CFD study of fluid flow and natural convection heat transfer from a helically coiled tube in a confined enclosure Part II numerical simulation

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1 CFD study of fluid flow and natural convection heat transfer from a helically coiled tube in a confined enclosure Part II numerical simulation DIACONU BOGDAN MARIAN* CRUCERU MIHAI * JUCAN IOAN DANIEL ** *Faculty of Engineering, University Constantin Brancusi of Tg-Jiu, Geneva,, Targu Jiu, Gorj ** ITP GRUP Teilor, Targu Carbunesti, Gorj ROMANIA diaconu@utgjiu.ro cruceru@utgjiu.ro itpgrup@clicknet.ro Abstract: - A numerical study of fluid flow and natural convection heat transfer from helically coiled tubes under constant wall heat flux density, with vertical axis in water was carried out. The effect of helix diameter and helix pitch on the local and average Nusselt number was assessed. A complex influence of the two parameters on Nusselt number was found. The heat transfer device was immersed in a cylindrical enclosure with vertical axis. The proximity of the wall enclosure was found to influence the buoyancy induced flow profile and as a consequence, Nusselt number value. Key-Words: - Natural convection; helically coiled tube Introduction Helically coiled tubes (HCTs) are simple and robust heat transfer devices used in many industrial applications in chemical and nuclear engineering, process plants, air conditioning and refrigeration. Simple fabrication technology, low cost and relatively high heat transfer surface area volume ratio are the main advantages of such devices. In spite of the wide scale usage, little information is available concerning the heat transfer from such devices. Most of the studies in the literature are concerned with the forced convection heat transfer inside HCTs. Ali [] developed natural heat transfer correlation for HCTs with vertical axis in water. Two types of coils with diameters and mm and various values of the pitch, number of turns and helix diameter were investigated. A power law type Nu-Ra correlation was developed. Moawed [] investigated experimentally the natural convection heat transfer from HCTs with vertical helix axis in air under constant heat flux. Four HCTs having various values of tube diameter, helix diameter, pitch and number of turns were investigated. Higher values of Nusselt number were found at the ends of the helix and lower, constant values in the middle helix section. A heat transfer correlation was developed considering geometric parameters of the HCT: Nu = Ra ( D / d) ( p / d) ( L / d Valid for. Ra. and: p / d.,. D / d. and. L / d. Diaconu et al [] developed a correlation for natural heat transfer from a HCT with vertical helix axis in water for a specific geometry. Conjugated heat transfer conditions rather than constant heat flux or constant temperature were considered. A HCT with the following dimensions was used: d= mm, D=0 mm, p= mm and N=. The following Nu- Ra (with tube length as characteristic length) heat transfer correlation for natural heat transfer from HCT in water was developed: 0. Nu = 0.0Ra for < < Ra () Praghanjan et al [] investigated the natural convection heat transfer from a HCT with vertical axis in water. A conjugated heat transfer approach was used circulating water in the coiled tube and calculating the natural convection heat transfer coefficient (external) based on overall heat transfer coefficient and internal forced convection heat transfer coefficient (internal, Rogers and Mayhew []). Three coils with various values of the tube ) 0. ISBN:

2 diameter, helix diameter and pitch were used. The number of turns was. for all coils. Problem Formulation The theoretical premises of the problem were presented in the first part of the paper.. Simulation premises The diameter of the cylindrical enclosure was 0. m. The bulk temperature value was considered K in all cases. The helically coiled tube was considered coaxial with the cylindrical enclosure axis. The CFD commercial code ANSYS CFX (ANSYS Workbench.0.) was used to carry out the simulation. ANSYS CFX is a general purpose CFD code based on finite volume method for unstructured grids. 0 p=0.0 m Ra=0 0 p=0.0 Ra= p=0.0 Ra= p=0.0 Ra= Figure. Circumferential values of Nusselt Due to the symmetry of the problem a circular sector of the system with the center angle of deg. with vertical symmetry planes including the helix axis was considered in order to reduce the size of the problem. The computational domain (D water domain and D helically coiled tube wall surface) ISBN:

3 was meshed using an unstructured volumetric mesh. The number of elements ranged from approximately 00,000 to,000,000, depending on the size of the computational domain. A five-layer inflated boundary was applied on the surface of the helically coiled tube in order to account for the thermal and dynamic boundary layers. Ra number was varied by modifying the value of the heat flux on the surface of the helically coiled tube. Values ranging from to W/m were considered.circumferential Nusselt number is shown in Fig. (circumferential Nusselt) for d=0.0, D=0.0, N= corresponding to four values of p. A similar circumferential Nusselt number profile can be found with a peak at θ values between 0 and 0 deg. The angular position of the peak value increases with the turn number suggesting that the velocity influence on local Nu is more significant than the influence of temperature. Ra=0 Ra=.E+0 Ra=.E+0 Ra= Ra=.E+0 0 p=0.0 m 0 p=0.0 m Ra=0 Ra=.E+0 Ra= Ra=.0E+0 p=0.0 m p=0.0 m 0 0 Fig.. value on each turn For small values of p the local Nu value on upper turns is influenced by the lower turns. For large values of p this effect is no longer present, each turn having similar Nu profile. Averaged Nu value on each turn is plotted in Fig. (average Nusselt turns) along the turn number. The helix diameter influences the flow profile, presented in Fig. (heat flux.0 W/m, p=0.0 m). The plume develops predominantly at the interior of the helix for D values ranging from 0 mm to ISBN:

mm. At D=0 mm an exterior plume develops for the upper

almost symmetrical on both sides of the helix.

predominantly at the exterior side of the helix.

diameter The influence of plume shape on average Nusselt

Nusselt number on the uppermost turn (Fig.

