Experimental Investigation of the Effect of Curvature Ratio on Heat Transfer in Double Pipe Helical Heat Exchanger

Different parameters of double pipe helical coil were investigation experimentally. Four coils were used; three with a curvature ratio (0.037, 0.031, and 0.028) and 11mm diameter of the inner tube while the fourth with 0.033 curvature ratio and 13 mm diameter of the inner tube. The hot water flow in the inner tube whereas the cold water flows in the annulus. The inlet temperatures of hot and cold water are 50 C and 18 C respectively. The inner mass flow rate ranges from 0.0167 to 0.0583 kg/s. The results show the Nusselt number increase with increase curvature ratio. The Nusselt number of the coil with 0.037 curvature ratio increases by approximately 12.3 % as compare with 0.028 curvature ratio. The results also reveal that the Nusselt number of the coil with curvature ratio 0.033 increases by approximately 11.6 % as compare with 0.028 curvature ratio for 400 mm coil diameter.


Introduction
One of most favorable passive techniques is helical coiled.The secondary flow motion induced due to centrifugal force resulting from the curvature of the tube makes the heat transfer rate greater than in a straight tube [1, 2, and 3].The heat transfer and flow characteristic in curved tubes such as spiral and helical coiled tubes have been investigated.Jamal-Abad et al [4] have studied experimental investigation on heat transfer performance and pressure drop characteristics in spiral coil.They found that the geometry of spiral coil is much effective in enhancing the thermal performance.Kubir and Kuloor [5,6] found that friction factor in spiral coil greater than that in straight tubes.Rennie [7] and Rennie and Raghavan [8] experimentally studied the heat transfer in double-pipe helical heat exchanger comprised of one loop.They showed that the overall heat transfer coefficient increase with increase in tube Dean number or annulus Dean numbers.Kumer et al [9] numerically and experimentally investigated the heat transfer in double-pipe helical heat exchanger comprised of four turns of coils.They found that the numerical results of friction factor agree fairly well with the experimental data and an error of 5-8% was observed.Also annulus Nusselt number values increases with increase in the annulus flow rate.The heat transfer characteristic in helical coiled tubes with different design parameter such as tube diameter, coil diameter and coil pitch have rarely been investigated experimentally and numerically [10, 11, 12 and13].Mohammed et al [14] performed a numerical study to investigate the heat transfer and fluid flow characteristics in a helical coiled tube heat exchanger using finite volume method.The study was carried out with different geometrical parameter.The results show that the geometrical parameters such as the helix radius and inner tube diameter have significant effect on the heat transfer under laminar flow conditions.Akhavan-Behabadi et al [15] investigated experimentally the heat transfer characteristics of helically coiled tubes.The experiments were carried out for different geometrical parameter.It was concluded that the coils with greater curvature ratio had higher performance.Pawar et al [16] study experimentally the heat transfer characteristics in a helically coiled heat exchanger for Newtonian as well as non-Newtonian fluids.The experiments were performed for different curvature ratio.They found that overall heat transfer coefficient is higher for smaller helix diameter as compared to larger helix diameter.
In the present work four coils were considered; three coils with a curvature ratio (0.037, 0.031, and 0.028) and 11mm diameter of the inner tube while the fourth with 0.033 curvature ratio and 13 mm diameter of the inner tube and all with same coil length.The purpose of this work is to study the effect of curvature ratios and inner tube diameter on heat transfer and pressure drop characteristics in a helical double pipe heat exchanger and compare the result with previous work.

Experimental Set Up and Procedure 2.1. Material
The test section is a double pipe helical coil it was made of copper.Four coils with different coil diameter (D ) were considered, each coil having 1260 mm long but the coil diameter were changed as shown in the figure (1).The inner diameter of outer pipe (D ) and inner diameter of inner pipe (d ) are 22 mm and 11 mm respectively for three coils and the fourth with 13 mm inner diameter of inner pipe (d ) and all with 1 mm thickness.The geometry dimensions were putting in table (1).

Experimental Apparatus
The experimental set up mainly consist of a test section, hot water closed loop, cold water open loop as shown in the figure (2) and figure (3).The water is heated in hot tank by 3000 W thermostatic electrical heater then pumped to the inner helically coiled tube of test section for circulation, then returns to the hot tank.The cold water was driven by pump from the cold water tank to flow through annulus as counter flow configuration.Two flow meter with rang (1-10 lit/min) with 0.2 % accuracy were used to measure the flow rate of hot and cold fluid .The flow rates were controlled by ball valve.The pressure drop through the inner tube was measured with mercury U-tube manometer.Four T-type thermocouples with ±0.1 0 C accuracy were inserted at inlet and outlet of the test section and connected to a digital temperature recorder to measure the cold and hot fluid temperature.The experimental were conducted by changing for six different flow rates in the inner tube from (1-3.5 lit/min) with annulus cold water flow rate was kept constant at 2 lit/min.The inlet hot water temperature was set to (50 ± 1 0 C) whereas the inlet cold water was set to (18 ± 0.5 0 C).The test section is isolated by rubber tube to minimize the heat losses with surrounding.

