Thermal hydraulic analysis of supercritical water reactor cooled by TiO₂ nanofluid

ABSTRACT

Heat transfer study of nanofluids as coolant in SCWRs core has been performed at Helwan University. A thermal hydraulic code has been produced to study the effect of TiO₂ nanofluid water based as a coolant with comparison with pure water as a coolant. Various volume fractions of nanoparticles TiO₂ (2, 6 and 10%) were used in order to investigate its effects on reactor thermalhydraulic characteristics. Based on Parameters of a SCW Canadian Deuterium Uranium nuclear reactor (CANDU), the fuel assembly was modeled to study the effect of nanoparticles volume fraction on thermos-physical properties of basic fluid and the temperature distribution of fuel, cladding surface and coolant in axial direction. The theoretical results showed that the density, viscosity and thermal conductivity of the coolant increases with the increase of nanoparticles volume fraction, contrasting to specific heat, which decreases with the increase in nanoparticles volume fraction.

KEYWORDS:

• Supercritical water reactor
• nanofluids heat transfer
• thermalhydraulic analysis

Thermal conductivity increases with 2, 6 and 10% volume fraction of nanoparticles by 5.5, 18.1 and 32.1%, respectively, at constant pressure 25 (MPa). For 10% volume percentage of nanoparticles the coolant temperature difference with pure water is about 24.2°C, 62.5°C and 94°C at constant pressure 25, 30 and 35 (MPa), respectively. On the other hand, using nanofluid with 10% volume percentage of nanoparticles as coolant has significant effect on fuel temperature that the maximum fuel temperature reduced by 26.2, 23.8 and 18.9% at constant pressure 25, 30 and 35 (MPa), respectively.

1. Introduction

Recent advancements in nanotechnology have originated the new emerging heat transfer fluids called nanofluids. Nanofluids are prepared by dispersing and stably suspending nanometer-sized solid particles in conventional heat transfer fluids. Previous researches have shown that a very small amount of suspending nanoparticles have the potential to enhance the thermophysical, transport and radiative properties of the base fluid. Due to improved properties, better heat transfer performance is obtained in many energy and heat transfer devices as compared to traditional fluids, which open the door for a new field of scientific research and innovative applications [1].

Nanofluids clearly exhibit improved thermo-physical properties such as thermal conductivity, thermal diffusivity, viscosity and convective heat transfer coefficient. The property change of nanofluids depends on the volumetric fraction of nanoparticles, shape and size of the nanomaterials [2,3].

Thermal hydraulic effects of nanofluid as coolant in VVER-1000 nuclear reactor with annular fuel are investigated. The fuel assembly has been simulated in the hot channel using computational fluid dynamics (CFD) simulation codes, and thermalhydraulic calculations (maximum fuel temperature, fluid outlet, minimum departure from nucleate boiling ratio (MDNBR) etc.) are done. As one of the most important results of the analysis, using the nanoparticles increases the heat transfer coefficient [4].

Analytical modeling [5] of the thermalhydraulic in small modular reactor (SMR) CAREM-25 has been applied when the Al₂O₃-water-based nanofluid is used as cooling fluid in the cooling system. Further to this analytical modeling, the reactor has been modeled by using CFD to determine the flow phenomena and distribution as well as the effect of nanoparticles of Al₂O₃-water based on the volume fraction (1 and 3%) on the heat transfer by natural convection.

SCWR reactor thermalhydraulic analysis with a new geometry design has been discussed [6,7]. In the new design, coolant and moderator circuits are separated and nanofluid has been used as reactor core coolant. The thermalhydraulic analysis has been performed for various Al₂O₃ nanoparticles mass fraction and moderator velocities. The calculations showed that the core outlet temperature grows up with increasing nanoparticle mass fraction.

VVER-1000 reactor cooled by Al₂O₃ nanofluid has been studied. The effects of fluctuations in coolant temperature and velocity at the inlet of a fuel assembly have been investigated. The analysis were performed by using a Fourier transformed conservation equation (mass, momentum and energy) in frequency space. The thermalhydraulic effects of nanofluid on noise fluctuations were calculated based on different concentrations of Al₂O₃ nanoparticles and noise frequencies. The calculations showed that any increment in nanoparticles mass fraction will result in reduction of fluctuations in coolant temperature and velocity [8].

