Proceedings of the 2nd Thermal and Fluid Engineering Conference, TFEC2017 4th International Workshop on Heat Transfer, IWHT2017 April 2-5, 2017, Las Vegas, NV, USA
TFEC-IWHT2017-18120
NUMERICAL INVESTIGATION ON THE TURBULENT CONVECTIVE HEAT TRANSFER OF NANOFLUID FLOWS IN AN UNIFORMALY HEATED PIPE G. Sekrani*, S. Poncet 1
Mechanical Engineering Department, Université de Sherbrooke 2500 boulevard de l’Université, Sherbrooke (QC), J1K 2R1, Canada
ABSTRACT Turbulent convective heat transfers of Al2O3-water nanofluid flowing in a circular tube subjected to a uniform and constant wall heat flux are numerically investigated using different turbulence models. Three nanoparticle volume concentrations, namely φ=0.02, 0.1 and 0.5% are considered for different bulk Reynolds numbers within the range 3000˂Re˂20 000. The effects of the nanoparticle concentration and the Reynolds number on the convective heat transfer and friction factor are reported. Two different numerical approaches including the single-phase and the mixture two-phase models with variable thermophysical properties are favorably compared to experimental results obtained from the literature. Adding nanoparticles to the base fluid was found to significantly improve the average heat transfer coefficient. The Nusselt number increases with increased nanoparticle volume concentration and increased Reynolds number, whereas the friction factor decreases with increased Reynolds number. Seven turbulence models in their lowReynolds number formulation were also compared to assess their ability to predict the effect of turbulence on the convective heat transfer. The SST k-ω model was found to perform the best with errors in terms of the average Nusselt number and friction coefficient of 0.44% and 1.82% respectively. On the contrary, the Reynolds Stress Model completely failed to provide the good values with discrepancies of 41.91% and 133.54%, respectively.
KEYWORDS: Convective heat transfer, nanofluid, single-phase model, mixture model, turbulence modeling.
1. INTRODUCTION Convective heat transfer plays an important role in various industrial sectors such as air-conditioning, transportation, chemical production, microelectronics and power generation. The conventional heat transfer fluids such as water, ethylene glycol or oil exhibit relatively limited heat transfer properties, which hinders the efficiency of the thermal systems. The recent advance in the field of nanotechnology gave rise to a new type of nanometeric metallic or non-metallic particles characterized by their substantially higher thermal conductivities. These particles, referred as nanoparticles, are dispersed into a conventional fluid, creating a new class of heat transfer fluids named nanofluids. Since the pioneering work of Choi and Eastman [1], the particularly increased thermal efficiency of nanofluids, compared to conventional fluids, has attracted the attention of researchers and engineers. One of the most common canonical experiments used to study the convective heat transfer performance of nanofluids, is the turbulent flow through a straight uniformly heated pipe as considered for example by Sundar and Sharma [2]. In their study, both the average heat transfer coefficient and the friction factor of an Al2O3water based nanofluid were measured in a straight pipe (with and without inserts) subjected to a constant heat flux at the wall for different axial Reynolds numbers Re and nanoparticle volume fractions φ. They observed *Corresponding Author:
[email protected]
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TFEC-IWHT2017-18120 that, for φ=0.5 %, the heat transfer coefficient increased by 15.62% and 54.54% at Reynolds numbers of 3000 and 18000, respectively, compared to pure water. Li and Xuan [3] measured the heat transfer coefficient and friction factor for Cu/water nanofluid flowing inside a tube in both laminar and turbulent flow regimes. They noted an enhancement up to 60% for φ=2%. Noghrehabadi and Pourrajab [4] investigated experimentally the convective heat transfer of γ-Al2O3-water nanofluid in a circular tube with constant heat flux at the wall. Their results showed that the average heat transfer coefficient was increased by 16.8% for φ=0.9 % compared to pure water. They observed that the enhancement