Impact of Nanoparticles on Heat Transfer Enhancement and Thermal Performance Improvement in HTS Power Transformers

Abstract

Despite the numerous benefits of high-temperature superconducting (HTS) power transformers, they are highly sensitive and vulnerable from a thermal perspective, particularly under fault current conditions due to their fault current tolerance properties. Ensuring the proper operation of the cooling system can enhance the transformer’s performance during fault and overload conditions. To improve the thermal management of this transformer in both convective heat transfer and nucleate boiling conditions, utilizing liquid nitrogen (LN₂) nanofluid instead of conventional LN₂ is a promising solution. In this study, a two-phase Eulerian model using ANSYS Fluent software is employed to analyze the impact of different volume fractions (VFs) of Al₂O₃ nanoparticles with a 40 nm diameter on the cooling performance of a power HTS transformer. The numerical simulations are conducted using the Ranz–Marshal method for heat transfer and the finite element method for solving the governing equations. Nanoparticle concentrations ranging from 0 to 1% are evaluated under various fault conditions. Additionally, the influence of nanoparticles on bubble behavior is examined, partially mitigating the blockage of cooler microchannels. The simulation reveals that adding nanoparticles to the fluid reduces the temperature of the hotspot by 29% in steady state and by 34–52% under different fault currents as a result of 0–46% enhancement of nucleate boiling heat transfer, thereby improving the cooling efficiency of the transformer.

1. Introduction

Transformers are essential components in power systems, as their continuous performance in distribution and transmission lines is crucial for minimizing transportation losses and adjusting voltage/current levels from generation to the distribution sector. Therefore, their reliable and uninterrupted operation is of utmost importance for ensuring continuous power delivery in any bulk power system [1,2,3].

High-temperature superconducting (HTS) technology is an attractive, promising, and beneficial technology for electrical applications such as transmission cables, fault current limiters, magnetic levitation, electrical machines, and transformers [4,5,6,7]. To transfer power on a large scale and at low voltage levels, superconducting transformers have been considered [8,9,10,11,12]. Due to their compact structure and permanent usage in the power grid, although the HTS transformer is a useful device compared to other HTS equipment [13,14,15,16,17], temperature can significantly affect its performance.

The thermal performance of HTS transformers is crucial in terms of total construction cost and thermal stability during operating conditions [18,19,20]. Thermal improvement of the HTS transformer involves two major aspects: reducing heat generation in heat sources and enhancing heat transfer between heat sources and coolant [21,22,23,24]. The heat produced in HTS cables includes AC loss (in steady state) and ohmic loss (in fault current conditions) [25,26,27,28,29,30]. Various approaches, such as using flux diverters or optimizing the structure of windings and tapes, have been explored to reduce AC loss [31,32,33,34,35,36,37,38].

Improving the heat transfer coefficient mainly depends on tape surface characteristics and the thermal properties of the cooling liquid. One effective solution is the use of nanoparticles in the cooling liquid to enhance convective heat transfer and the efficiency of the cooling system [39,40,41]. Previous research has investigated the effects of different nanoparticles such as Al₂O₃, TiO₂, ZnO, and Fe₂O₃ on various base fluids, including water, oil, and liquid nitrogen (LN₂) [42,43,44]. The results indicate that convective heat transfer is primarily influenced by the volume fraction, shape, and material of the nanoparticles [45].

Liquid nitrogen (LN₂) is widely used in cryogenic cooling applications due to its excellent thermal properties and ability to maintain superconducting conditions. In HTS transformers, LN₂ serves as an efficient coolant, enhancing both convective and nucleate boiling heat transfer processes. The low boiling point and high heat capacity of LN₂ enable effective temperature regulation and thermal stability [46]. Incorporating nanoparticles into LN₂ can further improve its thermal conductivity and heat transfer capabilities, making it a suitable choice for high-performance cooling systems in HTS applications.

Although nanoparticles improve convective heat transfer, their effect under fault conditions, characterized by short durations, has not been extensively investigated [27,29]. The main component of heat transfer in these conditions is nucleate boiling heat transfer [14,23]. The bubbles formed during the boiling process can obstruct the flow of LN₂ within the microchannels, making it crucial to understand bubble behavior in nucleate boiling heat transfer.

Thermal analysis results indicate that the most sensitive parts of the HTS transformer under fault current conditions are the microchannels between two tapes of a disc [19]. Blockage of these thin channels by nitrogen bubbles during a fault can severely disrupt heat transfer, increasing the risk of tape damage [42]. Various solutions, such as using porous surfaces [14,23] or increasing fluid turbulence [22,24], have been proposed to address this issue by enhancing bubble dispersal. However, these solutions primarily affect bubble dispersal rates and not the radius, breakup frequency, or nucleate boiling heat transfer coefficient (NBHTC), which are critical factors in boiling heat transfer.

Numerous studies have examined the impact of nanoparticles on the heat transfer coefficient in boiling conditions, revealing both promising results and challenges. For instance, nanofluids can enhance the NBHTC by 77.7% at low nanoparticle volume fractions but reduce it by 30.3% at higher concentrations [47]. Non-spherical nanoparticles, particularly blade-shaped ones, significantly improve heat transfer compared to spherical nanoparticles [48]. Additionally, nanofluids have been shown to significantly increase critical heat flux, although nucleate boiling heat transfer coefficients remain similar to those of pure water [49]. The impact of sedimentation layers on the heat transfer coefficient has also been investigated, indicating that while nanofluids enhance heat transfer, sedimentation can reduce the heat transfer coefficient by 31% and critical heat flux by 16% [50]. Several other studies have explored the effect of nanoparticles on bubble behavior, including parameters like bubble diameter, generation frequency [51], bubble spacing [52], and molecular simulations of these impacts [53]. However, the effects of nanoparticles on nucleation site density, bubble generation frequency, waiting time, and breakup and coalescence frequencies remain underexplored.

