LAMINAR FORCED CONVECTION HEAT TRANSFER IN HELICAL COILED TUBE HEAT EXCHANGERS

LAMINAR FORCED CONVECTION HEAT TRANSFER IN HELICAL COILED TUBE HEAT EXCHANGERS Hesam Mirgolbabaei ia, Hessam Taherian b a Khajenasir University of Technology, Department of Mechanical Engineering, Tehran, Iran, b Mazandaran University, Department of Mechanical Engineering, Babol, Iran, Abstract A numerical investigation of the forced convection heat transfer from vertical helical coiled tubes at various Reynolds numbers, various coil-to-tube radius ratios and non-dimensional coil pitch was studied. The particular difference in this study compared to other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid-to-fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell-side mass flow rate over the performance coefficient and on shell-side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data. It was deduced that tube diameter was best choice for the characteristic length. Keywords: helical coil- heat exchanger- forced convection- heat transfer- effectiveness 1.Introduction Shell-and-coil heat exchangers are used in refrigerators, HVAC application, chemical plants, solar energy systems, nuclear engineering and food industries. They offer several advantages such as compactness, easy maintenance, improved thermal efficiency, high operating pressure and extreme temperature gradients. A literature survey on the subject produced no fully relevant citations. Heat transfer inside the coiled tube have been investigated by many researchers experimentally and numerically [1]. Though much investigation has been performed on heat transfer coefficients inside coiled tubes, little work has been reported on the outside heat transfer coefficients. Ali [] studied natural convection heat transfer from helical coil. He obtained average outside heat transfer coefficients for turbulent heat transfer from vertical helical coils submersed in water. In these experiments water was pumped through the coil. Five different pitch- to-helical diameter ratios were used, along with two tube diameters and with different numbers of turns. The outside Nusselt number was evaluated using the length of the tube, L, as the characteristic length. Ali [] stated that from the observations, h o decreases slightly with boundary layer length for an outside diameter of 0.01m while it increases rapidly with the boundary layer length for a diameter of 0.008m. Ali [] also suggested that increasing the tube diameter for the same Rayleigh number and tube length will enhance the outer heat transfer coefficients. Xin and Ebadian [1] used three different helicoidal pipes to determine the outside heat transfer coefficients for natural convection. The coils were oriented both vertically and horizontally. The tube wall was heated by passing a high DC current through the tube wall, resulting in a constant heat flux boundary condition. The relationship of the Nusselt number, as a function of the Rayleigh number, was based on the outer diameter of the tube. For the case of a horizontal coil, local Nusselt numbers were higher on the top and the bottom of the coil than on the sides. The correlations of Xin and Ebadian [1] showed that the average heat transfer coefficient of the vertical coil was about 10% higher than for the horizontal coil in the laminar flow regime. Ali [3] performed experiments to measure the average Nusselt number, for a coil with a constant heat flux. The correlation between the Nusselt number and the Rayleigh number was based on the outer tube diameter as the characteristic length. It was found that the Nusselt number decreased with increasing Rayleigh number. Ajele [4] studied shell and coil natural convection heat exchangers experimentally. Combinations of up to four coils, as well as, single coils were tested. For single coils, Ajele divided the data between two regions based on the dimensionless flow space and obtained two equations for the Nusselt number based on the hydraulic diameter of the heat exchanger. Taherian [5] investigated convection heat transfer from single enclosed helical coils in a vertical orientation in the case of natural circulation in shell-side. Coils had different diameter, pitch and tube diameters. It was concluded that tube diameter has a little effect on shell-side heat transfer coefficient. Also it was deduced that,the medium dimensionless coil pitch, 1. 8<p<1.80, is the optimum value. Also Taherian and Allen [6] obtained equation for the effectiveness as a function of shell side to coil side mass flow rate ratio and total length of tube to height of coil ratio.

. Numerical computation.1. Numerical method A numerical investigation of the forced convection heat transfer from vertical helical coiled tubes for various Reynolds number (Re), various coil-to-tube radius ratio, and non-dimensional coil pitch, the coil pitch-tube diameter ratio, was studied with CFD analysis software. The segregated method has been used to solve the governing equations. Also second-order scheme has been used for pressure interpolation. SIMPLEC algorithm has been used for pressure-velocity coupling. Second-order upwind scheme has also been applied for solving momentum and energy equations... Governing equations The equation for steady state conservation of mass, or continuity equation, can be written as follows: x i ( ) = 0 ρu i (1) The momentum conservation equation is described by: p u j ( ρ ) μ i j x uu = + + ρ g () i i x i x i x i The conservation of energy is described by: ( ρcut p i ) T = k x i x i x i (3) Coils having different tube diameter and pitch were placed inside a annular space of two coaxial shells. Coil pitches of 1.5 to tube diameter were studied. The shell side mass flow rates of water were 0.03, 0.04, 0.05 and 0.09 kg/s. The coil side mass flow rate of water was 0.03 kg/s. The material of the coil tube is cooper. The physical dimensions of heat exchanger are shown in Figure1.

