The Effect of Al₂O₃ Concentration in Annular Fuels for a Typical VVER-1000 Core

Abstract

In this study, the effect of Al2O3 with various volume percentages in annular fuels for a typical VVER-1000 core is investigated. CFD is used to simulate the fuel rod. The results of the present study are compared with those of other published studies. Furthermore, the mentioned analytical methods are validated by comparing the final safety analysis report (FSAR). By comparing the results, it was found that the results are in good agreement with other studies. The results show that using annular fuel instead of solid fuel in the core of the reactor will increase the security and efficiency of the nuclear power plant. By increasing the volumetric concentration of nanofluid from 0.1 to 0.2, the rate in decrease of the peak temperature in the central fuel increases from 9% to 13%. Moreover, the clad temperature decreases from 626 K to 620 K (the clad temperature with pure water is 635 K).

1. Introduction

In recent years, nanofluids in various industries have been considered because of their ability to improve heat transfer. Nanoparticles are typically used in the form of nanofluids that consist of nanoparticles and a base fluid. The effective thermal conductivity is increased by the nanoparticles in a nanofluid, which can significantly improve heat transfer [1]. Today, nanoparticles are present in nearly all science and engineering branches. Nanofluids are colloidal dispersions of nanometer-sized materials (stable metals, metal oxides, oxide ceramics, metal carbides, etc.). In particular, Al₂O₃ nanofluids have been widely investigated and used due to their high productivity, higher thermal properties, and stability [2]. Accordingly, many studies have been done on Al₂O₃ nanofluids in heat transfer applications [3, 4].

The characteristics of thermophysical for Al₂O₃ are essential to be examined to find how Al₂O₃ nanoparticles influence the heat transfer and hydraulic properties of nanofluids [5]. Pak and Cho [6] measured the thermophysical characteristics of TiO₂ and Al₂O₃ nanofluids. Viscosity was determined by changing the volume fraction from 1–10%. The results prove that the density and viscosity increase with the volume fraction. Also, viscosity is approximately independent of the shear rate. Agarwal et al. [7] produced Al₂O₃ nanoparticles and analyzed thermal conductivity. It is dispersed in ethylene glycol or water with different concentrations. At a temperature of 1000 C, the synthesized Al₂O₃ nanoparticles are primarily stable and improve thermal conductivity. Kiruba et al. [8] investigated the effect of adding polyethylenimine on the rheological properties of Al₂O₃ nanofluids. It was proposed that adding polyethylenimine makes the viscosity independent of the fluid temperature and improves gel formation. Kumar et al. [9] investigated the effect of temperature changes (30 C, 40 C, 50 C) on the thermal conductivity of Al₂O₃ nanofluid. The results showed that increasing the volume fraction of nanoparticles in water from 0.01 to 0.08% vol.% improves thermal conductivity, and with increasing temperature, thermal conductivity is further improved.

In a nuclear reactor, heat is released through fission in the fuel rod. Heat is then transferred to the cladding through thermal conduction from the fuel surface [10]. From the cladding surface, heat is transferred to the coolant through convection. The heated coolant is passed to heat exchangers, where steam is generated to operate a power cycle. Nuclear fuel rods are employed as heat sources. Most nuclear reactors run on fuel rods containing the uranium-238 and uranium-235 isotopes. Fuel fission rate and thermal neutron flux affect heat generation in a nuclear reactor. Also, by changing the mass flow rate of the reactor coolant and the temperature difference across the core, the thermal power produced by a reactor changes directly [11]. Uranium is usually in the form of pure metal, in a compound such as U0₂, uranium oxide, or in the form of an alloy with another metal such as aluminum or zirconium (in the form of rectangular plates or long cylindrical rods).

Optimal properties of a fuel that must be fissile include high thermal conductivity, good corrosion resistance, good mechanical resistance at high temperatures, good corrosion resistance, and a high limiting temperature for operation [12].

