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Heat transfer characteristics in horizontal tube bundles for falling film evaporation in multi-effect desalination system
Desalination 375 (2015) 129–137
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Heat transfer characteristics in horizontal tube bundles for falling film evaporation in multi-effect desalination system Raju Abraham a, A. Mani b,⁎ a b
Scientist-E, National Institute of Ocean Technology, Velachery-Tambram Road, Chennai 600 100, India Department of Mechanical Engg., Indian Institute of Technology Madras, Chennai 600 036, India
H I G H L I G H T S • • • • •
2 dimensional modelling of falling film evaporation Prediction of film coefficient and evaporation for different tube sizes Experimental studies on falling film evaporation Comparison of in-line staggered tube layouts in tube bundle Comparison of CFD, experimental data and published literature
a r t i c l e
i n f o
Article history: Received 20 November 2014 Received in revised form 20 June 2015 Accepted 22 June 2015 Available online xxxx Keywords: Falling film evaporation Single tube Tube bundle Dry out Local and average heat transfer coefficient Mass evaporation
a b s t r a c t Horizontal tube falling film evaporation finds wider applications in multi-effect distillation system in recent years. The latent heat released inside the tube due to condensation of vapor is transferred to the falling film on the outer surface of the tube resulting in convective evaporation of water film. The evaporator consists of multiple rows and columns of horizontal tubes. Heat transfer from condensing film inside the tube bundle is more or less uniform while there is a large variation in heat transfer outside the tube bundle. This paper focuses on Computational Fluid Dynamics (CFD) analysis of falling film evaporation of seawater on a single tube and bundle of tubes using ANSYS Fluent 13.0®. CFD results are validated with published data available in the literature and also with experimental studies carried out. The effect of feed rate, tube diameter, wall temperature, etc. on the heat transfer is studied. Local film coefficient around the tubes of 19.05, 25.4 and 50.8 mm ∅ for different film Reynolds numbers is discussed. It is observed that convective evaporation heat transfer performance increases with feed rate, but decreases with tube diameter. In-line tube configuration is found to be better compared to staggered tube configuration. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Falling film evaporators find more applications in refrigeration and desalination industries due to less liquid inventory, high heat transfer coefficient, low temperature drop, low pressure drop, etc. Falling film evaporation takes place outside the tube geometry with two-phase heat transfer. Convective evaporation as well as nucleate boiling occurs in the film as it flows over the tube depending on the heat flux conditions. There are three modes of flowing film which are drop mode, column mode and sheet mode which is related to the fluid flow rate. Heat transfer coefficient around tube surface is influenced by the film Reynolds number and the mode of the film. Film mode in turn depends on film Reynolds number. Heat transfer in tube bundles compared to a single tube is significant as evaporators and condensers ⁎ Corresponding author. E-mail address: [email protected] (A. Mani).
http://dx.doi.org/10.1016/j.desal.2015.06.018 0011-9164/© 2015 Elsevier B.V. All rights reserved.
made of in-line or staggered tubes of considerable numbers. Most of the theoretical and experimental research on falling film evaporation is based on a single tube. In multi-effect desalination (MED) system, seawater is sprayed over the tube bundle and flows as a thin film over the tubes due to gravity under vacuum conditions. Liquid maldistribution and local dry out are common problems in such systems. Normally upper tubes experience excess flow rate and film thickness while the lower strata in tube bundle have dry out conditions. Experimental investigations conducted in the past show different trends in heat and mass transfer due to the simultaneous occurrence of nucleate boiling and convective evaporation. At lower heat flux only convective evaporation takes place and normally film coefficient increases with film Reynolds number. At high heat flux conditions nucleate boiling takes place as observed in experimental studies and the film Reynolds number has no significant influence. Falling film evaporators normally work under low heat flux conditions with convective evaporation. This paper discusses the Computational Fluid
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Dynamics (CFD) studies as well as experimental investigation on horizontal tube bundle for heat and mass transfer under various operating conditions. A review of investigations on tube bundle was published by Ribatski and Jacobi [1]. Working fluids used in most of the investigations are refrigerants such as R 134a and ammonia. Fujita and Tsutsui [2] carried out experimental studies on 5 vertical tubes with refrigerant R-112 and the highest film coefficient was observed at the topmost tube. Zeng et al. [3] carried out experimental studies on in-line and staggered tubes with ammonia. It was reported that rectangular pitch configuration gave better results. Experimental studies of Moeykens et al. [4] carried out with R-134a and R-123 reported that staggered pitch gave better results compared with in-line tubes at high heat flux conditions. Roques et al. [5] carried out experimental studies with 10 tubes in vertical array using R-134a and observed that film coefficient reaches a stabilized value at Ref = 500. It is also reported that the lower tubes showed a higher film coefficient. Habert M. [6] carried out experimental with R134a and R236fa to study the effects different working fluids, type of tubes, feed rates and heat flux conditions. It was reported that tubes present in the 4th to 6th row gave better film coefficients. Sharma R. and Mitra S.K. [7] conducted studies on tube bundles with 120 rows of 22 mm tube size adopting triangular tube configuration for brackish water at atmospheric conditions. Tube drying and reduction in heat transfer coefficient was observed below Ref = 400. Lower tubes in the bundle experienced reduction in film coefficient and liquid evaporation. Theoretical and experimental investigations on tube or tube bundles were presented by Yang and Wang [8], We Li et al. [9,10], Mu et al. [11], Jani et al. [12] and Shen et al. [13] in recent times. In certain cases the film coefficient increased with feed rate, stabilized or decreased beyond a limit. There observed a gradual reduction in heat transfer coefficient with bundle depth and film dry out occurred in low feed rates. Present study, using CFD and experimental methods, was due to the lack of information on tube bundles compared to single tube and to study the reduction in performance in tubes in the vertical direction in the bundle. A comparison of in-line and staggered tubes were carried out with sea water and fresh water which has applications in seawater desalination. 2. Factors influencing film heat transfer In falling film evaporation, seawater is sprayed on the top of the tube and allowed to flow along the curved tube surface. According to Chyu and Bergles [14] flow region can be divided into four. Liquid jet is impinging on top of the tube where stagnation region is formed. At the impingement zone, the flow takes a sharp turn and because of this the film coefficient is high due to the high velocity gradient. This is followed by the developing region, where the heat transfer coefficient decreases with increase in thermal boundary layer thickness. Heat transfer coefficient further reduces as the thermal layer is fully developed. At the bottom of the tube the thickness of film increases and flow is detached from the tube bottom surface and the schematic details of falling film with four regions is reported earlier by Raju Abraham and Mani [15]. Falling film evaporation is governed by conduction heat transfer across the thin film and convective evaporation from liquid to vapor at the interface. If the heat flux is sufficiently high nucleate boiling takes place at the tube surface in addition to the convective evaporation and bubbles start to form in the film. This further enhances the heat transfer coefficient. As the flow proceeds around the tube, it is accelerated by the gravity force and decelerated by the viscous force. A viscous boundary layer develops until it is extended to the free surface of the film. Chyu and Bergles [14] developed models for heat transfer prediction in the distinct flow regions along the tube surface. This model was later used by Sharma and Mitra [7] for heat transfer prediction for film evaporation of sea water. According to Chyu and Bergles, local heat
transfer coefficient at the tube surface at the stagnation flow zone can be estimated as 2 30:5 d uumax uj 5 j 4 : hs ¼ 1:03 Pr k d wx v w 1 3
ð1Þ
Velocity gradient is constant in stagnation zone and the angle for the region of stagnation is given by θs ¼ 0:6ðw R Þ. Similarly the local surface heat transfer coefficient at the impingement zone is given by Nui ¼
1 hi x ¼ 0:73 Pr3 Rex 0:5 k
ð2Þ
for laminar boundary layer and Nui ¼
1 hi x ¼ 0:037 Pr3 Rex 0:8 k
ð3Þ
for turbulent boundary layer. Impingement angle is estimated by w θi ¼ 2:0 : R
ð4Þ
Film Reynolds number, the ratio of inertia force to viscous force within film, is estimated based on half liquid mass flow rate per meter length of tube. In the thermal developing region, film thermal gradient is developed and major part of heat is utilized for heating of film. The film heat transfer coefficient is estimated based on the heat fluxes at impingement and developing region. The angle for film development is given by 1 3μΓ 4 θd ¼ παR gρ5
hd;ðθi −θd Þ ¼
!13
qd;ð0−θd Þ θd− qd;ð0−θiÞ θi : ðθd −θi ÞðTw −Ts Þ
ð5Þ
ð6Þ
Heat flux is related with film thickness as proposed by Nusselt's theory which is given by "
δðθÞ
#13 3μΓ ¼ : gρ f ρ f − ρg sinθ
ð7Þ
Liquid film thickness gradually reduces from the top of the tube and reaches a constant near the middle and increases then as the film flows toward the bottom of the tube. Theoretical and experimental studies with better measurement techniques in the recent past have proved wide variations in predictions. Mustafa and Negeed [16] proposed correlation for film thickness with tube diameter as a parameter influencing the film thickness. Correlation for film thickness developed by Hou et al. [17], based on experimental studies, incorporates the influence of tube diameter and inter-tube spacing. "
δðθÞ
#13 s n 3μΓ ¼C d ρ f ρ f − ρg g sinθ
ð8Þ
The constants C and n are depending on the angular position of film. In the fully developed thermal region, the thermal gradient is stabilized and heat is transferred to the film surface for convective evaporation. The following correlations are suggested by Chyu and Bergles [14].