L 1 =70mm D=0mm H=360mm D is =90mm D os =160mm D C =15mm Fig.1. geometry and dimensions of helical_coiled tube heat exchanger investigation In this numerical solution, 7geometries were considered and 4 different boundary conditions for each geometry were studied. Table1. contains the specifications of 8 coils. Table 1. coil specification No. 1 3 4 5 6 7 Tube Diameter r (mm) 9.5 9.5 9.5 9.5 1.5 1.5 1.5 Coil Pitch b(mm) 14.3 16. 17.1 19 1.3.5 5 Number of Turns 4 1 0 18 16 15 13 Hydraulic Diameter (mm) 84.5 91.73 94.37 99.83 87.44 91.04 101.7 Coil Surface Area A c (m ) oil 0.840 0.475315 0.359066 0.13133 0.495047 0.341903 0.035593 3. Results and discussion The heat transfer coefficient, h, is an indicator of how well heat can be transferred to or from a flow stream. Therefore it is desirable to understand which parameter affect it and in which manner. The following paragraphs will address this matter. 3.1. Effect of coil pitch on the shell side heat transfer coefficient Another parameter of interest is the coil pitch. In Figures -3, the average heat transfer coefficient as a function of mass velocity of shell side of heat exchanger for each tube diameter, at different pitches are illustrated. As it is shown, with increasing dimensionless coil pitch from 1.5-1.8, the heat transfer coefficient decreases while with increasing pitch to, heat transfer coefficient is increased.

150 100 1150 1100 have (w/m.k) 1050 1000 950 900 Figure. average heat transfer coefficient vs. mass velocity for Dt=9.5 mm 1100 1050 1000 have 950 (w/m.k) 900 850 800 Figure 3. average heat transfer coefficient vs. mass velocity for Dt=1.5 mm In Fig.4., h 0 from all the coils are plotted against heat transfer per unit coil surface area, q'', thus eliminating the effect of area on the heat transfer coefficient. As it can be seen, the coil pitch parameter, do not have significant effect on heat transfer coefficient at fix quantity of heat flux. 1300 100 1.5=<P=<1.8 1100 1000 have (w/m.k) 900 800 700 600 1000 14000 16000 18000 0000 000 q"(w/m) Figure4. Effect of coil pitch for all models

3.. Effect of tube diameter on the shell side heat transfer coefficient In Figure.5. the heat transfer coefficient of coils is plotted as a function of q. in this figure, all coils have the same surface area of approximately 0.5 m, but different tube diameters as indicated in the figure. Heat transfer coefficient decreases by increasing the tube diameter, as the increasing of q, results in rise in reduction of h 0. 110 1100 Dt=1.5mm Dt=9.5mm 1080 have (w/m.k) 1060 1040 100 1000 980 3500 4000 4500 5000 q (w) Figure5. Effect of tube diameter 3.3. Effect of coil pitch on rise in temperature of the shell side fluid In Figures 6 and 7, the rise in temperature of target fluid as a function of shell side mass velocity, has been shown in different coil pitches. The T decreases slightly by increasing the coil pitch. As it was illustrated, the coils with pitches of, have greater quantity of h 0, but have less surface area compared to that of coils which have coil pitches in medium range. Therefore the T of these coils is not greater than other ones. 35 30 5 0 T(k) 15 10 5 0 Figure6. Effect of coil pitch for Dt=9.5mm

