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Performance of flow and heat transfer in vertical helical baffle condensers
International Communications in Heat and Mass Transfer 72 (2016) 64–70
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Performance of flow and heat transfer in vertical helical baffle condensers☆ Li Lin a,b, Yaping Chen a,⁎, Jiafeng Wu a, Ya Guo a, Cong Dong a,c a b c
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, Jiangsu, China Yantai Architectural Design and Research Co., Ltd, Yantai 264600, Shandong, China Zhejiang University of Science and Technology, Hangzhou 310023, China
a r t i c l e
i n f o
Available online 01 February 2016 Keywords: Vertical feed water heaters Vertical condensers Helical baffled heat exchangers Trisection helical baffles Variable incline angled baffles Liquid dams
a b s t r a c t The feed water heaters in power plants are actually the condensers using turbine extracting steam to heat feed water. The vertical feed water heater occupies less area than the horizontal one and convenient to lift tube bundles out in maintenance. However, the lower heat transfer coefficient due to thick condensate film limits its application. A novel trisection helical baffled vertical condenser (feed water heater) is proposed with liquid dams and gaps for facilitating condensate drainage. The flow and condensation heat transfer characters of two vertical condensers with variable angled trisection helical baffles of both single-thread and dual-threads and a variable spanned segmental baffled one were numerically studied with Mixture model of Fluent software. The distributions of velocity, pressure, volume fraction of condensate, and local heat transfer coefficient in these heat exchangers were demonstrated. The simulation results show that the inclined baffles with liquid dam and drainage gaps could drain condensate effectively from tube bundle surfaces and prevent liquid film from entraining into vapor, and that the variable angled trisection helical baffled vertical condenser with dual-threads could greatly improve the condensation heat transfer coefficient up to 35.7% higher than that of the variable spanned segmental baffled one. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The feed water heaters in power plants are actually the condensers that the steam extracted from turbines condenses at their shell-side for heating the tube-side feed water. The vertical feed water heaters occupy less area than the horizontal ones and the large steam turbine workshop has available lifting equipment as well as sufficient height for lifting tube bundles out vertically. However, the film thickness of condensate gathered on the vertical tube surface in a segmental baffled vertical shell-and-tube heat exchanger is thicker and the heat transfer coefficient is lower than those of the horizontal one, which limits the application of vertical feed water heaters. Nevertheless, the horizontal heater has higher heat transfer coefficient but occupy larger area, and also needs space for dragging the tube bundle out with comparable size as the heat exchanger. To solve this dilemma, promoting the vertical feed water heaters with enhanced condensation heat transfer technique can be a savage, as the features of simpler structure, less occupied area, and reduced maintenance time are quite attractive to the power generation industry as well as petroleum and chemical industry. Steam vapor condensation takes place at the shell-side of the feed water heater, thus the key to improve the shell-side heat transfer coefficient of a vertical feed water heater is to reduce film thickness on ☆ Communicated by W. J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (Y. Chen).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2016.01.014 0735-1933/© 2016 Elsevier Ltd. All rights reserved.
outside of vertical tubes. Many experts proposed different enhanced heat transfer structures for vertical tube condensation. Gregorig [1] proposed a method to reinforce the heat transfer of laminar film condensation on vertical wall by applying a series of drainage plates along a longitudinal grooved tube. Thomas [2] studied film condensation heat transfer on vertical tubes by vertical wires. An et al. [3] studied condensation heat transfer enhancement in spiral grooved tube with staggered tube bundle. Hafiz and Adrian [4] and Zhu [5] theoretically studied respectively the condensation phenomenon on pin-fin tubes and a vertical fluted tube. Most of these enhanced technologies are utilizing surface tension effect to drive the condensate flow into the groove valley and then to reduce the film thickness on the protrusion surfaces of tubes. There are also some enhanced methods worth considering other than on vertical surfaces. Chang and Yeh [6] studied condensation heat transfer enhancement in horizontal elliptical tube. Cavallini et al. [7] and Hicham et al. [8] investigated respectively condensation heat transfer enhancement in minichannels and in a horizontal non-circular microchannel. Chen et al. [9] numerically studied condensation flow of the refrigerant FC-72 in a rectangular microchannel with a 1 mm hydraulic diameter using the volume of fluid model. Caruso et al. [10] experimentally studied film condensation in inclined tubes with noncondensable gases. Peng et al. [11] proposed an idea of condensing on series short channels and draining the condensate before the wet vapor enters the next channel, which takes advantage of the initial thin film part during condensation with higher heat transfer coefficient. Cvengros et al. [12] studied a divided condenser that drains the condensate from different heights.
L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
Nomenclature Latin Symbols E Energy, kJ F Volume force, kN G Mass flow, kg/s, kg/h h Enthalpy, kJ/kg k Turbulence kinetic energy, m2/s2 _ m Mass flux, kg/(m2·s) p Pressure, Pa q Specific heat, kJ/kg S Source term T Temperature, K u Velocity component in x direction, m/s v Velocity, velocity component in y direction, m/s w Velocity component in z direction, m/s Greek symbols α Volume fraction β Incline angle, ° ε Turbulence kinetic energy dissipation rate, m2/s3 ΔH Condensation enthalpy, kJ Effective thermal conductivity, W/(m·s) λeff μ Dynamic viscosity, kg/(m·s) ρ Density, kg/m3 Subscript c E i k m M o v dr sat
Condensate Energy Tube inside Phase number Mixture Mass Tube outside Vapor Drift Saturation
65
