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Distribution of brine temperature in a large-scale horizontal-tube falling film evaporator
Applied Thermal Engineering 164 (2020) 114437
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Distribution of brine temperature in a large-scale horizontal-tube falling film evaporator Luyuan Gong, Shihe Zhou, Yali Guo, Shengqiang Shen
T
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Key Laboratory of Liaoning Province for Desalination, Dalian University of Technology, Dalian 116024, Liaoning, China
H I GH L IG H T S
zoning distribution character of the brine temperature is depicted in detail. • The distribution characteristics of the brine temperature are analyzed. • Special • Thermodynamic losses are presented representing the high sensitivity of the evaporator.
A R T I C LE I N FO
A B S T R A C T
Keywords: Falling film evaporator Horizontal tube bundle Distributed parameter model Brine temperature distribution
Falling film evaporator applied in multi-effect evaporation device is normally operated under small temperature differences. Considering the high sensitive of the evaporator, the distribution of the brine temperature, as one of the parameters that determines the distribution of the local temperature difference, is studied in this paper using parameter distributed model. The three-dimensional distributions of the brine temperature as well as the location of the maximum brine temperature are presented under different operating conditions. Results show that the maximum variation range of the brine temperature in the evaporator decreases with the increment of the brine inlet spray density and salinity but increases with the increment of the apparent temperature difference. In the aim of avoid design failure of the local temperature difference, the variation of the location of the maximum brine temperature as well as the thermodynamic losses in the brine film are analyzed, providing theoretical basis for the more accurate design of the falling film evaporator.
1. Introduction Water shortage problem has become a serious problem all around the world due to demographic and industrial growth. The fresh water demand is estimated to reach 6300 billion cubic meters by the year of 2030 which exceeds 40% of the supply of water from the natural water cycle [1]. By removing salt from seawater, desalination has emerged as an important source of fresh water [2]. There are three major types of desalination technologies: multi-stage flash (MSF), multi-effect evaporation (MEE), and reverse osmosis (RO) [3]. Among the two dominant thermal technologies: MSF and MEE [4], MEE is currently considered as competitive to MSF for its higher thermodynamic efficiency and less investment [5]. Falling film evaporator due to its high heat transfer coefficient under relative low flow rates and allowing small temperature difference, is a preferred technique and is widely applied in MEE desalination plant [6]. In falling film evaporators, heat flux, film flow rate, geometry of the
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tube, liquid properties and distribution system are the major parameters that affect the performance of the evaporator [7]. For the impact of the liquid flow rate on the heat transfer coefficient, different results were found in open literatures. In convection-dominated conditions, some literatures shows that the falling film evaporation heat transfer coefficient on a single tube increases with the increase of the liquid flow rate mainly due to the more severe fluctuation of the liquid film [8–10]. According to experimental result of Shen et al. [11], the heat transfer increase firstly and reaches a plateau. They considered that with the increase of the spray density, the increase of the turbulence firstly dominate the heat transfer process but then the increase in the film thickness offsets the impact of the turbulence. As for the impact of the liquid flow rate on the heat transfer coefficient of a tube bundle, some literatures reported that it has no significant with single tube [12,13]. Other literatures fond that due to the partial dry-out, the heat transfer coefficient exhibits smaller values [6,14,15]. For the paramedic distribution in a falling film evaporator, the heat
Corresponding author. E-mail address: [email protected] (S. Shen).
https://doi.org/10.1016/j.applthermaleng.2019.114437 Received 4 January 2019; Received in revised form 31 July 2019; Accepted 23 September 2019 Available online 24 September 2019 1359-4311/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Applied Thermal Engineering 164 (2020) 114437
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Nomenclature
BPE ∇BPE G¯e PLcolumn40
p ∇p S Sinlet T Tsat ΔT ΔTapp ∇T δTbr,p
the maximum brine temperature variation caused by the change of BPE velocity, m·s−1 velocity gradient, m·s−1 per row or column
δTbr,BPE v ∇v
boiling point elevation of brine, °C the gradient of BPE , °C per row, column or meter average inter-tube vapor mass flow rate of the evaporator, kg·m−2·s−1 the plane composed of the tubes with the column number of 40 pressure, Pa pressure gradient, Pa per row or column local brine salinity of the evaporator, g·kg−1 brine salinity at the liquid inlet of the evaporator, g·kg−1 local temperature of the evaporator, °C saturated evaporation temperature, °C local temperature difference, °C apparent temperature difference of the evaporator, °C local temperature gradient, °C per row or column the maximum brine temperature variation caused by the change of vapor pressure
Greeks symbols local brine spray density, kg·m−1·s−1 brine spray density at the inlet of the evaporator, kg·m−1·s−1
Γ Γinlet
Subscripts br column vp length row vf
brine along the tube column direction vapor on the shell side along the tube length direction along the tube row direction along the vapor flow direction
large falling film tube bundle. Recently, based on the experimental database of Liu et al. [24], Gong et al. [25] added the influence of the inter-tube vapor flow resistance on the heat transfer performance of large-scale falling film evaporators. The three-dimension parameters distributions in the evaporator were obtained. The non-uniform distributions of steam inlet velocity under different operating conditions were studied by Shen et al. [26]. The low-temperature multi-effect evaporation desalination plant is run under relative small temperature difference (normally between 2 and 4 °C). The relatively small deviation of the calculated temperature difference distribution might lead to the total failure of the evaporator. Moreover, small thermal dynamic losses caused by the non-uniform distribution of heat transfer parameters might cause the local temperature difference to be zero [27,28]. Despite some studies on the nonuniform distribution of thermal parameters outside a single tube or a tube bundle, the detailed temperature distribution of the brine temperature, as one of the major factors that directly affects the distribution of the temperature difference in a falling film evaporator, has rarely been presented. The precise regulation of the falling film evaporator requires the detailed distribution of the parameters that cause local thermodynamic losses. In this paper, the distributions the brine temperature in the horizontal-tube falling film evaporator are studied in detail under different operating parameters. The detailed analysis of the variation of the brine temperature is beneficial for the better understanding of the parametric distribution of large-scale falling film