1.1 Supercritical water cooled nuclear reactors

SuperCritical Water-cooled nuclear Reactors (SCWRs) are a renewed technology being pursued as one of the six Generation IV International Forum (GIF) reactor concepts. The reactor coolant is light water at pressures and temperatures above its critical point. Some fossil generation power plants use SuperCritical Water (SCW) as the working fluid. However, SCWRs are the only Generation IV reactor concept to be cooled with SCW. These elevated operating conditions will improve SCW Nuclear Power Plant (NPP) thermal efficiency by 10–15% compared to those of current NPPs. Also, SCWRs will have the ability to employ a direct cycle, thus decreasing NPP capital and maintenance costs. A demonstration unit has yet to be designed and constructed. Fuel materials and configurations suited to supercritical conditions are currently being studied. Typical SCWR coolant operating parameters are 25 MPa and 350–625°C. These SCWR operating conditions significantly increase the thermal efficiency of current NPPs from 33–35% to approximately 45–50% [9,10,11,12,13,14,15,16].

1.2 Fuel bundle geometry

Figure(1) shows the fuel bundle, which consists of a heated length of 5.772 m. The central rod has an outer diameter (OD) of 20 mm and is assumed to be unheated. The remaining 42 elements have the OD of 11.5 mm. The hydraulic-equivalent diameter of the bundle is 7.83 mm [9].

Figure 1. Fuel bundle geometry [9].

2. Mathematical model and validation

In current study the considered design parameters showned in Table 1 has been used in the calculations and the considered nanofluid is a mixture of water and nanoparticles of TiO₂. Table 2 illustrate thermos-physical properties of TiO₂.

Table 1. Major parameters of SCW-CANDU and channel reactor with supercritical pressure water [10]

Country	Canada
Coolant	Light Water
Moderator	Heavy Water
Thermal Power, MWth	2540
Electric Power, MWe	1220
Thermal Efficiency, %	48
Presssure, MPa	25
Inlet Temperature, °C	350
Outlet Temperature, °C	625
Flowrate, Kg/s	1320
Number of Fuel Channels	300
Number of Fuel Element in Bundle	43
Maximum Cladding Temperature, °C	850

Table 2. Density-specific thermal conductivity of TiO_2.

PARTICLES	$\rho -\left(kg/m^3\right)$	$C_P-\left(J/kgK\right)$	$K-\left(W/mK\right)$
TiO2	4250	686.2	8.9538

Equations (1(1) ${\rho }_{nf}=\left(1-\mathrm{\varnothing }\right){\rho }_{bf}+\mathrm{\varnothing }{\rho }_p$(1) )–(5(5) $/(k_{np}+2k_{bf}+(k_{np}-k_{bf}){\left(1+\beta \right)}^3\mathrm{\varnothing })k_{bf}$(5) ) were used to study the effect of using nanofluid as a coolant in supercritical condition on coolant thermos-physical properties and temperature distribution across fuel rod.

Correlation (1) is used to calculate density of TiO₂ [6,17,18,19],

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

where ρ_nf is the density of the nanofluid, ϕ is the volume fraction of the nanofluid, ρ_bf is the density of the base fluid and ρ_p is the density of particle.

Correlation (2) is used to calculate Specific heat of TiO₂ [6,17,18,19].

(2) $\rho {c_p}_{nf}=\left(1-\mathrm{\varnothing }\right)\rho {c_p}_{bf}+\mathrm{\varnothing }{\left(\rho c_p\right)}_p$(2)

where Cp_nf is the specific heat of the nanofluid, Cp_bf is the specific heat of the base fluid and (Cp)_p is the specific heat of the nanoparticle.

Correlation (3,4) is used to calculate viscosity of TiO₂ [6,17,18,19].

(3) ${\mu }_{nf}=\left(108{\mathrm{\varnothing }}^2+5.45\mathrm{\varnothing }+1\right){\mu }_{bf}$(3)

(4) ${\mu }_{nf}=\frac{{\mu }_f}{{\left(1-\mathrm{\varnothing }\right)}^{2.5}}$(4)

where μ_nf is the viscosity of the nanofluid, μ_bf is the viscosity of the base fluid.

Correlation (5) is used to calculate conductivity of TiO₂ [18].