of 16 tubes and 3 rods with equilateral triangular layout and a cylindrical shell with inlets and outlets for steam/condensate and cooling water. In account to the decreasing trend of volumetric flow of vapor during condensation, the two helical baffled schemes both have three sections with baffle incline angles of 35°, 25°, and 15°, and the segment baffled scheme has also three sections of different spanned baffles, forming decreased cross-section area. Each helical baffle scheme has dual-thread helical baffles at first and second sections of incline angles of 35° and 25°, while its 15° incline angled third section remains single-thread. The detailed diagrams and structural parameters of these schemes are shown in Figs. 1, 2, Tables 1 and 2. Gambit software is used in building and meshing the 3D models of vertical trisection helical baffle condensers and segmental baffle condenser. Considering the complexity of the geometry, unstructured grids are adopted in the meshing. Fig. 3 is a grid graph of VTHBC at the shell side. The mesh refinement was conducted at the boundary layer of tubes. With the consideration of both independence of the grid number and computational time consumption, the grid numbers around 2.5 million for both VTHBC and VSBC schemes were finally adopted. 2.2. Governing equations Considering the velocity difference of vapor and liquid phase, the Mixture model of Fluent was selected for the two-phase flow models in simulation, which assumes the local equilibrium in the control volumes. By solving the continuity equation, momentum equation and energy equation of the mixed phases, the two-phase flow features of relative velocity, the liquid phase volume fraction and the heat transfer coefficient could be acquired. The conservation equations of continuity, momentum, and energy are as follows [14,15], ! ∇ ρk v k ¼ SMk
ð1Þ
h i ! ! ! ! T ! ! þ ρm g þ F ∇ ρm v m v m ¼ −∇p þ ∇ μ m ∇ v m þ ∇ v m ! 2 X ! ! α k ρk v dr;k v dr;k þ∇
ð2Þ
k¼1
Similar to the ideas of Gregorig [1], Cvengros et al. [12] and Peng et al. [11], Chen et al. [13] proposed a vertical trisection helical baffle condenser (VTHBC) scheme. The VTHBC is a modified shell-and-tube heat exchanger with circumferential overlap trisection helical baffles [14,15]. The inclined baffle plates not only support the tube bundle but also divide the tubes into short segments and scrape the condensate from tube surface successively. Also the downstream straight edge of each sector baffle plate is widened and bent to form a liquid dam to prevent the accumulated condensate from blown into the vapor stream. The draining gaps are set at the curved edge of each sector baffle plate to drain the condensate along the inner surface of the shell to the bottom, thus to enhance the condensation heat transfer coefficient of the vertical feed water heater. Numerical simulation has become an effective tool in understanding the heat transfer performance of a heat exchanger design. Recently, CFD modeling has been gradually applied to two-phase flow cases [16–20]. The CFD numerical simulation method is adopted in this paper to study the flow and heat transfer features of vertical feed water heaters with trisection helical baffles and segmental baffles. 2. Condensation models 2.1. Geometry and meshing As shown in Fig. 1, there are three vertical condenser schemes for calculation and comparison, each condenser consists of a tube bundle
∇
2 h X
i ! α k v k ðρk Ek þ pÞ ¼ ∇ ðλeff ∇T Þ þ SEm
ð3Þ
k¼1
where, the subscript m stands for the mixture; k is the phase ! sequence number, and 1 for vapor and 2 for liquid; F is the volume ! force; α k ; v dr;k ; ρk and λeff k are respectively the volume fraction, the drift velocity, the density, and the effective thermal conductivity of ! phase k; ρm, μm, and v m are, respectively, density, viscosity, and velocity of the mixture, which are expressed respectively as ρm ¼
2 X
α k ρk ; μ m ¼
k¼1
2 1 X ! ! αk μ k ; v m ¼ α ρ v ρm k¼1 k k k k¼1
2 X
ð4Þ
For incompressible phase, Ek = hk, where hk is the sensible enthalpy of phase k. For compressible phase, Ek ¼ hk −
p v2k þ ρk 2
ð5Þ
For a vapor and condensate two-phase flow system, the vapor and condensate are set as the primary and secondary phases, respectively. ! The relative velocity v cv , which is also the slip velocity, and the drift ! velocity v dr;c are defined respectively as ! ! ! v cv ¼ v c − v v
ð6Þ
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L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
(a)
(b)
(c)
(d)
(e)
1-shell; 2-tube bundle; 3-baffle; 4-steam inlet; 5-condensate outlet; 6/7-cooling water inlet/outlet Fig. 1. Structural schematic diagram of vertical trisection helical baffled condensers (VTHBCs) and vertical segmental baffled condenser (VSBC): (a) condenser shell, (b)/(c) tube bundle with single-/dual-thread trisection helical baffles, (d) tube bundle with segmental baffles, and (e) photo of tube bundle.
1 ! ! ! ! v dr;c ¼ v cv − α v ρv v v þ α c ρc v c ρm
ð7Þ
The liquid volume fraction equation is ! ! _ vc −m _ cv Þ ∇ α c ρc v m ¼ −∇ α c ρc v dr;c þ ðm
ð8Þ
_ vc and m _ cv are respectively the mass fluxes transferred at interwhere m face from vapor to condensate and from condensate to vapor. The volume fraction of condensate αc could be acquired by solving Eq. (8), and then the volume fraction of vapor αv can be calculated by using Eq. αc + αv =1. During condensation, the vapor mass decreases and the same amount liquid mass is created accompanied with certain amount of latent heat released and transmitted to the coolant side. The mass and energy source terms are necessary in the condensation models to
describe the heat and mass transfer process. The mass source terms of both liquid and vapor phases and energy source term of mixture are respectively as follows [16], T v −T sat SMc ¼ −SMv ¼ 0:1α v ρv T sat
ð9Þ
T v −T sat ΔH SEm ¼ SMc ΔH ¼ 0:1α v ρv T sat
ð10Þ
where ΔH is the condensation enthalpy (latent heat). The mass source terms are introduced in Eq. (1) for both vapor and condensate phases, while the energy source term is introduced in Eq. (3) for the mixture. 2.3. Boundary conditions Velocity and outflow boundary conditions are applied as the inlet and outlet conditions of the computational domain, respectively. The steady and homogeneous turbulent vapor flow is assumed at the inlet of the shell side with certain temperature T, pressure p, and velocity v. Non-permeable and adiabatic boundary conditions are set at the inner side of shell and the baffle plates. And the constant temperature Table 1 Parameters of both VTHBC and VSBC.
(a)
(b)
1-rod hole; 2-tube hole; 3-draining gap; 4-liquid dam Fig. 2. Structural diagrams of baffles: (a) trisection helical baffle and (b) segmental baffle.
