Numerical simulation of heat transfer improvement in the divertor of fusion reactors by using Al_{2}O_{3} nanofluid
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Abstract
The objective of this work is to study the effect of using nanofluids as coolant on divertor system of fusion reactors which is known to be subjected to high heat loads coming from the plasma. Turbulent force convective heat transfer of waterbased Al_{2}O_{3} nanofluid flowing through the CuCrZr cooling tube of a small scale of mock up made of five tungsten monoblocks has been numerically investigated using single phase model. Computational fluid dynamic approach has been applied by using CFD software FLUENT 6.3.26. The computed results have been validated by traditional corrections expression reported by previous works. The dependence of temperature contours and profiles on volume fraction of nanofluids for different walls of this monoblock has been studied and compared with pure water. The maximum allowed temperature of the candidate material under unusual situation of a fusion reactor has been considered and compared with the maximum temperatures resulted from the CFD results. The effects of various nanofluid concentrations and Reynolds numbers on average Nusselt number have been also investigated. The results show a significant improvement in heat removal from the divertor under the cooling of alumina/water nanofluid with respect to pure water.
Keywords
Fusion reactor Divertor Nanofluid Heat transfer Single phase CFDList of symbols
 c_{p}
Specific heat capacity at constant pressure (J/kg K)
 k
Thermal conductivity (W/m K)
 q
Heat flux, W/m^{2}
 h
Heat transfer coefficient (W/m^{2} K)
 Nu
Nusselt number
 T
Temperature (K)
 Re
Reynolds number \(\left( {\frac{\rho DV}{\mu }} \right)\)
 P
Pressure (Pa)
 V
Velocity (m/s)
 T
Temperature (K)
 D
Tube diameter (m)
 Pr
Prandtl number \(\left( {\frac{{c_{p} \mu }}{k}} \right)\)
 w
Wall
 L
Length of the tube (m)
Greek letters
 Ρ
Density (kg/m^{3})
 ε
Rate of dissipation per unit mass (m^{2}/s^{3})
 κ
Turbulence kinetic energy (J)
 µ
Dynamic viscosity (Pa.s)
 ϕ
Volume fraction (vol.%)
Subscripts
 np
Nanoparticles
 nf
Nanofluid
 f
Fluid
 w
Wall
Introduction
On the other hand, the heat management requirements give a great importance to coolant specification in divertor area of a fusion reactor. Water has always been a promising coolant, and there are lots of literature focusing on water and its characteristic [6, 8, 9, 10], but there are some disadvantages for water such as high pumping power and limited power handling caused by critical heat flux (CHF) [11].
Fortunately, these problems can be removed by the use of nanofluids. Using nanofluids leads to a great enhancement in CHF [12] and decreases the pumping power requirement. A nanofluid is a suspension of low concentration (below 10% vol.) of nanoparticles like aluminums oxide (Al_{2}O_{3}), titanium oxide (TiO_{2}) and copper oxide (CuO) and a base fluid (such as water or ethylene glycol) [13]. Using nanofluid to improve thermal properties of cooling fluid is dated back to 1990s by Choi [14, 15]. He reported a noticeable improvement in thermal properties and coined the nanofluid term. Since then, many researches have showed the favorable results of adding nanoparticles to base fluids both numerically and experimentally [16]. The proven advantage of using nanofluid is better heat characteristics like higher heat transfer coefficients even in low volume fractions of nanoparticles. Regarding these suitable properties of nanofluid, using nanofluid in high heat flux systems such as solar collectors, electronic cooling systems and nuclear reactors to reduce temperature and making a more uniform temperature distribution seem attractive.