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Laminar 1 −1 h fd v2 3 ¼ 1:10Re f 3 k g
Γ ≤ 0:61 ≤ μ
μ4g ρσ 3
−1 11
ð9Þ
Wavy-laminar 1 h fd v2 3 −1 ¼ 0:822Re f 3 k g
4 −1 μ g 11 Γ 0:61 ≤ μ ρσ 3
≤1450 Pr−1:06
ð10Þ
Turbulent 1 h fd v2 3 1 ¼ 3:8 10−3 Re f 0:4 Pr0:65 k g
Γ N 1450 Pr−1:06 μ
ð11Þ
Local and average heat transfer coefficients of tube surface and average liquid film thickness for tube diameter 19.05, 25.4 and 50.8 mm are computed for different film Reynolds numbers using the above correlations as given in Table 1. The film thickness increases with feed rate and it marginally increases with larger tube diameter for the same flow rate. The region of the development zone is increased with feed rate and sometimes the complete film consists of developing region. Average heat transfer coefficient of tube increases with feed rate especially for smaller diameter tubes due to the increased developing region. Flow of liquid film inside the bundle is complex due to the nonuniform distribution and dripping effects or interstitial drizzles and hence very difficult to predict. Flow mal-distribution results in either reduction in heat transfer coefficient due to higher film thickness or local dry out of falling film. Higher tube spacing has the liquid impact effect and hence higher heat transfer coefficient is expected. Similarly the flow of vapor generated in the tube bundle can play an active role in the convective evaporation heat transfer. Thin film is influenced by the vapor shear effects. Increase in tube diameter shows a decrease in film coefficient under non-boiling conditions. Film thickness may increase or decrease depending on the direction of flow of vapor. Summarizing previous analytical and experimental studies, the heat transfer characteristics in a falling film is found to be influenced by feed flow rate, heat flux, position in tube bundle, tube size, inter tube spacing, surface geometry, vapor flow direction, etc. 3. CFD modeling CFD is a modern tool to study complex two-phase heat transfer phenomenon such as falling film evaporation of water under vacuum conditions. For the present studies, horizontal tube of 19.05, 25.4 and 50.8 mm OD are considered. Tube wall is maintained at constant temperature of 64.6 °C and thin film of sea water is made to flow over
Fig. 1. Contour of falling film around a horizontal tube.
it by gravity. The saturation temperature of vapor at 62.6 °C and the feed water temperature are at 58.6 °C respectively. Convective evaporation takes place under vacuum pressure of 217.4 kPa at the corresponding saturation temperature of 62.6 °C. This is typical operating condition for the first effect in a multi-effect desalination system and studies are carried out by varying feed rate, wall super heat, etc. Liquid seawater is assumed to flow from the top to bottom over a single tube as well as bundle of tubes under gravity. Liquid enters through velocity inlet at top and leaves at the bottom boundary pressure outlet. Typical CFD model of falling film over single tube is shown in Fig. 1 for 25.4 mm tube with a uniform velocity 0.09 m/s or film Reynolds number 1250. Thin film is developed around the tube and finally getting detached at the bottom of the tube. ANSYS Fluent® with two-phase Volume of Fluid (VOF) model [18] was used to carry out the flow modeling of a horizontal tube falling film with convective evaporation. Quad-Pave scheme with 10,138 meshes were used for single tube studies. A grid dependence analysis was carried out from grid sizes 2000 with an increment of about 1000. Beyond 10,138 meshes, the accuracy was not improved considerably further, however computing time increased. A time dependence analysis was carried out with a time step of 0.001 s and there was no variation in results beyond 5 s. A mixture of water vapor and liquid is considered in the domain under vacuum conditions. Primary phase was considered as vapor and secondary phase as liquid. Heat and mass transfer due to
Table 1 Details of falling film on tube surface for different tube sizes. do, mm
19.05
25.4
50.8
Ref
173 340 760 1512 173 340 760 1512 173 340 760 1512
δ, mm (90 °C)
0.167 0.210 0.274 0.345 0.175 0.220 0.287 0.367 0.197 0.247 0.323 0.406
Stagnation zone
Impingement zone
∅s, °
hs, W/m2K
0.37 0.73 1.64 3.26 0.28 0.55 1.23 2.45 0.14 0.28 0.61 1.22
4
7.85 × 10 5.59 × 104 3.74 × 104 2.65 × 104 7.85 × 104 5.59 × 104 3.74 × 104 2.65 × 104 7.85 × 104 5.59 × 104 3.74 × 104 2.64 × 104
Developing zone
Developed zone
∅d, °
hd, W/m2K
∅d, °
hd, W/m2K
∅rd, °
hfd, W/m2K
1.24 2.44 5.45 10.9 0.93 1.83 4.09 8.15 0.47 0.92 2.05 4.08
43,280 30,830 7621 6639 43,280 30,830 7621 6639 43,280 30,830 7621 6639
34.86 86.14 ≥180 ≥180 26.15 64.61 ≥180 ≥180 13.07 32.30 94.20 ≥180
6331 7098 8631 10,120 6043 6605 8094 9546 5513 5609 6727 8053
143.5 90.69 0 0 152.6 113.0 0 0 166.3 146.5 83.1 0
6034 5198 4356 3743 6034 5198 4356 3743 6034 5198 4356 3743
Av. h, W/m2K
6510 6572 6734 7081 6286 6225 6417 6783 5898 5570 5614 6001
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variation in feed rate, tube diameter, variation in local and average film coefficient, wall shear stress, tube bundle effects, etc. is discussed in this paper. Heat flux has no significant influence on heat transfer under convective evaporation conditions. More details of CFD modelling is reported in the earlier works by Raju Abraham and Mani A. [19,20]. 4. Experimental studies on tube bundles Experimental studies were carried out on tube bundle with the same configuration as in CFD studies with aluminum tubes of 25.4 mm OD. The set up consisted of an evaporator with 0.5 m OD × 1.5 m long shell with 6 mm thickness. There were 15 numbers of aluminum 6061 tubes of mm OD × 1.4 m long. The tubes could be interchanged as it is fitted with special grommets. Tube configurations could be changed by replacing the tube sheets in the evaporator. Falling water film over the evaporator tubes was heated using electrical heaters inside the tubes. The heater was fixed with temperature controller based on the tube wall temperature. Feed flow rate was varied in the ranges of 800 to 3000 kg/h and feed water temperature in the ranges of 55 to 75°C. Two different configurations of in-line and staggered tube layout as shown in Fig. 2 were used for experiments. Details of experimental set up and measurement are reported in reference [15]. Copper–Constantine thermocouple was used for temperature measurements with an uncertainty of ±0.1 °C. Vacuum transmitter with ±0.2% accuracy was used to measure the vacuum in the evaporator. Glass Rota meters were used to measure water flow rate in circuits with an uncertainty of ±2.0%. An error analysis was carried out for measurement of heat transfer coefficient and it was found that results are within the error limits of ±5.8%. 5. Results and discussion 5.1. Single tube CFD studies were carried out on single tube as well as bundle of in-line and staggered configuration. Experimental study was carried out on tube bundle with in-line and staggered configuration. Both the studies used fresh water (ground water) and seawater at 35,000 ppm salinity as working fluid. 5.1.1. Development of liquid film thickness Table 1 shows the estimated results of water film thickness at 90° of the tube for three different tube sizes using the model suggested by Chyu and Bergles [14]. Higher film thickness is predicted for higher diameter tubes. Increase in film Reynolds number predicts an increase in film thickness. Film thickness doesn't vary considerably with tube
Fig. 3. CFD results of average film thicknesses for different tube sizes.
