Abstract

Since the events at the Fukushima–Daiichi nuclear power plant, there has been increased interest in developing accident tolerant fuel (ATF) to avoid accidents for light water reactors where Uranium-Silicide-based fuel has an excellent field to minimize the hydrogen hazards. Similarly, steel cladding is at the center of attraction for researchers nowadays. In this research, the feasibility of using Uranium-Silicides (i.e., U3Si, U3Si2, and U3Si5) combined with different types of austenitic steel (i.e., AISI) was investigated to improve the safety performance. A three-dimensional (3D) computational fluid dynamics (CFD)-coded star ccm+ model was used to assess heat transfer performance in the hexagonal fuel assembly of a supercritical water-cooled reactor VVER-1200. Utilizing the computational environment of star ccm+, the test analysis was conducted for a portion of fuel height using the realizable K-Epsilon Two-Layer Wall turbulence model. This analysis showed that the combination of U3Si2 fuel with AISI-348 cladding got superiority over other ATF-AISI fuel-claddings assemblies to use in the reactor core of VVER-1200 because of their lower central fuel temperature value with good mechanical and thermal advantages. This work also derived an empirical heat transfer coefficient equation to guide the relevant future investigations on the thermal analysis of the core.

1 Introduction

The nuclear fuel system of all light water reactors (LWRs) worldwide is currently based on the combination of slightly enriched UO2 pellets confined in Zirconium-alloy-based fuel-cladding. In March 2011, a magnitude of 9.0-grade earthquake occurred in Japan’s coastal area, causing a tsunami in that area [1]. The cost of this occurrence was more than hundreds of million dollars [2]. The tsunami results in a surge flooding in the backup power generator rooms at the Fukushima–Daiichi in Nuclear Power Plants (NPP). The loss of power to coolant systems leads to high temperatures, oxidation of Zr-based alloys, hydrogen production, melted fuel, and hydrogen explosions.

Moreover, during the loss of coolant in the core when the cladding is exposed to high-temperature steam, Zr alloys experience exothermic oxidation, which accelerates the progression of an accident, and the core may meltdown [3]. The economic impacts, both directly related to the clean-up and those generally affecting the nuclear energy sector, are significant [4].

The hydrogen production phenomenon was described by A.R. Massih [5], indicating the margin of safety to withstand hydrogen production, which causes cladding failure (i.e., cracking, melting, and cladding degradation) at high temperatures. Moreover, if any breakdown in any zone of fuel-cladding occurs, then water and steam go in touch with the UO2. So, it oxidized and caused the production of hydrogen.
Zr+2H2O800CZrO2+2H2

The oxidation of UO2 fuel under normal and abnormal to severe accidental conditions occurs when fuel-cladding fails caused by using Zirconium as cladding material by specific characteristics based on their design specifications. The radiation exposure probability is highest as soon as the meltdown scenario starts. So, an alternative way of using Uranium needed to be checked to avoid any other circumstances. In this regard, many researchers sought an excellent Silicide as a perfect option to compete with conventional fuel for securing safety and lowering hydrogen production in NPPs. However, the thermal stability within its melting points (Tables 1 and 7) is the major challenge which is a disadvantage of ura-silicides and steel cladding, whereas UO2 and Zr are 2840 °C, and 1825 °C, respectively. But to improve tolerance of loss of cooling accidents (LOCA) in current reactor systems, modern reactor technology urge a new fuel system with improved fuel and cladding behaviors at high fuel temperatures, against hydrogen generation, fission product release, and fuel melting [6].

Table 1

Thermal properties of austenitic stainless steels

AISIMelting point (°C)Conductivity (W m−1K −1)Expansion (10–6 K)
304143316.316.6
310146614.216
316142715.916–18
347142516.316–18
348144319.118.5
AISIMelting point (°C)Conductivity (W m−1K −1)Expansion (10–6 K)
304143316.316.6
310146614.216
316142715.916–18
347142516.316–18
348144319.118.5

Moreover, Bischoffs [7] and his team developed a fuel concept of accident tolerant fuel (ATF) and related properties to be considered during fuel development such as melting temperature, thermal conductivity, oxidation reaction kinetics with high-temperature steam to reduce the heat and hydrogen production, and fuel thermo-mechanical properties to maintain cool able geometry at high-temperature fuel pellet.