The fuel rod surface heat flux is the most critical factor in developing or designing a new fuel rod because it must be measured as the maximum fuel centerline temperature. As shown in Figure 1, the generated heat in the fuel pellet flows into a coolant through only one rod surface in the solid-type fuel, whereas the annular fuel has two surfaces and a dual coolant channel. Thus, the heat generated in the annular fuel can flow into the inner or outer surface.

Figure 1.

Schematic of solid (left) and annular fuel (right).

The internally and externally cooled annular fuel increases power density in the standard Westinghouse PWR while keeping or increasing the safety margin [13, 14]. In 2017, the thermal–hydraulic analyses of externally and internally cooled annular fuel were investigated. This study identified the geometry that allows the largest possible power density while maintaining or increasing the minimum departure from nucleate boiling ratio (MDNBR) margin in current PWRs [15]. The DUO THERM program investigated the design analysis of a dual-cooled annular fuel. The program studied pellet and cladding deformations caused by irradiation and power variation to predict the inner and outer heat fluxes and fuel temperature. Using the DUO THERM program, the fuel temperature and heat flux were estimated for a reference annular fuel design. The results showed that the annular fuel heat flux was significantly influenced by the inner and outer gap conductance behaviors. At zero burnup, the heat flux of the inner cladding was maximum. Furthermore, the location of maximum fuel temperature was altered by gap conductance asymmetry [16].

KAERI (Korea Atomic Energy Research Institute) developed a power-uprated annular fuel reloading. This project aimed to develop annular fuel that can be used in the current OPR-1000 pressurized water reactor. It was considered a 12 × 12 annular fuel to evaluate the thermal–hydraulic performance and compared its efficiency against a 16 × 16 cylindrical fuel assembly. The aim of this study was to evaluate dual-cooled annular fuel at normal power for OPR-1000 and finally to measure the possibility of 120% core power. The results illustrated that annular fuel has sufficient margin available on DNB and fuel pellet temperature relative to cylindrical fuel [17, 18]. Two significant safety coefficients (prompt reactivity and power coefficients) of a typical PWR were considered for the annular fuel core using the MCNP-5 code. The optimized 13 × 13 arrays performed the calculations for annular configuration [19]. Moreover, an internally and externally cooled annular fuel was simulated and adapted to a typical VVER-1000 reactor. The results demonstrated that an annular pin configuration, called annular-8, was suggested based on the fully neutronics and MDNBR evaluations [20].

One of the main components of a nuclear reactor is the cooling system. The coolant enters the core at a low temperature and exits at a high temperature after the fission energy is transferred to it. Heat is then transferred from the high-temperature fluid to other thermodynamic components, and eventually, electrical power is generated. High-performance cooling plays a vital role in the efficiency and security of the nuclear power plant. Consequently, the investigation of the effects of nanofluids has been one of the important subjects in recent years. Nanofluids have been found to possess improved thermo-physical properties such as thermal conductivity. Several studies have shown that nanofluids have great potential for increasing heat transfer rates in various application cases while incurring either little or no penalty in pressure drop [21, 22, 23].

In an experimental study, it was investigated different volume concentrations of ${\mathrm{Al}}_2{\mathrm{O}}_3$ nanofluid flowing in a horizontal shell and tube heat exchanger. The results show that the nanofluid’s convective heat transfer coefficient is slightly higher than the base fluid at the same mass flow rate [24]. Also, the nanofluids were simulated as the coolant in the VVER-1000 reactor core to analyze thermal–hydraulic performance using the porous media approach. The results displayed that the temperature of the coolant increases with the concentration of nanoparticles. Due to nanofluids’ higher heat transfer coefficient than pure water, the coolant flow rate can be reduced [25].