35 30 5 T(k) 0 15 10 5 0 Figure7. Effect of coil pitch for Dt=1.5mm 3.4. Effect of tube diameter on rise in temperature of the shell side fluid In Fig. 8. the rise in shell side fluid temperature of coils is plotted as a function of shell side mass flow rate. In this figure, all coils have the same surface area of approximately 0.5 m, but have different tube diameter. It can be seen that tube diameter has little effect on T. 35 30 Dt=9.5 mm Dt=1.5 mm 5 0 T(k) 15 10 5 0 Figure8. Effect of tube diameter 4. Nusselt-Reynolds diagram Although graphs of h 0 are valuable, analyzing the data in non-dimensional form is also of great importance. Heat transfer parameters, when presented in form of a dimensionless quantity, offer a broader and generalized picture. Dimensionless analysis of forced convection heat transfer involves some form of Nusselt and Reynolds number, fine tuned for that specific problem. Both of the main dimensionless numbers of forced convection, are defined, based on a specific characteristic length. The characteristic length, must be a good representative of the geometry of the flow. Different characteristic lengths were used in the Nusselt number calculations to determine which dimension best fits the data. The characteristic lengths used were hydraulic diameter of heat exchanger, the diameter of the tube, the diameter of the coil, the height of the coil (including space between coil turns), and as a normalized length, respectively. The normalized length was calculated by assuming the coil as a cylinder. The normalized length was the outer surface area of this cylinder divided by the total tube length[7]. In Figures 9-1, the plots of Nu vs. Re based on the above-mentioned characteristic length, have been illustrated. Heat exchanger hydraulic diameter,, as proposed by Kays and London[8]is the characteristic length in Figure 9. D hx

In Figures 9-11, it can be seen that data do not correlate well through these cases. The plot of Nu vs. Reynolds based on tube diameter, is presented in Figure14. As can be seen, tube diameter is a satisfactory characteristic length. 10 00 190 180 Nu Dhx 170 160 150 140 130 0 100 00 300 400 500 600 700 800 Re Dhx Figure 9. Nu vs. Re based on Dhx 55 50 45 Nu Ln 40 35 30 5 0 0 50 100 150 00 50 Re Ln Figure 10. Nu vs. Re based on normalized length 750 700 650 Nu H 600 550 500 0 500 1000 1500 000 500 3000 Re H Figure 11. Nu vs. Re based on coil height

Nu Dt 3 1 0 19 18 17 16 15 14 0 0 40 60 80 100 10 Re Dt Figure 1. Nu vs. Re based on tube diameter 5. effectiveness Heat Exchanger heat transfer effectiveness is: ε = q q max (1) Which is the ratio of the actual heat transfer rate in a heat exchanger to the thermodynamically limited maximum possible heat transfer rate if an infinite heat transfer surface area were available in a counterflow heat exchanger. In this section, the effect of different parameter on performance coefficient of heat exchanger is investigated. 5.1. Effect of coil pitch on effectiveness coefficient In Fig. 13 and 14, the thermal effectiveness for two coil tube diameter and four different dimensionless coil pitches, p, have been illustrated. It can be seen c that the thermal effectiveness decreases by the increment of coil pitch and increases by the raise of shell-side mass velocity. Effectiveness 0.67 0.65 0.63 0.61 0.59 0.57 0.55 0.53 0.51 0.49 0.47 0.45 Fig13. heat exchanger Thermal effectiveness for tube diameter of 9.5mm

Effectiveness 0.67 0.65 0.63 0.61 0.59 0.57 0.55 0.53 0.51 0.49 0.47 0.45 Fig.14. heat exchanger Thermal effectiveness for tube diameter of 1.5mm 5.. Effect of tube diameter on effectiveness coefficient In Fig. 15.the effectiveness of heat exchanger is plotted as a function of shell side mass velocity. In this figure, all coils have the same surface area of approximately 0.5 m, but different tube diameters as indicated in the figure. Tube diameter has little effect on effectiveness. 0.65 Dt=9.5 mm 0.6 Dt=1.5 mm Effectiveness 0.55 0.5 0.45 0.4 0.35 0.3 3.3. Effectiveness-NTU relation NTU is the number of heat transfer unit as described by: AU NTU = () C min C min Fig.15. Effect of tube diameter Where is the smaller of the two magnitudes of hot and cold heat capacity rate and the overall heat transfer coefficient, U, is related to the thermal resistance between the two streams of fluid as described by: 1 1 ln( r / r ) 1 o i = + + (3) UA h A π kl h A i i 0 0 In order to establish the effectiveness-ntu relations for the shell-and-coïl heat exchangers, the data were plotted together with the plots for some standard configurations in Figure 3. In Figure16 the effectiveness relationship for counter flow concentric tube heat exchangers, cross flow with C both fluids unmixed and cross flow with the max fluid mixed are plotted for the case =0.5 as an average value. C

effectiveness 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0 C*=0.7 0 1 3 4 5 NTU current study cross flow shell-tube( TEMA E) counter flow cross flow(cmax mixed) Fig.16. comparison of the effectiveness with standard heat exchanger configuration C In Figure 17 the results of the current study are compared with the standard shell and tube relations for values of 0.33, 0.6, 0.75and 1. It is clear that the current data are reasonably correlated by the shell and tube heat exchanger (TEMA E) relations, for C values of greater than 0.6. effectiveness 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0 current study C*=0.33 C*=0.6 C*=0.75 0 1 3 4 NTU Fig.17. comparison of the effectiveness with shell and tube heat exchanger configuration The standard shell and tube relation is as follow [9]: C*=1 5