Hence, this research aims to identify the best ATF combination which can generate high temperature but in the margin of its melting point using star ccm+. Moreover, categorizing and integrating different heat transfer coefficient (HTC) equations, another objective of this article is to state a simple HTC equation along with the height of the core.

1.1 UxSix as Fuel Material.

The information about Uranium–Silicide pellets was investigated by many researchers in different branches of science. The U–Si compounds varied in different forms, such as U3Si2, U3Si, U–Si, and U3Si5. Its (U–Si) thermal conductivity is higher than that of uranium dioxide at operating temperatures where Uranium dioxide’s thermal conductivity decreases as a function of temperature [8,9]. This thermal conductivity offsets its melting point (2865 °C), such that the fuel is operating and has safety margins.

In this regard, White et al. [1012] identified that U3Si5 and U3Si2 have similar onset oxidation temperatures, whereas the oxidation of U3Si2 is faster. Moreover, U3Si2 is recognized as a better option, because of its higher resistance to irradiation-induced macroscopic swelling and amorphization [1316].

Antonia and Gofryka calculated the thermal conductivity of U3Si2 in the temperature range of 2–300 K, and magnetic fields up to 9 T were about 8.5 W/m-K at 300 K, which was idealized by electronic and lattice contributions. In this case, the lattice part of the total thermal conductivity was relatively minor in U3Si [17].

Besides, U3Si5 has a lower U density (7.5 gU/cm3) than U3Si (14.8 gU/cm3) and U3Si (12.2 gU/cm3), causing a higher melting point (1770 °C) than those of U3Si (925 °C) and U3Si2 (1665 °C). Under the oxidizing atmosphere at rising temperatures at 1500 °C, U3Si5 was suspected as less susceptible to rapid oxidative pulverization temperatures at which the samples are fragmented [1012,18]. Based on the analysis, U3Si2 will remain crystalline without complete amorphization above ∼230–330 °C, the temperatures relevant to the LWR reactor operations [19]. Moreover, U3Si2 as an LWR fuel requires satisfactory thermal performance across 22 areas [20].

Besides, the Uranium density of U3Si5 with a lower U/Si ratio of 0.58 also suggests that the use of such fuel could be broadly envisioned if a higher U was allowed for specialty reactor designs or as a second fissile phase in a composite fuel [11]. Chen and Yuan [21] also suggested that U3Si2 fuel is an excellent candidate for ATF due to its high thermal conductivity and high Uranium density. It also transfers heat four times faster, allowing the fuel to last longer in accident conditions [22].

1.2 Austenitic Steel as a Cladding Material.

In nuclear reactors, the use of steel as fuel-cladding material has some advantages such as (i) good mechanical and (ii) corrosion resistance [23,24]. But during a loss-of-coolant accident, the main benefit is signified as reducing the amount of hydrogen released.

Moreover, steel 304 was used as a cladding material in the first pressurized water reactor (PWR) with a good performance in the 1960s. Then, alternated cladding materials such as alloys (AISI-304, AISI-310, AISI-316, and AISI-347) were checked to realize their performance and safety [25]. The mechanical properties of austenitic steel were also analyzed by Chawla [23], Beeston [26], Peckner and Berstein [27], and Pasupathi [28], which are combined in Table 1.

Furthermore, the elastic modulus of 348 is higher than Zircaloy-4, which means that the cladding deformation is much smaller than those of Zircaloy-4 cladding. This behavior was confirmed using simulations carried out using adapted fuel performance codes to evaluate fuel rods with AISI 348 as cladding and comparing to the performance of Zircaloy-4 under a common power history [24,29].

