Mourad Belghazi

André Bontemps

Christophe Marvillet

Condensation heat transfer on enhanced surface tubes: experimental results and predictive theory

Keywords: Bundles, Condensation, Finned Surfaces, Zeotropic Mixture, Horizontal Tubes

Introduction

A large number of specifically designed enhanced surface tubes have been tested to find the best surface geometry for condensing either pure fluids or vapor mixtures. These surfaces can be classified according to three types: one-dimensional surfaces ͑smooth tubes͒, two-dimensional surfaces ͑with transverse plain fins͒ and three-dimensional surfaces ͑with interrupted fins, spines, etc . . . ͒. Theoretical models to predict the heat transfer coefficient for single low-finned tubes with trapezoidal ͑or rectangular͒ fins have been well developed since the 1940s, in particular by the pioneering work of Beatty and Katz ͓1͔. Their model assumed that condensate is drained via gravity only. They neglected surface tension forces, which generally have an important role at the fin tip, since they are responsible for the draining of condensate from the tip to the fin flanks, and because the major part of heat transfer occurs at the fin tip. The surface tension forces also have a non-beneficial effect due to condensate retention along the underside of the tube. Theoretical models combining both gravity and surface tension forces, are used to predict the Heat Transfer Coefficient ͑HTC͒ of a single horizontal tube with sufficient accuracy ͑Karkhu and Borovkov ͓2͔, Webb et al. ͓3͔, Honda and Nozu ͓4͔, Adamek and Webb ͓5͔, Rose ͓6͔, Sreepathi et al. ͓7͔͒. The most simple proposed by Rose ͓6͔, is a semi-empirical model for a horizontal tube having trapezoidal fins. An enhancement ratio ⌬T is defined as the ratio of the heat transfer coefficient for a finned tube to that for a plain tube, based on plain tube area at the fin root diameter for the same ⌬T (⌬TϭT sat ϪT w ). To compare his model to experimental results, Rose used various finned tubes with different pitches, heights and diameters as well as various fluids ͑water, ethylene glycol, methanol, R113, R11, R12 . . . ͒.

Since the work of Gregorig, ͓8͔, many theoretical studies to optimize the fin profiles of two-dimensional circumferential fins have been carried out. Adamek ͓9͔ in his theoretical approach assumed the condensate to be drained by surface tension forces only and showed that around the fin crest the best heat transfer is given by a profile curvature depending on the path length at a power of Ϫ0.5 instead of 2.0 as proposed by Gregorig. More recently, Zhu and Honda ͓10͔ and Honda and Kim ͓11͔ have performed numerical calculations to optimize the fin profiles of twodimensional circumferential fins.

There are other numerical approaches to optimize enhanced surfaces. Honda and Makishi ͓12͔ in a two dimensional adaptation showed that by creating a circumferential rib on a fin, the values of the HTC can be 27 to 58 percent higher than the best performing fin profile proposed in the previous studies. Further threedimensional adaptations to extended surfaces have been carried out. The first systematic investigation was by Webb et al. ͓13͔ but does not allow a conclusive opinion to be drawn. Honda et al. ͓14,15͔ compared the heat transfer performance of several twodimensional and three-dimensional fin geometries. Their results showed that the heat transfer performance of the best twodimensional and those of the tested three-dimensional tubes are comparable. A specific type of three-dimensional fin was realized by Wang et al. ͓16͔ by creating radial ridges on the fin flanks. They found that the heat transfer performance was 30 to 40 percent higher than commercially available three-dimensional fin tubes.

The results obtained for a single tube cannot be extended to a tube bundle and a fin profile optimized for a single tube can be non-optimized for a tube bundle making, these models for a single tube inapplicable to tube banks, since the heat transfer in the lower rows is affected by condensate inundation and the HTC is lower for these tubes. It has been shown that, in this case, threedimensional geometries are not favorable ͑Webb and Murawski ͓17͔, Honda et al. ͓14,15͔͒. In the literature there are several approaches to this problem. The simplest consists of multiplication of the heat transfer for a single tube by a factor less than unity, taking into account the row position in the bundle.

In this paper, experiments were carried out to determine the HTC during condensation of R134a and a zeotropic mixture of R23 and R134a, on horizontal tubes with three-dimensional enhanced surfaces. A new type of notched fin tube ͑called Gewa Cϩ tube͒ has been studied and the results have been compared to those obtained for smooth tubes or integral-fin tubes with trapezoidal fins. This notched tube can be considered as a combination Studies covering the condensation of zeotropic mixtures are essentially confined to flat plates and smooth tubes. Hijikata and Himeno ͓22͔ conducted experiments using horizontal finned tubes during condensation of the binary mixture ͑90 percent R113ϩ 10 percent R114͒, and they found that the tube with high fins ͑3 mm͒ is better than the one with small fins ͑0.8 mm͒. Honda et al. ͓23͔ conducted experiments during condensation of a downwardflowing zeotropic mixture HFC123/HFC134a ͑about 9 percent HFC134a at the test section inlet͒, on a 13ϫ15 (columns ϫrows) staggered bundle of horizontal low finned tubes. Their experimental data show that both the heat and the mass transfer coefficients increased with the row number up to the third ͑or the second͒ row, then decreased monotonically with increasing row number, finally to increase at the last row.

