Available online at www.sciencedirect.com Energy Procedia 17 (2012 ) 791 800 2012 International Conference on Future Electrical Power and Energy Systems Fluid Flow and Heat Transfer Characteristics in Helical Tubes Cooperating with Spiral Corrugation LI Ya-xia 1, WU Jian-hua 1, WANG Hang 1, KOU Li-ping 1, TIAN Xiao-hang 2 1 School of Mechanical Engineering Shenyang University of Chemical Technology Shenyang, Liaoning, China 2 Thermal Unit 2 Liaoning Electric Power Survey & Design Institute Shenyang, Liaoning, China Abstract Cooperating with spiral corrugation on the inner wall is a passive further heat transfer enhancement method for the smooth helical tube. Numerical simulation was performed to give the turbulent flow and temperature fields in helical tubes cooperating with spiral corrugation. The effects of the spiral corrugation parameters and Reynolds number on the flow and heat transfer were studied. The results show that the spiral corrugation can further enhance heat transfer of the smooth helical tube due to the additional swirling motion. Decrease of the pith of spiral corrugation can enhance heat transfer in the tube. Within the research scope, helical tubes cooperating with spiral corrugation show 50-80% increase of heat transfer while the flow resistance is 50-300% larger than that in the smooth helical tube. 2012 2011 Published by Elsevier Ltd. Selection and/or peer-review under under responsibility of Hainan of [name University. organizer] Open access under CC BY-NC-ND license. Keywords-spiral corrugation; helical tube; secondary flow; heat transfer enhancement. 1. Introduction Helically coiled heat exchangers are extensively used in the power, chemical, pharmaceutical and food industries for the virtue of compact size, high film coefficients, strong structure and good adaptability. In power plant, they are used in steam generator and condenser designs due to their large surface area per unit volume. Heat transfer rate of helical tube is significantly higher because of the secondary flow caused by the centrifugal force. A survey of the open literature [1-4] indicates that a large number of papers have been published to include the flow and heat transfer characteristic in helical tube including laminar and turbulent flow condition. 1876-6102 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Hainan University. Open access under CC BY-NC-ND license. doi:10.1016/j.egypro.2012.02.172
792 LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 Further enhancement of heat transfer rate in helical tubes has great importance in several industrial applications. There are two different concepts to increase the rate of heat transferred basically, one is the active method and the other is the passive method. The active technique requires external forces and the passive technique requires special surface geometries or fluid additives. A few examinations have been considered for helical tubes with both techniques. Chen [5] studied the effect of rotation of helical tubes on the fluid flow and heat transfer characteristic. Cengiz [6] studied the heat transfer rate and pressure drop in a heat exchanger constructed by placing spring-shaped wires with varying pith within a helical tube. Zachar [7] simulated the laminar flow and heat transfer of coiled-tube exchangers to improve heat transfer rate with spirally corrugated on the outer wall. Longjian Li [8] performed a experiment to investigate the single-phase flow and flow-boiling heat transfer augmentation in 3D internally finned and micro-finned helical tubes. Helical tube cooperating with spiral corrugation on the inner wall is another further heat transfer enhancement method, which has been applied in practice such as helix screw thread pipe heat exchanger [9]. For the reason of expensive and difficult fabrication, no research on the fluid flow and heat transfer characteristic in it has been reported to our knowledge. With the development of computer, numerical method has become a new measure to study the performance of heat exchangers. It has the virtue of short research cycle and low cost. In this article, fluid flow and heat transfer in helical tube cooperating with spiral corrugation on the inner wall were numerically studied. The flow and temperature fields were given and the effects on the flow and heat transfer characteristics of Reynolds number and spiral corrugation parameters were investigated. 