In the reactor core, the cladding material should have a high tensile strength [30], and the tensile strength of AISI 348 is highest at 655 MPa. According to Beston’s analysis, considering its other mechanical properties is also an intolerable range. Thus, the AISI 348 would be a good choice. The early investigation found that irradiation of PWR is operated for a period using annealed 348 as cladding, confirming its good performance [31]. Moreover, the void formation probability in AISI steel cladding is lower due to the neutron fragments when irradiated in a fast neutron flux at a higher temperature (more than 650 °C). Since 1960, stainless steel as a cladding material has allowed PWR efficiency due to the lower absorption cross-section of thermal neutrons [24]. Considering such potential aspects, this research investigates steel’s thermal characteristics as cladding materials with the ATF.

1.3 Heat Transfer Coefficient Equation.

The HTC equations from several renowned researchers are well categorized for checking the sustainable heat transfer in the tables (Tables 2 and 3). In this analysis, correlations were implemented, and their prediction capabilities of heat transfer for supercritical water and HTCs need to be assessed.

Table 2

Heat transfer correlations derived from the Dittus–Boelter equation

Eqn. No.ReferencesCorrelationsFlow Geometry
(1)Dittus and Boelter [37]Nub = 0.025 Reb0.8Prb0.4For the case of heating the tube
(2)Griem [38]Nub = 0.0169 Reb0.8356Prb0.432Tubes
(3)Shitsman [41]Nub=0.023Prmin0.8Reb0.8Tubes (D = 7.8, 8.2 mm)
(4)Dwyer [42]Nu=6.66+3.126(SD)+1.184(SD)2+0.0155(ψPe)0.86S = distance between two fuel rod pitch
D = fuel diameter
(5)Kalinin and Dreitser [39]Nu=(0.032X0.0144)Re0.8Pr13; Here X=SDFor bundle fuel rod
(6)Churchill, and Bernstein [43]Nu=0.3+0.62Re0.5Pr13[1+(0.4Pr)23]14[1+(Re282,000)58]45Cylindrical fuel rod (for Pr.Re ≥ 0.2)
Eqn. No.ReferencesCorrelationsFlow Geometry
(1)Dittus and Boelter [37]Nub = 0.025 Reb0.8Prb0.4For the case of heating the tube
(2)Griem [38]Nub = 0.0169 Reb0.8356Prb0.432Tubes
(3)Shitsman [41]Nub=0.023Prmin0.8Reb0.8Tubes (D = 7.8, 8.2 mm)
(4)Dwyer [42]Nu=6.66+3.126(SD)+1.184(SD)2+0.0155(ψPe)0.86S = distance between two fuel rod pitch
D = fuel diameter
(5)Kalinin and Dreitser [39]Nu=(0.032X0.0144)Re0.8Pr13; Here X=SDFor bundle fuel rod
(6)Churchill, and Bernstein [43]Nu=0.3+0.62Re0.5Pr13[1+(0.4Pr)23]14[1+(Re282,000)58]45Cylindrical fuel rod (for Pr.Re ≥ 0.2)
Table 3

Heat transfer correlations with frictional factor

Eqn No.ReferencesCorrelationsFlow Geometry
(7)Petukhov [32]Nu=ζ8Re.Pr900Re+K+12.7ζ8(Pr2/2331)
Here, ζ = (1.82log(Re)1.64)−2 and K=1+900Re
Tubes, upward, downward, and horizontal (D = 10 mm, L = 3.67 m
(8)Gnielinski [40]Nu=f8(Re1000)Pr1+12.7(f8)0.5(Pr231)
Here, f = [0.79ln(Re) − 1.64]−2
Tubes, upward, downward, and horizontal (D = 15 mm, L = 4.29 m
(9)Krasnoshchekov Protopopov [33]Nuo=ζ8Re.Pr1.07+12.7ζ8(Pr2/2331)
where ζ = (1.82log(Re)−1.64)2
Tubes (D = 1.6–20 mm)
Eqn No.ReferencesCorrelationsFlow Geometry
(7)Petukhov [32]Nu=ζ8Re.Pr900Re+K+12.7ζ8(Pr2/2331)
Here, ζ = (1.82log(Re)1.64)−2 and K=1+900Re
Tubes, upward, downward, and horizontal (D = 10 mm, L = 3.67 m
(8)Gnielinski [40]Nu=f8(Re1000)Pr1+12.7(f8)0.5(Pr231)
Here, f = [0.79ln(Re) − 1.64]−2
Tubes, upward, downward, and horizontal (D = 15 mm, L = 4.29 m
(9)Krasnoshchekov Protopopov [33]Nuo=ζ8Re.Pr1.07+12.7ζ8(Pr2/2331)
where ζ = (1.82log(Re)−1.64)2
Tubes (D = 1.6–20 mm)