Experimental Apparatus and Reduction of Data

The experimental apparatus consists of a thermosyphon refrigerant loop and a forced circulation coolant ͑water͒ loop ͑Fig. 2͒. The test rig used in this investigation is basically the same as that used in the previous study by Belghazi et al. ͓24͔. In the refrigerant loop the vapor is generated in a boiler heated with hot water which is itself heated electrically. The vapor flows towards the test section, passes vertically downwards and condenses outside the water cooled tubes. The test section ͑Fig. 3͒ is a stainless steel duct and contains a staggered copper tube bank consisting of 13 rows, each of 2 ͑even rows͒ or 3 tubes ͑odd rows͒. The cross-hatched tubes are dummies ͑no heat exchange͒, while the others are active. Half tubes are attached to the vertical walls of the test section in order to eliminate vapor by-pass. A metallic rod with a diameter of 11 mm was inserted in each active tube in order to increase the water velocity. In this way the heat transfer is enhanced on the coolant side. The horizontal tube pitch is 24 mm, whereas the vertical pitch is 20 mm. The length of the tubes is 300 mm. The characteristics of the tested tubes are given in Table 1. Since the water flow rate is equally distributed in all active tubes ͑it is controlled by means of 13 rotameters, one on each row͒, it is deduced from the water flow rate in the coolant loop, measured by an electromagnetic flow meter, with an accuracy of Ϯ0.5 percent. The vapor velocity is less than 2 m/s and the vapor temperature inlet was maintained at 40°C. Temperatures were measured by type E thermocouples ͑Chromel-Constantan͒ with a precision of Ϯ 0.05°C. The vapor temperature is measured by five thermocouples ͑T06, T07, T08, T09, and T10͒ in the test section. These thermocouples indicate the same temperatures (T sat ) during the condensation of HFC134a, in contrast to the condensation of HFC23/HFC134a, where the vapor temperature decreases from the inlet to the outlet of the test section. The temperatures indicated by the five thermocouples are interpolated in order to obtain the vapor temperature in the neighborhood of each row.

In this study, commercial tubes ͑Wieland-Werke AG͒ are used, having a wall thickness of about 1 mm. An indirect Wilson plot method which measures the vapor-side heat transfer coefficient without measuring the wall temperature is employed.

From the measured water temperatures in the mixing chambers at the inlet and the outlet of each tube and from the measured vapor temperature in the neighborhood of each row, the overall HTC is calculated as follows:

ͩ T v, j ϪT c, j,in T v, j ϪT c, j,out ͪ (1)
where j refers to the row number, c to the cooling water, v to the vapor, in and out to the cooling water input and output respectively. The reference area is that outside a bare tube, D r being either the external diameter of a smooth tube or the diameter at the fin root for enhanced tubes.

The vapor-side HTC, ␣ e , is calculated via the following relation:

1 ␣ e ϭ 1 U Ϫ 1 ␣ i D r D i Ϫ D r 2 w ln ͩ D r D i ͪ (2)
␣ i is the inner heat transfer coefficient determined with the Gnielinski correlation ͑Gnielinski ͓25͔͒:

Nu G ϭ ͑ f /2͒͑Re c Ϫ1000͒Pr c 1ϩ12.7͑ f /2͒ 1/2 ͑ Pr c 2/3 Ϫ1 ͒ ( 3
)
where f is the friction factor determined from the following expression:

f ϭ͑1.58 Ln͑Re c ͒Ϫ3.28͒ Ϫ2 (4)
Re c is the hydraulic Reynolds given by:

Re c ϭ c V ˙cD h c (4-bis)
The Gnielinski correlation has been chosen because it has a wide range of applicability, 2300ϽRe c Ͻ5 10 6 and 0.5ϽPr c Ͻ2000. Thus, it covers both the transition and the turbulent flow regimes.

In our case, the Reynolds number was varied between 2,400 and 12,000. The inner HTC ␣ i is expressed as:

␣ i ϭB•Nu G • C D h (5)
where the coefficient B is determined by the Wilson plot procedure ͑Wilson ͓26͔͒. To determine the B coefficient a specific loop was built with a water/water countercurrent double pipe heat exchanger. The inner tube is the same as used in the condensation experiments. To enhance the accuracy on the ␣ i value, the outer HTC in this specific loop was maintained to a high value. The uncertainty ␦B was determined using Moffat's method ͓27͔. Table 2 gives the B values for all tubes tested. The relative uncertainty of the vapor-side HTC is strongly depending on the experimental conditions. For example, for condensation on the first row the uncertainties are less than 20 percent, 17 percent, 21 percent, 17 percent, 14 percent, and 15 percent for the K11, K19, K26, K32, K40, and Gewa Cϩ, respectively. For the whole bundle, the uncertainties are reported on the figures. Details of the uncertainty calculations are given in the appendix.

Experimental Results

Pure Fluid "HFC 134a… Single Tube. Figure 4 shows the evolution of the HTC of the first row with temperature difference ⌬T, during condensation of pure HFC134a on all tubes tested and on a smooth tube ͑Belghazi et al. ͓24͔͒. It can be seen that K32 has the best performance compared to the other trapezoidal fin tubes. A fin spacing of about 0.6 mm is then an optimum in order to have the best heat transfer coefficient during condensation of HFC134a. The notched fin tube presents a better HTC than the K32 tube, because notches located at the middle of the fin height enhance surface tension effects at the fin tip. The film condensate is thinner and heat transfer performances are better.