transfer coefficient along the peripheral direction of a single tube was studied by Parken et al. [16], Hu et al. [17] and Shen et al. [18,19]. They came out with similar result that the highest falling film evaporation heat transfer coefficient locates at the top of the tube where the liquid impinging effect enhances the local heat transfer. The coefficient then shows a decreasing trend along the peripheral direction until it is near the bottom of the tube where the liquid from both sides of the tube collides. For a falling film tube bundle, Zeng et al. [20] found in their experiment that upper tubes have the higher heat transfer coefficient than rest of the tubes. Due to narrower flow passages of triangular-pitch bundle than rectangular-pitch bundle, bubbles are more likely to be in contact with tube walls which makes higher heat transfer coefficient in a triangular-pitch bundle [21]. Hou et al. [22] numerically simulated the performance of a large horizontal-tube falling film evaporator for desalination. The heat transfer coefficient and seawater salinity distributions were given along the tube row and length directions. Their simulation results exhibit a deceasing trend of local heat transfer coefficient with the increment of the tube row number and the tube length mainly due to the decrease of the fluctuation in the brine film on the shell side and the decrease of the local vapor quality on the tube side. Yang [23] adopted similar method to simulate the falling film evaporator for large compression refrigeration systems and the similar variation trend of the heat transfer coefficient distribution were found along the tube row direction. Above simulations concentrated on the two-dimensional parametric distributions of a
vapor out
Inter-tube vapor
Inter-tube vapor
vapor out
liquid in
calculating area (a) Cross-section of the falling film evaporator
(b) Three-dimensional grid generation
Fig. 1. Schematic of falling film evaporator and grid generation. 2
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direction is determined by the constraint condition that the vapor always flows along the streamline that has the smallest total flow resistance from the current position to the boundary of the tube bundle. Taking Fig. 3 as an example, it is easy to know that the vapor flow direction at node M should be horizontal flow to the left point b because of the smallest total vapor flow resistance along this streamline compared with along the other two alternative flow directions.
evaporator and the better design of the evaporator. 2. Physical and mathematical model 2.1. Physical model The structure of a large-scale falling film evaporator is shown in Fig. 1(a). It is a shell and tube heat exchanger. On the shell side of the evaporator, the brine is sprayed onto the out surface of the heat transfer tubes. The brine flows downward in the evaporator by gravity, forming falling films outside the heat transfer tubes. Part of the brine turns into vapor when absorbs the heat inside the tube. The vapor accumulates among tubes and flows to the next effect evaporator, or to the condenser. Rest of the brine is extract from the evaporator for recycling. On the tube side of the evaporator, cooled by the brine, the steam gradually condenses, forming stratified flow pattern inside the tubes.
3.1. The distributions of tbr Fig. 4 demonstrates the zoning of the tube bundle of a falling film evaporator. The tube bundle is divided into three zones: the upper zone, the middle zone and the lower zone according to the flow directions of the vapor. In the upper zone and lower zones, the vapor flows vertically towards either the top boundary or the bottom boundary of the tube bundle. In the middle zone, the vapor flows horizontally to the side boundary. It is worth noting again that when the column number is 40, the calculation node is at the symmetric plane of the tube bundle along the tube column direction. When the column number is 1, the calculation node is at the side boundary of the tube bundle. In each of the three divided zones, pvp decreases along the vapor flow directions and reaches its minimum value at the boundary of the tube bundle. In the upper zone and lower zones, the vapor pressure gradient, ∇pvp, vf , shows larger values compared with in the middle zone. It is because that for the tube bundle of triangular arrangement, the flow area of vertical vapor flow, Fvt, is smaller than that of the horizontal vapor flow, Fvt, as shown in Fig. 3. Generally when the vapor flow vertically, it is more apt to generate larger vapor velocity compared with flowing horizontally. Thus ∇pvp, vf shows larger values in the upper and lower zones than in the middle. The detailed evaporation process of the brine film outside the tube surface is depicted in Fig. 5. When the vapor pressure in the vapor area increases, apparently the brine film need to be heated to a higher temperature in order to make partial pressure of the vapor molecular in the brine film equal to the vapor pressure on the vapor side, and to make the brine film boil. On the other hand, if the salinity of the brine is increased, the partial pressure of the vapor molecular in the brine decreases. In this case, the temperature of the brine film also need to be heated to a higher temperature that the partial pressure of the salt molecular is equal to that of the vapor molecular above the liquid. In the evaporator, it is above two parameters that need to be considered to clarify the distribution of the local brine temperature. Fig. 6 demonstrates the distribution of Tbr with Γinlet of 0.05 kg·m−1·s−1, Sinlet of 30 g·kg−1 and ΔTapp of 3 °C. It indicates that Tbr decreases along the vapor flow directions in the three zones. This is directly caused by the non-uniform distribution of pvp as depicted in Fig. 4. On the other hand, due to the concentration of brine from top to bottom of the evaporator, BPE shows an increasing trend along this direction. In consequence, Tbr,max is located in the lower part of the tube bundle rather than the upper where the maximum of pvp locates.