4 mm. At D=0 mm an exterior plume develops for the upper turns of the helix and at D=00 mm the plume profile grows almost symmetrical on both sides of the helix. At helix diameter values above 0 mm the plume develops predominantly at the exterior side of the helix. D=0 mm D=0 mm D=0 mm D=00 mm D= mm D=0 mm D=00 mm D=0 mm D=0 mm Fig.. Flow profile and velocity for various ratios coil / tube diameter The influence of plume shape on average Nusselt number was investigated plotting the local circumferential Nusselt number on the uppermost turn (Fig. a) and average Nusselt number on each turn against turn index (Fig. b) for constant value of the wall heat flux q =.0 W/m and coil pitch p = m Symmetrical development of the plume that occurs in the case D=0.00 m ensures a higher and more uniform value of the local circumferential Nusselt number value (Fig a) and also a higher average Nusselt number value (Fig. b).. ISBN:

D=0.0 m D=0.0 m D=0.00 m D=0.00 m D=0.0 m number on helix turn 0 0.0 m 0.0 m 0.00 m 0.00 m 0.0 m 0 0 0 0 0 0 0 00 0 0 0 CIrcumferential angular position (deg) a b Fig.

5 D=0.0 m D=0.0 m D=0.00 m D=0.00 m D=0.0 m number on helix turn m 0.0 m 0.00 m 0.00 m 0.0 m CIrcumferential angular position (deg) a b Fig.. Local circumferential Nusselt and average Nusselt The asymmetrical profile of the plume found in the case of large D values can be explained by the influence of enclosure wall proximity. The flow profile for D=0.0 m and a larger enclosure diameter (D E =0. m) is presented in Fig.. number on the whole helix D/D E Fig.. number on the HCT against D/D E Peak value of average Nusselt number was reached for D/D E =0.. Fig.. Flow profile for a larger enclosure diameter number on the helically coiled tube was plotted against D/D E (wall heat flux.0 W/m, pitch coil 0.0 m) in Fig... Conclusions The influence of helix diameter, helix pitch and helix / enclosure diameter ratio on the natural convection from a helically coiled tube was investigated numerically. It was found that both helix diameter and helix pitch values influence the Nusselt number values. The influence is insignificant at low Ra values and increases with Ra. Significant variation of the local Nusselt number on the tube circumference was found. Various patterns of the helix pitch influence on Nusselt number were found, depending on the helix diameter. The helix diameter was also found to influence significantly both Nusselt number and ISBN:

6 flow profile. As the helix diameter increases the plume that develops at low D values at the interior of the helix develops gradually on both sides of the helix and at high D values the plume develops predominantly at the exterior of the helix. The influence of D/D E on average Nusselt number values was assessed by varying helix diameter. It was found that helix diameter has an optimum value (0.00 m) for which Nusselt number has a peak value for which a symmetrical plume was observed (for identical values of the heat flux density). Proximity of the enclosure wall influences the shape of the plume and as a result, average Nusselt number. It was found that Nusselt number is higher for upper turns than for lower turns and the increase of the helix pitch increases also the average Nusselt number for any value of D. For any real application the effect of enclosure wall proximity cannot be neglected as it was shown in this study that D E is a parameter that influences the efficiency of the heat transfer system and not only its compactness. Therefore, a conventional Nu-Ra heat transfer correlation should also include the term D/D E. It is thought that alternative approaches such as Artificial Neural Networks (Colorado et al []). The results presented could be considered as some guidelines for sizing helically coiled tubes for natural convection heat transfer applications. The complex influence of the helix parameters and enclosure diameter on the Nusselt value makes difficult to apply the conventional approach of developing a generalized heat transfer correlation based on helix geometry. Other analysis methods such as machine learning algorithms (artificial neural networks, genetic algorithms, etc.) could be applied successfully in modeling the natural convection heat transfer from such devices. However, is has to be mentioned that a larger volume of data than the one used in this study could be required. A large database including the effect of tube diameter, enclosure diameter and number of turns could be developed and used in conjunction with a machine learning algorithm in order to provide fast and reliable information regarding the natural convection heat transfer from HCTs. References [] D. C. Wilcox, Turbulence Modelling for CFD, DCW Industries, 0 [] D. Colorado, M.E. Ali, O. Garcia-Valladares, J.A. Hernandez, Heat transfer using a correlation by ANN for natural convection from vertical helical coil in oil and glycerol/water solution, Energy () - ISBN:

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel *1 Hüseyin Kaya, 2 Kamil Arslan 1 Bartın University, Mechanical Engineering Department, Bartın, Turkey