Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model
Introduction
Heat exchangers have a vital role in industrial applications. Due to compactness and high heat transfer coefficient, helical coils are extensively used as heat exchangers such as steam generators [1]. They are also used in chemical mixing systems, cooling systems, waste heat recovery, environmental engineering, cryogenic processes and biomechanical engineering fields [2], [3].
Adding millimeter or micrometer sized solid particles with high conductivity to a fluid, a solid–liquid mixture is created. Although thermal conductivity is high in this mixture, poor suspension stability, corrosion, channel clogging, and great pressure drop are some of the disadvantages of this system [4]. Adding nanometer sized particles to a fluid was first tried by Choi [5], causing higher thermal conductivity. Thanks to the use of extreme fine particles, this mixture did not suffer from previously experienced defects [5].
Dean [6] was the first researcher in curved pipe field who studied the flow in a toroidal pipe employing perturbation method. He reported that the flow could be characterized by a dimensionless parameter named Dean number, the ratio of centrifugal force to inertial force [6].
In curved pipes, centrifugal force creates secondary flow which significantly affects heat transfer characteristics of these pipes, making the flow and convective heat transfer studies more complicated [3].
Investigations of heat transfer in coiled tubes date back to 1950; for example, Fostowskii, Micheeff, Kubair, and Schmidt presented empirical correlations for average forced convective heat transfer coefficient at a constant wall temperature. Seban, Dravid and Bell provided empirical correlations for uniform peripherally averaged heat flux boundary condition [7]. Manlapaz and Churchill studied the effect of torsion ratio on laminar flow in helical coils and reported that torsion ratio could be neglected if the coil pitch was lower than the coil radius [8].
Cioncolini and Santini studied pressure drop for the transition from laminar to turbulent flow in 12 helical pipes with different curvature ratios and negligible torsion ratios. Empirical correlations for friction factor were obtained from those results [9]. Hüttl et al. numerically studied the laminar, steady flow in helically tubes with various curvature and torsion ratios. In that work, Hydrodynamically periodic boundary condition was employed in axial direction. The effect of torsion and curvature ratio on axial velocity and secondary flow field was presented [10]. Jayakumar et al. developed correlations for Nusselt number based on coiled parameters using commercial software [1]. Kim et al. numerically investigated developing laminar flows in the entrance region of helical pipes. They presented a new correlation for the entrance region angles [2]. Amani and Nobari analyzed entropy generation in curved pipes in a toroidal coordinate system based on the projection algorithm at a constant wall temperature [11].
Single phase approach and two-phase approach are two different methods applied in heat transfer behavior investigations of the two phase mixtures such as nanofluids. One of the nanofluid single phase approaches is homogenous model which only differs from pure fluid in the effective properties. The other approach is dispersion model suggested by Xuan and Roetzel in 2000 [12]. In this model, the effect of chaotic movement of the nanoparticles in the nanofluid flow is taken into account. This model also is similar to the method used in porous media modeling. Dispersion model is able to predict higher heat transfer for nanofluid, adding a term to thermal conductivity of fluid known as dispersed thermal conductivity. Different correlations have been suggested for this term. For example, Xuan and Roetzel have suggested two relations. In the first one, nanoparticles volume fraction and size were ignored and the second one was not dimensionally compatible [12]. Xuan and Li implemented the Beckman formulas for axial dispersion thermal diffusivity proposing the axial velocity was constant that was not a proper assumption [13]. Khanafer used Xuan and Roetzel’s second relation for modeling the behavior of natural convective heat transfer in a two-dimensional enclosure [14].
Mokmeli and Saffar-Avval presented a new dispersion model to explain considerable enhancement of nanofluids heat transfer caused by the irregular movements of the nanoparticles [4]. The axial dispersed thermal diffusivity suggested by Xuan and Roetzel was ignored in mokmeli and Saffar-Avval study; however, dispersed thermal conductivity in radial direction was applied.
Zeinali-Heris et al. experimentally investigated laminar flow of CuO and Al2O3 in water as a base fluid in straight pipe at a constant wall temperature. The results were compared to the homogeneous model. At low volume fraction the results were in good agreement; however, at higher volume fraction results were not close to each other [15].
Akbarinia and Behzadmehr studied laminar mixed convection of a nanofluid in curved tubes using homogeneous model and concluded that concentration had positive effect on the heat transfer enhancement [16]. Akbarinia and Laur investigated the effect of solid particles diameter on a laminar nanofluid flow in a curved tube using a two phase approach and control volume technique. This research proved that the increase of the diameter of nanoparticles did not change the flow behavior [17].