was particularly significant in the entrance region and decreased with the axial distance. Turbulent convective heat transfers and pressure drop of γ-Al2O3-water nanofluid inside a circular tube were investigated experimentally by Fotukian and Nasr Esfahany [5]. They affirmed that the addition of small quantity of alumina nanoparticles to pure water increased heat transfer remarkably. For example, for Re=10000 and φ=0.045%, the heat transfer coefficient was increased by 48%. Heyhat et al. [6] experimentally studied the turbulent heat transfer behavior of alumina/water nanofluid in a circular pipe under constant wall temperature condition. Their results showed that the heat transfer coefficient of Al2O3-water nanofluid was increased by 23% for φ=2% compared to pure water. The thermal enhancement by the use of nanofluids has been then widely demonstrated experimentally mainly by global temperature and pressure measurements. Numerical simulations are then required to have a better insight into the flow dynamics and heat transfer processes of nanofluids. For comparison, the experimental data of Sundar and Sharma [2] will be used in the following. Due to their excessive computational cost, only limited attention has been paid to use direct numerical simulations (DNS) [7, 8] or even large eddy simulations (LES) to investigate nanofluid turbulent flows in pipes or channels. Sajjadi et al. [9] were the first to use a lattice Boltzmann based LES model to study the turbulent flows of Cu-water nanofluid in tall enclosures under the natural convection regime. Peng et al. [10] performed LES of turbulent nanofluid flows inside a cylindrical pipe and compared the predictions of Eulerian-Eulerian, Euler-Lagrangian, and Lagrangian multiphase models, in an attempt to better explain the flow field behavior and the mechanisms responsible for the heat transfer enhancement. The Lagrangian model was found to perform better than the two former models due to its capability to provide a more detailed information about the development and the interaction of the turbulent eddies with the nanoparticles. The use of advanced DNS or LES models in the context of turbulent nanofluid flows in realistic geometries remains marginal and most authors focus on Reynolds Averaged Navier Stokes (RANS) turbulence closures. Though being more simple and requiring less computational resources, they are able to provide accurate data if the appropriate single or twophase model and the appropriate correlations for the properties of the nanofluid are used. As there is clear consensus about the best model (turbulence closure + two-phase approach + correlations for the nanofluid properties) to use confidently to study turbulent nanofluid flows inside a cylindrical pipe, a careful numerical benchmark is still required and is the main objective of the present work. The most popular model to investigate turbulent nanofluid flows and heat transfers inside a cylindrical pipe is the standard standard k-ε (S k-ε) model [11,12,13], while Akbari et al. [14] used the Realizable k-ε (R k-ε) model to evaluate the turbulent forced convection in a horizontal heated tube filled with a Al2O3-water based nanofluid. A relatively good agreement was found compared to the experimental data of [2]. Roy et al. [15] considered turbulent water-based nanofluid flows inside a radial cooling system and compared the predictions of several turbulence models. They claimed that the shear stress transport SST k-ω model was the appropriate model for their specific case exhibiting a good agreement with the experimental data more than the RNG k-ε, k-ω and ϑ²-f models. Saha and Paul [16] considered numerically the heat transport behavior of water based alumina and titanium nanofluids in a circular pipe under turbulent flow condition. They compared the predictions of three k-ε models and they concluded that the R k-ε model was the appropriate turbulence closure. Recently, Boertz et al. [17] simulated the turbulent flow of SiO2-ethylene-glycol/water nanofluid in a tube with constant heat flux boundary condition. They assessed the predictions of the Nusselt number and the friction factor by three turbulence models including the S k-ε, k-ω and SST k-ω models. They concluded that the SST k-ω was the appropriate turbulence closure level in their simulation. Many researchers tend to model the flow and heat transfer of nanofluids using a suitable numerical approach. The models may be divided into two categories: the single-phase (SP) and the two-phase models. The singlephase model treats the nanofluid as a homogenous fluid, since the nanoparticles suspended in the base fluid are very small (10 ≤ dnp ≤ 100 nm) and have almost the same diameter than the base fluid molecules. For example,