Some researchers have used nanofluid in nuclear systems for study. Wu and Zhao [13] in reviewing nanofluid heat transfer and critical heat flux enhancement especially in nuclear reactor have claimed that to turn nanofluid application from vision to reality, we need to first overcome some challenges, like a precise database of nanofluid thermophysical properties and nanofluid stability in real working condition. Zarifi et al. performed a neutronic simulation of different nanofluids in VVER1000 reactor [13]. Their research aimed at optimization of type and characteristics. They also studied thermal–hydraulic modeling of nanofluid in this reactor, showing remarkable differences between nanofluid and pure water by increasing the concentration of nanoparticles [17]. Few researches have been done on using nanofluids in fusionbased systems. Barret et al. [11] experimentally investigated using nanofluid in fusionrelevant geometries with focus on studying nanofluid behavior in such environment. They showed an initial assessment of suitability of nanofluids as coolant in a fusion reactor.
In this study, a numerical investigation of the turbulent forced convection flow of aluminum oxide (Al_{2}O_{3}) nanofluid in the cooling tube of a monoblock of a divertor has been under consideration. The CFD analysis has been done by FLUENT software based on finite volume method.
Mathematical formulation and numerical procedure
Geometry and material
The geometry of the divertor W monoblock considered here is shown in Fig. 2. It is a 22 × 26 × 11 mm rectangular tungsten which is subjected to a heat flux load of 10 MW/m^{2} from the top surface in contact with plasma. Cooling tube is made of CuCrZr with the diameter of 10 mm. The inlet coolant has the pressure of 4.2 MPa and the temperature of 120 °C, and the velocity between 8 and 15 m/s associated with different mass flow rates (Reynolds number, Re). The 1 mm CuOFHC, as an interlayer, bonds the cooling tube to W monoblock.
Physical properties of nanofluid
Governing equations
Singlephase approach has been chosen here to numerically simulate forced convective heat transfer behavior of alumina nanofluids inside a heated tube under steady heat flux coming from a divertor of fusion reactor. Equations (1), (2), (3) and (4) are used to define the nanofluid properties in UDF codes imported in FLUENT software.
The popular singephase model assumes that nanoparticles have been uniformly distributed in the base fluid and these two parts of nanofluids are in thermal equilibrium and move with the same velocity. Also, as it can be seen from the relations of physical properties of nanofluids, they are based on the mixture of nanoparticles and base fluids [28, 29, 30]
The general forms of governing equation for steadystate flow and heat transfer of nanofluids are as follows
Boundary conditions
The problem is investigating a threedimensional, steadystate, forced turbulent convection of alumina nanofluid with different volume fractions (1–4%) inside a circular tube with length of 100 mm and diameter of 10 mm and also comparing the result with pure water. This tube is a part of monoblocks of a divertor acting as heat sink for removing high heat loads from the plasma which in direct contact with monoblock surface.
Impermeable boundary and noslip wall conditions are implemented over the surfaces of walls. The top surface (tungsten) is subjected to high heat flux of 10 MW/m^{2}. In fact, a constant heat flux is considered for the top wall in order to absorb the heat. The fluid (pure water with ϕ = 0 or nanofluid with ϕ = 1–4%) flowing inside the tube enters with a uniform temperature (T_{inlet}) and also an axial uniform velocity profile (V_{inlet}) of different values associated with a range of Reynolds numbers, here varied from 80,000 to 150,000. The uniform velocity profile is a common way of considering the inlet flow condition in order to determine the Reynolds number according to its formula. The pressure outlet has been chosen for the tube outlet boundary condition, while the velocity gradients are fixed to zero value. This pressure has been set at 4.2 MPa.
The wall (here means the inner surface of the CuCrZr tube) is in the stationary state and no slip for motion and shear stress, respectively.
Numerical method
Physical model

The fluid is incompressible, nonNewtonian and turbulent in steady state.

The fluid along the cooling channel remains in single phase.

There is a thermal equilibrium between nanoparticles and base fluids and the relative velocity is equal to zero.

Thermophysical properties of fluids are constant.
CFD simulation
The governing equations (flow, turbulence and energy) with mentioned boundary conditions have been numerically solved using the finite volume method (FVM). It was done by using computational fluid dynamic (CFD) approach. CFD is a technique with the aim of studying fluid flow, heat transfer and other related phenomena based on computer simulations.