ε = 1 * * 1 + C + (1 + C ) 1 * 1+ exp[ NTU (1 + C ) ] 1 * 1+ exp[ NTU (1 + C ) ] (4) 6. Conclusions Forced convection heat transfer from vertical helical coils to water was investigated. It was concluded that coil pitch has significant effect on shell-side heat transfer coefficient, as with increasing dimensionless coil pitch in medium range, the heat transfer coefficient decreases while with increasing pitch to tube diameter, heat transfer coefficient is increased. Also it was concluded that heat transfer coefficient decreases by increasing the tube diameter and coil pitch and tube diameter have no great effect on the rise in the target fluid temperature. Different characteristic lengths were used and it was deduced that tube diameter was the best choice for the characteristic length in this study. It has been concluded that the heat exchanger thermal effectiveness decreases by the increment of coil pitch and increases by the raise of shell-side mass velocity. Also, it has been deduced that tube diameter has little effect on thermal effectiveness of helical coiled tube heat exchanger. In conclusion, it is suggested to use the ε-ntu relations of the shell-tube heat exchanger to predict the effectiveness of the forced convection shell-and coil heat exchangers. Nomenclatures A c A p b Flow cross-sectional area on the shell side [m ] Wetted surface area on the shell side [m ] Coil Pitch, [m] Heat flux[w ] ] Length of coil [m] Coil Diameter [m] Temperature [K] q H Height of heat exchanger [m L D T D hx Hydraulic diameter, 4AcH/A p [m] K Thermal conductivity [W/ m.k] p Pressure [P a] P Dimensionless pitch, b/r r Tube Diameter [m] x Dimension of Position [m] g [m/s ] h 0 Gravity acceleration Heat transfer coefficient G Mass velocity [kg/m.s] Nu Nusselt number, hd/k o Δ T Temperature difference [K] C p -1-1 [J kg K ] Heat Capacity C Heat capacity [ ] J/kg.K [W/m.K] C /C * C Heat capacity ratio [ min max ]

Re Reynolds number, [ ρvd/μ] NTU Heat transfer unit u i j Velocity component in x-direction -1 [m.s ] -1 u,u Velocity component in i and j directions [m.s ] Greek symbols ρ Density 3 [kg/m ] μ Dynamic Viscosity [ kg/m.s] ε Subscripts c os is n t max min Effectiveness Coil Outer Shell Inner Shell Normalized Tube Maximum Minimum References [1] Xin R.C., Ebadian M.A.,1996, Natural convection heat transfer from helicoidal pipes, J. Thermophys. Heat Transfer, Vol. 1,97 30. [] Ali M.E.,1994, Experimental investigation of natural convection from vertical helical coiled tubes, Int. J. Heat Mass Transfer, vol 37,665 671. [3] Ali M.E., 1998, Laminar natural convection from constant heat flux helical coiled tubes, Int. J. Heat Mass Transfer, vol 41,175 18. [4] Ajele, natural convection heat transfer from enclosed helical coils, Ph.D. Thesis, thecnical university of Nova Scotia,1995. [5] Taherian,H., 1998, Natural convection heat transfer in heat exchanger with vertical helical coils'', Ph.D. Thesis, Dalhousie University Daltech, Halifax,Nova Scotia, Canada. [6] Taherian,H., 1998,''Natural convection heat transfer in heat exchanger with vertical helical coils'', Ph.D. Thesis, Dalhousie university Daltech, Halifax,Nova Scotia, Canada. [7] Prabhajan D.G., Rennie T.J., 004, Raghavan G.S.V., Natural convection heat transfer from helical coiled tubes, Int. J. Thermal Sciences, vol 43,359 365. [8]Kays, W. M., and London, A. L., 1984, Compact Heat Exchangers, 3rd ed., McGraw-Hill, New York. [9] S. Kakac, G. Liu, 00, (Heat Exchangers Selection, Rating, and Thermal Design), CRC. i Corresponding author, Email: mirgolbabaei@gmail.com