Parameters
Units
Values
Shell inner diameter Baffle outer diameter Tube outer diameter Tube effective length Tube pitch Tube number Rod number
mm mm mm mm mm — —
81 80 8 832 16 16 3
L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70 Table 2 Baffle number for different inclined angle of single-thread and dual-thread trisection helical baffle and segmental baffle condensers. Scheme
Item
1st section
2nd section
3rd section
Helical baffle
Inclined angle Helical pitch (mm) Baffle number Single-thread Dual-threads Pitch(mm) Baffle number
35° 150 6 11 75 4
25° 99.4 9 18 50 6
15° 60 10 10 30 6
segmental baffle
67
condenser, and there is a low velocity zone in the back of each baffle especially in the single-thread scheme. However, in the dual-thread scheme, a quite perfect spiral flow is formed. Nevertheless, Fig. 4c shows that in the segmental baffled condenser, steam flows quite uneven along the zigzagged path that the magnitude of the velocity at the baffle gaps is very large while that at the dorsal side of each baffle is very small. The main steam collides on the next baffle with high velocity after passing through the baffle gap and forms a big stagnant zone at the back of each baffle. 3.2. Pressure
boundary condition is applied on the tube walls for simplicity in calculation to reflect the heat transfer from the steam vapor to the cooling water through the tube walls. The inlet steam is assumed saturate with temperature of 90 °C and pressure of 70 kPa, the inlet velocity is set as 10 m/s through the inlet tube with inner diameter of 50 mm corresponding to a vapor flow of 30 kg/h or Reynolds number of 18,220. The constant temperature of 85 °C tube wall boundary condition is adopted. 2.4. Options in calculation The segregated solver and unsteady implicit solving form were used. The RNG k–ε turbulence model was used for turbulence on flow and heat transfer. SIMPLE algorithm was selected on the coupling calculation of pressure and velocity. The momentum, energy, and turbulence parameters were solved with second-order upwind scheme. The iteration can be regarded as convergence when the residuals of continuity and momentum variables u, v, w, k, ε were less than 10−4 and the residuals of energy parameters were less than 10−7, and simultaneously the mass conservation condition of outlet and inlet fluids was satisfied and the fluid pressure at outlet stabilized. 3. Simulation results and discussion 3.1. Velocity Fig. 4 shows the front view of the local velocity nephograms and vectors of steam at the conjunction of the first and second sections in the three vertical condensers, i.e. single-thread and dual-thread variable angled helical baffle schemes and variable spanned segmental one. The zoomed figures in helical baffled schemes and segmental baffled one were respectively at the sectors ranging 0.16–0.42 m and 0.16–0.40 m from the top. From the figures, it can be seen that the steam flows spirally along the helical baffled channel in each trisection helical baffled
Fig. 5 shows the longitudinal and transverse pressure distributions in vertical condensers of the single-thread and dual-thread variable angle helical baffled schemes and the segmental baffled ones. It can be seen from the longitudinal slices that the pressure drop in vertical condenser of segmental baffled scheme is much larger than that of the trisection helical baffled ones. Compared with the single-thread scheme, the pressure drop of dual-thread scheme increased slightly due to added baffle constraints. The transverse zoomed slice of each scheme of the pressure nephogram with velocity vector distribution was at 0.31 m from the top. It can be seen that the pressure of the helical baffled schemes not only decreases along the flow path but also has radial gradient which balances the centrifugal force of the helical vapor flow in the shell side. 3.3. Volume fraction of condensate The volume fraction of condensate is an index reflecting the condensation heat transfer. Fig. 6 shows the volume fraction of condensate distributions in the three vertical condensers. The zoomed figures in two helical baffled schemes and segmental baffled one were respectively at the meridian sectors ranging 0.49–0.61 m and 0.48–0.58 m from the top. It could be seen from the figures that the volume fraction of condensate increases along the flow path of each condenser, and the condensate from tubes accumulates at baffles and eventually to the vessel bottom. By comparing Fig. 6a the single-thread scheme with Fig. 6b, the dual-thread one, it can be seen that more condensate is generated on the latter than on the former that mainly due to shorter tube span between two baffles, which made liquid film on the tubes thinner and condensation effect better. The scraped condensate in the helical baffle scheme flows along the incline baffle surface and is blocked at the liquid dam of each baffle, which guides condensate flows toward to the inner surface of the shell. The centrifugal force of helical flow in two helical baffle schemes also has separation effect for condensate droplets from the vapor. Then the condensate flows down directly along the inner surface of the shell through draining gaps of
Fig. 3. Grid graph of VTHBC at the shell side: (a) part of meridian section and (b) transverse section.
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L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
Fig. 4. Front views of velocity distributions of three schemes: (a)variable angle single-thread, (b) variable angle dual-threads, and (c)segmental baffle (sectional view).
baffles to the next cycle and eventually to the bottom of the vessel. Nevertheless, from Fig. 6c, it could be seen that the condensate gathered on both sides of segmental baffles but little on the shell inner surface,
indicating that the draining effect on the horizontal surfaces of segmental baffles is quite poor, thus the condensate accumulated on the segmental baffle surface is easily entrained into the main vapor stream.
(a) L: single-thread; M: dual-threads; R: segmental
(b) U: single-thread; M: dual-threads; B:segmental
Fig. 5. Pressure distributions of single-thread, dual-thread helical baffled schemes and segmental baffled scheme (zoomed view position: 0.31 m from top): (a) on meridian slices and (b) on transverse slices.
L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
69
Fig. 6. Volume of condensate fraction distributions on front views and meridian slices: (a) single-thread helical baffled scheme, (b) dual-thread helical baffled scheme, and (c) segmental baffled scheme.
3.4. Heat transfer coefficient Fig. 7 shows the heat transfer coefficients of steam to the five meridian tubes of each of the three vertical condensers. The figures in helical baffled schemes and segmental baffled one were respectively at the range of 0.3–0.5 m and 0.15–0.35 m from the top. From Fig. 7, it could be seen that the heat transfer coefficient of each scheme has periodical distribution that the high value zone is just under the baffle plates with fresh surfaces. By comparing Fig. 7a and b, it is clearly shown that the heat transfer coefficient of the dual-thread scheme is uniform with larger high value zone than that of the single-thread one. The heat transfer coefficient at upper half of each helical cycle of the single-head scheme is similar to that of the dual-thread scheme, but its value at lower half is
much smaller. As the velocity distributions are similar in both cases, the heat transfer enhancement is mainly caused by the added incline baffles. Fig. 7c shows that the heat transfer coefficient of segmental baffled condenser is lower than that of the helical baffled schemes. It is clearly revealed that the baffles play a very important role on scrapping the liquid film from the tubes and the incline baffles in helical schemes could significantly reduce the film thickness on the tubes, and thus augmenting heat transfer coefficient. In general, the average values of heat transfer coefficient of the single-thread and the dual-thread variable angle trisection helical baffled schemes are 10,634 W/(m2·K), 11,790 W/(m2·K), respectively, which are 22.4% and 35.7% higher than that of the variable spanned segmental baffled one with average heat transfer coefficient of 8688 W/(m2·K).
4. Experimental verification
Fig. 7. Heat transfer coefficient distributions on meridian tubes of three schemes: (a) single-thread helical baffled scheme, (b) dual-thread helical baffled scheme, and (c) segmental baffled scheme.
The heat transfer performance test of a vertical condenser with dual-thread variable angle helical baffles with identical geometry was performed for verifying the simulation model. The schematic diagram of the test rig is shown in Fig. 8. An electric heater is used to produce saturated steam for condensation in the condenser and the working medium is circulated under thermal siphon principal. The working parameters of steam in the condenser are controlled with heating power, flow rate, and inlet temperature of cooling water. The heat transmitted in the condenser is measured only at cooling water side and 3% dissipation heat is considered. The uncertainties of flow meter and platinum resistance thermometers and vacuum pressure sensor are 0.5% and 0.2 °C and 0.1%, respectively, and the maximum uncertainties of both overall h.t.c. and shell side h.t.c. are, respectively, 3.77% and 6.26%, which are acceptable at engineering sense. The inverse of the shell-side heat transfer coefficient is obtained by subtracting both tube-wall thermal resistance and the tube-side thermal resistance calculated with Gnielinski equation [21] from the inverse of overall heat transfer coefficient. Fig. 9 shows the comparison of curves of three simulated data with four experimental ones of the shell-side heat transfer coefficients of the vertical condenser with dual-thread variable angle helical baffles. It shows that the average deviation is less than 3.4% and it is within engineering acceptance, which verifies the simulation model to be reliable.