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TFEC-IWHT2017-18120 the diameter of water molecules is 0.384 nm [18]. For this reason, the nanoparticles can be easily fluidized and it is assumed that the base fluid and the solid nanoparticles are in thermal equilibrium and the relative velocity between the phases is zero. Salman et al. [19] showed the ability of the SP model to predict the heat transfer and fluid flow characteristics by introducing the effect of the Brownian motion on the thermal conductivity and the nanoparticle size on the dynamic viscosity. Using a single phase approach, Akbari et al. [14] compared six different combinations of thermal conductivity and viscosity in the case of turbulent Cu-water and Al2O3-water nanofluid flows inside a horizontal tube. They found that the combination between the Maiga et al. [20] correlation for the dynamic viscosity and the Nan et al. [21] equation for thermal conductivity leads to the better agreement with an average error for the Nusselt number less than 2% compared to the experimental data of Xuan and Li [22] and 27% far from the results of Sundra and Sharma [23]. The hydrodynamic and thermal behaviors of Al2O3-water nanofluids were numerically investigated by Bianco et al. [24] using a SP model with either constant or temperature-dependent properties, and showed an acceptable prediction compared to the experimental data with temperature-dependent properties. In order to reach more realistic results and better understand the heat transfer phenomena within nanofluids, researchers have used also two-phase models where the slip velocity between the particles and the fluid may not be zero due to different factors such as the Brownian force, the Brownian diffusion, sedimentation and dispersion. The mixture model has been successfully applied for the first time by Behzadmehr et al. [12], improving the predictions of the single-phase model. Mirmasoumi and Behzadmehr [25] demonstrated that the mixture model can give significant information on the alumina nanoparticle distribution within water at given tube cross-sections contrary to the single-phase model, which considers a uniformly distribution along the tube. Bianco et al. [11] also compared the predictions of the SP and mixture models leading to the same conclusion. The mixture model is more appropriate while the SP model underestimates the wall temperature. Davarnejad and Jamshidzadeh [26] investigated numerically a turbulent flow and heat transfer characteristics of MgO-water nanofluid comparing the predictions of the SP, VOF (Volume Of Fluid) and mixture approaches. Their results showed that the two-phase models provide similar results and are more accurate than the SP model, the average deviation from the experimental data being about 2% and 11%, respectively. An excellent review on different numerical approaches for the simulation of nanofluid flows can be found in references [27, 28]. To the best of our knowledge, there is no detailed study evaluating the performance of seven RANS turbulence models on the turbulent fluid flow and heat transfer of alumina-water based nanofluids flowing inside a horizontal heated tube. The aim of the present paper is to investigate numerically a turbulent forced convection flow of Al2O3-water nanofluid in a circular pipe with constant heat flux boundary condition. A comparative study of the single-phase and mixture models was done using the experimental data of Sundar and Sharma [2]. Investigation is conducted for three nanoparticle volume fractions for a wide range of Reynolds numbers (3000 ≤ Re ≤ 20000). The distributions of the average Nusselt number are also compared to three empirical correlations [29, 30, 31] found in the literature, and the numerical friction factor was compared to the Blasius analytical equation [32].