diameter. Experimental studies of Hou et al. [17] reported that there is no obvious change in the film thickness within a range of 20 to 32 mm tube diameter with Ref in the range of 70 to 574. CFD results of three tube sizes 19.05, 25.4 and 50.8 mm ∅ are plotted and compared with the predictions of Chyu and Bergles and Hou et al. as shown in Fig. 3. No marked difference is obtained for 19.05 mm and 25.4 mm ∅ tubes. However, film thickness is reduced for 50.8 mm ∅ tube and this can be attributed to large contact area for large size tubes. It was difficult to get uniform film thickness below film Reynolds number 400. 5.1.2. Local and average heat transfer coefficient around the tube Local heat transfer coefficient (under non-boiling conditions) is highest at the impinging zone and is gradually reduced as reported by Parken et al. [21] based on the experimental studies on 25.4 and 50.8 mm ∅ electrically heated horizontal brass tubes with distilled water. However, for 50.8 mm ∅ tube, the heat transfer coefficient decreased steadily up to 90° of the tube and then tends to increase as flow approaches the bottom. Heat transfer coefficient increases with feed flow rate and feed temperature. It is reported that the effect of heat flux on heat transfer coefficient is negligible. In the present CFD study, temperature gradient for the thin film around the tube is plotted at a distance of 1 mm as shown in Fig. 4 for film Reynolds number 1250. Steepest gradient is observed at the top of the tube at 0° and the slope gradually reduces until 165° from the tube surface. This shows the gradual reduction of local film coefficient around the tube surface. However, after 165° there is a sharp reversal in the slope of the profile which increases and becomes close to the slope at 0°. At the bottom of the
Fig. 2. Photograph of tube sheet with staggered and in-line layout.
R. Abraham, A. Mani / Desalination 375 (2015) 129–137
Fig. 4. CFD results of temperature gradient around tube wall.
133
Fig. 6. Variation of local heat transfer coefficient around the tube surface with increase in Film Reynolds number.
tube at 180°, heated liquid leaves at temperature higher than the feed inlet temperature indicating sensible heating. Local heat transfer coefficient in the CFD studies were estimated using the temperature gradient at the wall and the temperature difference between tube wall and vapor (Tw − Ts). In the experimental studies, it is estimated from the heat flux measured from heat input to the heater. It is evident from the temperature profile that the heat transfer coefficient is increased at the bottom of the tube due to the effects of film detachment. This is contrary to many of earlier analytical predictions of variations in local film coefficient [22]. CFD results of the local film coefficient around 19.05, 25.4 and 50.8 mm ∅ tubes from the top to the bottom for film Reynolds number 671 is plotted as in Fig. 5. The variations in film coefficient at stagnation, impingement, developing and developed zones, etc. are clearly visible. The top of the tube shows highest value of film coefficient due to the impingement effects. Impingement effect is comparatively less for 50.8 mm ∅ tube due to large fraction of surface area compared to smaller diameter tubes. Local film coefficient is gradually reduced till the bottom end of tube where there is a sharp increase which is highest for the larger tube size. Film coefficient is highly unpredictable in this section and this can be attributed to the dynamic effects of film detachment from the tube surface. Fig. 6 shows the local heat transfer coefficient around the tube for Ref = 1250. It is observed that the local film coefficient for 50.8 mm ∅ tube is increased beyond 90° similar to the observations reported by Parken et al. This must be due to the acceleration of the fluid due to gravity in this section. The local film coefficients match with the correlation discussed by Rogers [22] for four different
Reynolds numbers namely 152, 305, 458 and 611 as given in Table 1. As the feed rate increases the length of region of the development is reduced. The wall shear stress around the tube surface is plotted as in Fig. 7. Wall shear stress is highest at the impingement region and reduces to a minimum value at about 20–30° and gradually increases due to the acceleration of the film. The shear stress gradually increases at the bottom of the tube as liquid flow approaches the bottom of the tube. Undue fluctuations are observed due to the film detachment at the bottom. Average heat transfer coefficient around the tube for 19.05, 25.4 and 50.8 mm ∅ is shown in Fig. 8. Higher film coefficient is observed for lower diameter tubes from CFD as well as empirical relations. This is due to the higher developed length for the higher diameter tubes which reduces the average film coefficient. Decrease in average heat transfer coefficient for lower Reynolds numbers is seen in the empirical results. This is in line with the experimental results of Hu and Jacobi [23] where a gradual increase in film coefficient observed all around the tube when Ref is increased. The increase in Re f increases film thickness and heat transfer is dominated by convection. Conduction resistance and convection play opposite role and hence, film coefficient stabilizes beyond a limit.
Fig. 5. CFD results of variation of local heat transfer coefficient around the tube surface.
Fig. 7. CFD results of variation of wall shear stress around the tube surface.
5.1.3. Effect of wall superheat Evaporation of falling film is not only dependent on the falling film thickness but also on wall superheat. Driving temperature differential for heat transfer increases with wall super heat which enables better film evaporation. Fig. 9 shows the variation in local Nusselt number with varying temperature difference. Saturation temperature and pressure of the vapor region was changed while keeping wall temperature at 64.6 °C and film Reynolds number constant at 1250. The increase in wall super heat (ATe) doesn't have much influence on local Nusselt
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R. Abraham, A. Mani / Desalination 375 (2015) 129–137
compared with experimental results of falling film evaporation presented by Sharma and Mitra [7] conducted at atmospheric conditions at about 80°C. Splashing of water was reported at higher Reynolds numbers causing reduction in evaporation in the experimental studies. 5.2. Tube bundle effects
Fig. 8. Variation of average heat transfer coefficients with film Reynolds number for different tube sizes.
number especially at the impingement or developing region of the tube. Increase in wall super heat must yield higher evaporation of liquid due to the reduction in viscosity due to change in temperature and reduction of film thickness. Thinning of film in-turn improves film heat transfer coefficient. Nusselt number is influenced at the bottom of the tube due to the change in fluid properties. CFD studies show that increase in wall super heat enhances the Nusselt number; however it is at the bottom region of the tube i.e. fully developed region of the tube only. 5.1.4. Mass transfer during evaporation Falling film evaporation occurs by convective evaporation as well as nucleate boiling inside the film depending upon the wall super heat or heat flux conditions. It is difficult to separate both the effects or to model it. The influence of heat flux, feed temperature, feed flow rate, etc. is totally different for both the phenomenon. Mass of liquid evaporated from the thin film is related to film thickness, temperature of the feed, wall superheat and saturation pressure. Mustafa and Negeed [16] used the following correlation for estimating the mass evaporation. me ¼
hAðTw − Ts Þ Cp f ðTs − Twi Þ þ hfg
ð12Þ
Computational results of mass transfer rate from the film for different tube sizes are presented in Fig. 10. Mass evaporation increases with film Ref due to better turbulence, reaches a peak value and then reduces. The increase in film thickness with Reynolds number suppresses the heat transfer and reduces the evaporation rate beyond Ref =750. Average value of evaporation for 25.4 mm ∅ tube is plotted and
Fig. 9. Variation of local Nusselt number around the tube surface for different wall superheat.
