Effect of Vapour Velocity on Condensate Retention Angle , Sample of Term Papers

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International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier.com/locate/ijhmt

Technical Note

Effect of vapour velocity on condensate retention between ﬁns during condensation on low-ﬁnned tubes

Claire L. Fitzgerald, Adrian Briggs, John W. Rose, Hua Sheng Wang ⇑

School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK

a r t i c l e

i n f o

a b s t r a c t

The paper reports experimental results using simulated condensation on horizontal ﬁnned tubes in a vertical wind tunnel. Condensation was simulated using three liquids (water, ethylene glycol and R113) supplied to the tube via small holes between the ﬁns along the top generator of the tubes. Eight tubes with different ﬁn dimensions were used. The results indicate that when the retention angle (measured from the top of the tube to the position where the interﬁn space is completely ﬁlled with liquid) is less than about p/2 at zero air velocity, it increases with increasing air velocity. On the other hand, for cases where the retention angle is greater than about p/2 at zero air velocity it decreases with increasing air velocity. In all cases (all ﬂuids and all tubes tested) the retention angle approaches a value near p/2 with increasing air velocity. Satisfactory agreement was found with observations taken during condensation. Ó 2011 Elsevier Ltd. All rights reserved.

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Article history: Received 1 September 2011 Accepted 29 September 2011 Available online xxxx Keywords: Condensation Low-ﬁnned tube Retention Vapour velocity

1. Introduction Low-ﬁnned tubes are widely used in many condenser applications, particularly in refrigeration and air conditioning. Owing to surface tension effects heat-transfer enhancement in excess of area increase due to the ﬁns may be obtained. As well as enhancing heat transfer by providing an additional drainage mechanism, surface tension has an adverse effect on heat transfer due to capillary retention of condensate between ﬁns inhibiting heat transfer on the lower ‘‘ﬂooded’’ parts of horizontal condenser tubes. For quiescent vapour the problem is now well understood. The extent of retention, characterized by the retention angle measured from the top of the tube to the position where the interﬁn space is ﬁlled with retained condensate, can be calculated with good accuracy (see [1,2]).

For trapezoidal section ﬁns the retention angle, uf (see Fig. 1) is given by Eq. (1),

terms of the ﬁn and tube geometry and the relevant ﬂuid properties [3,4]. The model is theoretically based, involves only two empirical constants and incorporates Eq. (1) to evaluate the retention angle. In industrial condensers, velocity of the vapour can be appreciable. In this case a complete model requires inclusion of vapour velocity in the prediction of both retention angle and heat transfer for the exposed parts of the ﬁn and tube surface. The combined effects of surface tension, gravity and vapour shear stress on condensation on integral-ﬁn tubes are only recently receiving attention. Experimental data are becoming available and are summarized by Briggs [5]. At present there are no reliable models or correlations. A correlation of Briggs and Rose [6] attempted to include these factors in a simple way but with limited success.

uf ¼ cosÀ1

4r cos b À1 qgsdo

ð1Þ

2. Apparatus and procedure The present work is focused on the effect of vapour velocity on retention angle by using simulated condensation readily to obtain extensive data for ﬂuids having different physical properties and for a range of geometrical parameters. Condensation is simulated using three liquids (water, ethylene glycol and R113) supplied to the tube via small holes between the ﬁns along the top generator. The tube under test was located horizontally in a vertical wind tunnel. Eight tubes with different ﬁn dimensions and diameter at the ﬁn root 12.7 mm were tested.

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where r is surface tension of the condensate, b is the half angle at the ﬁn tip, q is density of the condensate, g is the speciﬁc force of gravity, s is the spacing between ﬁns and do is the tube diameter at the ﬁn tip. For quiescent vapour the heat-transfer coefﬁcient is satisfactorily predicted by an algebraic equation in

⇑ Corresponding author.

E-mail address: h.s.wang@qmul.ac.uk (H.S. Wang).