2.2. Mathematical model In the large-scale falling film evaporator, the tube bundle contains hundreds of tubes. For investigating the heat transfer and flow characteristics, the tube bundle is divided into a three-dimensional network as shown in Fig. 1(b). For each grid, three modules, which includes the brine module on the shell side, the steam module on the tube side and the inter-tube vapor module, are calculated respectively. The geometric parameters are described in Table 1. The operating conditions selected in this paper are listed in Table 2. Considering the symmetric distribution of thermal parameters along the tube column direction, half of the tube bundle is selected as the calculation area with column 1 representing the side boundary of the tube bundle and column 40 the center. A comprehensive distributed parameter model (DPM) is used to study the heat transfer performance of large-scale horizontal-tube falling film evaporators. In previous work, the experimental work, the related correlations, the algorithm, the mesh independency of the model were described in detail [25,26,29]. The initial and boundary conditions are given are as follows: (1) The brine inlet flow rate (spray density), the brine inlet salinity and the inter-tube vapor pressure at the boundaries of the tube bundle are specified. (2) The stem inlet velocity, the steam inlet temperature are given. (3) The temperature of the wall on shell side is assumed to be constant. The validation of the model is shown in Fig. 2. The simulation results of the current model are compared with the model of Hou et al. [22] and the operating data from Huanghua power plant in China. The calculated value of the average vapor mass flow rate and pressure are coincident with the relative deviation less than 4.2% compared with the operating data of the power plant. Hou et al. adopted similar distributed parameter model, indicating the feasibility of the distributed parameter model for simulating the large-scale falling film evaporator. 3. Results and discussions
3.2. The location of the maximum brine temperature
In the horizontal-tube falling film evaporator for desalination, the distribution of the brine temperature is mainly determined by two parameters: the local pressure of the inter-tube vapor and the local brine salinity. Both parameters are non-uniformly distributed in the tube bundle. The higher local vapor pressure results in higher local saturated temperature of brine. On the other hand, higher local brine salinity, enhancing the boiling point of the brine, tends to result in higher evaporation temperature of the brine [30] as well. Both the variation of pvp and S in the tube bundle determine the distribution of Tbr . For each node of the calculating area, the inter-tube vapor (vapor generated outside of the tubes, hereinafter referred to as vapor) has three possible flow directions: vertical upflow, horizontal flow and vertical downflow as depicted in Fig. 3. For each node, the vapor flow
Fig. 7 demonstrates the locations of Tbr,max under different operating Table 1 Geometry parameters.
3
Name
Description
Tube length/m Row number (RN) Column number (CN) Number of tube Tube external diameter/mm Tube inside diameter/mm Tube arrangement
8 160 80 1 25.4 24 Triangular
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Table 2 Operating conditions. Name
Range −1 −1
Brine inlet spray density/kg·m ·s Brine inlet salinity/g·kg−1 Evaporation temperature/°C Apparent temperature difference/°C Average steam inlet velocity/m·s−1
0.05–0.09 30–50 60 2–5 40
10-3 Hou et al. [22] Operating results Present simulation
3.0
Ge / kg·m-2·s-1
2.7
Fig. 4. Zoning of the heat transfer tube bundle.
2.4
2.1
1.8
10
12
14
16
18
20
22
24
pvp / kPa
s
Fig. 2. Validation of the present model.
1 2 3
Fhz
M
... ...
side boundary
b
upper boundary 1 2 3 ... ... CN/2 a
RN
symmetrical plane
j i
M
Fig. 5. Schematic of evaporation process of brine film outside a horizontal tube.
inter-tube vapor
F vt
M
c lower boundary
inter-tube vapor
Fig. 6. Distributions of the brine temperature.
rear part of the tubes. However, with the increment of Γinlet , the location of the maximum q remains almost unchanged along the tube length direction [25]. This explains the locations of Tbr,max with the increase of Γinlet . Along the tube length direction, it is shown in Fig. 7(b) that with the increase of Sinlet , Tbr,max gradually moves to the steam inlet. As Sinlet is increased, the variation range of h decreases mainly due to the decreases of the heat transfer coefficient on the evaporation side of the tube. On the other hand, less steam is condensed inside the tube which directly results in relatively higher average steam velocity and larger variation range of ΔT along the tube length direction. The impact of ΔT on the distribution of q gradually surpass the impact of h . The maximum of q thus gradually moves backwards to the steam inlet where ΔT has larger values. Consequently, Tbr,max gradually moves toward the same direction as shown in Fig. 7(b).
Fig. 3. The determination of the vapor flow direction for a certain calculation node.
conditions. Along the tube column direction, due to the symmetry characteristics of vapor flow, Tbr,max is always located in the central symmetric plane of the tube bundle. It is the plane composed of the tubes with the column number of 40, denoted by PLcolumn40 in this paper. Along the tube length direction, it is demonstrated in Fig. 7(a) that with the increase of Γinlet , the location of Tbr,max remains almost unchanged. Along the tube length direction, the location of Tbr,max is mainly determined by the distribution of q . Where it has larger q , the brine has relatively higher S and larger BPE , which leads Tbr to be larger. It is found that q reaches its maximum value near the middle4
Applied Thermal Engineering 164 (2020) 114437
L. Gong, et al.
Fig. 8. Impact of Γinlet on Tbr , max , δTbr,p and δTbr,BPE .
Fig. 9. Impact of Sinlet on Tbr , max , δTbr,p and δTbr,BPE .
Fig. 10. Impact of ΔTapp on Tbr , max , δTbr,p and δTbr,BPE .
Along the tube length direction, Fig. 7(c) demonstrates that with the increase of ΔTapp , Tbr,max moves firstly forwards the steam outlet, then backward to the inlet. When ΔTapp is of 2.0 °C, compared with under the conditions of larger ΔTapp , less steam is condensed inside tubes. It causes higher average steam velocity and higher steam pressure drop inside tubes. The distribution of ΔT dominates the distribution of the local heat flux along the tube length direction. The maximum q is located
Fig. 7. Location of Tbr,max under different operating parameters.