$k_{nf}=\left((k_{np}+2k_{bf}+2(k_{np}-k_{bf}){\left(1+\beta \right)}^3\mathrm{\varnothing }\right)$

(5) $/(k_{np}+2k_{bf}+(k_{np}-k_{bf}){\left(1+\beta \right)}^3\mathrm{\varnothing })k_{bf}$(5)

where K_nf is the thermal conductivity of the nanofluid, K_np is the thermal conductivity of the nanoparticle, K_bf is the thermal conductivity of the base fluid and $\beta$ is the ratio of the monolayer thickness to the original particle radius, normally$\beta$ = 1.

The coolant temperature distribution can be calculated using Equation (6)(6) $T_{C,Z}=T_{C,i}+\left(\left(q_i\times L_i\times H_e\right)/\left(\pi \times C_{P-nano}\times \dot{m}\right)\right)\times \left(1-cos\left(\pi \times z/H_e\right)\right)$(6) [20,21].

(6) $T_{C,Z}=T_{C,i}+\left(\left(q_i\times L_i\times H_e\right)/\left(\pi \times C_{P-nano}\times \dot{m}\right)\right)\times \left(1-cos\left(\pi \times z/H_e\right)\right)$(6)

where T_c,z is the axial coolant temperature, T_c,i is the coolant inlet temperature, q_i is the maximum heat flux rate, L_i is the full heated length of the fuel rod, H_e is the extrapolated length, C_p-nano is the specific heat of the nanofluid, $\dot{m}$ is the coolant mass flow rate and z is the fuel increment.

The cladding outer surface temperature distribution can be calculated using Equation (7)(7) $T_{CL,Z}=T_{C,i}+\left(\left(q_i\times L_i\times H_e\right)/\left(\pi \times C_{p-nano}\times \dot{m}\right)\right)\times \left(1-cos\left(\pi \times z/H_e\right)\right)+\left(\left(q_i/h\right)\times sin\left(\pi \times Z/H_e\right)\right)$(7) [20,21].

(7) $T_{CL,Z}=T_{C,i}+\left(\left(q_i\times L_i\times H_e\right)/\left(\pi \times C_{p-nano}\times \dot{m}\right)\right)\times \left(1-cos\left(\pi \times z/H_e\right)\right)+\left(\left(q_i/h\right)\times sin\left(\pi \times Z/H_e\right)\right)$(7)

T_CL,Z is the axial cladding surface temperature, T_C.i is the Coolant inlet temperature and h is the heat transfer coefficient.

The fuel temperature distribution was calculated using Equation (8)(8) $T_{f,Z}=T_{C,i}+\left(\left(q_i\times L_i\times H_e\right)/\left(\pi \times C_{p-nano}\times \dot{m}\right)\right)\times \left(1-cos\left(\pi \times Z/H_e\right)\right)+\left(\left(q_i\times R_t\times L_i\right)\times sin\left(\pi \times Z/H_e\right)\right)+\left(\left(q_i/h\right)\times sin\left(\pi \times Z/H_e\right)\right)$(8) [20,21]., thus

(8) $T_{f,Z}=T_{C,i}+\left(\left(q_i\times L_i\times H_e\right)/\left(\pi \times C_{p-nano}\times \dot{m}\right)\right)\times \left(1-cos\left(\pi \times Z/H_e\right)\right)+\left(\left(q_i\times R_t\times L_i\right)\times sin\left(\pi \times Z/H_e\right)\right)+\left(\left(q_i/h\right)\times sin\left(\pi \times Z/H_e\right)\right)$(8)

where T_f,Z is the axial center line fuel temperature and R_t is the total thermal resistance.

Equation (9)(9) $q_i=\left(Q/A_h\right)$(9) is used to calculate the maximum heat flux rate ($q_i$) [21].

(9) $q_i=\left(Q/A_h\right)$(9)

where Q is the thermal power and A_h is the heated area.

Equation (10)(10) $A_h=\pi \times L_i\times D\mathrm{\_}i\times N\mathrm{\_}assm\times N\mathrm{\_}fuel\mathrm{\_}pin$(10) is used to calculate the heated area ($A_h$) [21].

(10) $A_h=\pi \times L_i\times D\mathrm{\_}i\times N\mathrm{\_}assm\times N\mathrm{\_}fuel\mathrm{\_}pin$(10)

where D_i is the diameter of the heated fuel rod, N_assm is the number of fuel assemblies and N_fuel_pin is the number of fuel pins in the assemblies.

Equation (11)(11) $A_f=\left(A_{pt}-A_{fb}\right)$(11) , is used to calculate the flow area ($A_f$) [21].