Integrating frictional factors, the developed correlation equations for heat transfer in supercritical fluids have been developed by Russian researchers Petukhov et al. [32] and Krasnoshchekov Protopopov [33], where the factors of the tube or surface are under consideration. The correlations and conditions are listed in Table 3, which uses various HTC applications.

2 Materials and Methods

The theoretical calculation of the average and surface temperature of the fuel was needed to identify the maximum temperature trends to give the proper justification for using a specific combination of fuel and cladding. The model in star ccm+ was developed for 30 cm, which needs to be verified by the theoretically calculated results. Similar characteristics (i.e., cladding temperature) between the simulated and theoretical data were found in the earlier investigation. The recommendation for fuel-cladding combinations and empirical HTC equation needs to be formulated for the first half of the uniform full-size core.

2.1 Fuel Center Temperature Distribution of Different Accident Tolerant Fuels.

The conductivity of Uranium Carbide, Uranium Nitride (UN), and Uranium Silicide (U3Si2) are appreciably higher than that of UO2 and increases with temperature rather than decreases. High thermal conductivity will reduce the centerline temperature to avoid melting the pellets and claddings. These theories justified the acquired results in this work were explained in star ccm+ by these theories.

To compare the ATF with conventional fuel, thermal distribution is one of the main parameters of this work. The comparison of temperature distribution of ATFs with conventional fuel in the center of the fuel pellet depending on the coordinate of the height of the core has been observed. Furthermore, according to Goldberg [34] and Rahgoshay and Rahmani [35], the total length of the reactor is 375 cms.

The distribution of Tc, with the Tsh and the height and the Tavg of fuel, was calculated every 5 cm. However, the temperature of coolant and cladding was previously calculated where no significant dependency on fuel height was found.

Moreover, to draw the periphery temperatures, Tw(z) distribution, and the fuel resistance effect Rf = 0 in the following equation:
Tc(z)=Tsh(z)+qocos(πzHeff)(Rsh+Rg+Rf)
Thus, the average temperature distribution at each point between the fuel center and the surface becomes
Tavg(z)=Tc(z)+Tw(z)2

In this case, Tc equations correlates with Goldberg’s theories. However, the fuel’s center temperature varies due to thermal resistance and conductivity. Hence, an increase in thermal conductivity will reduce the melting point of each fuel. However, the distribution with the height needs to be clarified within the melting margin. Furthermore, the thermal distribution to use ATF compared to conventional fuel and cladding will be investigated based on the theoretically calculated and found a symmetric distribution as in Fig. 1.

Fig. 1
Temperature distribution at the center of different fuel pellets depends on the coordinate of the height of the core for different cladding material and fuel material combinations
Fig. 1
Temperature distribution at the center of different fuel pellets depends on the coordinate of the height of the core for different cladding material and fuel material combinations
Close modal

2.2 Specification of the Model.

In this analysis, the dimensions used for the model were obtained from an extract of the hexagonal fuel assembly configuration design. The overall computational meshed 3D model output from star ccm+ is visualized in Figs. 2(a)2(c).

