EFFECT OF DEAN NUMBER ON THE HEAT TRANSFER CHARACTERISTICS OF A HELICAL COIL TUBE WITH VARIABLE VELOCITY & PRESSURE INLET

The heat transfer, friction factor, pressure difference, Nusselt number of a helical coil tube using variable pressure and velocity during inlet for various values of Dean number [ratio of coil diameter (D) to tube diameter (d)] has been studied using commercially available computational tool. A validation is performed using the computational tool through the experimental data and it was observed that the results are in good agreement. The helical coil of 0.3 m diameter with four (4) turns of inner diameter 0.01 m with length 3.77 has been modelled, meshed and analyzed for both laminar and turbulent flows of constant wall temperature and heat flux. A grid independence test is also performed. The results show that increase in Dean number increases the heat transfer of the helical tube. The increases in pressure have less effect on heat transfer during laminar flow while adverse effect can be observed during turbulent flow.


INTRODUCTION
Heat exchangers were an inevitable component in modern mechanical systems. In order to effectively use energy being generated through various methods, various heat exchangers in various forms like, economizer, air preheater, super heater, waste heat recovery boilers, etc were used. Even though heat exchangers serves the purpose of transferring heat from one fluid to another, lack of effective heat transfer results in loss of heat from the fluid and hence useful energy is being wasted. For this reason, various methodologies were being studied and adapted in increasing the heat transfer effectiveness of various heat exchangers. In many cases where experimental study is not feasible or economically viable, numerical study have been forecasted by many researchers to be a useful tool. The thermal performance of vertical spiral ground heat exchangers (GHE) for extracting ground source heat using a heat pump was performed for nine (9) spiral GHE and two (2) u-tube GHE with ore holes, using experimental method and numerical method. The experiment was performed for all the test samples for 150hrs. The results of the experiments were compared with predicted numerical results using commercially available solver COMSOL [1]. Another combined experimental and numerical approach was performed for investigating the heat transfer and friction flow characteristics of three (3) mini channel regenerative heat exchangers with hydraulic diameter of the channels as 1.5, 1 and 0.5 mm. The study was conducted for measuring the transient thermal responses and pressure drop at the outlet and inlet of each of the heat exchangers. The authors concluded that heat exchanger with 0.5 mm have the highest interstitial coefficient of heat transfer, which can be explained due to the increase in the specific surface area of the heat exchanger [2]. Other combined study suggests that desiccant coated heat exchanger have reduced heat transfer coefficient of 30%, as compared to conventional heat exchangers during heat transfer between air and water. The researchers suggested that the reduction in the heat transfer is due to the resistance provided by the desiccant coating [3]. Corrugated inner tubes with pitch of 5mm and depth 1.5mm have been found to have the highest heat transfer and Nusselt number subjected to different flow rates of 0.03 to 0.13 kg/s and 0.04 to 0.14 kg/s for cold and hot fluids respectively. The experimental result is verified by the prediction of artificial neural network (ANN) which have R2 values of 0.99999, 0.999997 and 0.999993 for heat transfer, Nusselt number and Reynolds number respectively [4].
The thermo hydraulic performance of air to water heat exchange on a double pipe heat exchanger with helical fins (with fin spacing in the range of 0.05 to 2 m) was studied using commercially available numerical solver ANSYS FLUENT [5]. The study have concluded that helical fin with fin spacing of 0.1 m provides the optimum thermo hydraulic performance. The study also denotes the improvement of compactness and overall performance with use of helical fins. Another study using the software proposed that helical wire inserts can increase the Nusselt number by 1.77 times. Some studies also suggested that circular obstacles in heat exchangers can increase the overall performance, compared to other form of obstacles like rectangular or triangular [6][7]. A study using CFD-segmented heat exchanger model using open sourced solver Open FOAM have recommended that velocity scaling between different fin geometries must be avoided. The maximum capacity loss observed was 9.75% from bare-tube heat exchangers. They have concluded that the severity of the Mal-distribution of the refrigerant leads to larger capacity loss in heat exchangers [8]. Other applications of CFD can be found in solving complex equations and geometry of internal combustion engines. CFD solver such as Forte Reaction Design (Chemkin) has been used for studying 3dimension simulations of reactions. Engine emissions simulations were effectively being predicted using numerical solver also [9][10]. Other studies on heat exchangers using commercial codes have been extensively studied by various researchers [11-18 16] for different applications. They have found that commercial CFD codes and tools can be used for studying the characteristics of heat exchangers. Other study involves thermal analysis and multi dimensional modeling of various thermal systems including IC engines, emission dispersion studies, slurry flow, flame study thermal comfort etc. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].
In view of the above literatures, the authors have found that there are fewer studies in the combined effect of Dean number, velocity and pressure inlet with conditions of constant wall temperature and heat flux on the heat transfer, friction factor, pressure difference and Nusselt number of a helical tube. Hence a correlative study on the combined effects has been studied numerically using commercially available tool, ANSYS. To increase the accuracy in predicting the results, a validation has been performed using experimental results and the prediction holds good for both values of heat transfer co-efficient and Nusselt number.