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It is also noted in Fig. 8 that δTbr,BPE decreases with the increment of Γinlet . With the increment of Γinlet , the concentration ratio of the brine between the inlet and the outlet of the evaporator decreases which causes the slower increase of S and smaller variation range of BPE . When Γinlet is increased from 0.05 to 0.09 kg·m−1·s−1, the brine temperature variation range caused by the variation of BPE decreases from 7.5% to 4.1% of the apparent temperature difference. With the increment of Γinlet , the increase of δTbr,p helps to increase the value of Tbr,max . On the other hand, the decrease of δTbr,BPE goes against the increase of Tbr,max . Under the effects of both the variation of pvp and BPE , Tbr,max shows a slight decreasing trend followed by a significant increasing trend as Γinlet is increased from 0.05 to 0.09 kg·m−1·s−1. Fig. 9 demonstrates the thermodynamic losses caused by vapor flow resistance and boiling point elevation under different Sinlet . As the increment of Sinlet , it is noted that Tbr,max increases almost linearly with the increment of Sinlet . Apparently it mainly results from the increase in the BPE . Both δTbr,p and δTbr,BPE decreases with the increment of Sinlet . When Sinlet is increased, the falling film evaporation heat transfer coefficient decreases significantly because of the increase in the brine viscosity and surface tension [25]. The decrease of heat transfer coefficient leads q to be smaller so that less amount of vapor is produced among tubes. When Sinlet is increased from 30 to 50 g·kg−1, the thermodynamic loss caused by the variation of pvp decreases from 6.2% to 3.5% of ΔTapp and the thermodynamic loss caused by the variation of BPE decreases from 6.3% to 5.9% of ΔTapp . Fig. 10 shows that both δTbr,p and δTbr,BPE increase significantly with the increment of ΔTapp due to the increase of heat flux. When ΔTapp is increased from 2 to 5 °C, the thermodynamic loss caused by the variation of pvp increases from 4.9% to 7.4% of ΔTapp . Meanwhile, the thermodynamic loss caused by the variation of BPE increases from 4.5% to 8.7% of ΔTapp . It is the increase of both δTbr,p and δTbr,BPE that directly lead to the increase of Tbr,max .
near the steam inlet and so does Tbr,max . When ΔTapp is increased to 3 °C, the impact of ΔT on the distribution of q becomes weaker and the distribution of h gradually dominates the distribution of q . Tbr,max gradually moves to the middle-rear part of the tube where h has the maximum value. As ΔTapp further increases to 5 °C, more condensate is generated at the bottom of the tube and the shear force of the steam on the condensate near the steam outlet becomes smaller. The maximum h gradually moves towards the steam inlet; Moreover, the steam condenses completely before reaching the steam outlet which shortens the effective heat transfer length of the tubes. Both the above two aspects result in that Tbr,max moves back to the steam inlet. Along the tube row direction, Tbr,max is always located at the interface of the middle zone and the lower zone where both pvp and BPE have relative larger values. The location of the interface between the middle zone and lower zone has close relation to the local vapor output of the evaporator. With the increase of Γinlet and ΔTapp , or the decrease of Sinlet , it is shown in Fig. 7 that the location of Tbr,max moves upwards. Such variation of the above three parameters are beneficial for the vapor output amount of the evaporator. More vapor near the lower part of the tube bundle changes the flow direction from horizontal flow to vertical flow. The interface plane of middle zone and lower zone gradually moves upward. Fig. 7 also demonstrates the isothermal lines under different operating parameters. Each isothermal line represents the Tbr equaling to Tbr,max minus a micro increment of temperature. It is indicated that with the increment of Γinlet and the decrease of ΔTapp , the length of the isothermal line along the tube row direction increases. It indicates that the brine temperature is more uniformly distributed along this direction. With the decrease of Γinlet , ΔTapp , or the increase of Sinlet , the length of the isothermal line along the tube length direction indicates that the brine temperature is more uniformly distributed along this direction. 3.3. The variation of thermodynamic loss of the brine
4. Concluding remarks
Falling evaporator applied in MEE devices are normally operated under small temperature difference. The local effective temperature difference is sensitive to the variation of the heat transfer parameters. The thermodynamic loss is defined as the difference between the apparent temperature difference and the local effective temperature difference [31]. In this paper, the following parameters are defined to better present the thermodynamic losses caused by the vapor pressure and BPE in such typical small temperature heat exchangers. δTbr,p is defined as the difference between the maximum and the minimum of the saturated vapor temperatures in the evaporator which represents the maximum variation range of Tbr that the variation of pvp contributes; δTbr,BPE is defined as the difference between the maximum and the minimum of BPE which represents the maximum variation range of Tbr that the variation of BPE contributes.
δTbr,p = Tbr,sat |pvp = max − Tbr,sat |pvp = min
(1)
δTbr,BPE = BPEmax − BPEmin
(2)
The distribution of the brine temperature in a horizontal-tube falling film evaporator is studied using distributed parameter model. The conclusions are summarized as follows: 1. In the upper zone of the tube bundle, the brine temperature has larger gradient than the middle zone and the lower zone along the vapor flow directions. It is because of the increase of the boiling point elevation of the brine that the maximum brine temperature is located near the lower rather than the upper part of the tube bundle. 2. Along the tube length direction, with the variation of the brine inlet spray density and inlet brine salinity, the major factors that determine the distribution of the maximum brine temperature are the local heat transfer coefficient inside the tube and the local temperature difference, respectively. With the increase of the apparent temperature difference, the above parameters dominates the distribution of the maximum temperature alternatively. 3. Along the tube row direction, the amount of vapor, by changing the location of the interface of the center and lower zones, indirectly affects the location of the maximum brine temperature. 4. The thermodynamic losses caused by the variation of vapor pressure and brine point elevation shows different variation trends with the change of brine inlet spray density, salinity as well as the apparent temperature difference. Comprehensive consideration of the distribution above parameters must be taken to prevent excessive thermodynamic losses.
From Fig. 8 it can be seen that δTbr,p increases almost linearly with the increment of Γinlet . It is because of the following reasons: (1) The overall heat transfer coefficient of the evaporator is enhanced with the increment of Γinlet due to the increase in the wavy effect of brine films [25]. It leads to remarkable increase of the vapor output. (2) With the increment of Γinlet , the brine film outside the tube surfaces as well as the brine falling among tubes occupy more space which narrows the flow area of the vapor. The increase of Γinlet also result in the change of the liquid flow pattern from droplet flow to jet flow and even to jet-sheet flow which further decrease the flow area of the vapor. Both above two phenomena lead to the increment of the local vapor velocity and finally causes the increase of local vapor pressure gradient. When Γinlet is increased from 0.05 to 0.09 kg·m−1·s−1, the thermodynamic loss caused by the variation of pvp increases from 5.3% to 8.7% of ΔTapp .