(11) $A_f=\left(A_{pt}-A_{fb}\right)$(11)

where A_f is the coolant channel flow area, A_pt is the pressure tube area and A_fb is the fuel bundle area.

Equation (12)(12) $A_{pt}=\left(\pi /4\right)\times d_i^2$(12) , is used to calculate the pressure tube area ($A_{pt}$) [21],

(12) $A_{pt}=\left(\pi /4\right)\times d_i^2$(12)

where d_i is the flow tube inner diameter.

Equation (13)(13) $P_{wetted}=\pi \times \left(\left(N\mathrm{\_}fuel\mathrm{\_}pin\times d_b\right)+d_i\right)$(13) , is to calculate the wetted perimeter ($P_{wetted}$) [21].

(13) $P_{wetted}=\pi \times \left(\left(N\mathrm{\_}fuel\mathrm{\_}pin\times d_b\right)+d_i\right)$(13)

where P_wetted is the wetted perimeter, N_fuel_pin is the number of fuel pins in the assemblies and d_b is the flow bundle diameter.

Equation (14)(14) $D_{hy}=\left(4\times A_f\right)/P_{wetted}$(14) , is used to calculate the hydraulic diameter ($D_{hy}$) [21].

(14) $D_{hy}=\left(4\times A_f\right)/P_{wetted}$(14)

where D_hy is the hydraulic diameter.

Equation (15)(15) $A_{fb}=N\mathrm{\_}fuel\mathrm{\_}pin\times \left(\pi /4\right)\times d_b^2$(15) is used to calculate the fuel bundle area ($A_{fb}$) [21].

(15) $A_{fb}=N\mathrm{\_}fuel\mathrm{\_}pin\times \left(\pi /4\right)\times d_b^2$(15)

Equation (16)(16) $R_{e-nano}=\left(\left(G\times D_{hy}\right)/{\mu }_{nano}\right)$(16) is used to calculate the Reynolds number of coolant ($R_{e-nano}$) [20].

(16) $R_{e-nano}=\left(\left(G\times D_{hy}\right)/{\mu }_{nano}\right)$(16)

where R_e-nano is the Reynolds number for nanofluid, G is the mass flux.

Equation (17)(17) $P_{r-nano}=\left(\left({\mu }_{nf\times }{C}_{P-nano}\right)/K_{nano}\right)$(17) is used to calculate the Prandtle number of nanofluid/water-based coolant ($P_{r-nano}$) [17].

(17) $P_{r-nano}=\left(\left({\mu }_{nf\times }{C}_{P-nano}\right)/K_{nano}\right)$(17)

P_r-nano is the Prandtl number of coolant.

Equation (18)(18) $G=\frac{\dot{m}}{A_f}$(18) is used to calculate the mass flux ($G$) [21].

(18) $G=\frac{\dot{m}}{A_f}$(18)

Total thermal resistance ($R_t$) is the sum of thermal resistance of cladding ($R_{cond}$), thermal resistance of coolant ($R_{conv}$) and thermal resistance of fuel ($R_f$).

(19) $R_t=R_{cond}+R_{conv-nano}+R_f$(19)

Equation (20)(20) $R_{cond}=\left(ln\left(r_c/r_f\right)/\left(2\times \pi \times L_i\times K_c\right)\right)$(20) can be used to calculate the thermal resistance of cladding ($R_{cond}$) [22].

(20) $R_{cond}=\left(ln\left(r_c/r_f\right)/\left(2\times \pi \times L_i\times K_c\right)\right)$(20)

where r_f is the outer radius of fuel.

The outer radius of cladding ($r_c$) is the sum of cladding thickness ($t_c$) and the outer radius of fuel ($r_f$).

(21) $r_c==r_f+t_c$(21)

The thermal conductivity of SS-304 is calculated using Equation (22)(22) $K_c=\left(2\times {10}^{-6}\times T^2\right)+\left(0.0134\times T\right)+\left(10.689\right)$(22) [21].

(22) $K_c=\left(2\times {10}^{-6}\times T^2\right)+\left(0.0134\times T\right)+\left(10.689\right)$(22)

where K_c is the cladding thermal conductivity, T is the Mean temperature of coolant.

The thermal resistance of nanofluid water-based coolant ($R_{conv-nano}$) can be calculated using Equation (23)(23) $R_{conv-nano}=\left(1/\left(h_{nano}\times A_f\right)\right)$(23) .