2. NUMERICAL APPROACH
2.1 Geometrical Configuration The present work investigates the steady, forced turbulent convection flows and the corresponding heat transfers of Al2O3 nanoparticles (average diameter dnp of 47 nm) dispersed in water. The nanofluid flows inside a straight cylindrical pipe of length L=1.5 m and diameter D=2R=0.019 m. The nanofluid enters with a constant temperature and uniform velocity. A constant heat flux is imposed at the tube wall. The numerical set-up is based on the experiments performed by Sundar and Sharma [2]. 2.2 Single-Phase and Mixture Models The physical properties of water are considered to be temperaturedependent while those of the alumina nanoparticles are constant. The following equations hold for the density [33], the specific heat [12], the thermal conductivity [34] and the dynamic viscosity [35] of pure water (index f) and they are used for both models under consideration:
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TFEC-IWHT2017-18120
f 2446 20.674T 0.11576T 2 3.12895 10 4 T 3 4.0505 10 7 T 4 2.0546 1010 T 5 8.29041 0.012557T Cp f exp 1 1.52373 10 3 T 3 k f 0.76761 7.535211 10 T 0.98249 105 T 2
f 2.414 10 10 5
247.8 T 140
(1) (2) (3) (4)
The single-phase model, frequently used to model nanofluid flows, along with the mixture model were implemented in order to compare their ability to predict the flow dynamics of an alumina-water nanofluid turbulent flow through a heated pipe. They are fully described in [36]. The mixture model takes into account drag effects and the Brownian motion of the particles among other things. Despite its simplicity, the main challenge in the single-phase model remains in the determination of the nanofluid properties using the appropriate correlations. The following expressions were used to evaluate the density [37], the specific heat [37], the dynamic viscosity [20], and the thermal conductivity [21] of the single-phase nanofluid:
nf 1 f np Cpnf
1 Cp f Cp np nf
nf 1 39.11 533.9 2 f knp 1 2 2k f 2 k f knp 1 kf knp 1 2 2k f k f knp 1
knf
(5) (6) (7) (8)
where α=2 Rb knp / dnp is the particle Biot number and Rb=0.77×10-8 m²K/W is the interface thermal resistance. φ denoted the Al2O3 concentration, the indexes np and nf referred to the nanoparticles and to the nanofluid, respectively. Note that these expressions yielded to the closest results to the experimental data [2] when compared to other correlations available in the literature.
2.3 Turbulence Modeling A comparison between seven different turbulence models was performed in order to assess their ability to predict the flow dynamics and the heat transfer of nanofluid turbulent flows through a cylindrical pipe. These models include the standard k-ε (S k-ε) model [38], the realizable k-ε (R kε) model [39], the renormalization-group k-ε (RNG k-ε) model [40], the standard k-ω (k-ω) model [41], the Shear Stress Transport k-ω (SST k-ω) model [42], the Shear Stress Transport (SST) model [42] and finally the Reynolds-Stress Model (RSM) [43]. All these models are used in their low-Reynolds number formulation.
2.4 Computational Domain and Boundary Conditions Several different grid arrangements were tested to ensure that the computed results were grid independent. The selected computational domain was a structured mesh which consisted of 68, 138 and 1500 nodes in the circumferential, radial and axial directions, respectively. A mesh refinement close to the pipe wall was deemed necessary to capture the development of the turbulent boundary layer and ensure a wall coordinate always lower than r+10000). Similarly, the numerical results for the friction factor are found to be in conformity with the theoretical values evaluated using the Blasius equation. Nevertheless, a slight discrepancy is obtained at relatively lower Re for all volume fractions. The average friction coefficient decreases with increasing Re. However the addition of alumina nanoparticles to water has not noticeable effect on it.
(a) (b) (c) Fig. 4 Comparison between the predicted average friction factor using both single-phase and mixture models, the experimental results of Sundar and Sharma [2] and the theoretical equation of Blasius [33] for: (a) φ=0.02%, (b) φ=0.1% and (c) φ=0.5%. Evolution as a function of the Reynolds number.
