Experimental and Numerical comparison between the performance of Helical cone coils and ordinary helical coils used as dehumidifier for humidification dehumidification in desalination units Abo Elazm M.M. 1, Ragheb A.M. 1, Elsafty A.F. 1, Teamah M.A. 2 1 Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt. 2 Faculty of Engineering, Alexandria University, Alexandria, Egypt. Ragheb_9@yahoo.com ABSTRACT Helical and spiral coils were used for too long as heat exchangers in power and chemical processes. This Numerical research is introducing the concept of helical cone coils and comparing the performance of helical cone coils as heat exchangers to the ordinary helical coils. Helical and spiral coils are known to have better heat and mass transfer than straight tubes, that s attributed to the generation of a vortex at the helical coil known as Dean Vortex, this vortex is a secondary flow superimposed on the primary flow. The Dean Number which is a dimensionless number used in describing the dean vortex is a function of Reynolds Number and the square root of the curvature ratio, so varying the curvature ratio for the same coil would vary the Dean Number. Experimental and Numerical investigation based on the commercial CFD software fluent was made to understand the difference between ordinary helical coils and helical cone coils. Two coils having different heights of 40 and 50 mm and thicknesses 0.6 mm and 0.7 mm were used in the investigation. It was found that as the taper angle enhances the heat transfer characteristics of the coil this increase is presented in an increase in the coil exit temperature, the numerical simulation showed that the heat transfer characteristics of the helical cone coil is better than the ordinary helical coils. Keywords: Experimental, Numerical, Helical, Heat Exchanger, Heat Transfer Nomenclature a: Pipe radius (mm). H: Helical coil height (mm). h: Heat transfer coefficient (w/m 2 K). I: Inclined height (mm). M urf : Relaxation factor of momentum. P: Helical Pitch (mm). P urf : Relaxation factor of pressure. R: Coil radius of curvature (mm). t: Tube Thickness (mm). T: Temperature (k). T wall : Wall temperature (k). u: Inlet velocity (m/s). De: Dean Number. Nu: Nusselt Number. Re cr : Critical Reynolds number. Re : Reynolds number. 104
Greek Symbol Θ: Taper angle. Ρ: Density. 1. Introduction Helical coils have been long and widely used as heat exchangers in power, petrochemical, HVAC, chemical and many other industrial processes. Helical and spiral coils are known to have better heat and mass transfer compared to straight tubes, the reason for that is the formation of a secondary flow superimposed on the primary flow, known as Dean Vortex (Rohsenow et al., 1998). The Dean Vortex was first observed by Eustice; then numerous studies have been reported on the flow fields that arise in curved pipes (Dean, White, Hawthorne, Horlock, Barua, Austin and Seader)( Adrian and Allan, 2003). The first attempt to mathematically describe the flow in a coiled tube was made by Dean, he found that the secondary flow induced in curved pipes (Dean Vortex) is a function of Reynolds Number and the curvature ratio, the Dean Number is widely used to characterize the flow in curved tubes: De = Re * (1) It has been widely observed that the flow inside coiled tubes remains in the viscous regime up to a much higher Reynolds Number than that for straight tubes Srinivasan et al. (Rohsenow et al., 1998). The curvature induced helical vortices (Dean Vortex) tend to suppress the onset of turbulence and delay transition. The critical Reynolds Number which describes the transition from laminar to turbulent flow is given by any correlations; the following correlation is given by Srinivasan et al.( (Rohsenow et al., 1998): Re cr = 2100 * (1+12 ) (2) Dennis and Ng (Dennis and Ng, 1982) numerically studied laminar flow through a curved tube using a finite difference method with emphasis on two versus four vortex flow conditions. They ran simulations in the Dean range of 96 to 5000. The four vortex solutions would only appear for a Dean number greater than 956. Dennis and Riley (Dennis and Riley, 1991) developed an analytical solution for the fully developed laminar flow for high Dean Numbers. Though they could not find a complete solution to the problem, they stated that there is strong evidence that at high Dean Numbers the flow develops into an inviscid core with a viscous boundary layer at the pipe wall. The effect of pitch on heat transfer and pressure drop was studied by Austin and Soliman (Austen and Soliman. 