Hashemi and Akhavan-Behabadi studied pressure drop and heat transfer characteristics of CuO nanoparticles and oil as a base fluid flow inside horizontal helically coiled pipe under constant heat flux. They defined a parameter called performance index so as to find the optimum work conditions of two enhanced heat transfer techniques, nanofluid and helical pipe. They compared applying pure fluid flows in helical pipe vs. using nanofluid in straight pipe. The results showed first method is a more effective way to enhance the force convective heat transfer coefficient than the second method. Their results were valid for one coil with specific torsion and curvature ratio [18].
As it was reviewed pressure drop and the forced convective heat transfer behavior of nanofluid in helical pipes at a constant wall temperature was not investigated by previous works experimentally and numerically. This investigation is productive and applicable with regard to shell and coil heat exchangers, particularly, in the case that the fluid in the shell is a two-phase fluid. This sort of heat exchangers are used in refrigeration, chemical and HVAC industries such as condensers and evaporators. In this research, convective heat transfer of nanofluid in helically coiled tubes at a constant wall temperature was studied numerically and experimentally. Homogeneous model with constant effective properties was used to predict the enhancement of nanofluid heat transfer behaviors. To make the experimental and numerical results similar, dispersion model was used which had not been examined in previous studies of helical pipes.
Section snippets
Experimental setup
Fig. 1 schematically shows the designed and constructed experimental apparatus which provides constant wall temperature boundary condition. The flow loop comprised a reservoir tank, test chamber, cooling section, centrifugal pump with inverter, flow meter and thermocouples. The 40 × 60 × 40 cubic test chamber was constructed of 2 mm thickness stainless steel plates. Three heaters were installed at the bottom of the chamber to provide 10.5 kW power to make boiling water as a two phase fluid. This
Nanofluid preparation
In the current study, nanofluid oxide including 68 nm average size CuO nanoparticles in water as base fluid with 0.1% and 0.2% volume fraction was prepared using Electrical Explosion of Wire (EEW) technology. Fig. 2 shows scanning electron microscope (SEM) micrograph of the CuO nanoparticles. SEM and TEM images have been taken from the nanoparticle of CuO which show a little agglomeration, but using the combination of some surfactant such as Stearic acid and sodium hexa metaphosphate can make a
Nanofluid properties and dispersion model
Single phase approach and the two-phase approach are two different methods for studying heat transfer behavior of the two phase mixtures. Homogenous model is one of the nanofluid single phase approaches which is different from pure fluid only in terms of effective properties [4].
Considerable differences between nanofluid and base fluid make the calculation of thermo physical properties of the nanofluid necessary. Two classical formulas were used to calculate effective thermal capacity and
Geometry and governing equations
Fig. 3 shows the geometry of a helical pipe with radius R, pitch ps, and coil radius ra. The curvature ratio κ and the torsion τ of the helical pipe axis can be calculated by Eqs. (19), (20), respectively.
The basic governing equation in helical tubes could be represented in a orthogonal helical coordinate system, suggested by Germano [25]. Where (s, r, θ) are the directions in helical coordinate system representing of axial, radial and circumferential directions,
Numerical method
An orthogonal staggered grid was generated to solve the three dimensional governing equations including continuity, momentum and energy equations in the helical coordinate system. Projection algorithm with Second order finite difference discretization (forward in time and central in space) was employed. The continuity and momentum equations could be written in vector form as (Eqs. (34), (35)):
In this study, depending on Chorin projection algorithm [26], virtual
Results and discussion
In the current work, laminar, incompressible, steady state viscous flow in the helically coiled tubes at a constant wall temperature was studied. The experimental and numerical results for water were in good agreement. The difference between them was less than 3%. Experimental and numerical results using effective properties method were compared to each other. To observe no difference between experimental and numerical results, modified dispersion model was used. To understand this
Conclusions
In this paper, pressure drop and heat transfer behavior of nanofluid and water in helically coiled tubes was investigated experimentally and numerically. Heat transfer characteristics of nanofluid were predicted using homogeneous model with constant effective properties and dispersion model. These results were compared to the experimental data.
Heat transfer coefficient and pressure drop of nanofluid were compared to that of base fluid at a same flow conditions in different helically coiled
Acknowledgments
The authors would like to acknowledge Payamavaran Nanotechnology Fardanegar Company (PNFCo.) for preparation of nanofluid using EEW method with PNC1K setup. The authors also thank Iranian Nanotechnology Initiative Council and Mechanical Engineering Dept., Amirkabir University of Technology (Tehran polytechnic) for their financial supports through the setup construction and research implementation.
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