To predict the Gewa Cϩ HTC a theoretical model based on the Nusselt approach but taking the surface tension into account, has been developed. Tube Bundle. Figure 5 shows the evolution of the heat transfer coefficient along the bundle. It can be seen that the inundation effect ͑impinging of deep rows by condensate flowing from upper rows͒ is important for Gewa Cϩ tubes in contrast to trapezoidal fin tubes ͑Signe, ͓28͔͒ where the deterioration of the HTC is not important. It is also noticed that the higher the vapor mass velocity G, the greater the Gewa Cϩ HTC deterioration in the tube bundle, in contrast to the integral fin tubes where the deterioration of the HTC is more important when G decreases ͑Belghazi, ͓29͔͒. Indeed, the Gewa Cϩ has low notched fins and retains condensate formed on the upper rows. Then, even if the vapor mass velocity increases, the inundation effect controls the heat transfer because the condensate flow increases also.

Mixtures

Single Tube. Figure 6 shows the evolution of the HTC during condensation of two mixtures ͑3 percent and 6 percent HFC23͒ of HFC23/HFC134a on K19 and Gewa Cϩ tubes. A deterioration of the mixture HTC is noted due to the mass transfer induced by the more volatile component ͑HFC23͒ which accumulates in the liquid-vapor interface and constitutes a diffusion layer which acts as a thermal resistance. Such deterioration has been also observed by Hijikata and Hemino ͓22͔, who measured the vapor-side HTC during condensation of R113 and several compositions of the mixture R113/R114.

Contrary to the case of the pure fluid it can be seen from Fig. 6 that the Gewa Cϩ has a HTC comparable to that of the K19 tube. Indeed, as the Gewa Cϩ tube has low fins compared to the other fin tubes, its fins are flooded by the diffusion layer ͑Fig. 7͒, and performance is poorer. For 6 percent HFC 23 and for low ⌬T's, where the diffusion layer controls the heat transfer, the K19 and Gewa Cϩ HTC values tend to the smooth tube HTC values, since the diffusion layer is very thick and screens the fins. The finned tube is seen as a smooth tube.

Tube Bundle. During condensation of mixture outside the Gewa Cϩ bundle the HTC may increase or decrease from the top to the bottom of the tube bank, depending on the heat flux ͑Fig. 8͒. Such effects have already been observed by Signe ͓28͔ who noted that the HTC on a bundle of smooth tubes increases throughout the bundle. This effect was explained by the fact that the condensate formed on upper rows disturbs the diffusion layer, which gives an amelioration of the heat transfer.

Theoretical Model

As shown in Fig. 9, the Beatty and Katz model ͓1͔ underestimates the HTC of the Gewa Cϩ tube, because it neglects the surface tension effects which are enhanced by notches located at the fin flanks ͑Fig. 11͒. To develop a model predicting the HTC on the Gewa Cϩ tube, the tube circumference is divided into a flooded and an unflooded part.

The flooded part located at the bottom of the tube is referred to as an area submerged completely by the condensate because of capillary retention. It is assumed that there is no heat transfer in this part of the tube. The retention angle ⌽ ͑Fig. 10͒ is calculated by the Rudy and Webb equation ͓30͔: The model is based on the Nusselt expressions for condensation on a vertical plate ͑Eq. ͑7͒͒, and on horizontal smooth tubes ͑Eq. ͑8͒͒

␣ plate ϭ0.943 ͩ l 3 l ͑ l Ϫ ͒g⌬h l ͑ T sat ϪT w ͒L ͪ 1/4 (7) ␣ tube ϭ0.728 ͩ l 3 l ͑ l Ϫ ͒g⌬h l ͑ T sat ϪT w ͒D ͪ 1/4 . ( 8
)
where L and D are plate length and tube diameter, respectively. For regions I and III where only surface tension forces drain condensate, Nusselt's expression ͑Eq. ͑7͒͒ is modified by replacing l g, which is a gravity volume force, by an equivalent in terms of surface tension.

Generally the condensation of a fluid having a liquid-vapor interface radius ͑see Fig. 12͒ which varies along the wall, induces a pressure variation along that interface. An expression for this was given by ͑Gregorig, ͓7͔͒:

dP l ds ϭ d͑/r ͒ ds (9)
In term of a volume force Eq. ͑9͒ can be written:

dF ϭ d͑1/r ͒ ds dV ( 10
)
where dV is a condensate volume control. For a condensate film surface having two different radii r t and r b as shown in Fig. 12, the curvature derivative can be written as:

d͑1/r ͒ ds Ϸ 1 h ͩ 1 r b Ϫ 1 r t ͪ ( 11
)
where h is the fin height. This nevertheless represents a strong assumption, which will be justified a posteriori.

Combining Eq. ͑10͒ and ͑11͒ gives:

dF dV Ϸ h ͩ 1 r b Ϫ 1 r t ͪ (12)
The Gewa Cϩ HTC, calculated with reference to the surface of tube having D r as a diameter, is a function of the HTCs of regions I, II, III, and IV and is given by:

␣ p A r ϭ͑␣ I A I ϩ␣ II A II ϩ␣ III A III ͒ϩ␣ IV A IV ( 13
)
where is the fin efficiency, given by:

ϭ tanh͑mh͒ mh (14) with mϭ ͩ 2␣ p w t ͪ 1/2 (15)
␣ p being determined by an iterative procedure. Parameters given in Eq. ͑13͒ are defined as follows: where K is the number of elemental parts of the fin ͑region I, II, III plus notches. Fig. 11͒ on one side of a fin flank and p is the fin pitch.