Acknowledgements The authors are gratitude for the support of the National Natural Science Foundation of China (No.51936002). 6
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Appendix A. Supplementary material
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Distribution of brine temperature in a large-scale horizontal-tube falling film evaporator Luyuan Gong, Shihe Zhou, Yali Guo, Shengqiang Shen
T
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Key Laboratory of Liaoning Province for Desalination, Dalian University of Technology, Dalian 116024, Liaoning, China
H I GH L IG H T S
zoning distribution character of the brine temperature is depicted in detail. • The distribution characteristics of the brine temperature are analyzed. • Special • Thermodynamic losses are presented representing the high sensitivity of the evaporator.
A R T I C LE I N FO
A B S T R A C T
Keywords: Falling film evaporator Horizontal tube bundle Distributed parameter model Brine temperature distribution
Falling film evaporator applied in multi-effect evaporation device is normally operated under small temperature differences. Considering the high sensitive of the evaporator, the distribution of the brine temperature, as one of the parameters that determines the distribution of the local temperature difference, is studied in this paper using parameter distributed model. The three-dimensional distributions of the brine temperature as well as the location of the maximum brine temperature are presented under different operating conditions. Results show that the maximum variation range of the brine temperature in the evaporator decreases with the increment of the brine inlet spray density and salinity but increases with the increment of the apparent temperature difference. In the aim of avoid design failure of the local temperature difference, the variation of the location of the maximum brine temperature as well as the thermodynamic losses in the brine film are analyzed, providing theoretical basis for the more accurate design of the falling film evaporator.
1. Introduction Water shortage problem has become a serious problem all around the world due to demographic and industrial growth. The fresh water demand is estimated to reach 6300 billion cubic meters by the year of 2030 which exceeds 40% of the supply of water from the natural water cycle [1]. By removing salt from seawater, desalination has emerged as an important source of fresh water [2]. There are three major types of desalination technologies: multi-stage flash (MSF), multi-effect evaporation (MEE), and reverse osmosis (RO) [3]. Among the two dominant thermal technologies: MSF and MEE [4], MEE is currently considered as competitive to MSF for its higher thermodynamic efficiency and less investment [5]. Falling film evaporator due to its high heat transfer coefficient under relative low flow rates and allowing small temperature difference, is a preferred technique and is widely applied in MEE desalination plant [6]. In falling film evaporators, heat flux, film flow rate, geometry of the
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tube, liquid properties and distribution system are the major parameters that affect the performance of the evaporator [7]. For the impact of the liquid flow rate on the heat transfer coefficient, different results were found in open literatures. In convection-dominated conditions, some literatures shows that the falling film evaporation heat transfer coefficient on a single tube increases with the increase of the liquid flow rate mainly due to the more severe fluctuation of the liquid film [8–10]. According to experimental result of Shen et al. [11], the heat transfer increase firstly and reaches a plateau. They considered that with the increase of the spray density, the increase of the turbulence firstly dominate the heat transfer process but then the increase in the film thickness offsets the impact of the turbulence. As for the impact of the liquid flow rate on the heat transfer coefficient of a tube bundle, some literatures reported that it has no significant with single tube [12,13]. Other literatures fond that due to the partial dry-out, the heat transfer coefficient exhibits smaller values [6,14,15]. For the paramedic distribution in a falling film evaporator, the heat
Corresponding author. E-mail address: [email protected] (S. Shen).
https://doi.org/10.1016/j.applthermaleng.2019.114437 Received 4 January 2019; Received in revised form 31 July 2019; Accepted 23 September 2019 Available online 24 September 2019 1359-4311/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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Nomenclature
BPE ∇BPE G¯e PLcolumn40
p ∇p S Sinlet T Tsat ΔT ΔTapp ∇T δTbr,p
the maximum brine temperature variation caused by the change of BPE velocity, m·s−1 velocity gradient, m·s−1 per row or column
δTbr,BPE v ∇v
boiling point elevation of brine, °C the gradient of BPE , °C per row, column or meter average inter-tube vapor mass flow rate of the evaporator, kg·m−2·s−1 the plane composed of the tubes with the column number of 40 pressure, Pa pressure gradient, Pa per row or column local brine salinity of the evaporator, g·kg−1 brine salinity at the liquid inlet of the evaporator, g·kg−1 local temperature of the evaporator, °C saturated evaporation temperature, °C local temperature difference, °C apparent temperature difference of the evaporator, °C local temperature gradient, °C per row or column the maximum brine temperature variation caused by the change of vapor pressure
Greeks symbols local brine spray density, kg·m−1·s−1 brine spray density at the inlet of the evaporator, kg·m−1·s−1
Γ Γinlet
Subscripts br column vp length row vf
brine along the tube column direction vapor on the shell side along the tube length direction along the tube row direction along the vapor flow direction
large falling film tube bundle. Recently, based on the experimental database of Liu et al. [24], Gong et al. [25] added the influence of the inter-tube vapor flow resistance on the heat transfer performance of large-scale falling film evaporators. The three-dimension parameters distributions in the evaporator were obtained. The non-uniform distributions of steam inlet velocity under different operating conditions were studied by Shen et al. [26]. The low-temperature multi-effect evaporation desalination plant is run under relative small temperature difference (normally between 2 and 4 °C). The relatively small deviation of the calculated temperature difference distribution might lead to the total failure of the evaporator. Moreover, small thermal dynamic losses caused by the non-uniform distribution of heat transfer parameters might cause the local temperature difference to be zero [27,28]. Despite some studies on the nonuniform distribution of thermal parameters outside a single tube or a tube bundle, the detailed temperature distribution of the brine temperature, as one of the major factors that directly affects the distribution of the temperature difference in a falling film evaporator, has rarely been presented. The precise regulation of the falling film evaporator requires the detailed distribution of the parameters that cause local thermodynamic losses. In this paper, the distributions the brine temperature in the horizontal-tube falling film evaporator are studied in detail under different operating parameters. The detailed analysis of the variation of the brine temperature is beneficial for the better understanding of the parametric distribution of large-scale falling film