In the present study, the effect of Al₂O₃ with various volume percentages in annular fuels on a typical VVER-1000 core was investigated. The FLUENT 6.3.26 code is used together with Gambit mesh generation software to model the annular fuels. The prediction–correction method with a SIMPLEC algorithm is applied to numerical solutions. The k-ε model is used to consider the turbulence effect. The cosine form of generated heat in the axial direction of the fuel rod is defined using the User Defined Function (UDF). Firstly, the simulation accuracy is proved by comparing with other studies and the final safety analysis report (FSAR) for the solid fuel with the concentration of nanoparticles. Then, it is simulated annular fuels with various volume percentages of nanofluid. Finally, the temperature distribution in the fuel, clad, and coolant with nanoparticles and pure water concentration is presented.

2. Material and methods

It is essential to control the diameter tolerance of annular fuel for actualizing dual cooled fuel. Therefore, a comprehensive calculation of the optimal dimensions and array of annular fuel rods for a VVER-1000 is applied based on the moderator to fuel ratio, fuel rod pitch, and annular heat surface area to reference. Furthermore, some thermal–hydraulic limitations are considered to achieve a suitable configuration for the annular fuel rods. The annular-8 configuration is nominated as the most promising configuration based on fully thermal–hydraulic analysis and neutronic research [19].

There are 163 fuel assemblies in the core of the VVER-1000 reactor. It has been arranged in a hexagonal lattice with a lattice pitch of 23.6 cm. There are 311 fuel rods, 18 guiding channels for control rods and/or burnable absorber rods (BARs), and a central channel in each fuel assembly. Figure 2 shows the arrangement of the fuel assembly [26].

Figure 2.

The arrangement of fuel assembly [14, 15].

Table 1 presents significant specifications for the core of the VVER-1000 reactor.

Parameter	Parameter	Value
Core	Reference pressure (MPa)	15.7
	Reactor thermal power (MWt)	3000
	Inlet coolant flow rate ($m^3$/h)	84,800
	Inlet coolant enthalpy (kJ/kg)	1290
	Coolant temperature at the core inlet (K)	561.15
Fuel assembly	Fuel assembly form	Hexagonal
	Number of fuel assembly in the core	163
	Pitch between the assemblies	23.6
	Number of fuel rod in the fuel assembly	311
	Fuel rod pitch (mm)	12.75
Fuel rod	Hole diameter in the fuel pellet (mm)	1.5
	Fuel pellet outside diameter (mm)	7.57
	Cladding inner diameter (mm)	7.73
	Cladding outer diameter (mm)	9.1
	Fuel pellet material	UO2
	Cladding material	Alloy Zr + 1% Nb
	Fuel pellet density (g/${\mathit{cm}}^3$)	10.4–10.7

Table 1.

VVER-1000 reactor specifications [15].

The typical layout of a fuel assembly for the annular case with 8 × 8 arrays is demonstrated in Figure 3. There are 156 fuel rods and 12 guiding channels for control rods in each fuel assembly [20].

Figure 3.

The fuel assembly layout of annular pins and equivalent lattice cell [8].

Table 2 shows the details of the designed values of the annular fuel which have been calculated by Mozafari (2013) [20]. The MNCP5 and COBRA-EN codes were used to find many neutronics and thermo-hydraulics core parameters.

Type	Value
Fuel pellet outside radius (mm)	6.920
Outer cladding outer radius (mm)	7.685
Outer cladding thickness (mm)	0.685
Inner cladding inner radius (mm)	3.906
Inner cladding thickness (mm)	0.685
Outer gap width (mm)	0.08
Inner gap width(mm)	0.08
Predicted pitch (mm)	17.77

Table 2.

Dimensions of the Annular-8 fuel rods [8].

In the present study, the geometry is drawn with GAMBIT software. GAMBIT offers a concise and powerful set of solid modeling-based geometry tools. If you already employ a CAD package, GAMBIT runs both the geometry import and “clean-up” functions that you’ll require. Top down geometry construction using 3D primitives without the complexity of a full-fledged CAD package allows you to create geometries fast. Different CFD problems need different mesh types, and GAMBIT gives you all the options you need in a single package.

In this study, triangular cells are employed to generate the meshes. The number of computational cells is 1.01 million. Figure 4 displays the quality of the mesh in the fuel rod.