3.2 Numerical Benchmark of the Different RANS Turbulence Models Since the SP and the mixture models provide similar results for both the thermal and hydrodynamic fields, the comparative study between the different RANS turbulence models, namely the S k-ε, R k-ε, RNG k-ε, kω, SST k-ω, SST and RSM, is only based on the SP approach due to its simpler implementation as well as its less prohibitive computational cost. In the following section, the comparison between the different eddy viscosity models is performed for Re=13380 and φ=0.1%. The average Nusselt number (Nu) and the average friction factor (f) along the tube, predicted by the different turbulence models, are summarized in Table 1. The numerical results clearly showed that the SST k-ω model provides the closer predictions for both Nu and f compared to the experimental data of Sundar and Sharma [2], which confirms the former findings of Boertz et al. [18]. The average errors between the predicted values of Nu and f using the SST k-ω model, with respect to the experimental data [2], are about 0.43% and 1.8%, respectively. The R k-ε, S k-ε, SST and k-ω models show also a reasonable agreement with the experimental values [2] with average errors less than 4.21% and 7.27% for the predictions of Nu and f, respectively. Interestingly, the RNG k-ε model fails to predict the good Nusselt number value (error of 21.97%), whereas it predicts quite well the friction factor. More surprisingly, the RSM model (7 equation model) strongly overestimates both the hydrodynamic and the thermal fields. Table 1 Comparison in terms of the average Nusselt number and the friction factor between different turbulence models. Results obtained using the single-phase model for Re=13380 and φ=0.1%. Relative errors Nu f are given in (%) Experiment [2] 107.682 (-) 0.0321 (-) S k-ε 108.779 (1.02) 0.0304 (5.22) R k-ε 108.743 (0.99) 0.0305 (5.06) RNG k-ε 131.344 (21.97) 0.0305 (4.9) k-ω 103.145 (4.21) 0.0298 (7.27) SST- k-ω 108.152 (0.44) 0.0315 (1.82) SST 106.223 (1.35) 0.0309 (3.83) RSM 152.808 (41.91) 0.0751 (133.54)
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In order to closely inspect the hydrodynamic behavior obtained using the different turbulence models, the axial development of the centerline axial velocity is illustrated in Figure 5 for the seven turbulence models. The centerline mean axial velocities exhibit a significant increase due to the axial development of the flow field and especially of the boundary layers. Then they reach peak values at locations ranging from z/L=0.15 to 0.35. Then, the centerline velocities slightly decrease towards an asymptotic value marking the beginning of the hydrodynamic fully flow region, in agreement with Behzadmehr et al. [12] and Sekrani and Poncet [44]. This behavior may be attributed to the rapid growth of the boundary layer, in the entrance region, which tended to push the fluid towards the axis region resulting in an increased axial velocity to conserve mass. Additionally, Figure 5 clearly shows that the S k-ε, R k-ε and RNG k-ε models are the first to achieve the hydrodynamic fully developed state at a streamwise distance of about z/L=0.15. The k-ω, SST and SST k-ω models predict a fully developed flow at z/L=0.35. Despite the similar incoming flow conditions, different centerline velocities are reported in the asymptotic region for the different turbulence models: for example, the RSM model exhibits the highest centerline mean axial velocity among the other turbulence models with an average value of about 0.78 m/s, which is 6% higher than that of the SST k-ω model. It is corroborated by the radial distributions of the mean axial velocity at an axial position z/L=0.0733 located within the common fully developed region (Figure 6). Different behaviors are observed in the near wall region as well as close to the pipe axis. The S k-ε, RNG k-ε and R k-ε models provide a similar boundary layer growth in the viscous region, which may be attributed to their poor performance for boundary layer flows. The boundary layer appears thicker for the k-ω and the SST models compared to those obtained with any of the k-ε models. It may be explained by a larger sensitivity of the k-ω models to the free stream conditions. It is noteworthy, that the variants of the k-ω models have good attributes to predict boundary layer flows, much better than k-ε models. The predictions of the RSM model exhibit the highest velocity gradient in the boundary layer region.