Fig. 2
(a) Computational 3D meshed model in star CCM+, (b) detailed mesh configuration of fuel rod and cladding (cross-sectional view), and (c) detailed mesh configuration of fuel rod and cladding (top-sectional view)
Fig. 2
(a) Computational 3D meshed model in star CCM+, (b) detailed mesh configuration of fuel rod and cladding (cross-sectional view), and (c) detailed mesh configuration of fuel rod and cladding (top-sectional view)
Close modal

Prism layer meshes and surface re-meshes were applied with 16,401,947 small matrices or the modeling procedure to get a more accurate model for collecting basic information. The model was validated between temperature ranges 0 °C–5000 °C. Other specifications of the setting of the analytical model and flow and new heat transfer model of computational fluid dynamics (CFD) are prolonged in Tables 4 and 5, respectively.

Table 4

Initial conditions

Initial turbulence intensity0.01
Initial turbulent viscosity ratio10.0
Turbulence velocity1 m/s
Pressure0 Pa
Static temperature315 °C
Initial inlet temperature330 °C
Initial avg. the temperature of the wall surface470.656 °C
Initial turbulence intensity0.01
Initial turbulent viscosity ratio10.0
Turbulence velocity1 m/s
Pressure0 Pa
Static temperature315 °C
Initial inlet temperature330 °C
Initial avg. the temperature of the wall surface470.656 °C
Table 5

Specification of the model in star CCM+

SpecificationValue
Number of the fuel rod7 Psc.
Fuel rod materialU3SI/U3Si2/U3Si5/UO2
Number of cladding7 Psc.
Cladding materialAISI 310/348/Zr
Pressure16.2 MPa
ModeratorWater (properties ref. IAPWS-IF97)
Inlet temperature298.2 °C
Total number of matrix cells6 401 947
Constant field functions
Mass flowrate2.31 kg/s
Effective height4.299 m
Fuel length3.75 m
Assembly number163
Number of fuel rods312
Total thermal power3212 MW
Pellet diameter7.6 mm
Contact thermal resistance3.2 × 10−4 m2k/w
Configuration for mesh generators
Surface re-mesher
Size of the surface cells0.6 mm
The minimum size of the surface cells0.24
Surface growth rate1.2
Parallel messerFor cladding base size (8 mm)
Polyhedral Mesher (without cladding)Base size 12 mm
Number of prism layers8
Prism layer stretching1.2
The total thickness of the prism layer9.6 mm
The flow and heat transfer model
Three dimensionalRANS Turbulence model
Realizable k-epsilon two-layer wall treatment (2nd order gradient)Segregated Fluid Temperature (Convection second-order modeling).
The heat transfer model for cladding and fuel pellet
Three dimensionalSteady
Segregated solid energyConstantan density
SpecificationValue
Number of the fuel rod7 Psc.
Fuel rod materialU3SI/U3Si2/U3Si5/UO2
Number of cladding7 Psc.
Cladding materialAISI 310/348/Zr
Pressure16.2 MPa
ModeratorWater (properties ref. IAPWS-IF97)
Inlet temperature298.2 °C
Total number of matrix cells6 401 947
Constant field functions
Mass flowrate2.31 kg/s
Effective height4.299 m
Fuel length3.75 m
Assembly number163
Number of fuel rods312
Total thermal power3212 MW
Pellet diameter7.6 mm
Contact thermal resistance3.2 × 10−4 m2k/w
Configuration for mesh generators
Surface re-mesher
Size of the surface cells0.6 mm
The minimum size of the surface cells0.24
Surface growth rate1.2
Parallel messerFor cladding base size (8 mm)
Polyhedral Mesher (without cladding)Base size 12 mm
Number of prism layers8
Prism layer stretching1.2
The total thickness of the prism layer9.6 mm
The flow and heat transfer model
Three dimensionalRANS Turbulence model
Realizable k-epsilon two-layer wall treatment (2nd order gradient)Segregated Fluid Temperature (Convection second-order modeling).
The heat transfer model for cladding and fuel pellet
Three dimensionalSteady
Segregated solid energyConstantan density

In the heat transfer model, two-equation assumes that the turbulent fluctuations are locally isotropic with smaller eddies and high Reynolds. Moreover, the production and dissipation terms in the k-equation were considered for the localized heat equilibrium assumption for turbulence modeling. The finite element analytical model requires sophisticated facilities to integrate the gas gap. Hence, the contact resistance between the fuel pellet and the inner cladding surface was set as the gap conductance value of 3.2 × 10–44 to improve computational flexibility.