Figure 4.

The quality of mesh in the fuel rod.

FLUENT reads the generated mesh using GAMBIT. FLUENT is the world’s largest commercial Computational Fluid Dynamics (CFD) software. FLUENT is a Green-Gauss Finite Volume Method with a Cell-Centered formulation. The major point is the finite volume method (FVM).

The same boundary conditions, such as heat flux, outlet pressure, inlet temperature, and mass flow rate, are considered for nanofluids and pure water. The boundary conditions for the inlet of the fuel assembly, temperature, $T_0$ = 561 K and profiles of uniform axial velocity,$u_0$ are set. The non-slip conditions are considered for the fuel rod wall. The rate of 1.753 kg/m.s is considered for the net flow in the fuel assembly. Pressure is set at 15.7 MPa during reactor operation.

$q=q_{\mathit{max}}cos\left(\pi \mathrm{z}/\mathrm{L}\right)$ is the axial heat-generation distribution, where q, z, and L are the volumetric heat-generation, the axial length, and the active fuel rod length, respectively. To define the cosine function, it is written in the C programming language and compiled in FLUENT.

The governing equations of the nanofluid for the conservation of mass, momentum, and energy in a steady state are written below [27, 28]:

$$\nabla .\left({\rho }_{\mathit{nf}}V\right)=0$$E1

$$\nabla .\left({\rho }_{\mathit{nf}}\mathit{VV}\right)=-\nabla p+\nabla .\tau$$E2

$$\nabla .\left({\rho }_{\mathit{nf}}\mathit{Ve}\right)=-\nabla .\left(k_{\mathit{nf}}\nabla T\right)-\nabla .\left(\mathit{pV}\right)+\nabla .\left(\tau .V\right)$$E3

Where ρ is the density of the nanofluid, V is the velocity vector, p is the pressure, τ is the stress tensor, e is the specific total energy, and T is the temperature. $k_{\mathit{nf}}$ is the conductivity of the nanofluid.

The CFD is used to solve the denoted Navier–Stokes equations. In this code, the SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm, a modified form of the SIMPLE algorithm, is used for numerical procedures in CFD. The algorithm manipulates the same steps as the SIMPLE algorithm with a minor change in the momentum equations, allowing the SIMPLEC velocity correction equations to delete fewer important expressions than those deleted in SIMPLE. It tries to avoid the effects of reducing dropping velocity neighbor correction terms.

3. Thermophysical properties of nanofluid

In this study, it simulated the core of the VVER-1000 reactor with solid and annular fuel using ${\mathit{Al}}_2{O}_3$ nanofluid as coolant. Table 3 shows the physical and thermal properties of this nanoparticle and base fluid [29].

Property	C (J/kg K)	$\rho$(kg/$m^3$)	k (W/mK)	$\alpha$($m^2$/s)
water	4179	997.1	0.605	1.47
${\mathit{Al}}_2{O}_3$	765	3970	40	1317

Table 3.

Thermo-physical properties of nanoparticles and base fluids [16].

The correlations for density (${\rho }_{\mathit{nf}}$), specific heat$\left({\mathit{Cp}}_{\mathit{nf}}\right)$, viscosity (${\mu }_{\mathit{nf}}$), and thermal conductivity ($k_{\mathit{nf}}$) of the nanofluid can be obtained [28, 30, 31]:

$${\mathrm{\rho }}_{\mathrm{nf}}=\left(1-\mathrm{\phi }\right){\mathrm{\rho }}_{\mathrm{nf}}+\mathrm{\phi }{\mathrm{\rho }}_{\mathrm{bf}}$$E4

$${\mathrm{Cp}}_{\mathrm{nf}}=\left(1-\mathrm{\phi }\right){\mathrm{Cp}}_{\mathrm{bf}}+\mathrm{\phi }{\mathrm{Cp}}_{\mathrm{bf}}$$E5

$${\mathrm{\mu }}_{\mathrm{nf}}/{\mathrm{\mu }}_{\mathrm{bf}}=123{\mathrm{\phi }}^2+7.3\mathrm{\phi }+1$$E6

$$k_{\mathit{nf}}/k_{\mathit{bf}}=4.97{\phi }^2+2.72\phi +1$$E7

In this simulation, $\phi$ is the volume fraction of nanofluid considered 5,10, 20.