Fig. 5 Axial evolution of the centerline mean axial Fig. 6 Radial profiles of the mean axial velocity at velocity for Re=13380 and φ=0.1%. Comparison z/L=0.733 for Re=13380 and φ=0.1%. Comparison between the different RANS models. between the different RANS models. The predictions of the different turbulence models are also compared for the temperature along the pipe axis in Figure 7. For all the turbulence models considered here, the bulk temperature along the pipe centerline remains roughly constant up to a given distance from the pipe entrance, referred to as the thermal entrance length, before it starts to gradually increase with the increased streamwise distance. Furthermore, Figure 7 shows that the thermal entrance length is clearly sensitive to the selected turbulence model. The RSM, RNG k-ε, R k-ε and S k-ε models reach a thermally fully developed state at a shorter streamwise distance with respect to that of the SST k-ω model. In the contrary, both k-ω and SST models exhibit a relatively longer thermal entrance length compared to the SST- k-ω model, before they attain the thermal fully developed state. The axial development of the centerline temperature is a good indicator for the development of the
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TFEC-IWHT2017-18120 thermal boundary layer and the different behaviors are closely linked to the differences observed in terms of the average Nusselt number reported in Table 1. A close examination of the streamwise turbulence intensity shown in Figure 8 indicates a significantly increased turbulence intensity (Tw) in the entrance region for the RSM model compared to the other turbulence models. The k-ε variants also exhibit a relatively higher turbulence intensity than those of the k-ω variants and SST model. The difference in the turbulence level within the entrance region can tremendously affect the onset of both the hydrodynamic and the thermal fully developed region. This effect is clearly observed in Figure 8. The deficit in Tw close to the inlet is associated with the turbulent mixing region. The increased turbulent mixing in the case of both RSM and k-ε models strongly accelerates their transition to a fully developed flow regime.
Fig. 7 Axial evolution of the centerline Fig. 8 Axial development of the centerline temperature for Re=13380 and φ=0.1%. streamwise turbulence intensity for Re=13380 and Comparison between the different RANS models. φ=0.1%. Comparison between the different RANS models. The axial evolutions of the centerline turbulence kinetic energy k obtained by the different turbulence models is displayed in Figure 9. The turbulence kinetic energy slightly decreases right after the pipe inlet and then strongly increases in the mixing region. In the latter, the significant increase of the turbulent production is mainly attributed to the increased turbulent mixing caused by the interaction between the developing boundary layers. As soon as the fully fledged regime is attained, the flow starts to exhibit a rather more organized behavior and the velocity gradients caused by the shearing and stretching across the pipe are gradually smeared. Therefore, the turbulence kinetic energy starts to gradually decrease as there is no production mechanism to maintain a constant turbulence kinetic energy along the pipe. These observations are in agreement with the results of Akbari et al. [14], whereas Behzadmehr et al. [12] reported that the turbulence kinetic energy at the tube centerline exhibits an asymptotic behavior in the fully developed region. Additionally, the three k-ε models show similar profiles for k since these models share the same transport equation for the turbulence kinetic energy. The k-ω model predicts the lowest k values among the other turbulence models, which may be attributed to its strong sensitivity to the dissipation rate imposed at the pipe inlet. The highest values of k are obtained by the RSM model which was expecting from its over prediction of the turbulent intensity as illustrated in Figure 8. The streamwise development of the turbulence kinetic energy is roughly identical for the k-ω, SST k-ω and SST models with relatively higher values for the SST k-ω model. The SST k-ω model combines indeed the advantageous behavior of the k-ω and k-ε models, by using the free stream independence of the k-ε model in the outer part of the boundary layer and the accurate formulation of the k-ω model in the near wall region [42]. Therefore, the predictions of the SST k-ω model are more accurate than the k-ε and k-ω models, which was observed in the calculated values of the Nusselt number and friction factor.