A I ϭ2 ⌽ Kwe 1 /p (16) A II ϭ2 ⌽ Kwe 2 /p (17) A III ϭ2 ⌽ Kzh/pϭ2 ⌽ Kz͑e 1 ϩe 2 ϩe 3 ͒/ p (18) A IV ϭ2 ⌽ KD r b/ p (19)
Assuming that ͑Fig. 11͒: r t ϭt/2; r b1 ϭϪb/4; r b2 ϭϪb/2 the acting force in the region I is given by:

dF dV ͯ Region I ϭ e 1 ͩ 1 r t ϩ 1 r b1 ͪ ϭ e 1 ͩ 2 t ϩ 4 b ͪ (20)
Substituting l g in Eq. ͑7͒ by Eq. ͑20͒ leads to:

␣ I ϭ0.943 ͩ l 3 ͑ l Ϫ ͒⌬h l ͑ T sat ϪT w ͒e 1 ͪ 1/4 ͩ e 1 ͩ 2 t ϩ 4 b ͪͪ 1/4 (21)
In the same manner in region III:

dF dV ͯ Region III ϭ h ͩ 1 r t ϩ 1 r b2 ͪ ϭ 2 h ͩ 1 t ϩ 1 b ͪ (22) ␣ III ϭ0.943 ͩ l 3 ͑ l Ϫ ͒⌬h l ͑ T sat ϪT w ͒h ͪ 1/4 ͩ 2 h ͩ 1 t 1 b ͪͪ 1/4 . ( 23
)
In region II, the condensate is drained by gravity and the HTC is given by:

␣ II ϭ0.943 ͩ l 3 l ͑ l Ϫ ͒g⌬h l ͑ T sat ϪT w ͒e 2 ͪ 1/4 (24)
The HTC in the interfin channel is given using Eq. ͑8͒ by:

␣ channel ϭ0.728 ͩ l 3 l ͑ l Ϫ ͒g⌬h l ͑ T sat ϪT w ͒D r ͪ 1/4 (25)
The condensate formed on fins is collected within the interfin channel, so that the actual HTC corresponding to the region IV is smaller than the one calculated by Eq. ͑25͒ since film condensate is thicker. To take this phenomenon into account another version of the Nusselt formula is used ͑Eq. ͑26͒͒:

␣ IV ϭ1.51 Re f Ϫ1/3 ͩ l 2 l 3 g ͪ Ϫ1/3 (26)
where Re f ϭ4 ⌫ l and ⌫ϭ⌫ channel ϩ⌫ fin

⌫ channel ϭ ␣ channel ͑ T sat ϪT w ͒A IV ⌬h (27) ⌫ fin ϭ ͑ ␣ I A I ϩ␣ II A II ϩ␣ III A III ͒͑T sat ϪT w ͒ ⌬h (28)
Figure 9 shows that the present model predicts very accurately the Gewa Cϩ HTC, without adjusting any parameter. The deviation from experimental results is less than 10 percent.

Conclusion

The present investigation allows the following concluding remarks to be drawn:

• Experimental data for condensation of HFC134a on five commercially available copper integral fin tubes show an optimum fin spacing of about 0.6 mm.

• The Gewa Cϩ tube ͑notched tube͒ has been tested and gives an enhancement of about 30 percent compared to the best integral fin tubes ͑K32͒. Notches drawn on fin flanks enhance the surface tension effect. During condensation of HFC134a, the higher the vapor mass velocity, the greater the Gewa Cϩ HTC deterioration in the tube bundle. However, from an industrial point of view, the usual ⌬T is about 3K, and in this case the inundation effect is not significant.

• For the mixtures, experimental results show that, due to the zeotropic character of the mixture tested ͑HFC23/HFC134a͒, the HTC deteriorates dramatically. Contrary to the pure fluid case, the Gewa Cϩ tube gives no enhancement compared to the K19 tube.

• The model developed for a single Gewa Cϩ tube, takes into account surface tension effects, and predicts accurately the present experimental data.

• Work is currently in progress to develop a model, based on the condensation curve method, predicting heat transfer during condensation of binary mixtures outside a bundle of Gewa Cϩ.

Nomenclature

  of the enhanced tube with a circumferential rib ͑Honda and Kim ͓11͔͒ with the tube having radial ridges on the fin flank ͑Wang et al. ͓16͔͒. The notches seen in Fig.1can be considered as part of a rib and the space between notches as radial ridges. One can expect that such a fin geometry will be efficient in condensation heat transfer.There are few experiments on condensation of HFC134a on low finned tubes. In the work of Blanc et al. ͓18͔ the HTC on trapezoidal fin tubes ͑K26͒ is compared with another type of finned tube as well as with current theories. Honda et al. ͓19͔ measured the row-by-row heat transfer coefficients of HFC134a condensing on a bundle of tubes having 26 fins/inch and a diameter at the fin root of 15.8 mm. Their results are slightly lower than those of Blanc et al., Cheng and Wang ͓20͔, and Agrawal et al. ͓21͔ conducted experiments on condensation of HFC134a using several types of low finned tubes. For a vertical column of three tubes with trapezoidal fins no significant inundation effect is observed ͓20͔. The variation of the HTC in function of ⌬T for a single tube was carried out by Agrawal et al. ͓21͔.