${\rho }_{\mathit{bf}}$, ${\mathit{Cp}}_{\mathit{bf}}$, ${\mu }_{\mathit{bf}}$, and $k_{\mathit{bf}}$ are density, specific heat, viscosity, and thermal conductivity of the pure fluid, respectively.

4. Results and discussion

4.1 Validation

The simulation results are presented for a typical VVER-1000 reactor with the specifications listed in Table 1. To evaluate simulation accuracy, the obtained results for solid fuel are compared with three other studies. Firstly, the distribution of the axial coolant temperature with 5 and 10 volume fractions of nanofluid is presented in Figure 5.

Figure 5.

Axial coolant temperature distribution in the solid fuel [13].

The obtained results are compared with the porous media approaches solved by Zarifi et al. [25]. In the research of Zarifi, the conservation equations are solved by numerical methods using visual FORTRAN language; Furthermore, the nanofluids analysis was compared with an analysis of pure water. Finally, the applied approaches in the Zarifi study were validated using the COBRA-EN code for pure water [25].

Second, the distribution of the axial clad temperature in solid fuel with pure water is compared with the COBRA-EN code that Safaei has used (Figure 6) (In the simulation of Safaei, the COBRA-EN code is improved to make a thermal–hydraulic analysis for the VVER reactor. To validate it, this calculation is compared with reactor FSAR and analytical approaches.) [32].

Figure 6.

Axial clad temperature distribution in the solid fuel [21].

Third, Figure 7 presents the axial fuel temperature with 10 and 20 volume fractions of nanofluid. It is compared with the DRAGON/DONJON code used by Safarzadeh (In the simulation of Safarzadeh, the DRAGON, DONJON, and a thermal–hydraulic model are used for the coupled analysis of the nanofluid core. The results are compared with the final safety analysis report (FSAR).) [33].

Figure 7.

Axial fuel temperature distribution in the solid fuel [22].

Finally, as shown in Figure 8, the axial fuel temperature with pure water is demonstrated. It is evaluated with the plant’s final safety analysis report (FSAR) [26].

Figure 8.

Axial fuel temperature distribution in the solid fuel [15].

The comparison of the obtained results showed the calculations were in good agreement with other studies. Consequently, the accuracy of the validation is acceptable.

The results showed that due to the increase in heat transfer coefficient by increasing the concentration of ${\mathrm{Al}}_2{\mathrm{O}}_3$nanofluid, the coolant temperature increased, and the central fuel temperature decreased. It is observed that for 10% by volume of nanoparticles, the difference between the cooling temperature and pure water was about 21°C and the difference between the fuel temperature was about 26°C. This study describes the effect of nanofluid on the cooling system’s performance in the reactor core.

4.2 Results

Here, it is simulated annular fuel with pure water. In annular fuel, heat is transferred from internal and external surfaces. Figures 9 and 10 present the distribution of the fuel and clad temperature in annular fuel and solid fuel with pure water. As can be seen, the distribution of temperature would be cosine shaped, which is due to the cosine shape of the heat generated in the axial direction of the fuel rod.

Figure 9.

Comparison of axial fuel temperature distribution.

Figure 10.

Comparison of axial clad temperature distribution.

As can be observed in Figure 9, the maximum value of the fuel temperature in solid and annular fuel is 1201 K and 1012 K, respectively. As observed, an approximately 16% reduction in peak temperature at the fuel center was due to the use of annular fuel instead of solid fuel. As shown in Figure 10, there is a difference of about 26 degrees between the clad temperature in the annular fuel and the solid fuel.