2.3 Boundary Conditions.

The gradients were deployed using Green–Gauss/Weighted-Least-Squares Hybrid Gradient [36]. The symmetric non-slip boundary flow condition for the moderator took into account the intermolecular force and dragged between the fuel surface and the water moderator. Furthermore, the blended wall function values (rate of dissipation = 9.0, turbulence kinetic energy = 0.42) were chosen. They combined the moderator two-layer techniques with the usage of the function and resulted in a smoother transition flow. The constant mass flowrate of 2.31 kg/s was considered for the effective height of the models through the inlet to the outlet. According to the current VVER-1200 data references, all relevant values have been chosen without the wall configuration.

2.4 Model Evaluation.

For evaluating the model, Tavg and Tc for Zircaloy 4 cladding and UO2 fuel were also calculated and analyzed the similarity of the result to validate the model. In this regard, Tc and Tavg in minor errors which might occur due to the unavoidable assumptions (i.e., wall configuration, hydrogen gap). In Figs. 3(a) and 3(b) and Table 6, the variation in average temperature by theoretical and simulated value is observed. The average error was only 1.975% for Tavg distribution and 0.96% error for Tc distribution which validate the model for further analysis. Moreover, a similar approach was also made for all other combinations by validating and then investigating all along ways of this research to justify the model at each stage in Table 6.

Fig. 3
(a) Average fuel temperature comparison for Zircaloy-4 cladding and UO2 fuel and (b) center fuel temperature comparison for Zircaloy-4 cladding and UO2 fuel
Fig. 3
(a) Average fuel temperature comparison for Zircaloy-4 cladding and UO2 fuel and (b) center fuel temperature comparison for Zircaloy-4 cladding and UO2 fuel
Close modal
Table 6

Average temperature of the fuel for overall 30 cm of the fuel

CombinationAverage theoretically calculated Tc°CAverage simulated Tc°CTc error %Average theoretically calculated Tav,°CAverage simulated Tav,°CTavg error %
Zircaloy cladding and UO2 fuel555.61560.640.91492.73483.001.97
AISI 348 cladding and U3Si fuel468.49465.290.68453.98446.141.72
AISI 348 cladding and U3Si2 fuel473.21469.850.71455.74447.681.76
AISI 348 cladding and U3Si5 fuel506.18509.500.66472.22464.561.62
AISI 310 cladding and U3Si fuel471.86473.170.28456.75447.971.92
AISI 310 cladding and U3Si2 fuel476.58479.720.66459.10451.431.67
AISI 310 cladding and U3Si5 fuel509.52511.820.45475.58467.601.68
CombinationAverage theoretically calculated Tc°CAverage simulated Tc°CTc error %Average theoretically calculated Tav,°CAverage simulated Tav,°CTavg error %
Zircaloy cladding and UO2 fuel555.61560.640.91492.73483.001.97
AISI 348 cladding and U3Si fuel468.49465.290.68453.98446.141.72
AISI 348 cladding and U3Si2 fuel473.21469.850.71455.74447.681.76
AISI 348 cladding and U3Si5 fuel506.18509.500.66472.22464.561.62
AISI 310 cladding and U3Si fuel471.86473.170.28456.75447.971.92
AISI 310 cladding and U3Si2 fuel476.58479.720.66459.10451.431.67
AISI 310 cladding and U3Si5 fuel509.52511.820.45475.58467.601.68

3 Results and Analysis

The thermal analysis revealed the best combination of U–Si and steel cladding considering fuel center temperature within each margin of melting point and a simple HTC equation along with the height of the core.