CFD modeling of tube bundles with rectangular (in-line) and triangular (staggered) arrangements were considered. As shown in the CFD model in Fig. 11, a rectangular arrangement with 3 vertical columns and 5 rows of tubes is studied. The contour of vapor and liquid is shown and void fraction 1 represents completely vapor region and 0 represents completely liquid region. Interstitial dripping effects, film dry-out etc., are seen at the bottom rows. Film coefficient decreases as the film flows down over the bundle of 10 tubes and stabilizes as shown in Fig. 12. Three different film Reynolds numbers are compared. It can be noted that average film coefficient increases as the feed rate increases and gets stabilized. Numerical studies Jani et al. [12] with Li/Br solution on 20 rows for Reynolds number up to 1500 predicted decrease in heat transfer coefficient at entrance zone and stabilizes the coefficient beyond. Computational studies on different tube sizes also showed that stabilization for tube bundle takes place within the first 10 tubes in the row. The overall reduction in average heat transfer coefficient is related by hb ¼ ht N−0:25 :
ð13Þ
Experimental study of Shen [13] with 25.4 mm ∅, pitch ratio 1.3, aluminum brass tube bundle of 100 in-line rows reported the influence of feed rate and wall super heat. Fresh water was supplied for a range of feed rate 0.03 to 0.07 kg/ms (Ref = 450 to 1250) and a range of temperature 40 to 60 °C. Decrease in the difference in overall heat transfer coefficient was observed for the bundle depth from 15% to 5% for an increase in film Reynolds number from 450 to 1250 for a total temperature difference of 3°C between the inside and outside of the tube. Visual observations on in-line and staggered configuration show that in-line configuration gives a better flow pattern. Non-uniformity in flow is observed in CFD models in staggered tube arrangements compared to square pitch and thus there is large variation from top row tubes in film coefficient. This can be due to the shear effects on film due to the upward flow of vapor and it shall be more predominant in staggered tubes due to the physical proximity of tubes. Heat transfer coefficient with variation in feed flow rate for both the configurations for 25.4 mm ∅ tube with pitch 1.17d is shown in Fig. 13. As the film Reynolds number increases the bundle average heat transfer coefficient increases and stabilizes. The stabilized film coefficient at Ref = 1500 for the in-line bundle is nearly 15% lower than that of the single tube. The staggered arrangement shows 35% lower value for the bundle average
Fig. 10. CFD results of variation of average mass transfer with film Reynolds number.
R. Abraham, A. Mani / Desalination 375 (2015) 129–137
135
Fig. 11. Simulation of flow around a tube bundle.
heat transfer coefficient compared with in-line arrangement. The variation of mass transfer for staggered bundle is 31% lower than that of in-line arrangement. Variation of mass transfer rate for different tube wall temperature is plotted and compared with a single tube as shown in Fig. 14. Evaporation rate increases proportionately with wall temperature and in-line configuration gives better results.
lower values of fluid properties like viscosity and surface tension. Tubes coated with thermal spraying of aluminum particles also tested and enhancement in heat transfer was noticed as shown in Fig. 15. No visible bubbles were observed during experimentation showing the absence of nucleate boiling. More details of experimental investigation, measurements and results are reported in reference [15].
5.3. Experimental studies on bundle effect
6. Conclusions
From the experimental study, it was observed that the in-line configuration of tubes gives a better performance than staggered tubes. In general the film coefficient reaches a peak and then stabilizes or reduces with increase in film Reynolds number. Experimental studies were carried out up to film Reynolds number 800 due to limitations in the set up. Tests were repeated at different Reynolds number for seawater as well as with fresh water as shown in Fig. 15. Fresh water tests with in-line configuration showed better performance. Better distillate production was possible with fresh water compared to seawater due to
CFD study on single tube and a bundle of tubes was carried out and it shows that heat transfer coefficient is highest for the top tube in the bundle and decreases proportionately to the position of tube in the bundle. Bundle depth effect is observed within the first 10 rows of tubes. Heat transfer coefficient is stabilized within first ten rows. As the Reynolds number increases, the film heat transfer coefficient also increases and stabilizes due to the increase in film thickness. Film heat transfer coefficient decreases as tube diameter increases based on the observation on
Fig. 12. CFD results of variation of bundle average wall heat transfer coefficient for 10 tubes.
Fig. 13. Variation of heat transfer coefficient and mass transfer coefficient with Reynolds number for different tube configurations.
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Fig. 14. CFD results of mass transfer rate with tube. Fig. 15. Comparison of experimental results of tube bundle with fresh water and sea water.
three different tube sizes. A sharp increase in local heat transfer coefficient is observed from CFD studies at the bottom of the tube. In-line tube configuration of bundle gives better performance than staggered configuration with same pitch and diameter. Studies with seawater showed a reduction of 15–20% in film heat transfer coefficient compared to fresh water at the same operating conditions. An optimum film Reynolds number of 500–800 is recommended for effective mass transfer in the design of falling film evaporators. In a bundle of tubes heat transfer coefficient stabilizes at a film Reynolds number 1500 approximately and the bundle average film coefficient is approximately 85% of the film coefficient of a single tube for the same film Reynolds number. Nomenclature A heat transfer area, m−2 Ar Archimedes number, g d3o ν−3 Cp specific heat, J kg−1 K−1 do tube outside diameter, m g gravitational acceleration, m s−2 h heat transfer coefficient, Wm−2 K−1 hfg latent heat of vaporization, kJ/kg k thermal conductivity, Wm−1 K−1 N vertical position of tube Nu Nusselt number, hν2/3 k−1 g−1/3 Pr Prandtl number, μCpk−1 R outer tube radius, m film Reynolds number, 4Γμ−1 Ref s tube pitch, m T temperature, K u velocity, m/s w jet width, m Subscripts b bundle d developing e evaporation f liquid fd fully developed g vapor i impingement s saturated t top x local w wall wi water inlet ΔTe local temperature difference for evaporation, K HTC heat transfer coefficient, W/m2 K MTC mass transfer coefficient, kg/m2 s
Greek symbols α thermal diffusivity, m2 s−1 Γ half liquid mass flow rate per length of tube, kg m−1 s−1 δ film thickness, m θ angle along the tube perimeter measured from the apex, ° μ dynamic viscosity, kg m−1 s−1 Φ diameter, mm ρ density, kg m−3 σ surface tension N m−1 v kinematic viscosity, m2 s−1 Acknowledgment Authors acknowledge the financial support received from the National Institute of Ocean Technology, Chennai (NIOT/F&A/PROJ/ EFW01/2010) for the studies.
References [1] G. Ribatski, A.M. Jacobi, Falling film evaporation on horizontal tubes—a critical review, Int. J. Refrig. 28 (2005) 635–653. [2] Y. Fujita, M. Tsutsui, Experimental investigation of falling film evaporation on horizontal tubes, J. Heat Transf. 27 (8) (1998) 609–618. [3] X. Zeng, M.C. Chyu, Z.H. Ayub, Experimental investigation on ammonia spray evaporator with triangular pitch-tube bundle—part I tube bundle effects, Int. J. Heat Mass Transf. 44 (2001) 2299–2310. [4] S.A. Moeykens, John E. Kelly, Michael B. Pate, Spray evaporation heat transfer performance of R-123 in tube bundles, ASHRAE Trans. Am. Soc. Heat. Refrig. Aircondition. Eng. 102 (2) (1996) 259–272. [5] J.F. Roques, V. Dupont, J.R. Thome, Falling film transitions on plain and enhanced tubes, J. Heat Transf. 124 (2002) 491–499. [6] M. Habert, Falling film evaporation on a tube bundle with plain and enhanced tubes(Ph.D Thesis) Laboratory of Heat and Mass Transfer (LTCM), Swiss Federal Institute of Technology Lausanne (EPFL), 2009. [7] R. Sharma, Sushanta K. Mitra, Performance model for a horizontal tube falling film evaporator, Int. J. Green Energy 2 (2005) 109–127. [8] Y. Li, W. Wang, The heat transfer performance of horizontal tube bundles in large falling film evaporators, Int. J. Refrig. 34 (2011) 303–316. [9] W. Li, Xiao-Yu Wu, Zhong Luo, Shi-chune Yao, Jin-Liang Xu, Heat transfer characteristics of falling film evaporation on horizontal tube arrays, Int. J. Heat Mass Transf. 54 (9) (2011) 1986–1993. [10] W. Li, Xiao-Yu Wu, Zhong Luo, R.L. Webb, Falling water film evaporation on newly-designed enhanced tube bundles, Int. J. Heat Mass Transf. 54 (13) (2011) 2990–2997. [11] X. Mu, Shengqiang Shen, Yong Yang, Xiaohua Liu, Experimental study of falling film evaporation heat transfer coefficient on horizontal tube, Desalin. Water Treat. 50 (1–3) (2012) 310–316. [12] S. Jani, M.H. Saidi, A.A. Mozaffari, Tube bundle heat and mass transfer characteristics in falling film absorption generations, Int. Commun. Heat Mass Transfer 30 (4) (2003) 565–576. [13] S. Shen, G. Liang, Y. Guo, R. Liu, X. Mu, Heat transfer performance and bundle-depth effect in horizontal-tube falling film evaporators, Desalin. Water Treat. 51 (4–6) (2013) 830–836.