Please cite this article in press as: C.L. Fitzgerald et al., Effect of vapour velocity on condensate retention between ﬁns during condensation on low-ﬁnned tubes, Int. J. Heat Mass Transfer (2011), doi:10.1016/j.ijheatmasstransfer.2011.09.063

C.L. Fitzgerald et al. / International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

Nomenclature d di do dr g h s t u ua uv Rea Rev diameter inside diameter diameter at the ﬁn tip diameter at ﬁn root speciﬁc force of gravity ﬁn height space between adjacent ﬁns ﬁn thickness velocity air approach velocity vapour approach velocity Reynolds number for air, qauado/la Reynolds number for vapour, qvuvdo/lv Greek symbols b half angle at ﬁn tip l dynamic viscosity la dynamic viscosity of the air lv dynamic viscosity of the vapour q density of condensate qa density of air qv density of vapour r surface tension uf ‘‘ﬂooding’’ or retention angle measured from the top of the tube, see Fig. 1

Fig. 1. Retention angle.

The apparatus is shown in Fig. 2. The tubes had 0.4 mm diameter holes drilled between the rectangular section ﬁns along the top generator (see Fig. 3).

One end of the tube was connected to a ﬂuid reservoir via a ﬂexible tube and valve to control the ﬂow rate. A plane Perspex window, located in the tunnel wall opposite the test tube, facilitated visual and photographic observation to determine retention angle. The ﬂow rate was adjusted so that the ﬂuid spilled steadily and uniformly over the tube surface. A hot wire anemometer located above the tube in the centre of the channel was used to measure the air approach velocity. The anemometer was removed prior to photographing the tube. Five tubes (A1-A5, see Fig. 3), had a ﬁn height of 0.8 mm and spacings between ﬁns of 0.5 mm, 0.75 mm, 1.0 mm, 1.25 mm and 1.5 mm and three tubes (B1–B3, see Fig. 3) had ﬁn heights of 1.6 mm and ﬁn spacings of 0.6 mm, 1 mm and 1.5 mm. Tubes A1–A5 and tubes B2–B3 had ﬁn thickness of 0.5 mm. Tube B1 had ﬁn thickness 0.3 mm. The tube diameter at the ﬁn root was

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Fig. 2. Schematic and photo of the apparatus for simulated condensation experiment.

C.L. Fitzgerald et al. / International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

Fig. 3. Finned tubes for simulated condensation measurements.

Table 1 Dimensions of tubes used for both simulated and actual condensation experiments [7,8]. Tube A1 A2 A3 A4 A5 B1 B2 B3 Ca Da do (mm) 14.3 14.3 14.3 14.3 14.3 15.9 15.9 15.9 15.9 15.9 dr (mm) 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 di (mm) 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 s (mm) 0.50 0.75 1.00 1.25 1.50 0.60 1.00 1.50 0.6 1.0 h (mm) 0.8 0.8 0.8 0.8 0.8 1.6 1.6 1.6 1.6 1.6 t (mm) 0.5 0.5 0.5 0.5 0.5 0.3 0.5 0.5 0.3 0.5 Experiment Simulated Simulated Simulated Simulated Simulated Simulated Simulated Simulated Condensation Condensation

a Dimensions of tubes C and D are the same as those of tubes B1 and B2, respectively.

Fig. 4. Comparison of measured retention angle at zero air velocity with Eq. (1).

12.7 mm in all cases. Table 1 summarizes the tube and ﬁn dimensions. For each tube, experiments were conducted using three ﬂuids: water, ethylene glycol and R-113. Before a test, the tube was thoroughly cleaned using a sodium bicarbonate solution and observed to be fully wetted by the test ﬂuid. A small amount of red food colouring was added to water and ethylene glycol to enhance visibility of the retention position. The fact that measurements with zero air velocity agreed with closely with Eq. (1) (see Fig. 4) show that this did not affect the surface tension signiﬁcantly. Photographs were taken for each tube at air velocity intervals of 2 m/s in the range 0–24 m/s.

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3. Results and discussion Fig. 5 shows photographs for tube B2 at zero and at the highest air velocity 24 m/s. It is interesting to note the disturbed liquid ﬁlm at some distance below the retention meniscus at the highest velocity in all cases, presumably due to circulating ﬂow in the wake.

Graphs of retention angle versus air velocity are shown in Fig. 6 for tubes A1–A5 and in Fig. 7 for tubes B1–B3. It is seen that where the retention angle at zero air velocity is less than about 90° it increases (i.e. the retention level decreases) with increasing velocity. Conversely where the retention angle at zero air velocity is greater than about 90° it falls (i.e. the retention level rises) progressively with increasing air velocity. In all cases (i.e. for all ﬂuids and geometries) the retention angle appears to approach a value of around 80–90° with increasing air velocity. Where the retention angle at zero velocity is around 80–90° it is almost independent of velocity. The simulation data are compared with measurements taken during condensation [7,8] by plotting retention angle against Reynolds number for steam (Fig. 8) and for ethylene glycol (Fig. 9).