3.1 Fuel-Cladding Combination.

In Figs. 4(a) and 4(b), the simulated data are graphically compared between different combinations of fuel and cladding. Here, the analytical understanding from the turbulence model is that maximum Tavg and Tc for all varieties of ATF fuel-cladding are much lower than the conventional VVER-1200. Comparatively, the dependency on cladding type is slightly lower than the fuel. To expatiate the results, the overall average values are also mentioned for the first 30 cm of the fuel rod for different fuel-cladding material combinations in Table 6, which reassures the validation of the model and theoretical calculation and enable this research to state the best type of fuel combination calculation of full-size reactor from Fig. 1.

Fig. 4
(a) Fuel average temperature (Tavg) comparison between different fuel and cladding combinations and (b) Fuel maximum temperature (Tc) comparison between different fuel and cladding combination
Fig. 4
(a) Fuel average temperature (Tavg) comparison between different fuel and cladding combinations and (b) Fuel maximum temperature (Tc) comparison between different fuel and cladding combination
Close modal

Furthermore, comparing all the combinations, U3Si2 fuel with AISI 348 anAISI 348 cladding and U3Si2 fuel got the i2 fuel got third lowest Tc (1033.6 °C), which is within its melting margin. Among all other combinations, U3Si5 fuel and AISI 310, 348 cladding got a priority for reactor application for its higher Tc with high heat generation capabilities but within the melting limit (1775 °C). Precise indication has been noted in Table 7 properly comparing two sample combinations with the highest and lowest Tc.

Table 7

Comparable thermal characteristics analysis for declaration

Fuel typeMelting point of the fuel, °CCladding typeThe melting point of the cladding, °CSimulated maximum, Tc °C (for 30 cm)Theoretically calculated maximum Tc, °C (for full size)
U3Si925AISI 3481443465.291010.70
AISI 3101466473.171023.91
U3Si51775AISI 3481443509.661167.46
AISI 3101466515.981181.11
Fuel typeMelting point of the fuel, °CCladding typeThe melting point of the cladding, °CSimulated maximum, Tc °C (for 30 cm)Theoretically calculated maximum Tc, °C (for full size)
U3Si925AISI 3481443465.291010.70
AISI 3101466473.171023.91
U3Si51775AISI 3481443509.661167.46
AISI 3101466515.981181.11

However, for U3Si fuel, the fuel maximum temperature Tc is higher than its melting point. Thus, it will cause reactor failure even during normal operating conditions; hence U3Si, with any other cladding, should not apply to any reactor applications.

Moreover, earlier studies found that AISI 348 got higher mechanical and expansion advantages. Additionally, according to the thermal analysis for all the combinations, U3Si2 and U3Si5 with AISI 348 can be used in VVER-1200 considering its maximum temperature follows the fuel concept within melting point margin and low hydrogen production.

3.2 Heat Transfer Coefficient.

To calculate the referenced HTCavg in Fig. 6, different characterizing data such as conductivity, viscosity, Prandtl, and Reynolds numbers, etc., at each 0.005 cm were identified from NIST Reference Fluid Thermodynamic and Transport Pries Database (REFPROP).

Moreover, the average heat transfer coefficient (HTCavg) for the 30 cm was also computed using star ccm+ as 39,800.1 W/m2K after 103 iterations (Fig. 5). The considerable modal analysis for this iteration is 38,735.81 W/m2K. Hence, the comparison between simulated and theoretically calculated HTC is indicated in Fig. 6.

Fig. 5
Average HTC monitor plot in star ccm+
Fig. 5
Average HTC monitor plot in star ccm+
Close modal
Fig. 6
HTCoverall value comparison with simulated value
Fig. 6
HTCoverall value comparison with simulated value
Close modal
Here, the simulated values are very close to all the relations except for those of Dittus and Boelter [37], Greim [38], and Kalinin and Dreitser [39], due to their course of application and geometry and factor consideration which are concisely mentioned in Tables 2 and 3. Furthermore, the reliability interpretation R-squared values of the correlations considering residuals and the analytical results were found as 0.998, which is recommended as in the excellent range [40]. Therefore, the mean HTC value for the same element for these relations can be calculated with 310 data sets to indicate a simple HTC relation and the core height with the prementioned conditions
HTCnew=7.8835z2+397.19z+38,708
The graphical demonstration by GNUplot is in Fig. 7. A corrective factor, k at the center of the fuel, needs to be identified for further analysis to conclude this research.
Fig. 7
Graphical demonstration of HTCnew along with the height of the core
Fig. 7
Graphical demonstration of HTCnew along with the height of the core
Close modal