1988) for the case of uniform wall heat flux. The results showed significant pitch effects on both the friction factor and the Nusselt Number at low Reynolds Numbers, though these effects weakened as the Reynolds number increased. The authors suggested that these pitch effects are due to free convection, and thus decrease as the forced convection becomes more dominant at higher Reynolds Numbers. The effect of the pitch on the Nusselt Number in the laminar flow of helicoidal pipes was also investigated by Yang et al (Yang, Dong, and Ebadian. 1995) Numerical results for fully developed flow with a finite pitch showed that the temperature gradient on one side of the pipe will increase with increasing torsion; however, the temperature gradient on the opposite will decrease. Overall, the Nusselt Number slightly decreases with increasing torsion for low Prandtl Numbers, but 105
significantly decreases with larger Prandtl Numbers. On the other hand Germano (Germano, 1982) introduced an orthogonal coordinate system to study the effect of torsion and curvature on the flow in a helical pipe. In the results of the perturbation method indicated that the torsion had a second order effect and curvature had a first order effect on the flow. Further studies by Tuttle (Tuttle, 1990) indicated that the frame of reference (coordinate system) determines if the torsion effect is first or second order. Kalb and Seader (Kalb, and Seader. 1972) numerically studied the heat transfer in helical coils in case of uniform heat flux using an orthogonal toroidal coordinate system. They have found that for Prandtl Numbers greater than 0.7, it was shown that the local Nusselt Number in the area of the inner wall was always less than that of a straight tube, and increasing less as the Dean Number is increased till it reached a limiting value. The local Nusselt Numbers on the outer wall continued to increase with increasing Dean Number. Fully developed laminar flow and heat transfer was studied numerically by Zapryanov et al. (Zapryanov, Christov, and Toshev, 1980) using a method of fractional steps for a wide range of Dean (10 to 7000) and Prandtl (0.005 to 2000) numbers. Their work focused on the case of constant wall temperature and showed that the Nusselt number increased with increasing Prandtl numbers, even for cases at the same Dean number. Spiral coils have received little attention compared to helical coils, though the reported results of spiral coils show better performance than helical ones. Figueiredo and Raimundo (Figueiredo and Raimundo, 1996) experimentally investigated the thermal response of a hotwater store and the thermal discharge characteristics from heat exchanger coils placed inside. The classical cylindrical coil and the flat spiral coil were investigated. The results indicated that the efficiency of flat spiral coil was higher than that of a cylindrical one. The results from comparison between the model and experiments were in good agreement. Naphon and Suwagrai (Naphon and Suwagrai, 2007) studied the Effect of curvature ratios on the heat transfer in the horizontal spirally coiled tubes both experimentally and numerically, they have found that due to the centrifugal force, the Nusselt number and pressure drop obtained from the spirally coiled tube are 1.49, 1.50 times higher than those from the straight tube, respectively. Helical cone coils have even received lower attention than spiral coils, only very few researchers have investigated the capabilities of these coils due to the complexity of the structure, it was hard to investigate it both numerically and experimentally. Yan Ke et al. (Yan Ke, Ge, Sue and Meng, 2011) have investigated the helical cone tube bundles both numerically and still some foregoing experiments, the authors found that the cone angle has a significant effect on enhancing the heat transfer coefficient, also they ve found that the pitch has nearly no effect on the heat transfer. The aim of this paper is to experimentally and numerically investigate the effect of the taper angle on heat transfer characteristics. 2. Numerical Simulation 2.1 Helical Cone Coil Geometry The Geometry of the helical cone tube is shown in Fig.1; both the curvature and torsion are variable along the tube. The bottom radius of curvature is donated (R), the pipe diameter (a), 106