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L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
(2) The variable angle dual-thread helical baffled scheme with added baffle constraints has a little bit larger pressure drop than that of the single-thread one. However, the pressure drops in both helical baffle schemes were significantly lower than that of the segmental baffled one. (3) The scraped condensate in a helical baffle scheme flows along the incline baffle to the liquid dam then flows down directly along the inner surface of the shell through draining gaps of baffles to the next cycle and eventually to the bottom of the vessel. However, the draining effect on the horizontal surfaces of segmental baffles is quite poor, thus the condensate accumulated on the segmental baffle surface is easily entrained into the main vapor stream. (4) The heat transfer coefficient of the dual-thread scheme is uniform with higher heat transfer coefficient than that of the single-thread one. The average values of heat transfer coefficient of the single-thread and the dual-thread variable angle trisection helical baffled schemes are, respectively, 22.4% and 35.7% higher than that of the variable spanned segmental baffled one.
Acknowledgments This work is supported by the National Nature Science Foundation Programs of China (no. 51276035, no.51206022).
Fig. 8. Schematic diagram of condensation test rig.
References 5. Conclusions Mixture model in Fluent software was adopted to simulate the shellside distributions of steam velocity, pressure, local heat transfer coefficient, and condensate volume fraction in three vertical condensers with two single-thread and dual-thread variable angle helical baffled schemes and a variable spanned segmental baffled one. By performing comparison and analysis, conclusions are obtained as follows: (1) The steam vapor flows spirally along the helical baffled channel in each trisection helical baffled condenser. The variable angled baffles with decreased cross-section area can effectively compensate the decreased steam volume flow rate during condensation and enhance heat transfer. The stream in variable angle dualthread helical baffled scheme flows more evenly than in the other schemes. In the segmental baffled condenser, the steam flow is quite uneven and a big stagnant zone is formed at the back of each baffle.
12
-2
h o /kW m K
-1
11.5
11 h o,exp h o,sim
10.5
10 18
20
22
24
26
28
30
-1
G o /kg h
Fig. 9. Comparison of simulation data with experiment ones. (t = 90 °C, p = 70 kPa).
[1] R. Gregorig, Film condensation of fine grooved surfaces with consideration of surface tension, ZAMP 5 (1954) 36–49. [2] D.G. Thomas, Enhancement of film condensation heat transfer rates on vertical tubes by vertical wires, Ind. Eng. Chem. Fundam. 6 (1967) 97–103. [3] Y.L. An, L. Zhao, X.Y. Huang, Study on the heat transfer and flow resistance characteristics of spiral groove tube with staggered tube bundle, Therm. Power Eng. 21 (2006) 358–361 (in Chinese). [4] M.A. Hafiz, B. Adrian, Condensation heat transfer on pin–fin tubes: effect of thermal conductivity and pin height, Appl. Therm. Eng. 60 (2013) 465–471. [5] D.L. Zhu, Numerical heat transfer analysis of laminar film condensation on a vertical fluted tube, Appl. Therm. Eng. 30 (2010) 1159–1163. [6] T.B. Chang, W.Y. Yeh, Theoretical investigation into condensation heat transfer on a horizontal elliptical tube in stationary saturated vapour with wall suction, Appl. Therm. Eng. 31 (2011) 945–953. [7] A. Cavallini, D. Del Col, M. Matkovic, et al., Frictional pressure drop during vapour– liquid flow in minichannels: modelling and experimental evaluation, Int. J. Heat Fluid Flow 30 (2009) 131–139. [8] E.M. Hicham, A. Mohamed, L. Hasna, et al., Condensation heat transfer enhancement in a horizontal non–circular microchannel, Appl. Therm. Eng. 64 (2014) 358–370. [9] S.H. Chen, Z. Yang, Y.Y. Duan, et al., Simulation of condensation flow in a rectangular microchannel, Chem. Eng. Process. 76 (2014) 60–69. [10] G. Caruso, D.V.D. Maio, A. Naviglio, Film condensation in inclined tubes with noncondensable gases: an experimental study on the local heat transfer coefficient, Int. Commun. Heat Mass Transfer 45 (2013) 1–10. [11] X.F. Peng, D. Wu, Y. Zhang, Applications and principles of high performance condensers, Chem. Ind. Eng. Prog. 26 (2007) 97–104 (in Chinese). [12] J. Cvengros, M. Micov, J. Lutisan, Modeling of fractionation in a molecular evapourator with divided condenser, Chem. Eng. Process. 39 (2000) 191–199. [13] Y.P. Chen, C. Dong, L. Lin, et al., Feasibility of application of helical baffle heat exchangers in power plants, Boiler Tech. 45 (2014) 1–5 (in Chinese). [14] Y.P. Chen, A novel helix baffled heat exchanger suitable for tube bundle arrangement with equilateral triangles, Pet. Chem. Equip. 37 (2008) 1–5 (in Chinese). [15] Y.P. Chen, Y.J. Sheng, C. Dong, et al., Numerical simulation on flow field in circumferential overlap trisection helical baffle heat exchanger, Appl. Therm. Eng. 50 (2013) 1035–1043. [16] S. Ghorai, K.D.P. Nigam, CFD modeling of flow profiles and interfacial phenomena in two–phase flow in pipes, Chem. Eng. Process. 45 (2006) 55–65. [17] S.C.K. De Schepper, G.J. Heynderickx, Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker, Comput. Chem. Eng. 33 (2009) 122–132. [18] A. Asghar, R. Masoud, CFD modeling of flow and heat transfer in a thermosyphon, Int. Commun. Heat Mass Transfer 37 (2010) 312–331. [19] W. Liang, F. Song, C. Angelo, et al., A modular RANS approach for modeling laminarturbulent transition in turbomachinery flows, Int. J. Heat Fluid Flow 34 (2012) 62–69. [20] P. Mirzabeygi, C. Zhang, Three–dimensional numerical model for the two-phase flow and heat transfer in condensers, Int. J. Heat Mass Transf. 81 (2015) 618–637. [21] V. Gnielinski, New equations for heat mass transfer in turbulent pipe and channel flows, Int. Chem. Eng. 16 (1976) 359–368.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Performance of flow and heat transfer in vertical helical baffle condensers☆ Li Lin a,b, Yaping Chen a,⁎, Jiafeng Wu a, Ya Guo a, Cong Dong a,c a b c
Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, Jiangsu, China Yantai Architectural Design and Research Co., Ltd, Yantai 264600, Shandong, China Zhejiang University of Science and Technology, Hangzhou 310023, China