4 Conclusions

This study proposed a fuel material and measured thermal response under normal operation. It provides an overview of the lower part efforts underway to support the models to be included in the star ccm+ analysis. To summarize the article, the specifics result from these concepts are the following:

  • Among all types of UxSix fuels and AISI claddings, U3Si with any steel cladding is not applicable for reactor operating conditions. The combination of U3Si5, U3Si2, and AISI-348 is highly capable of reactor applications in the LWRs because of their high heat generation with maximum fuel center temperature and an average temperature within the melting point margin. Besides, integrating mechanical and thermal characteristics of U3Si2 and AISI-348 placed them as a perfect competitor with conventional fuels.

  • The following simple polynomial equation for the HTC has been formulated, with a dependency along with the height for the first half of the reactor and symmetric for the other half
    HTCnew=7.8835z2+397.19z+38,708±k

The corrective factor k indicates additional neutronic study such as the effect of inherent systems, burnable poison, control rod, fission gas release in U3Si5, and irradiation creep in AISI-348, are essential but urge advanced computational facilities for further investigation. However, the equation will be beneficial because of its simplicity during the calculation of the reactor heat transfer analysis for the recommended fuel assembly of VVER-1200.

Acknowledgment

The authors of this paper express their sincere appreciation to the Bangladesh Atomic Energy Commission for arranging the grant for this research, which allows theoretical knowledge to be used in real-world circumstances. The authors would also like to thank the honorable delegates Kirill V. Kutsenko and Demetri Kuzmenkov, as well as the lab facilities of the National Research Nuclear University (NRNU MEPhI), Department of Nuclear Physics and Technologies in Moscow, Russia, and show their gratitude for sharing their pearls of knowledge in this research.

Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent is not applicable. This article does not include any research in which animal participants were involved.

Data Availability Statement

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

     
  • h =

    enthalpy (J)

  •  
  • D =

    diameter (mm)

  •  
  • G =

    mass flow rate, (kg/s)

  •  
  • K =

    turbulent kinetic energy (J/kg)

  •  
  • L =

    length

  •  
  • M =

    molecular mass (kg/kmol)T =  temperature (k/°C)

  •  
  • hlg =

    latent heat of vaporization (kJ/ kg−1)

  •  
  • qo =

    maximum linear density of heat flux(W/m2)

  •  
  • Cp =

    specific heat capacity [kJ/kg]

  •  
  • Heff =

    effective height of the core

  •  
  • Kr =

    irregularity coefficient along the core radius

  •  
  • Kz =

    irregularity coefficient for the height of the core

  •  
  • Na =

    the number of fuel assemblies (Pcs.)

  •  
  • Qc =

    convection heat flux, W/m2

  •  
  • Rf =

    fuel resistance for cladding

  •  
  • Rg =

    gap thermal resistance

  •  
  • Rsh =

    cladding thermal resistance

  •  
  • Sij =

    mean flow quantity

  •  
  • Tc =

    fuel center temperature

  •  
  • Tsh =

    cladding temperature

  •  
  • Tw =

    fuel surface/periphery temperature

  •  
  • y+ =

    dimensionless wall distance

  •  
  • Nu =

    Nusselt number

  •  
  • Re =

    Reynolds number

  •  
  • ΔP =

    pressure drop (MPa)λ =  thermal conductivity (W/mK)

  •  
  • μlf =

    dynamic viscosity at the fluid temperature (kg/s.m)

  •  
  • μlw =

    dynamic viscosity the inner wall surface temperature (kg/s.m)ʋ =  kinematic viscosity (m2/s)

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