(23) $R_{conv-nano}=\left(1/\left(h_{nano}\times A_f\right)\right)$(23)

Equation (24)(24) $h_{nano}=\left(\left(k_{nano}\times N_{u-nano}\right)/D_{hy}\right)$(24) is used to calculate the heat transfer coefficient of nanofluid water-based coolant ($h_{nano}$) [17].

(24) $h_{nano}=\left(\left(k_{nano}\times N_{u-nano}\right)/D_{hy}\right)$(24)

Equation (25)(25) $N_{u-nano}=0.023\times \left(R_{e-nano}^{0.8}\right)\times \left(P_{r-nano}^{0.4}\right)$(25) is used to calculate Nusselt number ($N_{u-nano}$) [17].

(25) $N_{u-nano}=0.023\times \left(R_{e-nano}^{0.8}\right)\times \left(P_{r-nano}^{0.4}\right)$(25)

Equation (26)(26) $R_f=1/\left(8\times \pi \times {\mathrm{L}}_{\mathrm{i}}\times {\mathrm{K}}_{\mathrm{f}}\right)$(26) can be used to calculate the thermal resistance of fuel ($R_f$).

(26) $R_f=1/\left(8\times \pi \times {\mathrm{L}}_{\mathrm{i}}\times {\mathrm{K}}_{\mathrm{f}}\right)$(26)

where K_f is the thermal conductivity of nuclear fuels.

3. Results and discussion

In this study, nanofluids TiO₂ -Water with 2, 6 and 10% volume percentages of nanoparticles have been modeled in the supercritical reactor and the thermophysical properties of nanofluids have been investigated.

Figure 2 shows the validation of pure water density between current model and the results of Ref. [23] at supercritical pressure of 25 (MPa).It can be seen that the comparisons showed a good agreement with the data of Ref. [23] for temperature range from 350 (°C) to 400 (°C).

Figure 2. Pure water density at supercritical pressure 25 (MPa) compared with Ref. [23].

Figure 3 shows the validation of pure water specific heat between current model and Ref. [23] results at supercritical pressure of 25 (MPa). It can be seen that the comparisons showed a good agreement with maximum absolute deviations of (2.4%) with the data of Ref. [23] at temperature range from 350 (°C) to 400 (°C).

Figure 3. Pure water specific heat at supercritical pressure 25 (MPa) between current model and Ref. [23].

Figure 4 shows the validation of pure water viscosity between current model and Ref. [23] results at supercritical pressure of 25 (MPa). It can be seen that the comparisons showed a good agreement with the Ref. [23] data at temperature range from 350 (°C) to 400 (°C).

Figure 4. Pure water viscosity at supercritical pressure 25 (MPa) compared with Ref. [23].

In Figures 5 and 6 the current model nanofluid results at supercritical pressure 25 (MPa) ware compared with Ref. [24]. That results of LWR with 15 (MPa) pressurized water reactor cooled by nanofluid were used for validation. As there are no thermal properties of supercritical nanofluid water-based coolant in the literature. Comparisons illustrate good agreement in coolant profile taking into consideration the difference in operating conditions.

Figure 5. Coolant temperature distribution in axial direction compared with Ref. [24] at ϕ 6%.

Figure 6. Coolant temperature distribution in axial direction compared with Ref. [24] at ϕ 10%.

Figure 7 illuminates the temperature distribution of coolant along heated length of supercritical nuclear reactor cooled by nanofluid. Increasing volumetric ratio of TiO₂ particles at constant supercritical pressure P = 25 (MPa), increases the temperature of coolant along heated length. The maximum coolant temperature is as illustrated in Table 3.

Table 3. Maximum coolant temperature difference between SCWR cooled with pure water and SCWR cooled with TiO₂ -water nanofluid at P = 25 (MPa)

TiO2%	0%	2%	6%	10%
Maximum coolant temperature	570.6	575.1	584.5	594.8
Temperature difference	0	4.5	13.9	24.2

Figure 7. Coolant temperature at constant pressure 25 (MPa) different volume fractions of TiO₂ particles.