the helical pitch as (P), the straight height (H) and finally the inclined height (I). For a straight helical coil the height (H) will be equal to (I) but when changing the inclination angle (θ), the height of the coil (I) will change in accordance to that angle, while keeping (H) constant. Figure 1: Helical Coil Geometry The bottom radius of curvature (R) is 95 mm; the tube diameter (a) was 11 mm. two coil heights (H) were used 40 and 50 mm and two different tube thicknesses were used 0.6 and 0.7 mm. 2.2 Simulation Model The laminar flow in the helical spiral coil is simulated using the commercial CFD software Fluent. In the simulation of the laminar fluid flow, the flow and pressure equations were solved with SIMPLEC algorithm, which is one of the three widely, used velocity pressure coupling algorithm in Fluent. The Second Order Upwind algorithm was employed in the discretization of the equations because of its accuracy and iterating efficiency. The parameters of laminar fluid flow model were in accordance with the default values of the CFD software: P urf = 0.3 M urf = 0.7 (3) Where, the P urf and M urf respectively denote the Under Relaxation Factor of pressure and momentum of the fluid flow inside the tube during the iterating of the calculation. The commercial software Fluent uses both Navier Stocks equation, continuity equation and the energy equation in the solution, the equations are solved for laminar, steady and 3D flow. The second step was to make mathematical model verification, and as stated previously, very few experiments and mathematical simulations have been conducted on helical cone tubes. In order to verify the accuracy of the mathematical model we are investigating, the finite element model for the circular cross sectional area made by (Yan Ke et al)has been used in the verification. Unstructured, non uniform grid systems are used to discretize the main governing equations. The sweep grids were used to discretize the whole volume of the spiral coil. The skewness was kept below 0.5 for all of the models to have a good mesh quality. The constant temperature and non slip boundary conditions were applied. The results of the mathematical model were found in agreement with the results of Yan Ke et al. (Yan Ke, Ge, 107
Sue and Meng, 2011), this paper was discussing both elliptical and circular pipe cross section for the helical cone coils, in the verification the results was only compared to the circular pipe results and it was within 10% of these results. 3. Results and Discussion 3.1 Experimental and Numerical Results Two numerical models were used to simulate the actual coils at various operating conditions; table 1 shows the geometrical parameters for the experimental and numerical model. Coil 1 mathematical model data could be found in table 2 and coil 2 mathematical model data could be found in table 3. Five experiments and numerical simulation were conducted on each coil, vapor at various temperatures is used to heat the water in the coil. Table 1: Helical Cone Coils Experimental and Mathematical Model Geometrical Parameters Coil P (mm) R (mm) a (mm) Re u (m/s) t (mm) H (mm) I (mm) Coil 1 0.7 40 85 20 95 11 6360 0.58 Coil 2 0.6 50 95 Table 2: Coil 1 Mathematical Model Data Number of Nodes 283124 Number of Cells 252384 Inlet Outlet Thermal Boundary Condition Pressure, Momentum, Energy, Scheme Water Inlet Temperature Velocity inlet (0.58 m/s) Pressure Outlet Temperature = Vapor Temperature for each Second Order upwind Inlet Temperature in each Case Table 3: Coil 2 Mathematical Model Data Number of Nodes 341048 Number of Cells 310230 108
Inlet Outlet Thermal Boundary Condition Pressure, Momentum, Energy, Scheme Inlet Temperature Velocity inlet (0.58 m/s) Pressure Outlet Temperature = Vapor Temperature for each Second Order upwind Inlet Temperature each Case Figure 2: Coil 1 Experimental and Numerical Results Comparison Figure 2 shows the vapor temperature, the water temperature at the coil inlet, the water temperature at the coil outlet numerically and experimentally for coil 1. It can clearly conclude from the figure that the difference between the experimental and numerical results is less than 10 % so the numerical simulation is highly acceptable. Figure 3 shows the vapor temperature, the water temperature at the coil inlet, the water temperature at the coil outlet numerically and experimentally for coil 2. It can clearly conclude from the figure that the difference between the experimental and numerical results is less than 10 % so the numerical simulation is highly acceptable. It can be concluded from the previous results that the numerical simulation can be used to compare between the ordinary helical coils and helical cone coils. 109