a r t i c l e
i n f o
Available online 01 February 2016 Keywords: Vertical feed water heaters Vertical condensers Helical baffled heat exchangers Trisection helical baffles Variable incline angled baffles Liquid dams
a b s t r a c t The feed water heaters in power plants are actually the condensers using turbine extracting steam to heat feed water. The vertical feed water heater occupies less area than the horizontal one and convenient to lift tube bundles out in maintenance. However, the lower heat transfer coefficient due to thick condensate film limits its application. A novel trisection helical baffled vertical condenser (feed water heater) is proposed with liquid dams and gaps for facilitating condensate drainage. The flow and condensation heat transfer characters of two vertical condensers with variable angled trisection helical baffles of both single-thread and dual-threads and a variable spanned segmental baffled one were numerically studied with Mixture model of Fluent software. The distributions of velocity, pressure, volume fraction of condensate, and local heat transfer coefficient in these heat exchangers were demonstrated. The simulation results show that the inclined baffles with liquid dam and drainage gaps could drain condensate effectively from tube bundle surfaces and prevent liquid film from entraining into vapor, and that the variable angled trisection helical baffled vertical condenser with dual-threads could greatly improve the condensation heat transfer coefficient up to 35.7% higher than that of the variable spanned segmental baffled one. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The feed water heaters in power plants are actually the condensers that the steam extracted from turbines condenses at their shell-side for heating the tube-side feed water. The vertical feed water heaters occupy less area than the horizontal ones and the large steam turbine workshop has available lifting equipment as well as sufficient height for lifting tube bundles out vertically. However, the film thickness of condensate gathered on the vertical tube surface in a segmental baffled vertical shell-and-tube heat exchanger is thicker and the heat transfer coefficient is lower than those of the horizontal one, which limits the application of vertical feed water heaters. Nevertheless, the horizontal heater has higher heat transfer coefficient but occupy larger area, and also needs space for dragging the tube bundle out with comparable size as the heat exchanger. To solve this dilemma, promoting the vertical feed water heaters with enhanced condensation heat transfer technique can be a savage, as the features of simpler structure, less occupied area, and reduced maintenance time are quite attractive to the power generation industry as well as petroleum and chemical industry. Steam vapor condensation takes place at the shell-side of the feed water heater, thus the key to improve the shell-side heat transfer coefficient of a vertical feed water heater is to reduce film thickness on ☆ Communicated by W. J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (Y. Chen).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2016.01.014 0735-1933/© 2016 Elsevier Ltd. All rights reserved.
outside of vertical tubes. Many experts proposed different enhanced heat transfer structures for vertical tube condensation. Gregorig [1] proposed a method to reinforce the heat transfer of laminar film condensation on vertical wall by applying a series of drainage plates along a longitudinal grooved tube. Thomas [2] studied film condensation heat transfer on vertical tubes by vertical wires. An et al. [3] studied condensation heat transfer enhancement in spiral grooved tube with staggered tube bundle. Hafiz and Adrian [4] and Zhu [5] theoretically studied respectively the condensation phenomenon on pin-fin tubes and a vertical fluted tube. Most of these enhanced technologies are utilizing surface tension effect to drive the condensate flow into the groove valley and then to reduce the film thickness on the protrusion surfaces of tubes. There are also some enhanced methods worth considering other than on vertical surfaces. Chang and Yeh [6] studied condensation heat transfer enhancement in horizontal elliptical tube. Cavallini et al. [7] and Hicham et al. [8] investigated respectively condensation heat transfer enhancement in minichannels and in a horizontal non-circular microchannel. Chen et al. [9] numerically studied condensation flow of the refrigerant FC-72 in a rectangular microchannel with a 1 mm hydraulic diameter using the volume of fluid model. Caruso et al. [10] experimentally studied film condensation in inclined tubes with noncondensable gases. Peng et al. [11] proposed an idea of condensing on series short channels and draining the condensate before the wet vapor enters the next channel, which takes advantage of the initial thin film part during condensation with higher heat transfer coefficient. Cvengros et al. [12] studied a divided condenser that drains the condensate from different heights.
L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
Nomenclature Latin Symbols E Energy, kJ F Volume force, kN G Mass flow, kg/s, kg/h h Enthalpy, kJ/kg k Turbulence kinetic energy, m2/s2 _ m Mass flux, kg/(m2·s) p Pressure, Pa q Specific heat, kJ/kg S Source term T Temperature, K u Velocity component in x direction, m/s v Velocity, velocity component in y direction, m/s w Velocity component in z direction, m/s Greek symbols α Volume fraction β Incline angle, ° ε Turbulence kinetic energy dissipation rate, m2/s3 ΔH Condensation enthalpy, kJ Effective thermal conductivity, W/(m·s) λeff μ Dynamic viscosity, kg/(m·s) ρ Density, kg/m3 Subscript c E i k m M o v dr sat
Condensate Energy Tube inside Phase number Mixture Mass Tube outside Vapor Drift Saturation
65