Fig. 1

 1 Fig. 1 Optical microscope view of a notched fin tube "Gewa C¿…

Fig. 3

 3 Fig. 3 Test section

Fig. 6

 6 Fig. 6 Evolution of mixture HTC on Gewa C¿ and K19 tubes

Fig

  Fig. 10 Retention angle

A. Bontemps

	Professor,
	Laboratoire des Ecoulements Géophysiques et
	Industriels (LEGI/GRETh),
	Université Joseph Fourier,
	Grenoble, France,
	CEA Grenoble, 17, avenue des martyrs, 38054
	Grenoble cedex 9, France

  A ϭ heat exchange surface area, m 2 A r ϭ surface of a plain tube, m 2 b ϭ fin spacing, m C p ϭ heat capacity, J kg Ϫ1 K Ϫ1 D 0 ϭ diameter of the metallic rod, m D e ϭ diameter at the fin tip, m D h ϭ hydraulic diameter, m D i ϭ inner diameter, m D r ϭ tube diameter at the fin root, m e 1 ϭ distance from fin tip to notch, m e 2 ϭ distance from notch to fin root, m e 3 ϭ thickness of a notch, m f ϭ friction factor F ϭ force, N g ϭ gravity, m s Ϫ2 G ϭ vapor mass velocity, kg m Ϫ2 s Ϫ1 h ϭ fin height, m K ϭ number of elemental parts on fin's flank L ϭ plate length, m L tube ϭ tube length, m m ˙ϭ mass flow rate, kg s Ϫ1 p ϭ fin pitch, m P ϭ pressure, Pa Q ˙ϭ heat flow rate, W r ϭ curvature radius, m r b1 , r b2 , r t ϭ curvature radii, m s ϭ curvilinear coordinate, m t ϭ fin thickness, m T ϭ temperature, K U ϭ overall heat transfer coefficient, W m Ϫ2 K Ϫ1 V ˙ϭ volumetric flow rate, m 3 s Ϫ1 w ϭ notch width, m z ϭ space between notches, m Greek ␣ e ϭ vapor side HTC, W m Ϫ2 K Ϫ1 ␣ i ϭ inner HTC, W m Ϫ2 K Ϫ1 ␣ p ϭ predicted HTC, W m Ϫ2 K Ϫ1 ⌬T ϭ (T sat ϪT w ) or (T v,j ϪT w ), K ⌬h ϭ latent heat, J kg Ϫ1 ⌫ ϭ condensate lineic mass flow rate, kg s Ϫ1 m Ϫ1 ⌽ ϭ flooding angle, rad ϭ thermal conductivity, W m Ϫ1 K Ϫ1 ϭ dynamic viscosity, Pa s ϭ kinematic viscosity, m 2 s Ϫ1 ϭ density, kg m Ϫ3 ϭ surface tension, N m Ϫ1 ϭ fin efficiency

	Indices
	I, II, III, IV ϭ region's index
	c ϭ coolant
	e ϭ external
	f ϭ film condensate
	G ϭ refers to Gnielinski
	i ϭ internal
	in ϭ water inlet
	j ϭ row index
	l ϭ liquid
	out ϭ water outlet
	r ϭ at fin root
	t ϭ fin tip
	v ϭ vapor
	w ϭ wall
	ϭ refers to surface tension
	Dimensionless Numbers
	Nu ϭ Nusselt number
	Pr ϭ Prandtl number
	Re ϭ Reynolds number

Acknowledgment

The authors acknowledge with thanks Wieland-Werk AG for their contribution to this work.

Appendix

The single sample uncertainty of external heat transfer coefficient, ␦␣ e , is written as:

where ␣ץ e ץU ϭ 1

and ␣ץ e ␣ץ i ϭϪ 1

In the same way:

The flowmeter used has a precision of 0.5 percent, and the thermocouples have an uncertainty of 0.05 K.

Using Moffat's method ͓27͔ it was found that ␦B is equal to 0.1, 0.09, 0.04, 0.12, 0.03 and 0.05 for K11, K19, K26, K32, K40 and Gewa Cϩ respectively.

For each point ␦Nu G is calculated as follows:

where Nu G is given by equations ͑3͒ and ͑4͒.

␦ Reϭ

Finally the maximum relative uncertainty of the external HTC ␦␣ e /␣ e for the first row of the bundle is equal to 20 percent, 17 percent, 21 percent, 17 percent, 14 percent and 15 percent for the K11, K19, K26, K32, K40 and Gewa Cϩ respectively. For the bundle the uncertainties are reported on the figures 5 and 8.


Audrey Monnot

Primius Boldo

Nicolas Gondrexon

André Bontemps

Enhancement of Cooling Rate by Means of High Frequency Ultrasound

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Heat transfer processes are widely used in many industrial applications, such as in chemical, gas, oil, and food industries. Decreasing heat losses and increasing efficiency of the energy transfer processes are of major importance from both economic and ecological viewpoints. Among the new technical solutions that must be developed and optimized in order to improve heat transfer processes is the application of ultrasonic waves. Although the influence of ultrasound on heat transfer has already been reported in the literature, it is interesting to note that all previous studies have been carried out using waves in the lowfrequency range; no work has been published on the application of a high-frequency ultrasonic field.

PREVIOUS STUDIES

Ultrasound refers to waves with frequencies ranging from 16 kHz (human hearing threshold) to 10 MHz. The broad clas-Address correspondence to Professor Andre Bontemps, Université Joseph Fourier, LEGI/GRETh, CEA Grenoble, 38054 Grenoble cedex 9, France. E-mail: Andre.Bontemps@cea.fr sification of ultrasonic waves has been divided into two distinct regions, as illustrated in Figure 1 power ultrasound between 20 and 100 kHz and diagnostic ultrasound between 1 and 10 MHz.