The condensation data cover a range of pressures from 5 kPa to atmospheric pressure. Despite the fact that in the simulation case (no condensation) there is no transpiration effect on the shear stress at the gas–liquid interface, the simulation and

C.L. Fitzgerald et al. / International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

Fig. 5. Photographs of tube B2 in simulated tests at air velocities of 0 and 24.0 m/s for water, ethylene glycol and R113. Arrows indicate retention positions.

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C.L. Fitzgerald et al. / International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

Fig. 6. Retention angle against air velocity for tubes A1–A5.

C.L. Fitzgerald et al. / International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

Fig. 8. Comparison of retention angles observed during condensation [7,8] and simulated measurements for steam.

Where uf at zero velocity is less than p/2 it increases with velocity in both cases. Unfortunately no forced convection condensation data are available for case where uf at zero velocity is greater than p/2.

4. Concluding remarks A fully predictive heat-transfer theory must incorporate a method for calculating the retention angle. In the case of quiescent vapour the retention angle is determined by a balance of the surface tension pressure drop across the meniscus of the retained condensate and the gravity force on the retained liquid column and can be readily calculated with good accuracy. However, in the presence of signiﬁcant vapour velocity and consequent shear stress on the liquid surface the problem is affected both by the pressure variation around the tube and distortion of the meniscus. Work is currently in progress aimed at developing a model for predicting the retention angle in the presence of signiﬁcant vapour velocity. This should be valid for any ﬂuid and geometry and, on the basis of the present investigation, should satisfy Eq. (1) at zero velocity and approach a value of around p/2 with increasing velocity.

Fig. 7. Retention angle against air velocity for tubes B1, B2 and B3.

condensation data are seen to be in general agreement. It is noteworthy that for the ethylene glycol case where the retention angle is near p/2 at zero velocity it is essentially independent of Reynolds number for both actual and simulated condensation.

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C.L. Fitzgerald et al. / International Journal of Heat and Mass Transfer xxx (2011) xxx–xxx

References

[1] H. Honda, S. Nozu, K. Mitsumori, Augmentation of condensation on ﬁnned tubes by attaching a porous drainage plate, in: Proc. ASME-JSME Thermal Eng. Joint Conf., vol. 3, 1983, pp. 289–295. [2] H. Masuda, J.W. Rose, Static conﬁguration of liquid ﬁlm on horizontal tubes with low radial ﬁns: implications for condensation heat transfer, Proc. Roy. Soc. Lond. A410 (1987) 126–139. [3] J.W. Rose, An approximate equation for the vapour-side heat-transfer coefﬁcient for condensation on low-ﬁnned tubes, Int. J. Heat Mass Transfer 37 (1994) 865–875. [4] A. Briggs, J.W. Rose, Effect of ﬁn efﬁciency on a model for condensation on horizontal integral ﬁnned tube, Int. J. Heat Mass Transfer 37 (Suppl. 1) (1994) 457–463. [5] A. Briggs, Theoretical and experimental studies in shell-side condensation, keynote paper, in: Proc. 6th Int. Conf. on Heat Transfer, Fluid Mechanics, and Thermodynamics, Pretoria, 2008. [6] A. Briggs, J.W. Rose, Condensation on integral-ﬁn tubes with special reference to effects of vapour velocity, Heat Transfer Res. 40 (2009) 57–78. [7] C.L. Fitzgerald, A. Briggs, H.S. Wang, J.W. Rose, Effects of vapour velocity on condensation of ethylene glycol on horizontal integral ﬁn tubes: heat transfer and retention angle measurements, in: Proc. 14th Int. Heat Transfer Conf., Washington, USA, Paper No. IHTC14-22254. [8] C.L. Fitzgerald, Forced-Convection Condensation Heat-Transfer on Horizontal Integral-Fin Tubes Including Effects of Liquid Retention, Ph.D. Thesis, University of London, 2011.

Fig. 9. Comparison of retention angles observed during condensation [7,8] and simulated measurements for ethylene glycol.

Fig. 1. Retention angle.

Fig. 3. Finned tubes for simulated condensation measurements.

Fig. 6. Retention angle against air velocity for tubes A1–A5.

Fig. 7. Retention angle against air velocity for tubes B1, B2 and B3.

References

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