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Fig. 9 Axial evolution of the centerline turbulence Fig. 10 Radial profiles of the eddy viscosity at kinetic energy for Re=13380 and φ=0.1%. z/L=0.733 for Re=13380 and φ=0.1%. Comparison Comparison between the different RANS models. between the different RANS models. The radial profiles of the eddy viscosity μt are reported in Figure 10 at a streamwise distance z/L = 0.733. The three k-ε models provide the same profiles close to the wall. Away from the wall, at r/R=0.7, the eddy viscosity profiles predicted by the k-ε variants changed from one model to another. The turbulent viscosity calculated by the RNG k-ε model decreases until reaching a constant value of 0.04 Pa.s. The turbulent dissipation obtained by the S k-ε model is slightly higher close to the axis where μt reaches 0.05 Pa.s. Concerning the R k-ε model, the turbulent viscosity μt increases suddenly having a peak value of 0.103 Pa.s at the tube centerline. The same formulation is used by the S k-ε and RNG k-ε models to evaluate the turbulent viscosity [38, 40]. The main difference lies in the constant C2ε introduced in the transport equation of the dissipation rate ε of the turbulence kinetic energy-for the RNG k-ε model [40]. The values of ε predicted by the S k-ε are thus smaller than the ones predicted by the RNG k-ε model. Contrariwise to the former models, the R k-ε model possesses another transport equation for the dissipation rate derived from an exact equation for the transport of the mean square vorticity fluctuation. It includes also a different formulation for the turbulent viscosity, where the Cμ parameter takes into account the changes in both mean and fluctuating velocity fields [39]. This may explain the over-prediction of the turbulent viscosity by the R k-ε model, as seen in Fig.10. In the viscous flow region, the radial evolutions of the turbulent viscosity are nearly identical for the SST, SST k-ω and k-ω models. Towards the pipe axis, the radial profiles of the turbulent viscosity of both SST and SST k-ω models exhibit a perfect collapse with a peak value nearly twice higher than that of the k-ω model. This difference might be attributed to the strong sensitivity of the k-ω model to the freestream conditions. In average, the largest values of the turbulent viscosity are predicted by the RSM model. However, the latter shows the highest gradient of μt in the viscous region among the other models, which may be related to the fact that the RSM model is not based on the hypothesis of an isotropic eddy-viscosity [43].
4. CONCLUSIONS In this paper, a numerical investigation of the hydrodynamic and thermal behaviors of alumina-water nanofluid flowing inside a uniformly heated tube was carried out. Both single-phase and mixture approaches were evaluated and showed a good agreement with the experimental data of Sundra and Sharma [2]. Both models performed well leading to the same distributions of the average Nusselt number and friction factor for the three alumina volume fractions over a wide range of Reynolds numbers (3000 ≤ Re ≤ 20000). This can be explained by both the use of the appropriate correlations for the nanofluid properties using the singlephase approach and by the relatively low nanoparticle concentrations considered here.
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TFEC-IWHT2017-18120 The validity of the two models was assessed by comparing the present Nusselt number distribution to the correlations of Gnielinski [29], Dittus-Boelter [30], Pak and Cho [31] and Blasius [32]. A good agreement was found except with the equation of Dittus-Boelter [30]. A comparative study between the RANS models was also conducted using the single-phase approach for Re=13380 and φ=0.1%. The SST k-ω was found to be the appropriate turbulence model, in the present case, with average errors between the predicted values of Nu and f, with respect to the experimental data, of about 0.43% and 1.8%, respectively. On the contrary, the RSM model showed its inadequacy to predict both the thermal and hydrodynamic fields, with a predicted friction coefficient twice higher than the experimental one and a discrepancy of 42% in terms of the average Nusselt number. The RNG k-ε model overestimated the experimental Nusselt number by 20%. It is noteworthy that the R k-ε, S k-ε, SST and k-ω models showed a reasonable agreement with the experimental values. Further calculations are now required to investigate in details the coherent structures, which may appear in the turbulent regime and affect the heat transfer distribution within the pipe. their interactions with the nanoparticle concentration field. For this purpose, LES calculations using the WALE model associated with the mixture model are still running.
ACKNOWLEDGMENT The authors would like to thank the NSERC chair on industrial energy efficiency established at Université de Sherbrooke in 2014 and supported by Hydro-Québec, Ressources Naturelles Canada (CanmetEnergy in Varennes) and Rio Tinto Alcan. This project was also initiated thanks to the support of the company Sigma Energy Storage, which is also gratefully acknowledged. Calculations have been performed using the supercomputer Mammouth Parallèle 2 of Calcul Québec’s network.
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