The propagation of power ultrasound in a liquid results mainly in cavitation and acoustic streaming. Cavitation is generally defined as the formation of small bubbles due to local pressure decrease and their subsequent growth and collapse. The implosion of these bubbles near solid surface results in a microscopic hydrodynamic phenomenon such as micro-jet formation or micromixing of the liquid. Acoustic streaming refers to strong convective currents that occur when a liquid is subjected to an ultrasonic field. These convective currents also induce an overall mixing of the liquid [START_REF] Boucher | Sonochemistry at Low and High Ultrasonic Frequencies[END_REF][START_REF] Bergles | Survey and Evaluation of Techniques to Augment Convective Heat and Mass Transfer[END_REF].

The influence of ultrasound on heat transfer processes has been investigated and reported in several previous works [START_REF] Wong | Effects of Ultrasonic Vibrations on Heat Transfer to Liquids by Natural Convection and by Boiling[END_REF][START_REF] Yukawa | The Effect of Ultrasonic Vibrations on Free Convective Heat Transfer from Heated Wire to Water[END_REF][START_REF] Yukawa | Effect of Ultrasonic Vibration on Free Convective Heat Transfer from an Inclined Plate in Water[END_REF][START_REF] Iida | Natural-Convection Heat Transfer in a Field of Ultrasonic Waves and Sound Pressure[END_REF][START_REF] Komarov | Enhancement of Gas Phase Heat Transfer by Acoustic Field Application[END_REF][START_REF] Oh | A Study of the Effect of Ultrasonic Vibrations on Phase-Change Heat Transfer[END_REF][START_REF] Bonekamp | Influence of Ultrasound on Pool Boiling Heat Transfer to Mixtures of the Refrigerants R23 and R134a[END_REF][START_REF] Melkumov | Use of Ultrasound for Intensification of Heat Transfer Process in Heat Exchangers[END_REF][START_REF] Yamashiro | Effect of Ultrasonic Vibrations on Transient Boiling Heat Transfer during Rapid Quenching of a Thin Wire in Water[END_REF][START_REF] Renaudin | Etude et Caractérisation de la Zone Réactionnelle et de la Répartition Énergétique dans un Réacteur á Ultrasons[END_REF][START_REF] Boldo | New Operating Method Improves Calorimetric Measurement of Ultrasonic Power[END_REF]. All of these studies have been carried out using ultrasound operating at a low frequency (20-69.2 kHz) by applying an ultrasonic power ranging from 24 to 600 W. Because these studies have been performed with quite different experimental setups (e.g., frequency, ultrasonic power, heat transfer process), it is difficult to compare the corresponding results from one study to the others. However, the experimental approaches that have been developed can be divided into three main types: 1. the effect of ultrasonic vibration on natural convection heat transfer [START_REF] Wong | Effects of Ultrasonic Vibrations on Heat Transfer to Liquids by Natural Convection and by Boiling[END_REF][START_REF] Yukawa | The Effect of Ultrasonic Vibrations on Free Convective Heat Transfer from Heated Wire to Water[END_REF][START_REF] Yukawa | Effect of Ultrasonic Vibration on Free Convective Heat Transfer from an Inclined Plate in Water[END_REF], 2. the study of phase-change heat transfer by acoustic field application [6-9], 3. the influence of ultrasound on heat exchange process in heat exchangers [START_REF] Melkumov | Use of Ultrasound for Intensification of Heat Transfer Process in Heat Exchangers[END_REF].

Enhancement of Cooling Rate by Means of High Frequency Ultrasound

In all cases, the influence of experimental parameters (e.g., ultrasonic power, frequency, nature of the material) has been investigated with the aim to quantify the effect of the presence of ultrasonic waves on the heat transfer process. It has also been concluded that the application of ultrasound results in an enhancement of the heat transfer, regardless of the heat transfer mode (e.g., natural convection, phase change heat transfer). Moreover, it has been demonstrated that increasing the ultrasonic power leads to an increase of the ultrasonic enhancement. Furthermore, owing to previous studies devoted to the influence of the frequency, it seems that the lower the operating frequency, the higher the ultrasonic enhancement [START_REF] Bergles | Survey and Evaluation of Techniques to Augment Convective Heat and Mass Transfer[END_REF].

The only study related to the use of high frequency ultrasound was initiated in 1994 by Renaudin in order to validate the cooling rate in a sonochemical reactor she had designed [START_REF] Renaudin | Etude et Caractérisation de la Zone Réactionnelle et de la Répartition Énergétique dans un Réacteur á Ultrasons[END_REF]. This reactor operates with ultrasound at 500 kHz and a maximal power input of 100 W. The temperature of the liquid within the reactor is controlled by means of a cooling coil placed into the reactor. This work also demonstrated that high-frequency ultrasonic fields increase the overall heat transfer coefficient up to 37-fold.

All of previous works reported in the literature have shown that in the presence of an acoustic field, the heat transfer process can be greatly enhanced. In all cases, the proposed explanation for such an improvement is related to physical effects induced by the propagation of ultrasonic waves in the liquid. All of these effects create disturbances in the liquid that cause an increased heat transfer (e.g., bulk mixing of the liquid, micromixing near the heated surface).