METHODOLOGY Model Preparation and Geometry Creation
The helical tube has been modeled using commercial computational tool, ANSYS for which the dimensions of 0.3 meter, 3.77 meter and 0.01 meter for diameter of coil (D), length of tube (L) and diameter of tube (d), has been chosen for the study as shown in Fig. 1, since the present study will be helpful in analyzing compact heat exchange systems. During the process of the study, four (4) other models were also created by changing the value of 'd', keeping constant value of D and L in order to effectively study the effect of the change in dean number (D/d) on the heat transfer and fluid flow characteristics. The circles are initially created and SWEEP procedure is followed for generating the three dimensional model. The number of turns has been specified to be as four, while defining the body type to be fluid for outer and innermost tube and solid for middle tube. The domain or the cell zone conditions of the model have been defined as water-fluid & copper-solid. The tube of the heat exchanger is made up of copper to facilitate maximum heat transfer due to its superior thermal conductivity. The properties of copper remained constant throughout the analysis.

Grid Independence Test (GIT)
Grid independence tests are one of the most vital procedures which are mandatory in numerical problems, for checking the independence of the final results to the number of grids. Since, most of the results being generated are a function of the number of grids being generated; the results vary in accordance to the grids being specified. Hence, the minimum number of grids after which there is no change in the results of the problem is generally referred to as optimum grid size. At this stage, the results are independent of the grids.  In the present study, initializing from D/d= 10 with assumptions of insulated outer wall, inlet velocity of hot fluid as 1.5072 m/s (Re= 10000), temperature at 355K and variation of grid size from 65770 to 139770, the GIT is performed based on inlet pressure of hot fluid, outlet temperature of hot fluid and outlet temperature of cold fluid. From Fig. 3 (a), it can be observed that the results are independent after 137617, which shows that the results are independent of the grid after the specified value. Also from Fig. 3 (b) and (c), it can be seen that the results are independent after 138726 number of divisions, showing that the results are independent of the grid.

Governing Equations and Boundary Conditions
The models were analyzed using constant wall heat flux (20000 W/m2) and temperature (300 K) for both laminar and turbulent flows. The working fluid is assumed to be water and the corresponding properties of water are shown in Table.1 below. The initial temperature and pressure of the fluid are taken to be 360 K and 1 atm.  The flow was taken to be steady and incompressible and the density of the fluid is constant throughout the computational domain. The effect of conduction on the tube material is small. SIMPLE algorithm is used for the pressure correction approach and the relaxation factor has been kept to its default values (Pressure: 0.3; Momentum: 0.7; Energy: 01; Density: 01; Body force: 01). k-epsilon model is being used as the turbulence model. The governing equations for the study we shown in equations (1) to (7) Continuity equation Navier-Stokes field equation (Only equation is given below) Energy equation where ∅ is the Rayleigh dissipation function and is given by   The results of variation of (a) heat transfer co-efficient and (b) Nusselt number with Reynolds number is shown in Fig. 4. From the figures, it can be seen that the results of the computational tool is quite close to that of the experimental results. Hence the results of both experimental and computational are in good agreement. Thus, the computational tool can be effectively used for the study.   The Fig 5 (a) shows that the pressure distribution (pascals) on the helical tubes are more on the upper region, while less effect is being observed in the lower regions. Again, from Fig. 5 (b), the temperature (kelvin) contour shows that the whole length of the tube is subjected to the heat.   Fig. 7. From the graph, is can be seen that there is increase in Nusselt number with increase in Dean number and pressure. Accordingly, the heat transfer coefficient also increases with increase in inlet pressure. Thus, helical tubes will have higher performance, with increasing Dean number. In turbulent flow conditions, there is increase in all the parameters under study with increase in Dean number. Heat transfer co-efficient increases with increase in pressure inlet while, reduction in Nusselt number is observed. Increase in pressure difference with increase in inlet pressure is observed and for all values of inlet pressure, the pressure difference increases with Dean number.   Fig. 8 (laminar flow) and Fig. 9 (turbulent flow) respectively. The computational study shows higher value of Nusselt number in helical tubes, as compared to straight tubes. During constant heat flux conditions, in both laminar and turbulent flow conditions, the heat transfer co-efficient and pressure difference increases with increase in Dean number. In laminar flow, it can be observed that the Nusselt number for variable values of pressure inlet have less significant effect at lower Dean number. An increase in Nu is observed in increasing Dean number.     Fig. 13. It can be observed that the increase in Dean number results in increase in corresponding values. The increase in velocity increases the heat transfer co-efficient and pressure difference. But the Nusselt number decreases with decrease in velocity. Similar trend can be observed for Friction factor also.

CONCLUSION
Heat transfer phenomenon and fluid flow is studied using commercially available computational tool. The corresponding effects of inlet mass flow rate, pressure at inlet and ratio of curvature (Dean number) is studied. The following conclusions are drawn from the study:  The results of Nusselt number largely depends on the Dean number. The increase in Nusselt number is observed with the increase in Dean number and mass flow rate.  The friction factor is more for Turbulent flow, as compared to laminar flow in all cases.  The computational tool can be used for studying complex and expensive study, which are rather undesirable for experimental study.