It can be seen that for volume percentage (ϕ = 10%) of nanoparticles, the coolant temperature difference with pure water is about 24.2 (°C). This means that the heat exchange capacity of the supercritical coolant increased. Thus, to preserve equal design temperature difference, lower coolant flow rate is necessary for cooling the reactor core. Consequently, the reactor core can be more compact and the capital cost of the power plant will be reduced. This temperature difference can save reheat unit cost, which matches with Ref. [24] results.

Figure 8 illuminates the temperature distribution of coolant along heated length of supercritical nuclear reactor cooled by nanofluid. Increasing volumetric ratio of TiO₂ particles at constant supercritical pressure P = 30 (MPa), increases the temperature of coolant along heated length. The maximum coolant temperature is as illustrated in Table 4.

Table 4. Maximum coolant temperature difference between SCWR cooled with pure water and SCWR cooled with TiO₂ -water nanofluid at P = 30 (MPa)

TiO2%	0%	2%	6%	10%
Maximum coolant temperature	931	942.5	967	993.7
Temperature difference	0	11.5	36	62.7

Figure 8. Coolant temperature at constant pressure 30 (MPa) different volume fractions of TiO₂ particles.

It can be seen that for volume percentage (ϕ = 10%) of nanoparticles, the coolant temperature difference with pure water is about 62.7 (°C). This means that the heat exchange capacity of the supercritical coolant increased.

Figure 9 lights up the temperature distribution of coolant along heated length of supercritical nuclear reactor cooled by nanofluid. Increasing volumetric ratio of TiO₂ particles at constant supercritical pressure, P = 35 (MPa), increases the temperature of coolant along heated length. The maximum coolant temperature is as illustrated in Table 5.

Table 5. Maximum coolant temperature difference between SCWR cooled with pure water and SCWR cooled with TiO₂ -water nanofluid P = 35 (MPa)

TiO2%	0%	2%	6%	10%
Maximum coolant temperature	1237	1254	1291	1331
Temperature difference	0	17	54	94

Figure 9. Coolant temperature at constant pressure 35 (MPa) different volume fractions of TiO₂ particles.

It can be seen that for volume percentage, (ϕ = 10%) of nanoparticles, the coolant temperature difference with pure water is about 94 (°C). This means that the heat exchange capacity of the supercritical coolant increased.

Figure 10 illuminates the temperature distribution of fuel along heated length of supercritical nuclear reactor cooled by nanofluid. Increasing volumetric ratio of TiO₂ particles at constant supercritical pressure P = 25 (MPa), decreases the temperature of fuel along heated length. The maximum fuel temperature is as illustrated in Table 6.

Table 6. Maximum fuel temperature difference between SCWR cooled with pure water and SCWR cooled with TiO₂-water nanofluid at P = 25 (MPa)

TiO2%	0%	2%	6%	10%
Maximum fuel temperature	1176	873	867.6	867.5
Temperature difference	0	303	308.4	308.5

Figure 10. Fuel temperature at constant pressure 25 (MPa) different volume fractions of TiO₂ particles.

Table 5 clear up the maximum fuel temperature reduction with increasing nanoparticle volumetric ratio at constant supercritical pressure.

The fuel temperature distribution of the supercritical nuclear reactor cooled by nanofluid will have an extra safe margin 308.5 (°C). That reducing the probability to exceed the industrial acceptance temperature limit of 1850 (°C).

From Table 6 at constant pressure 25 (MPa), using water-based nanofluid as coolant has significant effect on fuel temperature that it reduced by 26.2% accordingly, using nuclear fuels with low melting point can be available and safe with nanofluids . Also it can be seen that for 6 and 10% volume percentage of nanoparticles the fuel temperature reduction is drastically deteriorated. It is because the reduction in specific heat that occur with increasing nanoparticles, and the increase in coolant temperature, which can also explain the propagation of maximum fuel temperature across the fuel rod to be near the end of heated length.

Figure 11 shows the temperature distribution of fuel along heated length of supercritical nuclear reactor cooled by TiO₂ nanofluid. In the case of cooling the reactor by pure water, the maximum fuel temperature reaches to 1545 (°C). By adding the TiO₂ with volume fraction of 2%, (ϕ = 2%) the maximum fuel temperature decreases to 1158 (°C). By increasing the volume fraction percentage, the fuel temperature almost constant and did not affected with these increase as illustrated in Table 6. On the contrary, the maximum fuel temperature tend to increase by increasing the volume fraction percentage after 3.8 (m) of the heated length, i.e. the adding nanoparticles to the pure water enhance the heat transfer coefficient till a certain limit after this limit the maximum fuel temperature tend to increase due to deterioration in the heat transfer.