The aim of the present study was then to compare heat transfer with and without high frequency ultrasound. Preliminary experimental results are reported in this paper.

EXPERIMENTAL SECTION Ultrasonic Reactor

Experiments were carried out using a homemade ultrasonic reactor, which is composed of a cylindrical, double-jacketed glass body, the bottom of which is inserted the emitting system. This emitter system is made of a piezoelectric disk and can be easily removed and changed to modify the ultrasound frequency to be 800, 600, 300, or 20 kHz. The reactor volume is three liters.

Overall Setup

The setup schematic is shown in Figure 2. A copper helical coil (length = 2.5 m, internal diameter = 6 mm, external diameter = 8 mm) is placed within the ultrasonic reactor. This coil is fed with cooling water from below at a constant volume flow rate. Eight sensors are used to measure and follow the evolution of the operating parameters versus time. Six RTD platinum 100 ohm sensors are used for temperature measurement. Cooling water flow rate is recorded using one or two MacMillian turbine flow meters, depending on low or high flow rates. A data acquisition system composed of two 16-bit digital converters (ADAM) is connected to a laptop computer. An ADAM 4015 is used for RTD temperature sensors, and an ADAM 4018 for the flow meter signal. Data transfer to a computer is done by a classical RS232 serial input using an ADAM 4522. In-house software written in Visual Basic is used to display real time values and store measurement values in an Excel spreadsheet-compatible data file. The real time display contains temperature-and flow rate-measured values together with calculated heat flow rates and overall heat transfer coefficients.

Particular attention is given to the evolution with time of the following parameters:

• temperature of the water that initially filled the reactor at several locations (top, middle, and bottom of the reactor), • temperature of the cooling water at the inlet of the coil,

• temperature of the cooling water at the outlet of the coil,

• flow rate of the cooling water in the coil.

EXPERIMENTAL PROCEDURE

Water contained within the ultrasonic reactor is preheated to a constant temperature (40 • C). The corresponding height of water is kept constant during all experiments and is equal to 35.3 cm, which is to say, 2.885 L. The copper coil is initially not filled with cooling water. The experiments start as soon as the coil is fed with cooling water at a constant flow rate (141 ± 2 L • h -1 ) defining the initial time (t = 0). The cylindrical, double-jacketed glass body remains empty in order to limit the heat transfer exchange between preheated water contained within the reactor and the ambient air. It also reduces any heat losses through the external walls of the reactor. Experiments are carried out under the same experimental conditions with and without ultrasound.

Determination of the Heat Transfer Coefficient

Energy Balance

The aim of this study is also to compare the heat transfer between preheated water contained within an ultrasonic reactor and the cooling water flowing through the coil placed inside the reactor, with and without ultrasound. The corresponding heat transfer coefficient (h g ) was estimated by solving the following energy balance in Eq. ( 1):

W = mC p dT dt + h g S ext (T -T ext ) + h g S ref (T -T ref ) (1)
where (T -T ref ) can be used instead of the LMTD due to the low coil water temperature variation.

Measurement of the Ultrasonic Power

In the above energy balance, the power induced by ultrasound (W) is required to solve Eq. (1). This ultrasonic power was determined experimentally by means of an improved calorimetric method developed by Boldo et al. [START_REF] Boldo | New Operating Method Improves Calorimetric Measurement of Ultrasonic Power[END_REF]. This method is classically used for the calibration of sonochemical reactors to estimate their energy conversion yield.

Heat Transfer Coefficient Calculations

Once the ultrasonic power in Eq. ( 1) is known, it is possible to determine the overall heat transfer coefficient of the coil (h g ). Taking into account that the system time constant τ is defined as: [START_REF] Bergles | Survey and Evaluation of Techniques to Augment Convective Heat and Mass Transfer[END_REF] and that the temperature reached in steady state is given by:

τ = mC p h g • S ext + h g • S ref
T eq = h g • S ref • (T ref -T ext ) + W h g • S ext + h g • S ref + T ext (3)
Equation ( 1) is then solved as:

T (t) -T eq = (T 0 -T eq ) exp(-t/τ) (4)
with T 0 being the initial temperature.

It is also possible from collected experimental data to calculate and plot for each time t the quantity ln T (t) -T eq T 0 -T eq = f (t). Assuming the experimental data to be in good agreement with the proposed modeling, the corresponding curve will be a straight line, the slope of which enables one to determine the value of the system time constant τ. It is therefore possible to deduce the value of the overall heat transfer coefficient of the coil (h g ).

First, write Eq. ( 2) in the form:

(h g • S ext + h g • S ref ) = C p • m τ (5)
Next, from Eq. ( 3), it can be deduced that:

h g = [(T eq -T ext ) × (h g • S ext + h g S ref )] -W S ref × (T ref -T ext ) (6)
The overall heat transfer coefficient of the coil is then obtained by substituting in Eq. ( 6) the experimental values for T ext , T ref , T zq , and the value of the term given on the left-hand side in Eq. ( 5). According to Eq. ( 4), calculations of the temperature of the water initially contained within the reactor T (t) can be deduced after integrating the experimentally deduced value of the system time constant τ.

These calculations are performed to ensure that the experimental values are in good agreement with the proposed modeling. A comparison between experimental and calculated curves will also check the validity of the procedure for the determination of the overall heat transfer coefficient of the coil.