2. Physical model z 2e h 2a H o x R c Figure 1. Physical model of helical tube cooperating with spiral corrugation The physical model of helical tube cooperating with spiral corrugation is shown in Fig. 1. The spiral corrugation is located on the inner wall of helical tube which makes a helical rib on the outer wall of the tube. In Fig. 1, R c is the curvature radius of smooth helical tube, H is the pitch of helical tube and a is the radius of tube. is the angle rotating along the helical line of the smooth helical tube. The shape of spiral corrugation cross section is semicircular and e is the depth of spiral corrugation. In order to study the effect of spiral corrugation on the further heat transfer enhancement of helical tube, the pitch of the spiral corrugation h is defined as h 1 2 2 N R H 2 c N 2 (1)
LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 793 Here N 1 is the number of the turns of smooth helical tube and N 2 is the number of the turns of spiral corrugation around the helical tube. In this article, two turns of smooth helical tube is selected, i.e. N 1 =2 or the computational domain in axial direction extends from =0 to =720. Three types of spiral corrugation pitch h are studied, the parameters of which are shown in Tab. 1. The depth of spiral corrugation is selected as e=1 mm. Table 1. Geometry dimension of the tubes Tube specification Geometry dimension R c (mm) 2a(mm) H(mm) N 2 h(mm) Smooth helical tube 30 10 20 - - Tube I 30 10 20 20 18.95 Tube II 30 10 20 50 7.59 Tube III 30 10 20 70 5.41 3. Numerical method The k- realizable turbulent model is adopted and the governing equations have been solved with a control volume method by the CFD software FLUENT 6.3. For the complexity of the physical models, the geometries of the helical tube cooperating with spiral corrugation are established by the software UG. 4.0 and the mesh is created by using GAMBIT 2.3 of FLUENT package starting from its primitives. Pressure velocity coupling is done based on SIMPLEC scheme. Moment, turbulent and energy equations are discretized by Second Order Upwind scheme. Constant temperature boundary condition is specified for the tube wall (T w =353 C). Uniform velocity and temperature for inlet (T in =288 C) and outflow for outlet boundary condition are set. Inlet turbulent intensity level I is estimated as I=5%. Incompressible fluid water is used as the work medium, the physical parameters of which are kinetic viscosity =0.001005Pa s, density =998.2kg/m 3. An unstructured non-uniform grid system is used to discretize the governing and energy equations. The three-dimensional grid system is shown in Fig. 2. Simulated results show that hundreds of thousands of grids number can meat the demand of computational accuracy. Figure 2. Computational grids Validation studies are also conducted for the numerical models used with the experimental data available on turbulent flow and heat transfer in smooth helical tubes. Numerical predictions of friction factor f and Nusselt number Nu m in the smooth helical tube with R c =200 mm, H=753.6mm, 2a=20mm are compared with experimental data given in (2) and (3) by [10] and [11]. From Fig. 3 and 4, it can be clearly observed that the numerical results agree well with the experimental results with the maximum deviation of fre is 6.67% and Nu m is 7.97%, which indicates that the simulated results are reliable and precise.
f 794 LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 f 0.076Re 0.25 +0.00725(R c /a) 0.5 (2) Nu m 0.023Re 0.85 Pr 0.4 (a/r c ) 0.1 (3) Re 15000, 5 R c /a 2000 0.014 0.012 Simulation data By eq.(2) in ref.[10] 0.010 0.008 0.006 0.004 16000 18000 20000 22000 24000 26000 Re Figure 3. Comparison of fre for smooth helical tube 240 220 200 By eq.(3) in ref.[11] Simulation data Nu m 180 160 140 120 100 16000 18000 20000 22000 24000 26000 Re Figure 4. Comparison of Nu m for smooth helical tube 4 Result and discussion 4.1 Flow Field A great deal of research results illustrate that in helical tube, the value of secondary flow velocity is less than that of axial velocity for 1 or 2 orders of magnitude. In order to get the secondary flow pattern on the cross section, the velocities based on the rectangular coordinate system should be translated to the velocities based on orthogonal helical coordinate system. According to the relations between rectangular and orthogonal helical coordinate systems [12], the translating equations can be obtained as u V x cos V y sin (4) v V x sin sin +V y cos sin +V z cos (5) w V x sin cos +V y cos cos +V z sin (6) arcsin[k(z z i )/(K 2 +R c x)], K H/(2 ) (7)
LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 795 sin 2 2 K/ R K, cos R / R K (8) 2 2 c c c Where V x, V y and V z are the velocities based on the rectangular coordinate system, u, v and w are the velocities based on orthogonal helical coordinate system. is helix angle of the smooth helical tube. For convenient contrast, the variables are expressed in dimensionless as w' w/v m, u' ud h /, v' vd h / (9) T'=(T-T w )/(T m -T w ) (10) d h =2a (11) Here, u', v', w' and T' are dimensionless velocities and temperature. is viscosity of the fluid and d h is the equivalent diameter of the smooth helical tube. v m and T m are the bulk velocity and temperature on the cross. 1.06 1.01 0.94 0.88 0.81 0.74 0.67 0.61 0.54 0.47 0.40 0.34 0.27 0.20 0.13 0.07 (a) Smooth helical tube (b) Tube I 1.08 1.01 0.94 0.86 0.79 0.72 0.65 0.58 0.50 0.43 0.36 0.29 0.22 0.14 0.07 (c) Tube II 1.19 1.11 1.03 0.95 0.87 0.80 0.72 0.64 0.56 0.48 0.40 0.32 0.24 0.16 0.08 (d) Tube III 1.25 1.17 1.09 1.00 0.92 0.83 0.75 0.67 0.58 0.50 0.42 0.33 0.25 0.17 0.08 Figure 5. Contour line of axial velocity w' at the condition of Re=22000 and =540 (left side of cross is the outside wall). (a) Smooth helical tube (b) Tube I
796 LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 (c) Tube II (d) Tube III Figure 6. Secondary flow pattern at the condition of Re= 22000 and = 540 (left side of cross is the outside wall). The contour lines of dimensionless axial velocity w' on the cross section of the smooth helical tube and three types of helical tubes cooperating with spiral corrugation are shown in Fig. 5 at the condition of =540 and Re=22000. It can be seen that for the smooth helical tube the contour line shape of w is saddle. The velocity gradient near the outside wall is much greater than that near the inside wall and the location of the maximum velocity near the outside wall. This is because in the curved or coiled ducts, the flowing fluid experience a centrifugal force caused by the duct curvature. The magnitude of the centrifugal force which depends on the local axial velocity of the fluid particles and the curvature of the coiled tube can causes secondary flows to develop in the flowing fluid. For the reason of the difference in axial velocity between fluid particles flowing in the core of the tube and fluid particles flowing close to the tube wall, the fluid particles flowing in the tube core have higher axial velocity and thus experience a higher centrifugal force than the fluid particles flowing near the tube wall. Fluid from the tube core region is then pushed towards the outside wall of the tube where it bifurcates and drives the fluid near the wall towards the inside wall of the tube, thus forming a pair of re-circulating counter-rotating vortices and making the location of the maximum axial velocity move to the outside wall. The secondary flow patterns are given in Fig.6. For the helical tube cooperating with spiral corrugation, the saddle shape of the axial velocity w' is destroyed due to the effect of the spiral corrugation. The secondary flow pattern is same to smooth helical tubes as two-vortices, but the scope of secondary flow enlarges at the same time, which is virtue for heat transfer. The locations of the vortices centers change with the different position of corrugation on the cross section. 4.2 Temperature Field 1.05 1.03 1.00 0.96 0.94 0.87 0.80 0.74 0.67 0.60 0.53 0.47 0.40 0.33 0.27 0.20 0.13 0.07 (a) Smooth helical tube (b) Tube I 1.05 1.04 1.02 0.99 0.96 0.93 0.86 0.79 0.73 0.66 0.60 0.53 0.46 0.40 0.33 0.26 0.20 0.13 0.07
LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 797 (c) Tube II 1.05 1.03 1.02 0.99 0.96 0.93 0.86 0.80 0.73 0.66 0.60 0.53 0.46 0.40 0.33 0.27 0.20 0.13 0.07 (d) Tube III 1.01 0.99 0.96 0.94 0.92 0.90 0.83 0.77 0.70 0.64 0.58 0.51 0.45 0.38 0.32 0.26 0.19 0.13 0.06 Figure 7. Temperature fields at the condition of Re= 22000 and = 540 (left side of cross is the outside wall). The contour lines of temperature T on the cross section of four tubes are displayed in Fig. 7. For smooth helical tube, the temperature gradient near the outside wall is much greater than that near the inside wall, which is the effect of secondary flow. For the spiral corrugation tube, the regular pattern of temperature distribution is destroyed by the spiral corrugation. It can also be found that decrease of the pitch of spiral corrugation can make the distribution of temperature more uniform. Fig. 8 displayed the fluid temperature distribution in axial direction. It can be clearly seen that the outlet temperature of the spiral corrugation tube is higher than that of the smooth helical tube. From Fig. 7 and 8, the conclusion can also be drawn that the smaller the spiral corrugation pitch is, the stronger the heat transfer ability of the tube is. Here this is the effect of additional swirling motion caused by the spiral corrugation, which makes heat transfer augment by destroying the boundary layer and enhancing disturbance. The pattern of additional swirling motion caused by the spiral corrugation is shown in Fig. 9. (a)smooth helical tube (b) Tube I (c) Tube II (d) Tube III Figure 8. Distribution of fluid temperature in axial direction