R. Abraham, A. Mani / Desalination 375 (2015) 129–137 [14] M.C. Chyu, A.E. Bergles, An analytical and experimental study of falling-film evaporation on a horizontal tube, J. Heat Transf. 109 (1987) 983–990. [15] Raju Abraham, A. Mani, Experimental studies on thermal spray coated tubes for falling film evaporation in multi-effect distillation system, Desalin. Water Treat. (2014) 1–12 (ahead-of-print). [16] M. Mostafa Awad, El-Sayed R. Negeed, Enhancement of evaporation of falling liquid film on horizontal tube bundle, International Water Technology Conference, IWTC12, Alexandria, Egypt, 2008. [17] H. Hou, Q. Bi, H. Ma, G. Wu, Distribution characteristics of falling film thickness around a horizontal tube, Desalination 285 (2012) 393–398. [18] ANSYS Fluent® Software Version 13.0. [19] Raju Abraham, A. Mani, L.S.S. Prakashkumar, CFD studies on falling film modes in tube bundles in multi-effect distillation system, Int. J. Environ. Sci. 1 (2013) 2.
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[20] Raju Abraham, A. Mani, Effect of flame spray coating on falling film evaporation for multi-effect distillation system, Desalin. Water Treat. 1–8 (2012) 1944–3994. [21] W.H. Parken, L.S. Fletcher, V. Sermas, J.C. Han, Heat transfer through falling film evaporation and boiling on horizontal tubes, Trans. ASME 112 (1990) 744–750. [22] J.T. Rogers, Laminar falling film flow and heat transfer characteristics on horizontal tubes, Can. J. Chem. Eng. 59 (1981) 213–222. [23] X. Hu, A.M. Jacobi, The inter-tube falling film flow: part 1—characteristics, mode transitions and hysteresis, ASME J. Heat Transf. 118 (3) (1996) 616–625.
Contents lists available at ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Heat transfer characteristics in horizontal tube bundles for falling film evaporation in multi-effect desalination system Raju Abraham a, A. Mani b,⁎ a b
Scientist-E, National Institute of Ocean Technology, Velachery-Tambram Road, Chennai 600 100, India Department of Mechanical Engg., Indian Institute of Technology Madras, Chennai 600 036, India
H I G H L I G H T S • • • • •
2 dimensional modelling of falling film evaporation Prediction of film coefficient and evaporation for different tube sizes Experimental studies on falling film evaporation Comparison of in-line staggered tube layouts in tube bundle Comparison of CFD, experimental data and published literature
a r t i c l e
i n f o
Article history: Received 20 November 2014 Received in revised form 20 June 2015 Accepted 22 June 2015 Available online xxxx Keywords: Falling film evaporation Single tube Tube bundle Dry out Local and average heat transfer coefficient Mass evaporation
a b s t r a c t Horizontal tube falling film evaporation finds wider applications in multi-effect distillation system in recent years. The latent heat released inside the tube due to condensation of vapor is transferred to the falling film on the outer surface of the tube resulting in convective evaporation of water film. The evaporator consists of multiple rows and columns of horizontal tubes. Heat transfer from condensing film inside the tube bundle is more or less uniform while there is a large variation in heat transfer outside the tube bundle. This paper focuses on Computational Fluid Dynamics (CFD) analysis of falling film evaporation of seawater on a single tube and bundle of tubes using ANSYS Fluent 13.0®. CFD results are validated with published data available in the literature and also with experimental studies carried out. The effect of feed rate, tube diameter, wall temperature, etc. on the heat transfer is studied. Local film coefficient around the tubes of 19.05, 25.4 and 50.8 mm ∅ for different film Reynolds numbers is discussed. It is observed that convective evaporation heat transfer performance increases with feed rate, but decreases with tube diameter. In-line tube configuration is found to be better compared to staggered tube configuration. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Falling film evaporators find more applications in refrigeration and desalination industries due to less liquid inventory, high heat transfer coefficient, low temperature drop, low pressure drop, etc. Falling film evaporation takes place outside the tube geometry with two-phase heat transfer. Convective evaporation as well as nucleate boiling occurs in the film as it flows over the tube depending on the heat flux conditions. There are three modes of flowing film which are drop mode, column mode and sheet mode which is related to the fluid flow rate. Heat transfer coefficient around tube surface is influenced by the film Reynolds number and the mode of the film. Film mode in turn depends on film Reynolds number. Heat transfer in tube bundles compared to a single tube is significant as evaporators and condensers ⁎ Corresponding author. E-mail address: [email protected] (A. Mani).
http://dx.doi.org/10.1016/j.desal.2015.06.018 0011-9164/© 2015 Elsevier B.V. All rights reserved.
made of in-line or staggered tubes of considerable numbers. Most of the theoretical and experimental research on falling film evaporation is based on a single tube. In multi-effect desalination (MED) system, seawater is sprayed over the tube bundle and flows as a thin film over the tubes due to gravity under vacuum conditions. Liquid maldistribution and local dry out are common problems in such systems. Normally upper tubes experience excess flow rate and film thickness while the lower strata in tube bundle have dry out conditions. Experimental investigations conducted in the past show different trends in heat and mass transfer due to the simultaneous occurrence of nucleate boiling and convective evaporation. At lower heat flux only convective evaporation takes place and normally film coefficient increases with film Reynolds number. At high heat flux conditions nucleate boiling takes place as observed in experimental studies and the film Reynolds number has no significant influence. Falling film evaporators normally work under low heat flux conditions with convective evaporation. This paper discusses the Computational Fluid
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Dynamics (CFD) studies as well as experimental investigation on horizontal tube bundle for heat and mass transfer under various operating conditions. A review of investigations on tube bundle was published by Ribatski and Jacobi [1]. Working fluids used in most of the investigations are refrigerants such as R 134a and ammonia. Fujita and Tsutsui [2] carried out experimental studies on 5 vertical tubes with refrigerant R-112 and the highest film coefficient was observed at the topmost tube. Zeng et al. [3] carried out experimental studies on in-line and staggered tubes with ammonia. It was reported that rectangular pitch configuration gave better results. Experimental studies of Moeykens et al. [4] carried out with R-134a and R-123 reported that staggered pitch gave better results compared with in-line tubes at high heat flux conditions. Roques et al. [5] carried out experimental studies with 10 tubes in vertical array using R-134a and observed that film coefficient reaches a stabilized value at Ref = 500. It is also reported that the lower tubes showed a higher film coefficient. Habert M. [6] carried out experimental with R134a and R236fa to study the effects different working fluids, type of tubes, feed rates and heat flux conditions. It was reported that tubes