RESULTS AND DISCUSSION

Modeling Validation

Sample results are shown in Figure 3 that refer to experiments performed with and without ultrasound operating at 800 kHz. Calculated curves (the solid and dashed lines) were computed from Eq. ( 4) following the procedure described earlier. A comparison of the experimental and calculated curves in Figure 3 indicates that the modeling is in good agreement with the experiments. Such a conclusion can also be extended to all other experiments carried out in this work. As a consequence, this makes the method for determining the heat transfer coefficient valid. Detailed results corresponding to experiments performed at 800 kHz are given in Table 1.

( f = 800 kHz, W = 57.6 W, Q = 141 L • h -1 ) P cal (W) T ref ( • C) T eq ( • C) T 0 ( • C) -1 τ (s -1 ) τ (s) h g (W • m -2 • K -1 )

Experimental Results and Discussion

The average values of heat transfer coefficients were estimated from the solution of the heat balance equation. All those values are reported in Table 2.

Comparison with and without Ultrasound

As it can be seen from values given in Table 2, the heat transfer coefficient of the coil is systematically enhanced by the presence of the ultrasonic field.

Without ultrasound and for given flow rate, the determined overall heat transfer coefficient h g is largely constant (as an example, the average value for 141 L • h -1 is equal to 580 W • m -2 • K -1 ). To quantify the effect of ultrasound, an enhancement factor EF is usually defined as the ratio of the value observed with ultrasound divided by the value under silent conditions. In this case:

EF = h g with ultrasound h g without ultrasound
Owing to values of this enhancement factor given in Table 2 (which range from 1.35 using 20 kHz ultrasound up to 2.04 using 800 kHz ultrasound), it might also be concluded that the presence of the ultrasonic field always results in an enhancement of the overall heat exchange transfer coefficient of the coil. It still remains difficult to compare these values because they were obtained under different operating conditions of ultrasonic power.

(kHz) Ultrasonic power (W) (L • h -1 ) ( W• m -2 • K -1 ) ( W • m -2 • K -1 ) EF (Enhancement

Influence of the Flow Rate

Measurements were performed at 1.6 MHz with a significant flow rate variation (from 7 to 190 L • h -1 ). The corresponding results, reported in Table 2 and Figure 4, confirm the trends observed at 800 kHz. In addition, it can been seen that increasing the coil flow rate allows an increase of the enhancement factor (EF). This result can be explained by comparing the three heat transfer resistances. The internal heat transfer resistance depends on the flow rate. The conduction term through copper is constant and can be neglected. The external heat transfer resistance can have two values, depending on whether the ultrasound power is switched on or off. Then, for low flow rates, even if the external heat transfer resistance is low, the high internal heat transfer resistance is limiting and the EF is low. Increasing the flow rate, however decreases the internal heat transfer resistance so that the enhancement can be detected. A limit appears as the internal heat transfer resistance becomes very low and can be neglected, as illustrated in Figure 4.

Influence of the Ultrasonic Power

According to experiments 3 and 4, a comparison can be made for experiments carried out with the same cooling water flow rate but using two different ultrasonic powers. Owing to values reported in Table 2, increasing ultrasonic power leads to an increase of the overall heat transfer coefficient of the coil. Thus, the EF increase from 1.68 to 1.95 illustrates that the enhancement due to ultrasound increases with the input power.

CONCLUSION

In this work, it has been shown that the heat transfer between a cooling flow and a liquid inside a vessel can be greatly increased by applying an ultrasonic field. The influence of ultrasonic vibrations on the rate of decrease of the bath temperature allowed the quantitative deduction of the increase of the heat transfer coefficient through an enhancement factor. This result, already demonstrated in previous studies with low-frequency waves, has been extended to the high-frequency range (up to 1600 kHz). For the highest frequency, the influence of the flow rate on the enhancement factor has been measured. This preliminary study clearly demonstrates the capacity of ultrasound to be used in thermal as well as chemical processes, and such methods could be of a great interest in batch processes.

Future stages of this work will be carried out under specific operating conditions for which it is expected that no cavitation will occur. This will also help distinguish the contribution of mechanisms induced by cavitation and acoustic streaming on the observed enhancement.

Figure 1

 1 Figure 1 Usual classification of ultrasound.

Figure 2

 2 Figure 2 Schematic of the experimental setup.

Figure 3

 3 Figure 3 Experimental and calculated temperatures as a function of time with and without 800 kHz ultrasound (W = 57.6 W, Q = 141 L • h -1 ).

Figure 4

 4 Figure 4 Influence of the flow rate on the enhancement factor ( f = 1600 kHz, W = 42.3 W).

NOMENCLATURE

  C p water-specific heat capacity, J • kg -1 • K -1 h g heat transfer coefficient at the external wall of the ultrasonic reactor, W• m -2 • K -1 h g overall heat transfer coefficient of the coil, W • m -2 • K -1 m mass ofwater contained in the ultrasonic reactor, kg S ext external exchange surface of the ultrasonic reactor, m 2 S ref heat exchange surface of the coil, m 2 T temperature of water initially contained inside the ultrasonic reactor, • C t time, s T ext temperature of ambient air, • C T ref average temperature (inlet and outlet) of cooling water in the coil, • C T 0 initial temperature, • C W thermal power induced by ultrasound, W cal

Table 1

 1 Example of experimental values of parameters used for the determination of the overall heat transfer coefficient

Table 2

 2 Experimentally determined overall heat transfer coefficients of the coil with and without ultrasound and corresponding enhancement factors

	N •	Frequency	Flow rate	h g without ultrasound	h g with ultrasound