of 16 tubes and 3 rods with equilateral triangular layout and a cylindrical shell with inlets and outlets for steam/condensate and cooling water. In account to the decreasing trend of volumetric flow of vapor during condensation, the two helical baffled schemes both have three sections with baffle incline angles of 35°, 25°, and 15°, and the segment baffled scheme has also three sections of different spanned baffles, forming decreased cross-section area. Each helical baffle scheme has dual-thread helical baffles at first and second sections of incline angles of 35° and 25°, while its 15° incline angled third section remains single-thread. The detailed diagrams and structural parameters of these schemes are shown in Figs. 1, 2, Tables 1 and 2. Gambit software is used in building and meshing the 3D models of vertical trisection helical baffle condensers and segmental baffle condenser. Considering the complexity of the geometry, unstructured grids are adopted in the meshing. Fig. 3 is a grid graph of VTHBC at the shell side. The mesh refinement was conducted at the boundary layer of tubes. With the consideration of both independence of the grid number and computational time consumption, the grid numbers around 2.5 million for both VTHBC and VSBC schemes were finally adopted. 2.2. Governing equations Considering the velocity difference of vapor and liquid phase, the Mixture model of Fluent was selected for the two-phase flow models in simulation, which assumes the local equilibrium in the control volumes. By solving the continuity equation, momentum equation and energy equation of the mixed phases, the two-phase flow features of relative velocity, the liquid phase volume fraction and the heat transfer coefficient could be acquired. The conservation equations of continuity, momentum, and energy are as follows [14,15], ! ∇ ρk v k ¼ SMk
ð1Þ
h i ! ! ! ! T ! ! þ ρm g þ F ∇ ρm v m v m ¼ −∇p þ ∇ μ m ∇ v m þ ∇ v m ! 2 X ! ! α k ρk v dr;k v dr;k þ∇
ð2Þ
k¼1
Similar to the ideas of Gregorig [1], Cvengros et al. [12] and Peng et al. [11], Chen et al. [13] proposed a vertical trisection helical baffle condenser (VTHBC) scheme. The VTHBC is a modified shell-and-tube heat exchanger with circumferential overlap trisection helical baffles [14,15]. The inclined baffle plates not only support the tube bundle but also divide the tubes into short segments and scrape the condensate from tube surface successively. Also the downstream straight edge of each sector baffle plate is widened and bent to form a liquid dam to prevent the accumulated condensate from blown into the vapor stream. The draining gaps are set at the curved edge of each sector baffle plate to drain the condensate along the inner surface of the shell to the bottom, thus to enhance the condensation heat transfer coefficient of the vertical feed water heater. Numerical simulation has become an effective tool in understanding the heat transfer performance of a heat exchanger design. Recently, CFD modeling has been gradually applied to two-phase flow cases [16–20]. The CFD numerical simulation method is adopted in this paper to study the flow and heat transfer features of vertical feed water heaters with trisection helical baffles and segmental baffles. 2. Condensation models 2.1. Geometry and meshing As shown in Fig. 1, there are three vertical condenser schemes for calculation and comparison, each condenser consists of a tube bundle
∇
2 h X
i ! α k v k ðρk Ek þ pÞ ¼ ∇ ðλeff ∇T Þ þ SEm
ð3Þ
k¼1
where, the subscript m stands for the mixture; k is the phase ! sequence number, and 1 for vapor and 2 for liquid; F is the volume ! force; α k ; v dr;k ; ρk and λeff k are respectively the volume fraction, the drift velocity, the density, and the effective thermal conductivity of ! phase k; ρm, μm, and v m are, respectively, density, viscosity, and velocity of the mixture, which are expressed respectively as ρm ¼
2 X
α k ρk ; μ m ¼
k¼1
2 1 X ! ! αk μ k ; v m ¼ α ρ v ρm k¼1 k k k k¼1
2 X
ð4Þ
For incompressible phase, Ek = hk, where hk is the sensible enthalpy of phase k. For compressible phase, Ek ¼ hk −
p v2k þ ρk 2
ð5Þ
For a vapor and condensate two-phase flow system, the vapor and condensate are set as the primary and secondary phases, respectively. ! The relative velocity v cv , which is also the slip velocity, and the drift ! velocity v dr;c are defined respectively as ! ! ! v cv ¼ v c − v v
ð6Þ
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(a)
(b)
(c)
(d)
(e)
1-shell; 2-tube bundle; 3-baffle; 4-steam inlet; 5-condensate outlet; 6/7-cooling water inlet/outlet Fig. 1. Structural schematic diagram of vertical trisection helical baffled condensers (VTHBCs) and vertical segmental baffled condenser (VSBC): (a) condenser shell, (b)/(c) tube bundle with single-/dual-thread trisection helical baffles, (d) tube bundle with segmental baffles, and (e) photo of tube bundle.
1 ! ! ! ! v dr;c ¼ v cv − α v ρv v v þ α c ρc v c ρm
ð7Þ
The liquid volume fraction equation is ! ! _ vc −m _ cv Þ ∇ α c ρc v m ¼ −∇ α c ρc v dr;c þ ðm
ð8Þ
_ vc and m _ cv are respectively the mass fluxes transferred at interwhere m face from vapor to condensate and from condensate to vapor. The volume fraction of condensate αc could be acquired by solving Eq. (8), and then the volume fraction of vapor αv can be calculated by using Eq. αc + αv =1. During condensation, the vapor mass decreases and the same amount liquid mass is created accompanied with certain amount of latent heat released and transmitted to the coolant side. The mass and energy source terms are necessary in the condensation models to
describe the heat and mass transfer process. The mass source terms of both liquid and vapor phases and energy source term of mixture are respectively as follows [16], T v −T sat SMc ¼ −SMv ¼ 0:1α v ρv T sat
ð9Þ
T v −T sat ΔH SEm ¼ SMc ΔH ¼ 0:1α v ρv T sat
ð10Þ
where ΔH is the condensation enthalpy (latent heat). The mass source terms are introduced in Eq. (1) for both vapor and condensate phases, while the energy source term is introduced in Eq. (3) for the mixture. 2.3. Boundary conditions Velocity and outflow boundary conditions are applied as the inlet and outlet conditions of the computational domain, respectively. The steady and homogeneous turbulent vapor flow is assumed at the inlet of the shell side with certain temperature T, pressure p, and velocity v. Non-permeable and adiabatic boundary conditions are set at the inner side of shell and the baffle plates. And the constant temperature Table 1 Parameters of both VTHBC and VSBC.
(a)
(b)
1-rod hole; 2-tube hole; 3-draining gap; 4-liquid dam Fig. 2. Structural diagrams of baffles: (a) trisection helical baffle and (b) segmental baffle.