Figure 11. Fuel temperature at constant pressure 30 (MPa) different volume fractions of $\mathrm{T}\mathrm{i}{\mathrm{O}}_2$ particles.

Table 7 clear up the maximum fuel temperature reduction with increasing nanoparticle volumetric ratio at constant supercritical pressure.

Table 7. Maximum fuel temperature difference between SCWR cooled with pure water and SCWR cooled with TiO₂ -water nanofluid at P = 30 (MPa)

TiO2%	0%	2%	6%	10%
Maximum fuel temperature	1545	1158	1163	1177
Temperature difference	0	387	382	368

The fuel temperature distribution of the supercritical nuclear reactor cooled by nanofluid will have an extra safe margin 387 (°C). That reduces the probability to exceed the industrial acceptance temperature limit of 1850 (°C).

From Table 7 at constant pressure 30 (MPa), using water-based nanofluid as coolant has significant effect on fuel temperature that it reduced by 26.2% accordingly, using nuclear fuels with low melting point can be available and safe with nanofluids . Also it can be seen that for 6 and 10% volume percentage of nanoparticles the fuel temperature reduction is drastically deteriorated. It is because of the reduction in specific heat that occurs with increasing nanoparticles, and the increase in coolant temperature, which can also explain the propagation of maximum fuel temperature across the fuel rod to be near the end of heated length.

Figure 12 shows the temperature distribution of fuel along heated length of supercritical nuclear reactor cooled by TiO₂ nanofluid. Increasing volumetric ratio of TiO₂ particles at constant supercritical pressure of, P = 35 (MPa), increases the maximum temperature of fuel along heated length, the maximum fuel temperature is as illustrated in Table 7.

Figure 12. Fuel temperature at constant pressure 35 (MPa) different volume fractions of $\mathrm{T}\mathrm{i}{\mathrm{O}}_2$ particles.

Table 8 explains the maximum fuel temperature reduction with increasing nanoparticle volumetric ratio at constant supercritical pressure.

Table 8. Maximum fuel temperature difference between SCWR cooled with pure water and SCWR cooled with TiO₂/water nanofluid at P =35 (MPa)

TiO2%	0%	2%	6%	10%
Maximum fuel temperature	1815	1423	1443	1471
Temperature difference	0	392	372	344

The fuel temperature distribution of the supercritical nuclear reactor cooled by TiO₂ nanofluid will have an extra safe margin of 392 (°C). That reduces the probability to exceed the industrial acceptance temperature limit of 1850 (°C).

4. Conclusion

Heat transfer of supercritical water cooled reactor cooled by TiO₂ – water-based nanofluid has been investigated at different volume fraction. The results showed that, by increasing the nanoparticles concentration the coolant temperature increased as a result of heat transfer coefficient improved. Also, nanofluids are efficient coolants than ordinary base fluids as they can remove more heat than ordinary base fluids. Accordingly using nuclear fuels with low melting point can be available and safe with nanofluids. The fuel temperature distribution of the supercritical nuclear reactor cooled by nanofluid will have an extra safe margin 307.6 (°C). That reduces the probability to exceed the industrial acceptance temperature limit of 1850 (°C).

Finally, the use of nanofluids in Supercritical nuclear systems seems promising. For volume percentage (ϕ = 10%) of nanoparticles, the coolant temperature difference with pure water and P = 25 (MPa) is about 24°C. Thus, to preserve equal design temperature difference, lower coolant flow rate is necessary for cooling the reactor core. Consequently, the reactor core can be more compact and the capital cost of the power plant will be reduced

