledges support through

a post-doctoral assistantship given by the Conselho

Nacional de Desenvolvimento Cientıfico e Tecnologico,

CNPq, Brazil. Both authors acknowledge support through

the Air Conditioning and Refrigeration Center at the

University of Illinois. We are also deeply grateful to Ms.

Xuli Tang who provided significant editorial assistance in

the preparation of this manuscript.

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Falling-film evaporation on horizontal tubes—a critical review

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