Parameters
Units
Values
Shell inner diameter Baffle outer diameter Tube outer diameter Tube effective length Tube pitch Tube number Rod number
mm mm mm mm mm — —
81 80 8 832 16 16 3
L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70 Table 2 Baffle number for different inclined angle of single-thread and dual-thread trisection helical baffle and segmental baffle condensers. Scheme
Item
1st section
2nd section
3rd section
Helical baffle
Inclined angle Helical pitch (mm) Baffle number Single-thread Dual-threads Pitch(mm) Baffle number
35° 150 6 11 75 4
25° 99.4 9 18 50 6
15° 60 10 10 30 6
segmental baffle
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condenser, and there is a low velocity zone in the back of each baffle especially in the single-thread scheme. However, in the dual-thread scheme, a quite perfect spiral flow is formed. Nevertheless, Fig. 4c shows that in the segmental baffled condenser, steam flows quite uneven along the zigzagged path that the magnitude of the velocity at the baffle gaps is very large while that at the dorsal side of each baffle is very small. The main steam collides on the next baffle with high velocity after passing through the baffle gap and forms a big stagnant zone at the back of each baffle. 3.2. Pressure
boundary condition is applied on the tube walls for simplicity in calculation to reflect the heat transfer from the steam vapor to the cooling water through the tube walls. The inlet steam is assumed saturate with temperature of 90 °C and pressure of 70 kPa, the inlet velocity is set as 10 m/s through the inlet tube with inner diameter of 50 mm corresponding to a vapor flow of 30 kg/h or Reynolds number of 18,220. The constant temperature of 85 °C tube wall boundary condition is adopted. 2.4. Options in calculation The segregated solver and unsteady implicit solving form were used. The RNG k–ε turbulence model was used for turbulence on flow and heat transfer. SIMPLE algorithm was selected on the coupling calculation of pressure and velocity. The momentum, energy, and turbulence parameters were solved with second-order upwind scheme. The iteration can be regarded as convergence when the residuals of continuity and momentum variables u, v, w, k, ε were less than 10−4 and the residuals of energy parameters were less than 10−7, and simultaneously the mass conservation condition of outlet and inlet fluids was satisfied and the fluid pressure at outlet stabilized. 3. Simulation results and discussion 3.1. Velocity Fig. 4 shows the front view of the local velocity nephograms and vectors of steam at the conjunction of the first and second sections in the three vertical condensers, i.e. single-thread and dual-thread variable angled helical baffle schemes and variable spanned segmental one. The zoomed figures in helical baffled schemes and segmental baffled one were respectively at the sectors ranging 0.16–0.42 m and 0.16–0.40 m from the top. From the figures, it can be seen that the steam flows spirally along the helical baffled channel in each trisection helical baffled
Fig. 5 shows the longitudinal and transverse pressure distributions in vertical condensers of the single-thread and dual-thread variable angle helical baffled schemes and the segmental baffled ones. It can be seen from the longitudinal slices that the pressure drop in vertical condenser of segmental baffled scheme is much larger than that of the trisection helical baffled ones. Compared with the single-thread scheme, the pressure drop of dual-thread scheme increased slightly due to added baffle constraints. The transverse zoomed slice of each scheme of the pressure nephogram with velocity vector distribution was at 0.31 m from the top. It can be seen that the pressure of the helical baffled schemes not only decreases along the flow path but also has radial gradient which balances the centrifugal force of the helical vapor flow in the shell side. 3.3. Volume fraction of condensate The volume fraction of condensate is an index reflecting the condensation heat transfer. Fig. 6 shows the volume fraction of condensate distributions in the three vertical condensers. The zoomed figures in two helical baffled schemes and segmental baffled one were respectively at the meridian sectors ranging 0.49–0.61 m and 0.48–0.58 m from the top. It could be seen from the figures that the volume fraction of condensate increases along the flow path of each condenser, and the condensate from tubes accumulates at baffles and eventually to the vessel bottom. By comparing Fig. 6a the single-thread scheme with Fig. 6b, the dual-thread one, it can be seen that more condensate is generated on the latter than on the former that mainly due to shorter tube span between two baffles, which made liquid film on the tubes thinner and condensation effect better. The scraped condensate in the helical baffle scheme flows along the incline baffle surface and is blocked at the liquid dam of each baffle, which guides condensate flows toward to the inner surface of the shell. The centrifugal force of helical flow in two helical baffle schemes also has separation effect for condensate droplets from the vapor. Then the condensate flows down directly along the inner surface of the shell through draining gaps of
Fig. 3. Grid graph of VTHBC at the shell side: (a) part of meridian section and (b) transverse section.
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Fig. 4. Front views of velocity distributions of three schemes: (a)variable angle single-thread, (b) variable angle dual-threads, and (c)segmental baffle (sectional view).
baffles to the next cycle and eventually to the bottom of the vessel. Nevertheless, from Fig. 6c, it could be seen that the condensate gathered on both sides of segmental baffles but little on the shell inner surface,
indicating that the draining effect on the horizontal surfaces of segmental baffles is quite poor, thus the condensate accumulated on the segmental baffle surface is easily entrained into the main vapor stream.
(a) L: single-thread; M: dual-threads; R: segmental
(b) U: single-thread; M: dual-threads; B:segmental
Fig. 5. Pressure distributions of single-thread, dual-thread helical baffled schemes and segmental baffled scheme (zoomed view position: 0.31 m from top): (a) on meridian slices and (b) on transverse slices.
L. Lin et al. / International Communications in Heat and Mass Transfer 72 (2016) 64–70
69
Fig. 6. Volume of condensate fraction distributions on front views and meridian slices: (a) single-thread helical baffled scheme, (b) dual-thread helical baffled scheme, and (c) segmental baffled scheme.
3.4. Heat transfer coefficient Fig. 7 shows the heat transfer coefficients of steam to the five meridian tubes of each of the three vertical condensers. The figures in helical baffled schemes and segmental baffled one were respectively at the range of 0.3–0.5 m and 0.15–0.35 m from the top. From Fig. 7, it could be seen that the heat transfer coefficient of each scheme has periodical distribution that the high value zone is just under the baffle plates with fresh surfaces. By comparing Fig. 7a and b, it is clearly shown that the heat transfer coefficient of the dual-thread scheme is uniform with larger high value zone than that of the single-thread one. The heat transfer coefficient at upper half of each helical cycle of the single-head scheme is similar to that of the dual-thread scheme, but its value at lower half is
much smaller. As the velocity distributions are similar in both cases, the heat transfer enhancement is mainly caused by the added incline baffles. Fig. 7c shows that the heat transfer coefficient of segmental baffled condenser is lower than that of the helical baffled schemes. It is clearly revealed that the baffles play a very important role on scrapping the liquid film from the tubes and the incline baffles in helical schemes could significantly reduce the film thickness on the tubes, and thus augmenting heat transfer coefficient. In general, the average values of heat transfer coefficient of the single-thread and the dual-thread variable angle trisection helical baffled schemes are 10,634 W/(m2·K), 11,790 W/(m2·K), respectively, which are 22.4% and 35.7% higher than that of the variable spanned segmental baffled one with average heat transfer coefficient of 8688 W/(m2·K).
4. Experimental verification
Fig. 7. Heat transfer coefficient distributions on meridian tubes of three schemes: (a) single-thread helical baffled scheme, (b) dual-thread helical baffled scheme, and (c) segmental baffled scheme.
The heat transfer performance test of a vertical condenser with dual-thread variable angle helical baffles with identical geometry was performed for verifying the simulation model. The schematic diagram of the test rig is shown in Fig. 8. An electric heater is used to produce saturated steam for condensation in the condenser and the working medium is circulated under thermal siphon principal. The working parameters of steam in the condenser are controlled with heating power, flow rate, and inlet temperature of cooling water. The heat transmitted in the condenser is measured only at cooling water side and 3% dissipation heat is considered. The uncertainties of flow meter and platinum resistance thermometers and vacuum pressure sensor are 0.5% and 0.2 °C and 0.1%, respectively, and the maximum uncertainties of both overall h.t.c. and shell side h.t.c. are, respectively, 3.77% and 6.26%, which are acceptable at engineering sense. The inverse of the shell-side heat transfer coefficient is obtained by subtracting both tube-wall thermal resistance and the tube-side thermal resistance calculated with Gnielinski equation [21] from the inverse of overall heat transfer coefficient. Fig. 9 shows the comparison of curves of three simulated data with four experimental ones of the shell-side heat transfer coefficients of the vertical condenser with dual-thread variable angle helical baffles. It shows that the average deviation is less than 3.4% and it is within engineering acceptance, which verifies the simulation model to be reliable.