transfer coefficient along the peripheral direction of a single tube was studied by Parken et al. [16], Hu et al. [17] and Shen et al. [18,19]. They came out with similar result that the highest falling film evaporation heat transfer coefficient locates at the top of the tube where the liquid impinging effect enhances the local heat transfer. The coefficient then shows a decreasing trend along the peripheral direction until it is near the bottom of the tube where the liquid from both sides of the tube collides. For a falling film tube bundle, Zeng et al. [20] found in their experiment that upper tubes have the higher heat transfer coefficient than rest of the tubes. Due to narrower flow passages of triangular-pitch bundle than rectangular-pitch bundle, bubbles are more likely to be in contact with tube walls which makes higher heat transfer coefficient in a triangular-pitch bundle [21]. Hou et al. [22] numerically simulated the performance of a large horizontal-tube falling film evaporator for desalination. The heat transfer coefficient and seawater salinity distributions were given along the tube row and length directions. Their simulation results exhibit a deceasing trend of local heat transfer coefficient with the increment of the tube row number and the tube length mainly due to the decrease of the fluctuation in the brine film on the shell side and the decrease of the local vapor quality on the tube side. Yang [23] adopted similar method to simulate the falling film evaporator for large compression refrigeration systems and the similar variation trend of the heat transfer coefficient distribution were found along the tube row direction. Above simulations concentrated on the two-dimensional parametric distributions of a
vapor out
Inter-tube vapor
Inter-tube vapor
vapor out
liquid in
calculating area (a) Cross-section of the falling film evaporator
(b) Three-dimensional grid generation
Fig. 1. Schematic of falling film evaporator and grid generation. 2
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direction is determined by the constraint condition that the vapor always flows along the streamline that has the smallest total flow resistance from the current position to the boundary of the tube bundle. Taking Fig. 3 as an example, it is easy to know that the vapor flow direction at node M should be horizontal flow to the left point b because of the smallest total vapor flow resistance along this streamline compared with along the other two alternative flow directions.
evaporator and the better design of the evaporator. 2. Physical and mathematical model 2.1. Physical model The structure of a large-scale falling film evaporator is shown in Fig. 1(a). It is a shell and tube heat exchanger. On the shell side of the evaporator, the brine is sprayed onto the out surface of the heat transfer tubes. The brine flows downward in the evaporator by gravity, forming falling films outside the heat transfer tubes. Part of the brine turns into vapor when absorbs the heat inside the tube. The vapor accumulates among tubes and flows to the next effect evaporator, or to the condenser. Rest of the brine is extract from the evaporator for recycling. On the tube side of the evaporator, cooled by the brine, the steam gradually condenses, forming stratified flow pattern inside the tubes.
3.1. The distributions of tbr Fig. 4 demonstrates the zoning of the tube bundle of a falling film evaporator. The tube bundle is divided into three zones: the upper zone, the middle zone and the lower zone according to the flow directions of the vapor. In the upper zone and lower zones, the vapor flows vertically towards either the top boundary or the bottom boundary of the tube bundle. In the middle zone, the vapor flows horizontally to the side boundary. It is worth noting again that when the column number is 40, the calculation node is at the symmetric plane of the tube bundle along the tube column direction. When the column number is 1, the calculation node is at the side boundary of the tube bundle. In each of the three divided zones, pvp decreases along the vapor flow directions and reaches its minimum value at the boundary of the tube bundle. In the upper zone and lower zones, the vapor pressure gradient, ∇pvp, vf , shows larger values compared with in the middle zone. It is because that for the tube bundle of triangular arrangement, the flow area of vertical vapor flow, Fvt, is smaller than that of the horizontal vapor flow, Fvt, as shown in Fig. 3. Generally when the vapor flow vertically, it is more apt to generate larger vapor velocity compared with flowing horizontally. Thus ∇pvp, vf shows larger values in the upper and lower zones than in the middle. The detailed evaporation process of the brine film outside the tube surface is depicted in Fig. 5. When the vapor pressure in the vapor area increases, apparently the brine film need to be heated to a higher temperature in order to make partial pressure of the vapor molecular in the brine film equal to the vapor pressure on the vapor side, and to make the brine film boil. On the other hand, if the salinity of the brine is increased, the partial pressure of the vapor molecular in the brine decreases. In this case, the temperature of the brine film also need to be heated to a higher temperature that the partial pressure of the salt molecular is equal to that of the vapor molecular above the liquid. In the evaporator, it is above two parameters that need to be considered to clarify the distribution of the local brine temperature. Fig. 6 demonstrates the distribution of Tbr with Γinlet of 0.05 kg·m−1·s−1, Sinlet of 30 g·kg−1 and ΔTapp of 3 °C. It indicates that Tbr decreases along the vapor flow directions in the three zones. This is directly caused by the non-uniform distribution of pvp as depicted in Fig. 4. On the other hand, due to the concentration of brine from top to bottom of the evaporator, BPE shows an increasing trend along this direction. In consequence, Tbr,max is located in the lower part of the tube bundle rather than the upper where the maximum of pvp locates.