Experimental Procedure
In the beginning, the heater is switch on to warm the water inside the hot tank and then the two pumps are turned on to allow hot and cold water to pass through the test section.The flow is adjusted through a control ball valve until flows reach an accurate value.Then, until the system reaches a state of stability, we begin to take the readings of the inlet and outlet temperature of the water in the inner and annulus of test section.The measurement readings are repeated to make sure they are correct.Six values of flow rate were considered from 1 lit/m to 3.5 lit/m and the experiments were repeated.

Data Reduction
The heat transfer rate is averaged between the heat supplied by inner hot water and the heat absorbed by the annulus cold water

…(5)
The outside heat transfer coefficient (ho) was estimated by correlation of Rennie for laminar flow [7].

Nu =
Where the annulus Dean number De is where D is the inner diameter of outer pipe, D is the outer diameter of inner pipe and R is the radius of coil.The hydraulic diameter D 6 is

Results and Discussion
Fig ( 4) and Fig ( 5) show the variation of pressure drop with inner mass flow rate and with different curvature ratio.The pressure drop increase with increasing mass flow rate because of increasing flow rate led to increase the turbulent between the fluid elements.Also when the flow increases, the flow becomes more turbulent, resulting in the loss of a large amount of energy due to the conversion of the energy of the pressure into kinetic energy.Also pressure drop increasing with increase curvature ratio because secondary flow intensifies in higher curvature ratio due to centrifugal force that led to increase the shear stress means that pressure drop will increase.The figure (5) shows at bigger diameter pressure drop reduces because pressure drops inversely proportion to the diameter tube and directly proportion to the velocity of flow which is responsible for lower pressure drop.6) and Fig (7) show the variation of overall heat transfer coefficient with mass flow rate and curvature ratio.The result show that increase overall heat transfer coefficient by increasing mass flow rate this can be attributed increasing the velocity of fluid flow that makes increasing of heat transfer coefficient.Also overall heat transfer coefficient increase with increase curvature ratio because the secondary flow is more effective due to centrifugal force at higher curvature ratio.But when increase the coil diameter the turbulence due to the effect of curvature ratio disappear and the fluid flow through coiled tube changed to become such as the flow through straight tube which in turn decrease overall heat transfer.Fig ( 8) and Fig ( 9) depicted the variation of Nussult number with mass flow rate and with different curvature ratio.The results show the Nussult number increasing with increase of mass flow rate due to increase the turbulent between the fluid elements which will enhance the rate of heat transfer.Also show Nussult number increase with increase of curvature ratio because at the high curvature ratio increase the centrifugal force, which in turn led to increase the effect of secondary flow that increase the rate of heat transfer and as a result increase the Nussult number.Also Secondary flow is more effective due to centrifugal force, which increases at higher mass flow rate.The Nusselt number of the coil with curvature ratio 0.037 increases by approximately 12.3 % as compare with 0.028 curvature ratio.From the figure (10), it was found that Nussult number increase with increase diameter of tube, as known that the increasing diameter of tube led to increase of curvature ratio.This leads to further improved heat transfer and then increases the Nusselt number because when the diameter of the tube is increased, the secondary flows will be stronger, and then more confused.The Nusselt number of the coil with curvature ratio 0.033 increases by approximately 11.6 % as compare with 0.028 curvature ratio for 400 mm coil diameter, or in other words as a comparison between inner tube diameter of 13 mm and 11 mm for the same coil diameter.In this work a critical Reynolds number approximate about 6943 and the maximum Reynolds number is about 6765 at high mass flow rate so the flow is laminar.From the figure Dean number slightly decreases with decreasing curvature ratio.The curvature ratio and the velocity of the flow are two factors to determine the Dean number.This can be explained with higher velocity and higher curvature ratio which increases mixing effect due to intensify secondary flow which in turn enhances heat transfer.The deviation between Nusselt number obtained from above correlation and experimental results for coil with 0.037 curvature ratio is about 5.7 %.The results of the present correlation are depicted in figures (12) with a deviation of about ± 4 %.

Fig. 10 .
Fig. 10.Variation of Nusselt number with inner mass flow rate for 400 mm coil diameter.

Fig ( 11 )
Fig (11) shows the comparison of the experimental work with the results of Dravid et al correlation for laminar flow [19].The Dravid et el correlation of the Nusselt number for helical coil can be expressed as follows Nu = ]0.76+ 0.65√De_Pr C.4bc for 50 < De < 2000 where D N = Re 0 e + ) , 3 C.c

Fig . 12 .
Fig .12. Comparison between experimental data and predictions present correlation.