798 LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 Figure 9. Pattern of additional swirling motion caused by spiral corrugation 4.3 Flow Resistance and Nusselt Number 240 220 smooth helical tube tube I tube II tube III 200 Nu m 180 160 140 0 100 200 300 400 500 600 700 Figure 10. The change of Nu m along axial direction. 1000 900 800 700 smooth tube tube I tubeii tubeiii 600 fre 500 400 300 200 100 9000 12000 15000 18000 21000 24000 27000 Re Figure 11. The variant of fre with Re for four tubes. Flow resistance fre and average wall Nusselt number Nu m of four types of tube are given in Fig. 10 and 11. Here the friction coefficient is defined as: f=-(dp/ds)/(2 v 2 m/d h ) (12) It can be found that spiral corrugation can further enhance heat transfer in the smooth helical tube and decrease of the spiral corrugation pitch makes the heat transfer enhance higher. In the research scope, heat
LI Ya-xia et al. / Energy Procedia 17 ( 2012 ) 791 800 799 transfer can be enhanced 50-80% for the smooth helical tube. However, the flow resistance fre increases 50-300%. 5. Conclusions Cooperating with spiral corrugation is a passive further heat transfer enhancement method for smooth helical tube. The spiral corrugation is located on the inner wall of helical tubes which makes a helical rib on the outer wall of the tube. Three-dimensional turbulent flow and heat transfer in three types of helical tube cooperating with spiral corrugation are numerically studied and the flow and temperature fields are compared with that in the smooth helical tube. The results show that the spiral corrugation can further enhance heat transfer in smooth helical tube due to the additional swirling motion and decrease of the pith of spiral corrugation makes heat transfer enhance higher. However the enhancement of flow resistance caused by the spiral corrugation can not be neglected. Acknowledgment This project is supported by a grant from the Key Program of Scientific Technology Research of Liaoning Province of China (No.2006223001), Key Research Fund for the Higher Education Program by Educational Commission of Liaoning Province of China (No. 2009T080). The authors are grateful for this support. References [1]J. S. Jayakumara, S. M. Mahajania and J. C. Mandala, CFD analysis of single-phase flows inside helically coiled tubes, Comput. Chem. Eng., vol.34, Apr. 2010, pp.430-446. [2]I. Conte, X. F. Peng, Numerical investigations of laminar flow in coiled pipes, Appl. Therm. Eng., vol.28, Apr. 2008, pp. 423 432. [3]G.Yang, Z. F. Dong and M. A. Ebadian, Laminar forced convection in a helicoildal pipe with finite pitch, Int. J. Heat Mass Tran., vol.38, Mar. 1995, pp.853-862. [4]T. J. Huttl and R. Friedrich, Influence of curvature and torsion on turbulent flow in helically coiled pipes, Int. J. Heat Fluid Fl., vol.21, Jun. 2000, pp.345 353. [5]H. Z. Chen and B. Z. Zhang, Fluid ow and mixed convection heat transfer in a rotating curved pipe, Int. J. Therm. Sci., vol.42, Nov. 2003,pp. 1047 1059. [6]Y. Cengiz, B.Yasar and P. Dursun, Heat transfer and pressure drops in a heat exchanger with a helical pipe containing inside springs, Energy Convers. Manage, vol.38, Apr.1997, pp. 619 624. [7]A. Zachár, Analysis of coiled-tube heat exchangers to improve heat transfer rate with spirally corrugated wall, Int. J. Heat Mass Tran.,vol. 53, Sep. 2010, pp.3928 3939. [8]L. J. Li, W. Z. Cui and Q. Liao, Heat transfer augmentation in 3D internally nned and micro nned helical tube, Int. J. Heat Mass Tran., vol.48, May.2005,pp.1916 1925. [9]C. Wei, Application of a new helix screw thread pipe exchanger, Chemical Technology Market, vol.32, Jul. 2009, pp. 33-34. Andrea Cioncolini, Lorenzo Santi, An experimental investigation regarding the laminar to turbulent flow transition in helically coiled pipes. Exp. Therm. Fluid Sci., vol. 30, Mar. 2006, pp. 367 380.
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