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(2) The variable angle dual-thread helical baffled scheme with added baffle constraints has a little bit larger pressure drop than that of the single-thread one. However, the pressure drops in both helical baffle schemes were significantly lower than that of the segmental baffled one. (3) The scraped condensate in a helical baffle scheme flows along the incline baffle to the liquid dam then flows down directly along the inner surface of the shell through draining gaps of baffles to the next cycle and eventually to the bottom of the vessel. However, the draining effect on the horizontal surfaces of segmental baffles is quite poor, thus the condensate accumulated on the segmental baffle surface is easily entrained into the main vapor stream. (4) The heat transfer coefficient of the dual-thread scheme is uniform with higher heat transfer coefficient than that of the single-thread one. The average values of heat transfer coefficient of the single-thread and the dual-thread variable angle trisection helical baffled schemes are, respectively, 22.4% and 35.7% higher than that of the variable spanned segmental baffled one.
Acknowledgments This work is supported by the National Nature Science Foundation Programs of China (no. 51276035, no.51206022).
Fig. 8. Schematic diagram of condensation test rig.
References 5. Conclusions Mixture model in Fluent software was adopted to simulate the shellside distributions of steam velocity, pressure, local heat transfer coefficient, and condensate volume fraction in three vertical condensers with two single-thread and dual-thread variable angle helical baffled schemes and a variable spanned segmental baffled one. By performing comparison and analysis, conclusions are obtained as follows: (1) The steam vapor flows spirally along the helical baffled channel in each trisection helical baffled condenser. The variable angled baffles with decreased cross-section area can effectively compensate the decreased steam volume flow rate during condensation and enhance heat transfer. The stream in variable angle dualthread helical baffled scheme flows more evenly than in the other schemes. In the segmental baffled condenser, the steam flow is quite uneven and a big stagnant zone is formed at the back of each baffle.
12
-2
h o /kW m K
-1
11.5
11 h o,exp h o,sim
10.5
10 18
20
22
24
26
28
30
-1
G o /kg h
Fig. 9. Comparison of simulation data with experiment ones. (t = 90 °C, p = 70 kPa).
[1] R. Gregorig, Film condensation of fine grooved surfaces with consideration of surface tension, ZAMP 5 (1954) 36–49. [2] D.G. Thomas, Enhancement of film condensation heat transfer rates on vertical tubes by vertical wires, Ind. Eng. Chem. Fundam. 6 (1967) 97–103. [3] Y.L. An, L. Zhao, X.Y. Huang, Study on the heat transfer and flow resistance characteristics of spiral groove tube with staggered tube bundle, Therm. Power Eng. 21 (2006) 358–361 (in Chinese). [4] M.A. Hafiz, B. Adrian, Condensation heat transfer on pin–fin tubes: effect of thermal conductivity and pin height, Appl. Therm. Eng. 60 (2013) 465–471. [5] D.L. Zhu, Numerical heat transfer analysis of laminar film condensation on a vertical fluted tube, Appl. Therm. Eng. 30 (2010) 1159–1163. [6] T.B. Chang, W.Y. Yeh, Theoretical investigation into condensation heat transfer on a horizontal elliptical tube in stationary saturated vapour with wall suction, Appl. Therm. Eng. 31 (2011) 945–953. [7] A. Cavallini, D. Del Col, M. Matkovic, et al., Frictional pressure drop during vapour– liquid flow in minichannels: modelling and experimental evaluation, Int. J. Heat Fluid Flow 30 (2009) 131–139. [8] E.M. Hicham, A. Mohamed, L. Hasna, et al., Condensation heat transfer enhancement in a horizontal non–circular microchannel, Appl. Therm. Eng. 64 (2014) 358–370. [9] S.H. Chen, Z. Yang, Y.Y. Duan, et al., Simulation of condensation flow in a rectangular microchannel, Chem. Eng. Process. 76 (2014) 60–69. [10] G. Caruso, D.V.D. Maio, A. Naviglio, Film condensation in inclined tubes with noncondensable gases: an experimental study on the local heat transfer coefficient, Int. Commun. Heat Mass Transfer 45 (2013) 1–10. [11] X.F. Peng, D. Wu, Y. Zhang, Applications and principles of high performance condensers, Chem. Ind. Eng. Prog. 26 (2007) 97–104 (in Chinese). [12] J. Cvengros, M. Micov, J. Lutisan, Modeling of fractionation in a molecular evapourator with divided condenser, Chem. Eng. Process. 39 (2000) 191–199. [13] Y.P. Chen, C. Dong, L. Lin, et al., Feasibility of application of helical baffle heat exchangers in power plants, Boiler Tech. 45 (2014) 1–5 (in Chinese). [14] Y.P. Chen, A novel helix baffled heat exchanger suitable for tube bundle arrangement with equilateral triangles, Pet. Chem. Equip. 37 (2008) 1–5 (in Chinese). [15] Y.P. Chen, Y.J. Sheng, C. Dong, et al., Numerical simulation on flow field in circumferential overlap trisection helical baffle heat exchanger, Appl. Therm. Eng. 50 (2013) 1035–1043. [16] S. Ghorai, K.D.P. Nigam, CFD modeling of flow profiles and interfacial phenomena in two–phase flow in pipes, Chem. Eng. Process. 45 (2006) 55–65. [17] S.C.K. De Schepper, G.J. Heynderickx, Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker, Comput. Chem. Eng. 33 (2009) 122–132. [18] A. Asghar, R. Masoud, CFD modeling of flow and heat transfer in a thermosyphon, Int. Commun. Heat Mass Transfer 37 (2010) 312–331. [19] W. Liang, F. Song, C. Angelo, et al., A modular RANS approach for modeling laminarturbulent transition in turbomachinery flows, Int. J. Heat Fluid Flow 34 (2012) 62–69. [20] P. Mirzabeygi, C. Zhang, Three–dimensional numerical model for the two-phase flow and heat transfer in condensers, Int. J. Heat Mass Transf. 81 (2015) 618–637. [21] V. Gnielinski, New equations for heat mass transfer in turbulent pipe and channel flows, Int. Chem. Eng. 16 (1976) 359–368.