Furthermore, it simulated the annular fuel with nanofluid. Then, it is compared with pure water. Figures 11 and 12 compare the distribution of the fuel and clad temperature in annular fuel with 10 and 20 volume nanofluid fractions with pure water.

Figure 11.

Comparison of axial fuel temperature distribution in the annular fuel.

Figure 12.

Comparison of axial clad temperature distribution in the annular fuel.

As can be seen in Figure 11, the maximum value of the fuel temperature in annular fuel with pure water is 1012 K, whereas the maximum value of the fuel temperature in annular fuel with 10 and 20 volume percentages of nanoparticles is 920 K and 885 K, respectively. It is concluded that by increasing the concentration of the nanofluid from $\phi =0.1$ to$\phi =0.2$, the decreasing peak temperature in the centre of the fuel changes from 9–13%. Also, Figure 12 illustrates that there is about a 13 degrees reduction in the clad temperature with nanofluid compared to the clad temperature with pure water. It was also found that the clad temperature gets closer to the coolant temperature when the nanofluid concentration increases.

In annular fuel, the maximum fuel temperature is reduced because the heat is removed from both sides of the fuel rod. Furthermore, as the heat transfer surface increases, the value of heat flux decreases; thus, it increases the minimum departure from the nucleate boiling ratio (MDNBR) margin. Finally, by increasing the use of the annular fuel, the critical heat flux can be increased.

In the steady-state operational condition, the MDNBR is one of the key limitations of thermal–hydraulic safety. DNBR is calculated from the relation,

$$\text{DNBR}=\frac{{{\mathrm{q}}^{"}}_{\mathrm{CHF}}}{{{\mathrm{q}}^{"}}_{\text{actual}}}$$E8

The nucleate boiling heat flux cannot be increased indefinitely, and it is called the critical heat flux (CHF) at some value. The reactor core must be designed to keep the DNBR larger than the minimum allowable value during steady-state operation, normal operational transients, and anticipated operational occurrences. In annular fuel, the minimum value of DNBR is 1.97, which is higher than the 1.75 value reported by the FSAR for the typical VVER-1000. In other words, the maximum actual heat flux in the annular fuel is 1389.93 kW/m², while in FSAR, this value is equal to 1570 kW/m² [15].

According to the description, it was found that by using the nanofluid as a coolant, the heat generated in the core from the fission reaction in the fuel could be further transferred by the nanofluid. Therefore, safety margins are improved for various transient accidents and crashes.

As observed in Figure 13 for the annular fuel, the pressure drop changes along the channel in different concentrations of nanoparticles. It is explained that as the concentration of nanofluids increases, the pressure drop increases.

Figure 13.

Comparison of the core pressure drop in the annular fuel.

5. Conclusions

This work studied the effect of the using annular fuel rods on thermal–hydraulic characteristics of a typical VVER-1000 reactor. The results of the annular fuel showed that the increase in the heated surface improves the margin from the peak temperature of the fuel to melting. The use of ${\mathrm{Al}}_2{\mathrm{O}}_3$ nanofluid as a coolant in the VVER-1000 nuclear reactor is also recommended. The results showed that by improving the heat transfer coefficient of Al₂O₃ nanofluid to increase the concentration of Al₂O₃ nanoparticles, the coolant temperature increases, and the central fuel temperature decreases. To explain more, there is about 127 K reduction in the maximum value of fuel temperature in the annular fuel with 20 volume percentages of nanoparticles compared to pure water. Furthermore, there is about 13 degrees reduction in the clad temperature with nanofluid compared to the clad temperature with pure water. The results showed the minimum value of DNBR for annular fuel was 1.97. Finally, it is determined that the use of nanofluid with annular fuel rods has the best efficiency in a nuclear reactor. By increasing the heated surfaces in the annular fuel and due to the higher heat transfer coefficient of nanofluids compared to pure water, the coolant flow rate can be reduced. As a result, the reactor core can be more compact, and the plant’s capital cost is reduced.