2.2. Mathematical model In the large-scale falling film evaporator, the tube bundle contains hundreds of tubes. For investigating the heat transfer and flow characteristics, the tube bundle is divided into a three-dimensional network as shown in Fig. 1(b). For each grid, three modules, which includes the brine module on the shell side, the steam module on the tube side and the inter-tube vapor module, are calculated respectively. The geometric parameters are described in Table 1. The operating conditions selected in this paper are listed in Table 2. Considering the symmetric distribution of thermal parameters along the tube column direction, half of the tube bundle is selected as the calculation area with column 1 representing the side boundary of the tube bundle and column 40 the center. A comprehensive distributed parameter model (DPM) is used to study the heat transfer performance of large-scale horizontal-tube falling film evaporators. In previous work, the experimental work, the related correlations, the algorithm, the mesh independency of the model were described in detail [25,26,29]. The initial and boundary conditions are given are as follows: (1) The brine inlet flow rate (spray density), the brine inlet salinity and the inter-tube vapor pressure at the boundaries of the tube bundle are specified. (2) The stem inlet velocity, the steam inlet temperature are given. (3) The temperature of the wall on shell side is assumed to be constant. The validation of the model is shown in Fig. 2. The simulation results of the current model are compared with the model of Hou et al. [22] and the operating data from Huanghua power plant in China. The calculated value of the average vapor mass flow rate and pressure are coincident with the relative deviation less than 4.2% compared with the operating data of the power plant. Hou et al. adopted similar distributed parameter model, indicating the feasibility of the distributed parameter model for simulating the large-scale falling film evaporator. 3. Results and discussions
3.2. The location of the maximum brine temperature
In the horizontal-tube falling film evaporator for desalination, the distribution of the brine temperature is mainly determined by two parameters: the local pressure of the inter-tube vapor and the local brine salinity. Both parameters are non-uniformly distributed in the tube bundle. The higher local vapor pressure results in higher local saturated temperature of brine. On the other hand, higher local brine salinity, enhancing the boiling point of the brine, tends to result in higher evaporation temperature of the brine [30] as well. Both the variation of pvp and S in the tube bundle determine the distribution of Tbr . For each node of the calculating area, the inter-tube vapor (vapor generated outside of the tubes, hereinafter referred to as vapor) has three possible flow directions: vertical upflow, horizontal flow and vertical downflow as depicted in Fig. 3. For each node, the vapor flow
Fig. 7 demonstrates the locations of Tbr,max under different operating Table 1 Geometry parameters.
3
Name
Description
Tube length/m Row number (RN) Column number (CN) Number of tube Tube external diameter/mm Tube inside diameter/mm Tube arrangement
8 160 80 1 25.4 24 Triangular
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Table 2 Operating conditions. Name
Range −1 −1
Brine inlet spray density/kg·m ·s Brine inlet salinity/g·kg−1 Evaporation temperature/°C Apparent temperature difference/°C Average steam inlet velocity/m·s−1
0.05–0.09 30–50 60 2–5 40
10-3 Hou et al. [22] Operating results Present simulation
3.0
Ge / kg·m-2·s-1
2.7
Fig. 4. Zoning of the heat transfer tube bundle.
2.4
2.1
1.8
10
12
14
16
18
20
22
24
pvp / kPa
s
Fig. 2. Validation of the present model.
1 2 3
Fhz
M
... ...
side boundary
b
upper boundary 1 2 3 ... ... CN/2 a
RN
symmetrical plane
j i
M
Fig. 5. Schematic of evaporation process of brine film outside a horizontal tube.
inter-tube vapor
F vt
M
c lower boundary
inter-tube vapor
Fig. 6. Distributions of the brine temperature.
rear part of the tubes. However, with the increment of Γinlet , the location of the maximum q remains almost unchanged along the tube length direction [25]. This explains the locations of Tbr,max with the increase of Γinlet . Along the tube length direction, it is shown in Fig. 7(b) that with the increase of Sinlet , Tbr,max gradually moves to the steam inlet. As Sinlet is increased, the variation range of h decreases mainly due to the decreases of the heat transfer coefficient on the evaporation side of the tube. On the other hand, less steam is condensed inside the tube which directly results in relatively higher average steam velocity and larger variation range of ΔT along the tube length direction. The impact of ΔT on the distribution of q gradually surpass the impact of h . The maximum of q thus gradually moves backwards to the steam inlet where ΔT has larger values. Consequently, Tbr,max gradually moves toward the same direction as shown in Fig. 7(b).
Fig. 3. The determination of the vapor flow direction for a certain calculation node.
conditions. Along the tube column direction, due to the symmetry characteristics of vapor flow, Tbr,max is always located in the central symmetric plane of the tube bundle. It is the plane composed of the tubes with the column number of 40, denoted by PLcolumn40 in this paper. Along the tube length direction, it is demonstrated in Fig. 7(a) that with the increase of Γinlet , the location of Tbr,max remains almost unchanged. Along the tube length direction, the location of Tbr,max is mainly determined by the distribution of q . Where it has larger q , the brine has relatively higher S and larger BPE , which leads Tbr to be larger. It is found that q reaches its maximum value near the middle4
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Fig. 8. Impact of Γinlet on Tbr , max , δTbr,p and δTbr,BPE .
Fig. 9. Impact of Sinlet on Tbr , max , δTbr,p and δTbr,BPE .
Fig. 10. Impact of ΔTapp on Tbr , max , δTbr,p and δTbr,BPE .
Along the tube length direction, Fig. 7(c) demonstrates that with the increase of ΔTapp , Tbr,max moves firstly forwards the steam outlet, then backward to the inlet. When ΔTapp is of 2.0 °C, compared with under the conditions of larger ΔTapp , less steam is condensed inside tubes. It causes higher average steam velocity and higher steam pressure drop inside tubes. The distribution of ΔT dominates the distribution of the local heat flux along the tube length direction. The maximum q is located
Fig. 7. Location of Tbr,max under different operating parameters.