3.2 Helical Cone Coils and Ordinary Helical Coils Numerical Comparison The comparison between the helical cone coils and the ordinary coils will be numerically as the numerical simulation has shown good agreement with the experimentally results. Two numerical models were built for the ordinary coils. Table 4 shows the geometric parameters of the ordinary helical coils. Figure 2: Coil 2 Experimental and Numerical Results Comparison Table 3: Ordinary Coils Geometric Parameters Coil P (mm) R (mm) a (mm) Re u (m/s) t (mm) H = I (mm) Coil 1 0.7 40 20 95 11 6360 0.58 Coil 2 0.6 50 Ordinary helical Coil 1 mathematical model data could be found in table 5 and ordinary helical coil 2 mathematical model data could be found in table 6. It s worth noting that in the helical cone coil having the structural parameters stated in table 1 that coil will be a six turns coil, while ordinary helical coil with the structural parameters found in table 4 will be only 110
three turn though they have the same height. The coil will be simulated using the same vapor temperature used in the previous section. Figure 4 shows a numerical comparison between the exit temperature of the ordinary helical coil and the exit temperature of the helical cone coil for coil 1, it can be clearly seen that the helical cone coil has better performance that the ordinary helical coil though it utilizes less space. Table 5: Coil 1 Mathematical Model Data Number of Nodes 141450 Number of Cells 125952 Inlet Outlet Thermal Boundary Condition Pressure, Momentum, Energy, Scheme Water Inlet Temperature Velocity inlet (0.58 m/s) Pressure Outlet Temperature = Vapor Temperature for each Second Order upwind Inlet Temperature in each Case Table 6: Coil 2 Mathematical Model Data Number of Nodes 197232 Number of Cells 178296 Inlet Velocity inlet (0.58 m/s) Outlet Thermal Boundary Condition Pressure, Momentum, Energy, Scheme Pressure Outlet Temperature = Vapor Temperature for each Case Second Order upwind Inlet Temperature Inlet Temperature each Case Figure 5 shows a numerical comparison between the exit temperature of the ordinary helical coil and the exit temperature of the helical cone coil for coil 2, it can be clearly seen that the 111
helical cone coil has better performance that the ordinary helical coil though it utilizes less space. Figure 4: Coil 1 Ordinary and Helical Cone Coil Exit Temperature Comparison 112
Figure 4: Coil 2 Ordinary and Helical Cone Coil Exit Temperature Comparison 4. Conclusion The heat transfer characteristics of the helical cone coil were found to be better than the heat transfer characteristics of the ordinary helical coils. The geometry of the coil was found to have a significant effect of the coil exit temperature. The taper angle of the helical cone coil has a significant effect on its heat transfer characteristics. 5. References 1. Austen, D. S., and H. M. Soliman. (1988), Laminar flow and heat transfer in helically coiled tubes with substantial pitch. Experimental Thermal and Fluid Science, 1,pp 183 194. 2. Adrian B. and Allan D, E.B.,(2003), Heat Transfer Handbook, First ed. John Wiley & Sons, New Jersey. 3. Dennis, S. C. R. and M. Ng. (1982), Dual solutions for steady laminar flow through a curved tube. Quarterly Journal of Mechanics and Applied Mathematics, 35(3),pp 305 324. 4. Dennis, S. C. R. and N. Riley. (1991), On the fully developed flow in a curved pipe at large Dean number. Proc. R. Soc. London Ser. A 43(4), pp 473 478. 113
5. Futagami, K. and Y. Aoyama. (1988), Laminar heat transfer in a helically coiled tube. International Journal of Heat and Mass Transfer, 31(2), pp 387 396. 6. Figueiredo AR, Raimundo AM. (1996), Analysis of the performances of heat exchangers used in hot water stores. Applied Thermal Engineering, 16,pp 605 11. 7. Germano, M. (1982), On the effect of torsion on a helical pipe flow, Journal of Fluid Mechanics, 12(5),1 8. 8. Kalb, C. E. and J. D. Seader, (1972), Heat and mass transfer phenomena for viscous flow in curved circular tubes. International Journal of Heat and Mass Transfer, 15,pp 801 817. 9. Paisarn Naphon, Jamnean Suwagrai, (2007), Effect of curvature ratios on the heat transfer and flow developments in the horizontal spirally coiled tubes, International Journal of Heat and Mass Transfer 50, pp 444 451. 10. Tuttle, E. R. (1990), Laminar flow in twisted pipes. Journal of Fluid Mechanics, 219,545 570. 11. Warren M. Rohsenow, James R Hartnett and Young I. Cho, (1998), Handbook of Heat Transfer, Third ed. McGraw Hill, New York. 12. Yan Ke, Ge Pei qi, Sue Yan cai and Meng Hai tao, (2011), Numerical simulation on heat transfer characteristic of conical spiral tube bundle, Applied Thermal Engineering 31, pp 284 292. 13. Yang, G., F. Dong, and M. A. Ebadian. (1995), Laminar forced convection in a helicoidal pipe with finite pitch. International Journal of Heat and Mass Transfer, 38(5), pp 853 862. 14. Zapryanov, Z., Christov, C. and E. Toshev. (1980) Fully developed laminar flow and heat transfer in curved tubes. International Journal of Heat and Mass Transfer, 23,pp 873 880. 114