In this work, the CFD commercially available software FLUENT 6.3.26 has been used by the following reasonable steps: prepress stage in which the geometry for the CFD region has been constructed and the componential created in GAMBIT as it is shown in Fig. 3. The mesh file has been then exported to FLUENT. Then the physical model, boundary condition and other assumptions required for an accurate analysis (next paragraph) have been defined in FLUENT. It has been followed by solving stage. The favorable results like Nusselt number needed for investigation have been defined in the postprocessing stage.
The main assumption considered in FLUENT is as follows. Pressurebased model has been used as solver, and semiimplicit method for pressurelinked equations (SIMPLE) model has been chosen for pressure–velocity coupling. κ–ε model with standard wall functions and default setting has been used to simulate turbulence. To discretize equations, secondorder upwind method has been selected. During the iteration process, the residuals for each variable have been monitored until the convergence criteria, restricted to be lower than 10^{−5}, has been assured.
Result and discussion
Hereinafter, the terms Nusselt and heat transfer coefficient refer to average amount, unless otherwise mentioned.
Validation
It is clear from this figure that numerical results obtained here are in good agreement with these two theoretical results, especially for larger Reynolds numbers, so that at the Reynolds number of 150 × 10^{3}, the deviation of the numerical results from the equation given by Gnielinski and Maiga is 0.07% and 3.5%, respectively. At lower Re numbers, Maiga correlation has better prediction of the numerical results with average deviation of 11%. These results agree well with the literature published by Lotfi [37] and Namburu [29].
Temperature distribution
After the validation done by comparison in the previous section and confirming that the componential model presented here is giving correct results with acceptable deviation, temperature distribution has been considered.
Temperature limitation on W and CuCrZr
One of the important issues in choosing appropriate material to be used in divertor part is the existence of some limitation especially for maximum temperature of these materials above which some failures might happen. According to high heat load test on W, above 1573 K recrystallization occurs and affects W thermomechanical properties [38]. On the other hand, the maximum temperature for CuCrZr must be lower than 823 K, the upper temperature limit below which CuCrZr has its optimum thermomechanical behavior.
As Figs. 8 and 9 show, in all Reynolds number and volume fractions of nanoparticles, the maximum temperatures for these two materials are in agreement with these limitations. Among all cases considered in these two figures, the maximum temperatures for W and CuCrZr have been seen at the lowest Reynolds number and volume fraction: 1323 °C and 792 °C, respectively.
Average Nusselt number
Experimental studies [39, 40] have shown that increments in heat transfer coefficients by inclusion of nanoparticles inside the base fluid are higher than what expected by numerical results, which means that improving the thermophysical properties is not the only phenomenon attributing to heat transfer improvement.
Conclusion
Numerical solution has been obtained to investigate heat transfer characteristics of alumina/water nanofluid flowing throw the horizontal cooling tube of a monoblock which is part of the important divertor system of fusion reactors. Steadystate turbulent convective heat transfer of this nanofluid under the high heat load of 10 MW/m^{2} was presented by CFD approach using FLUENT. The validity of CFD results was investigated by comparison with traditional expressions given by Maiga and Gnielinski and resulted in good agreement.
Temperature profiles for CuCrZr and tungsten sections of monoblock for the both cases of 1% Al_{2}O_{3} nanofluid and pure water revealed that adding even low concentration of nanoparticles can noticeably reduce temperature of these parts due to improvement in heat removal capacity. Also, maximum temperature profiles at W and CuCrZr for 1% and 4% volume fraction and base fluid illustrated that nanofluid can noticeably reduce maximum temperatures. It was concluded that using nanofluid can help the material to operate in their allowed temperature limitation. Moreover, average heat transfer study of nanofluids with different volume fractions (1–4%) showed enhancement in heat transfer with respect to pure water. The higher the concentration, the more the heat transfer improvement. Enhancement of heat transfer by increasing Reynolds numbers was also concluded from this study.
Notes
Acknowledgement
This work was supported by the Nuclear Science and Technology Research Institute (NSTR) and vice president research of University of Guilan.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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