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It is also noted in Fig. 8 that δTbr,BPE decreases with the increment of Γinlet . With the increment of Γinlet , the concentration ratio of the brine between the inlet and the outlet of the evaporator decreases which causes the slower increase of S and smaller variation range of BPE . When Γinlet is increased from 0.05 to 0.09 kg·m−1·s−1, the brine temperature variation range caused by the variation of BPE decreases from 7.5% to 4.1% of the apparent temperature difference. With the increment of Γinlet , the increase of δTbr,p helps to increase the value of Tbr,max . On the other hand, the decrease of δTbr,BPE goes against the increase of Tbr,max . Under the effects of both the variation of pvp and BPE , Tbr,max shows a slight decreasing trend followed by a significant increasing trend as Γinlet is increased from 0.05 to 0.09 kg·m−1·s−1. Fig. 9 demonstrates the thermodynamic losses caused by vapor flow resistance and boiling point elevation under different Sinlet . As the increment of Sinlet , it is noted that Tbr,max increases almost linearly with the increment of Sinlet . Apparently it mainly results from the increase in the BPE . Both δTbr,p and δTbr,BPE decreases with the increment of Sinlet . When Sinlet is increased, the falling film evaporation heat transfer coefficient decreases significantly because of the increase in the brine viscosity and surface tension [25]. The decrease of heat transfer coefficient leads q to be smaller so that less amount of vapor is produced among tubes. When Sinlet is increased from 30 to 50 g·kg−1, the thermodynamic loss caused by the variation of pvp decreases from 6.2% to 3.5% of ΔTapp and the thermodynamic loss caused by the variation of BPE decreases from 6.3% to 5.9% of ΔTapp . Fig. 10 shows that both δTbr,p and δTbr,BPE increase significantly with the increment of ΔTapp due to the increase of heat flux. When ΔTapp is increased from 2 to 5 °C, the thermodynamic loss caused by the variation of pvp increases from 4.9% to 7.4% of ΔTapp . Meanwhile, the thermodynamic loss caused by the variation of BPE increases from 4.5% to 8.7% of ΔTapp . It is the increase of both δTbr,p and δTbr,BPE that directly lead to the increase of Tbr,max .
near the steam inlet and so does Tbr,max . When ΔTapp is increased to 3 °C, the impact of ΔT on the distribution of q becomes weaker and the distribution of h gradually dominates the distribution of q . Tbr,max gradually moves to the middle-rear part of the tube where h has the maximum value. As ΔTapp further increases to 5 °C, more condensate is generated at the bottom of the tube and the shear force of the steam on the condensate near the steam outlet becomes smaller. The maximum h gradually moves towards the steam inlet; Moreover, the steam condenses completely before reaching the steam outlet which shortens the effective heat transfer length of the tubes. Both the above two aspects result in that Tbr,max moves back to the steam inlet. Along the tube row direction, Tbr,max is always located at the interface of the middle zone and the lower zone where both pvp and BPE have relative larger values. The location of the interface between the middle zone and lower zone has close relation to the local vapor output of the evaporator. With the increase of Γinlet and ΔTapp , or the decrease of Sinlet , it is shown in Fig. 7 that the location of Tbr,max moves upwards. Such variation of the above three parameters are beneficial for the vapor output amount of the evaporator. More vapor near the lower part of the tube bundle changes the flow direction from horizontal flow to vertical flow. The interface plane of middle zone and lower zone gradually moves upward. Fig. 7 also demonstrates the isothermal lines under different operating parameters. Each isothermal line represents the Tbr equaling to Tbr,max minus a micro increment of temperature. It is indicated that with the increment of Γinlet and the decrease of ΔTapp , the length of the isothermal line along the tube row direction increases. It indicates that the brine temperature is more uniformly distributed along this direction. With the decrease of Γinlet , ΔTapp , or the increase of Sinlet , the length of the isothermal line along the tube length direction indicates that the brine temperature is more uniformly distributed along this direction. 3.3. The variation of thermodynamic loss of the brine
4. Concluding remarks
Falling evaporator applied in MEE devices are normally operated under small temperature difference. The local effective temperature difference is sensitive to the variation of the heat transfer parameters. The thermodynamic loss is defined as the difference between the apparent temperature difference and the local effective temperature difference [31]. In this paper, the following parameters are defined to better present the thermodynamic losses caused by the vapor pressure and BPE in such typical small temperature heat exchangers. δTbr,p is defined as the difference between the maximum and the minimum of the saturated vapor temperatures in the evaporator which represents the maximum variation range of Tbr that the variation of pvp contributes; δTbr,BPE is defined as the difference between the maximum and the minimum of BPE which represents the maximum variation range of Tbr that the variation of BPE contributes.
δTbr,p = Tbr,sat |pvp = max − Tbr,sat |pvp = min
(1)
δTbr,BPE = BPEmax − BPEmin
(2)
The distribution of the brine temperature in a horizontal-tube falling film evaporator is studied using distributed parameter model. The conclusions are summarized as follows: 1. In the upper zone of the tube bundle, the brine temperature has larger gradient than the middle zone and the lower zone along the vapor flow directions. It is because of the increase of the boiling point elevation of the brine that the maximum brine temperature is located near the lower rather than the upper part of the tube bundle. 2. Along the tube length direction, with the variation of the brine inlet spray density and inlet brine salinity, the major factors that determine the distribution of the maximum brine temperature are the local heat transfer coefficient inside the tube and the local temperature difference, respectively. With the increase of the apparent temperature difference, the above parameters dominates the distribution of the maximum temperature alternatively. 3. Along the tube row direction, the amount of vapor, by changing the location of the interface of the center and lower zones, indirectly affects the location of the maximum brine temperature. 4. The thermodynamic losses caused by the variation of vapor pressure and brine point elevation shows different variation trends with the change of brine inlet spray density, salinity as well as the apparent temperature difference. Comprehensive consideration of the distribution above parameters must be taken to prevent excessive thermodynamic losses.
From Fig. 8 it can be seen that δTbr,p increases almost linearly with the increment of Γinlet . It is because of the following reasons: (1) The overall heat transfer coefficient of the evaporator is enhanced with the increment of Γinlet due to the increase in the wavy effect of brine films [25]. It leads to remarkable increase of the vapor output. (2) With the increment of Γinlet , the brine film outside the tube surfaces as well as the brine falling among tubes occupy more space which narrows the flow area of the vapor. The increase of Γinlet also result in the change of the liquid flow pattern from droplet flow to jet flow and even to jet-sheet flow which further decrease the flow area of the vapor. Both above two phenomena lead to the increment of the local vapor velocity and finally causes the increase of local vapor pressure gradient. When Γinlet is increased from 0.05 to 0.09 kg·m−1·s−1, the thermodynamic loss caused by the variation of pvp increases from 5.3% to 8.7% of ΔTapp .
Acknowledgements The authors are gratitude for the support of the National Natural Science Foundation of China (No.51936002). 6
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Appendix A. Supplementary material
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