present in the 4th to 6th row gave better film coefficients. Sharma R. and Mitra S.K. [7] conducted studies on tube bundles with 120 rows of 22 mm tube size adopting triangular tube configuration for brackish water at atmospheric conditions. Tube drying and reduction in heat transfer coefficient was observed below Ref = 400. Lower tubes in the bundle experienced reduction in film coefficient and liquid evaporation. Theoretical and experimental investigations on tube or tube bundles were presented by Yang and Wang [8], We Li et al. [9,10], Mu et al. [11], Jani et al. [12] and Shen et al. [13] in recent times. In certain cases the film coefficient increased with feed rate, stabilized or decreased beyond a limit. There observed a gradual reduction in heat transfer coefficient with bundle depth and film dry out occurred in low feed rates. Present study, using CFD and experimental methods, was due to the lack of information on tube bundles compared to single tube and to study the reduction in performance in tubes in the vertical direction in the bundle. A comparison of in-line and staggered tubes were carried out with sea water and fresh water which has applications in seawater desalination. 2. Factors influencing film heat transfer In falling film evaporation, seawater is sprayed on the top of the tube and allowed to flow along the curved tube surface. According to Chyu and Bergles [14] flow region can be divided into four. Liquid jet is impinging on top of the tube where stagnation region is formed. At the impingement zone, the flow takes a sharp turn and because of this the film coefficient is high due to the high velocity gradient. This is followed by the developing region, where the heat transfer coefficient decreases with increase in thermal boundary layer thickness. Heat transfer coefficient further reduces as the thermal layer is fully developed. At the bottom of the tube the thickness of film increases and flow is detached from the tube bottom surface and the schematic details of falling film with four regions is reported earlier by Raju Abraham and Mani [15]. Falling film evaporation is governed by conduction heat transfer across the thin film and convective evaporation from liquid to vapor at the interface. If the heat flux is sufficiently high nucleate boiling takes place at the tube surface in addition to the convective evaporation and bubbles start to form in the film. This further enhances the heat transfer coefficient. As the flow proceeds around the tube, it is accelerated by the gravity force and decelerated by the viscous force. A viscous boundary layer develops until it is extended to the free surface of the film. Chyu and Bergles [14] developed models for heat transfer prediction in the distinct flow regions along the tube surface. This model was later used by Sharma and Mitra [7] for heat transfer prediction for film evaporation of sea water. According to Chyu and Bergles, local heat
transfer coefficient at the tube surface at the stagnation flow zone can be estimated as 2 30:5 d uumax uj 5 j 4 : hs ¼ 1:03 Pr k d wx v w 1 3
ð1Þ
Velocity gradient is constant in stagnation zone and the angle for the region of stagnation is given by θs ¼ 0:6ðw R Þ. Similarly the local surface heat transfer coefficient at the impingement zone is given by Nui ¼
1 hi x ¼ 0:73 Pr3 Rex 0:5 k
ð2Þ
for laminar boundary layer and Nui ¼
1 hi x ¼ 0:037 Pr3 Rex 0:8 k
ð3Þ
for turbulent boundary layer. Impingement angle is estimated by w θi ¼ 2:0 : R
ð4Þ
Film Reynolds number, the ratio of inertia force to viscous force within film, is estimated based on half liquid mass flow rate per meter length of tube. In the thermal developing region, film thermal gradient is developed and major part of heat is utilized for heating of film. The film heat transfer coefficient is estimated based on the heat fluxes at impingement and developing region. The angle for film development is given by 1 3μΓ 4 θd ¼ παR gρ5
hd;ðθi −θd Þ ¼
!13
qd;ð0−θd Þ θd− qd;ð0−θiÞ θi : ðθd −θi ÞðTw −Ts Þ
ð5Þ
ð6Þ
Heat flux is related with film thickness as proposed by Nusselt's theory which is given by "
δðθÞ
#13 3μΓ ¼ : gρ f ρ f − ρg sinθ
ð7Þ
Liquid film thickness gradually reduces from the top of the tube and reaches a constant near the middle and increases then as the film flows toward the bottom of the tube. Theoretical and experimental studies with better measurement techniques in the recent past have proved wide variations in predictions. Mustafa and Negeed [16] proposed correlation for film thickness with tube diameter as a parameter influencing the film thickness. Correlation for film thickness developed by Hou et al. [17], based on experimental studies, incorporates the influence of tube diameter and inter-tube spacing. "
δðθÞ
#13 s n 3μΓ ¼C d ρ f ρ f − ρg g sinθ
ð8Þ
The constants C and n are depending on the angular position of film. In the fully developed thermal region, the thermal gradient is stabilized and heat is transferred to the film surface for convective evaporation. The following correlations are suggested by Chyu and Bergles [14].
R. Abraham, A. Mani / Desalination 375 (2015) 129–137
131
Laminar 1 −1 h fd v2 3 ¼ 1:10Re f 3 k g
Γ ≤ 0:61 ≤ μ
μ4g ρσ 3
−1 11
ð9Þ
Wavy-laminar 1 h fd v2 3 −1 ¼ 0:822Re f 3 k g
4 −1 μ g 11 Γ 0:61 ≤ μ ρσ 3
≤1450 Pr−1:06
ð10Þ
Turbulent 1 h fd v2 3 1 ¼ 3:8 10−3 Re f 0:4 Pr0:65 k g
Γ N 1450 Pr−1:06 μ
ð11Þ
Local and average heat transfer coefficients of tube surface and average liquid film thickness for tube diameter 19.05, 25.4 and 50.8 mm are computed for different film Reynolds numbers using the above correlations as given in Table 1. The film thickness increases with feed rate and it marginally increases with larger tube diameter for the same flow rate. The region of the development zone is increased with feed rate and sometimes the complete film consists of developing region. Average heat transfer coefficient of tube increases with feed rate especially for smaller diameter tubes due to the increased developing region. Flow of liquid film inside the bundle is complex due to the nonuniform distribution and dripping effects or interstitial drizzles and hence very difficult to predict. Flow mal-distribution results in either reduction in heat transfer coefficient due to higher film thickness or local dry out of falling film. Higher tube spacing has the liquid impact effect and hence higher heat transfer coefficient is expected. Similarly the flow of vapor generated in the tube bundle can play an active role in the convective evaporation heat transfer. Thin film is influenced by the vapor shear effects. Increase in tube diameter shows a decrease in film coefficient under non-boiling conditions. Film thickness may increase or decrease depending on the direction of flow of vapor. Summarizing previous analytical and experimental studies, the heat transfer characteristics in a falling film is found to be influenced by feed flow rate, heat flux, position in tube bundle, tube size, inter tube spacing, surface geometry, vapor flow direction, etc. 3. CFD modeling CFD is a modern tool to study complex two-phase heat transfer phenomenon such as falling film evaporation of water under vacuum conditions. For the present studies, horizontal tube of 19.05, 25.4 and 50.8 mm OD are considered. Tube wall is maintained at constant temperature of 64.6 °C and thin film of sea water is made to flow over
Fig. 1. Contour of falling film around a horizontal tube.