Nomenclature

$Q_{th}$	=	Thermal power, (W).
$A_f$	=	Coolant channel flow area, ($m^2$).
$A_{pt}$	=	Pressure tube area, ($m^2$).
$A_{fb}$	=	Fuel bundle area, ($m^2)$.
$d_i$	=	Flow tube inner diameter, $\left(m\right)$.
$d_b$	=	Flow bundle diameter, $\left(m\right)$.
$D_{hy}$	=	Hydraulic diameter of inner tube, $\left(m\right)$.
$P_{wetted}$	=	Wetted perimeter, $\left(m\right)$.
$A_h$	=	Heated area, ($m^2$).
$\dot{m}$	=	Coolant mass flow rate, (kg/s).
$\mu$	=	Viscosity of coolant, (kg/m. s).
$h$	=	Convection heat transfer coefficient, ($w$/m .k).
$G$	=	Mass flux, (kg/$m^{2.}$s).
$N_u$	=	Nusselt number,(-).
$r_f$	=	Outer radius of fuel, $\left(m\right)$.
$r_c$	=	Outer radius of cladding, $\left(m\right)$.
$t_c$	=	Cladding thickness, (mm).
$K$	=	Thermal conductivity of coolant at mean temperature,$\left(w/m^2.k\right)$.
$P_r$	=	Prandtl number of coolant, ($C_p\mu /K$).
$K_f$	=	Thermal conductivity of nuclear fuels, $\left(w/m^2.k\right)$.
$K_c$	=	Cladding thermal conductivity, $\left(w/m^2.k\right)$.
$L_i$	=	Full heated length of fuel rod, (m).
$D\mathrm{\_}i$	=	Diameter of heated fuel rod, (m).
$N\mathrm{\_}assm$	=	Number of fuel assemblies.
$N\mathrm{\_}fuel\mathrm{\_}pin$	=	Number of fuel pins in the assemblies.
$T$	=	Mean temperature of coolant, $(\circ C)$.
$T_{C,Z}$	=	Axial coolant temperature, $\left({ }^{\circ }C\right)$.
$T_{f,Z}$	=	Axial center line fuel temperature, ${(}^{\circ }C)$.
$T_{CL,Z}$	=	Axial cladding surface temperature, $\left({ }^{\circ }C\right)$
$T_{C,i}$	=	Coolant inlet temperature, ${(}^{\circ }C)$.
$T_{C,o}$	=	Coolant outlet temperature, ${(}^{\circ }C)$.
$H_e$	=	Extrapolated length, $\left(m\right)$.
$C_p$	=	Specific heat capacity of the coolant at constant pressure,(J/kg.k).
$h$	=	Coolant convective heat transfer coefficient,$\left(\frac{W}{m^2}.k\right)$.
$q_i$	=	Max heat flux rate, $\left(W/m^2\right)$.
$q_v$	=	Volumetric heat source,$\left(W/m^3\right)$.
Z	=	Axial location along heated length,$\left(m\right)$.
$R_{nano}$	=	The Reynolds number for nanofluid, (G.$D_{hy}/$${\mu }_{nano}$).
$P_{r-nano}$	=	Prandtle number for nanofluid, ($C_{p-nano}{\mu }_{nano}/$$K_{nano}$).
$K_{nano}$	=	Thermal conductivity of water-based nanofluid coolant, $\left(W/m^2.k\right)$.
$h_{nano}$	=	Water-based nanofluid coolant convective heat transfer coefficient, $\left(\frac{W}{m^2}.k\right)$.
$C_{P-NANO}$	=	Specific heat capacity of water-based nanofluid coolant (J/kg.k).
${\mu }_{nano}$	=	Viscosity of water-based nanofluid coolant, (kg/m .s).
$\mathrm{\varnothing }$	=	Volume fraction of the nanoparticles, (-).

Subscripts

c	=	center.
cr	=	critical (pressure).
el	=	electrical.
hy	=	hydraulic equivalent.
ir	=	inner ring.
in	=	inlet.
o	=	outer.
or	=	outer ring.
pc	=	pseudocritical point.
nano	=	nano coolant.
bf	=	base fluid.
np	=	nano particle.
nf	=	nanofluid.
pt	=	pressure tube.
fb	=	fuel bandle.

Acronyms

CANDU	=	Canada Deuterium Uranium (reactor).
ChUWR	=	Channel-type Uranium-graphite Water Reactor with annular-type elements cooled from inside.
CL	=	Centerline (related to fuel pellet).
HTC	=	Heat Transfer Coefficient.
CHF	=	Critical Heat Flux.
OD	=	Outer Diameter.
PC	=	Pseudocritical.
PT	=	Pressure Tube (reactor).
PV	=	Pressure Vessel (reactor).
PWR	=	Pressurized light-Water Reactor.
SCWR	=	Supercritical Water-cooled Reactor.
AHFP	=	Axial Heat Flux Profile.
NPP	=	Nuclear Power Plant.
ECCS	=	Emergency Core Cooling System.

Disclosure statement

No potential conflict of interest was reported by the authors.