it by gravity. The saturation temperature of vapor at 62.6 °C and the feed water temperature are at 58.6 °C respectively. Convective evaporation takes place under vacuum pressure of 217.4 kPa at the corresponding saturation temperature of 62.6 °C. This is typical operating condition for the first effect in a multi-effect desalination system and studies are carried out by varying feed rate, wall super heat, etc. Liquid seawater is assumed to flow from the top to bottom over a single tube as well as bundle of tubes under gravity. Liquid enters through velocity inlet at top and leaves at the bottom boundary pressure outlet. Typical CFD model of falling film over single tube is shown in Fig. 1 for 25.4 mm tube with a uniform velocity 0.09 m/s or film Reynolds number 1250. Thin film is developed around the tube and finally getting detached at the bottom of the tube. ANSYS Fluent® with two-phase Volume of Fluid (VOF) model [18] was used to carry out the flow modeling of a horizontal tube falling film with convective evaporation. Quad-Pave scheme with 10,138 meshes were used for single tube studies. A grid dependence analysis was carried out from grid sizes 2000 with an increment of about 1000. Beyond 10,138 meshes, the accuracy was not improved considerably further, however computing time increased. A time dependence analysis was carried out with a time step of 0.001 s and there was no variation in results beyond 5 s. A mixture of water vapor and liquid is considered in the domain under vacuum conditions. Primary phase was considered as vapor and secondary phase as liquid. Heat and mass transfer due to
Table 1 Details of falling film on tube surface for different tube sizes. do, mm
19.05
25.4
50.8
Ref
173 340 760 1512 173 340 760 1512 173 340 760 1512
δ, mm (90 °C)
0.167 0.210 0.274 0.345 0.175 0.220 0.287 0.367 0.197 0.247 0.323 0.406
Stagnation zone
Impingement zone
∅s, °
hs, W/m2K
0.37 0.73 1.64 3.26 0.28 0.55 1.23 2.45 0.14 0.28 0.61 1.22
4
7.85 × 10 5.59 × 104 3.74 × 104 2.65 × 104 7.85 × 104 5.59 × 104 3.74 × 104 2.65 × 104 7.85 × 104 5.59 × 104 3.74 × 104 2.64 × 104
Developing zone
Developed zone
∅d, °
hd, W/m2K
∅d, °
hd, W/m2K
∅rd, °
hfd, W/m2K
1.24 2.44 5.45 10.9 0.93 1.83 4.09 8.15 0.47 0.92 2.05 4.08
43,280 30,830 7621 6639 43,280 30,830 7621 6639 43,280 30,830 7621 6639
34.86 86.14 ≥180 ≥180 26.15 64.61 ≥180 ≥180 13.07 32.30 94.20 ≥180
6331 7098 8631 10,120 6043 6605 8094 9546 5513 5609 6727 8053
143.5 90.69 0 0 152.6 113.0 0 0 166.3 146.5 83.1 0
6034 5198 4356 3743 6034 5198 4356 3743 6034 5198 4356 3743
Av. h, W/m2K
6510 6572 6734 7081 6286 6225 6417 6783 5898 5570 5614 6001
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variation in feed rate, tube diameter, variation in local and average film coefficient, wall shear stress, tube bundle effects, etc. is discussed in this paper. Heat flux has no significant influence on heat transfer under convective evaporation conditions. More details of CFD modelling is reported in the earlier works by Raju Abraham and Mani A. [19,20]. 4. Experimental studies on tube bundles Experimental studies were carried out on tube bundle with the same configuration as in CFD studies with aluminum tubes of 25.4 mm OD. The set up consisted of an evaporator with 0.5 m OD × 1.5 m long shell with 6 mm thickness. There were 15 numbers of aluminum 6061 tubes of mm OD × 1.4 m long. The tubes could be interchanged as it is fitted with special grommets. Tube configurations could be changed by replacing the tube sheets in the evaporator. Falling water film over the evaporator tubes was heated using electrical heaters inside the tubes. The heater was fixed with temperature controller based on the tube wall temperature. Feed flow rate was varied in the ranges of 800 to 3000 kg/h and feed water temperature in the ranges of 55 to 75°C. Two different configurations of in-line and staggered tube layout as shown in Fig. 2 were used for experiments. Details of experimental set up and measurement are reported in reference [15]. Copper–Constantine thermocouple was used for temperature measurements with an uncertainty of ±0.1 °C. Vacuum transmitter with ±0.2% accuracy was used to measure the vacuum in the evaporator. Glass Rota meters were used to measure water flow rate in circuits with an uncertainty of ±2.0%. An error analysis was carried out for measurement of heat transfer coefficient and it was found that results are within the error limits of ±5.8%. 5. Results and discussion 5.1. Single tube CFD studies were carried out on single tube as well as bundle of in-line and staggered configuration. Experimental study was carried out on tube bundle with in-line and staggered configuration. Both the studies used fresh water (ground water) and seawater at 35,000 ppm salinity as working fluid. 5.1.1. Development of liquid film thickness Table 1 shows the estimated results of water film thickness at 90° of the tube for three different tube sizes using the model suggested by Chyu and Bergles [14]. Higher film thickness is predicted for higher diameter tubes. Increase in film Reynolds number predicts an increase in film thickness. Film thickness doesn't vary considerably with tube
Fig. 3. CFD results of average film thicknesses for different tube sizes.
diameter. Experimental studies of Hou et al. [17] reported that there is no obvious change in the film thickness within a range of 20 to 32 mm tube diameter with Ref in the range of 70 to 574. CFD results of three tube sizes 19.05, 25.4 and 50.8 mm ∅ are plotted and compared with the predictions of Chyu and Bergles and Hou et al. as shown in Fig. 3. No marked difference is obtained for 19.05 mm and 25.4 mm ∅ tubes. However, film thickness is reduced for 50.8 mm ∅ tube and this can be attributed to large contact area for large size tubes. It was difficult to get uniform film thickness below film Reynolds number 400. 5.1.2. Local and average heat transfer coefficient around the tube Local heat transfer coefficient (under non-boiling conditions) is highest at the impinging zone and is gradually reduced as reported by Parken et al. [21] based on the experimental studies on 25.4 and 50.8 mm ∅ electrically heated horizontal brass tubes with distilled water. However, for 50.8 mm ∅ tube, the heat transfer coefficient decreased steadily up to 90° of the tube and then tends to increase as flow approaches the bottom. Heat transfer coefficient increases with feed flow rate and feed temperature. It is reported that the effect of heat flux on heat transfer coefficient is negligible. In the present CFD study, temperature gradient for the thin film around the tube is plotted at a distance of 1 mm as shown in Fig. 4 for film Reynolds number 1250. Steepest gradient is observed at the top of the tube at 0° and the slope gradually reduces until 165° from the tube surface. This shows the gradual reduction of local film coefficient around the tube surface. However, after 165° there is a sharp reversal in the slope of the profile which increases and becomes close to the slope at 0°. At the bottom of the
Fig. 2. Photograph of tube sheet with staggered and in-line layout.
R. Abraham, A. Mani / Desalination 375 (2015) 129–137
Fig. 4. CFD results of temperature gradient around tube wall.
133
Fig. 6. Variation of local heat transfer coefficient around the tube surface with increase in Film Reynolds number.
tube at 180°, heated liquid leaves at temperature higher than the feed inlet temperature indicating sensible heating. Local heat transfer coefficient in the CFD studies were estimated using the temperature gradient at the wall and the temperature difference between tube wall and vapor (Tw − Ts). In the experimental studies, it is estimated from the heat flux measured from heat input to the heater. It is evident from the temperature profile that the heat transfer coefficient is increased at the bottom of the tube due to the effects of film detachment. This is contrary to many of earlier analytical predictions of variations in local film coefficient [22]. CFD results of the local film coefficient around 19.05, 25.4 and 50.8 mm ∅ tubes from the top to the bottom for film Reynolds number 671 is plotted as in Fig. 5. The variations in film coefficient at stagnation, impingement, developing and developed zones, etc. are clearly visible. The top of the tube shows highest value of film coefficient due to the impingement effects. Impingement effect is comparatively less for 50.8 mm ∅ tube due to large fraction of surface area compared to smaller diameter tubes. Local film coefficient is gradually reduced till the bottom end of tube where there is a sharp increase which is highest for the larger tube size. Film coefficient is highly unpredictable in this section and this can be attributed to the dynamic effects of film detachment from the tube surface. Fig. 6 shows the local heat transfer coefficient around the tube for Ref = 1250. It is observed that the local film coefficient for 50.8 mm ∅ tube is increased beyond 90° similar to the observations reported by Parken et al. This must be due to the acceleration of the fluid due to gravity in this section. The local film coefficients match with the correlation discussed by Rogers [22] for four different
Reynolds numbers namely 152, 305, 458 and 611 as given in Table 1. As the feed rate increases the length of region of the development is reduced. The wall shear stress around the tube surface is plotted as in Fig. 7. Wall shear stress is highest at the impingement region and reduces to a minimum value at about 20–30° and gradually increases due to the acceleration of the film. The shear stress gradually increases at the bottom of the tube as liquid flow approaches the bottom of the tube. Undue fluctuations are observed due to the film detachment at the bottom. Average heat transfer coefficient around the tube for 19.05, 25.4 and 50.8 mm ∅ is shown in Fig. 8. Higher film coefficient is observed for lower diameter tubes from CFD as well as empirical relations. This is due to the higher developed length for the higher diameter tubes which reduces the average film coefficient. Decrease in average heat transfer coefficient for lower Reynolds numbers is seen in the empirical results. This is in line with the experimental results of Hu and Jacobi [23] where a gradual increase in film coefficient observed all around the tube when Ref is increased. The increase in Re f increases film thickness and heat transfer is dominated by convection. Conduction resistance and convection play opposite role and hence, film coefficient stabilizes beyond a limit.
Fig. 5. CFD results of variation of local heat transfer coefficient around the tube surface.
Fig. 7. CFD results of variation of wall shear stress around the tube surface.
5.1.3. Effect of wall superheat Evaporation of falling film is not only dependent on the falling film thickness but also on wall superheat. Driving temperature differential for heat transfer increases with wall super heat which enables better film evaporation. Fig. 9 shows the variation in local Nusselt number with varying temperature difference. Saturation temperature and pressure of the vapor region was changed while keeping wall temperature at 64.6 °C and film Reynolds number constant at 1250. The increase in wall super heat (ATe) doesn't have much influence on local Nusselt
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R. Abraham, A. Mani / Desalination 375 (2015) 129–137
compared with experimental results of falling film evaporation presented by Sharma and Mitra [7] conducted at atmospheric conditions at about 80°C. Splashing of water was reported at higher Reynolds numbers causing reduction in evaporation in the experimental studies. 5.2. Tube bundle effects
Fig. 8. Variation of average heat transfer coefficients with film Reynolds number for different tube sizes.
number especially at the impingement or developing region of the tube. Increase in wall super heat must yield higher evaporation of liquid due to the reduction in viscosity due to change in temperature and reduction of film thickness. Thinning of film in-turn improves film heat transfer coefficient. Nusselt number is influenced at the bottom of the tube due to the change in fluid properties. CFD studies show that increase in wall super heat enhances the Nusselt number; however it is at the bottom region of the tube i.e. fully developed region of the tube only. 5.1.4. Mass transfer during evaporation Falling film evaporation occurs by convective evaporation as well as nucleate boiling inside the film depending upon the wall super heat or heat flux conditions. It is difficult to separate both the effects or to model it. The influence of heat flux, feed temperature, feed flow rate, etc. is totally different for both the phenomenon. Mass of liquid evaporated from the thin film is related to film thickness, temperature of the feed, wall superheat and saturation pressure. Mustafa and Negeed [16] used the following correlation for estimating the mass evaporation. me ¼
hAðTw − Ts Þ Cp f ðTs − Twi Þ þ hfg
ð12Þ
Computational results of mass transfer rate from the film for different tube sizes are presented in Fig. 10. Mass evaporation increases with film Ref due to better turbulence, reaches a peak value and then reduces. The increase in film thickness with Reynolds number suppresses the heat transfer and reduces the evaporation rate beyond Ref =750. Average value of evaporation for 25.4 mm ∅ tube is plotted and
Fig. 9. Variation of local Nusselt number around the tube surface for different wall superheat.
CFD modeling of tube bundles with rectangular (in-line) and triangular (staggered) arrangements were considered. As shown in the CFD model in Fig. 11, a rectangular arrangement with 3 vertical columns and 5 rows of tubes is studied. The contour of vapor and liquid is shown and void fraction 1 represents completely vapor region and 0 represents completely liquid region. Interstitial dripping effects, film dry-out etc., are seen at the bottom rows. Film coefficient decreases as the film flows down over the bundle of 10 tubes and stabilizes as shown in Fig. 12. Three different film Reynolds numbers are compared. It can be noted that average film coefficient increases as the feed rate increases and gets stabilized. Numerical studies Jani et al. [12] with Li/Br solution on 20 rows for Reynolds number up to 1500 predicted decrease in heat transfer coefficient at entrance zone and stabilizes the coefficient beyond. Computational studies on different tube sizes also showed that stabilization for tube bundle takes place within the first 10 tubes in the row. The overall reduction in average heat transfer coefficient is related by hb ¼ ht N−0:25 :
ð13Þ
Experimental study of Shen [13] with 25.4 mm ∅, pitch ratio 1.3, aluminum brass tube bundle of 100 in-line rows reported the influence of feed rate and wall super heat. Fresh water was supplied for a range of feed rate 0.03 to 0.07 kg/ms (Ref = 450 to 1250) and a range of temperature 40 to 60 °C. Decrease in the difference in overall heat transfer coefficient was observed for the bundle depth from 15% to 5% for an increase in film Reynolds number from 450 to 1250 for a total temperature difference of 3°C between the inside and outside of the tube. Visual observations on in-line and staggered configuration show that in-line configuration gives a better flow pattern. Non-uniformity in flow is observed in CFD models in staggered tube arrangements compared to square pitch and thus there is large variation from top row tubes in film coefficient. This can be due to the shear effects on film due to the upward flow of vapor and it shall be more predominant in staggered tubes due to the physical proximity of tubes. Heat transfer coefficient with variation in feed flow rate for both the configurations for 25.4 mm ∅ tube with pitch 1.17d is shown in Fig. 13. As the film Reynolds number increases the bundle average heat transfer coefficient increases and stabilizes. The stabilized film coefficient at Ref = 1500 for the in-line bundle is nearly 15% lower than that of the single tube. The staggered arrangement shows 35% lower value for the bundle average
Fig. 10. CFD results of variation of average mass transfer with film Reynolds number.
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Fig. 11. Simulation of flow around a tube bundle.
heat transfer coefficient compared with in-line arrangement. The variation of mass transfer for staggered bundle is 31% lower than that of in-line arrangement. Variation of mass transfer rate for different tube wall temperature is plotted and compared with a single tube as shown in Fig. 14. Evaporation rate increases proportionately with wall temperature and in-line configuration gives better results.
lower values of fluid properties like viscosity and surface tension. Tubes coated with thermal spraying of aluminum particles also tested and enhancement in heat transfer was noticed as shown in Fig. 15. No visible bubbles were observed during experimentation showing the absence of nucleate boiling. More details of experimental investigation, measurements and results are reported in reference [15].
5.3. Experimental studies on bundle effect
6. Conclusions
From the experimental study, it was observed that the in-line configuration of tubes gives a better performance than staggered tubes. In general the film coefficient reaches a peak and then stabilizes or reduces with increase in film Reynolds number. Experimental studies were carried out up to film Reynolds number 800 due to limitations in the set up. Tests were repeated at different Reynolds number for seawater as well as with fresh water as shown in Fig. 15. Fresh water tests with in-line configuration showed better performance. Better distillate production was possible with fresh water compared to seawater due to
CFD study on single tube and a bundle of tubes was carried out and it shows that heat transfer coefficient is highest for the top tube in the bundle and decreases proportionately to the position of tube in the bundle. Bundle depth effect is observed within the first 10 rows of tubes. Heat transfer coefficient is stabilized within first ten rows. As the Reynolds number increases, the film heat transfer coefficient also increases and stabilizes due to the increase in film thickness. Film heat transfer coefficient decreases as tube diameter increases based on the observation on
Fig. 12. CFD results of variation of bundle average wall heat transfer coefficient for 10 tubes.
Fig. 13. Variation of heat transfer coefficient and mass transfer coefficient with Reynolds number for different tube configurations.
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Fig. 14. CFD results of mass transfer rate with tube. Fig. 15. Comparison of experimental results of tube bundle with fresh water and sea water.
three different tube sizes. A sharp increase in local heat transfer coefficient is observed from CFD studies at the bottom of the tube. In-line tube configuration of bundle gives better performance than staggered configuration with same pitch and diameter. Studies with seawater showed a reduction of 15–20% in film heat transfer coefficient compared to fresh water at the same operating conditions. An optimum film Reynolds number of 500–800 is recommended for effective mass transfer in the design of falling film evaporators. In a bundle of tubes heat transfer coefficient stabilizes at a film Reynolds number 1500 approximately and the bundle average film coefficient is approximately 85% of the film coefficient of a single tube for the same film Reynolds number. Nomenclature A heat transfer area, m−2 Ar Archimedes number, g d3o ν−3 Cp specific heat, J kg−1 K−1 do tube outside diameter, m g gravitational acceleration, m s−2 h heat transfer coefficient, Wm−2 K−1 hfg latent heat of vaporization, kJ/kg k thermal conductivity, Wm−1 K−1 N vertical position of tube Nu Nusselt number, hν2/3 k−1 g−1/3 Pr Prandtl number, μCpk−1 R outer tube radius, m film Reynolds number, 4Γμ−1 Ref s tube pitch, m T temperature, K u velocity, m/s w jet width, m Subscripts b bundle d developing e evaporation f liquid fd fully developed g vapor i impingement s saturated t top x local w wall wi water inlet ΔTe local temperature difference for evaporation, K HTC heat transfer coefficient, W/m2 K MTC mass transfer coefficient, kg/m2 s
Greek symbols α thermal diffusivity, m2 s−1 Γ half liquid mass flow rate per length of tube, kg m−1 s−1 δ film thickness, m θ angle along the tube perimeter measured from the apex, ° μ dynamic viscosity, kg m−1 s−1 Φ diameter, mm ρ density, kg m−3 σ surface tension N m−1 v kinematic viscosity, m2 s−1 Acknowledgment Authors acknowledge the financial support received from the National Institute of Ocean Technology, Chennai (NIOT/F&A/PROJ/ EFW01/2010) for the studies.
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