The NP effect on physical properties of a bubble’s surface, such as in Figure 1, can create a significant impact on thermal behaviors of LN2. Building upon this literature, this paper focuses on investigating the impact of nanoparticles on the NBHTC in a practical model rather than the sample models examined in previous research. Furthermore, the study explores the effect of nanoparticles on bubble behavior in conjunction with their direct impact on nucleate boiling heat transfer. This approach helps identify various challenges and benefits, with one of the most significant issues being the potential blockage of HTS transformer microchannels by coalescing or overgrown bubbles. Additionally, the mechanism by which nanoparticles affect the NBHTC during very short periods (<100 ms) is also investigated.

In this paper, the influence of nanoparticles on LN2 heat transfer and HSPT under various operating conditions, including full load, overload, and fault conditions, is examined. Additionally, the impact of nanofluids on the convective heat transfer rate and the effect of enhanced convection heat transfer on cooling system performance is evaluated. Furthermore, the effect of the VF of nanoparticles on bubble formation inside the microchannels and NBHTC is investigated under fault current conditions with different amplitudes.

2. Governing Equations

In the thermal analysis, the influence of nanoparticles on the heat transfer performance of the HTS transformer was examined under both steady-state and transient conditions. In both of these modes, the first step is calculating the heat generated in the windings and other parts of the HTS transformer, and the second step is focused on analyzing the heat transfer rate. The flowchart shown in Figure 2 describes the process of this paper.

2.1. AC Loss Calculation

The AC loss of HTS tape includes hysteresis loss, which depends on the superconducting layer, eddy current loss, which mainly occurs in the stabilizer layer, and transporting loss. Equation (1) shows the AC loss of the coil with a unit of J/m/cycle [33,36,37]:

$$Q_{AC}=2{\int }_{T/2}^T{\int }_{S}E.JdSdt$$

(1)

2.2. Overload Losses

The overload condition in an HTS transformer is the flux flow mode in which electrical current is carried by the superconducting layer while the current is near critical current, making it more sensitive and fragile compared with the full load condition. The thermal stability of this mode is extremely important due to the relationship between critical current and temperature. Therefore, in order to operate the HTS transformer in this mode, the cooling system should be improved. By increasing heat transfer in this mode, the reliability of the transformer can be enhanced without entering fault current mode.

In fault current conditions, the resistance of the HTS tape suddenly increases due to the temperature of the tape exceeding its critical limit. The relationship between HTS layer resistance and the current in this mode can be calculated by Equation (2) [33,36,37]:

$${\rho }_t={{\displaystyle \frac{E_0}{J_c}}\left|{\displaystyle \frac{J}{J_c}}\right|}^{n-1}$$

(2)

$$J_c(B)={\displaystyle \frac{J_{c0}}{{\left(1+\frac{\sqrt{Z^2{B}_{\parallel }^2+B_{\perp }^2}}{B_0}\right)}^{\gamma }}}$$

(3)

where B₀, Z, $\gamma$, and n are fitting parameters, where B₀ = 0.137, Z = 0.001, γ $=2.2,\mathrm{a}\mathrm{n}\mathrm{d}n=25$.

Heat transfer in this mode depends on the thermal conductivity of the stabilizer and substrate layer, as well as the convective and evaporative heat transfer between LN2 and the tape surface.

2.3. Fault Current Loss

In the fault condition, the ohmic loss is the dominant part of the loss, and AC loss can be ignored. Ohmic loss is mainly created in the superconducting layer and stabilizer layer. Due to the lower resistance of the copper layer compared to the superconducting layer, in fault current conditions, the majority of the heat in the HTS tape is generated in the stabilizers. Moreover, stabilizers are located on the top and bottom of the tape so that convective heat transfer occurs here. Therefore, analyzing these layers is important in fault current conditions. By neglecting the resistance of other layers (such as the substrate, buffer, and Ag), the electric circuit of the HTS tape used to calculate the ohmic loss in fault current is shown in Figure 3.

Equation (4) is used to calculate the ohmic loss of the tape in fault current conditions [33,36,37]:

$$Q_F={\rho }_t{\displaystyle \frac{l{I}^2}{S}}$$

(4)

where ${\rho }_t={\rho }_{t.HTS}\parallel {\rho }_{t,copper}$, S is tape cross-area, and I is fault current.

2.4. Heat Transfer

Determining the temperature distribution in the winding of the HTS transformer is the primary objective of the thermal analysis, both in steady-state and transient conditions. In steady-state conditions, the hotspot temperature (HSPT) under overload conditions should not exceed the critical temperature. Conversely, under fault current conditions, the HSPT must remain below the quenching temperature of the tape. The energy conservation governing equation is applied in both numerical methods and finite element method (FEM) models to calculate the temperature distribution within the HTS winding. Equation (5) is employed in both steady-state and transient modes to determine the temperature distribution [19]:

$$V_{cd}{\rho }_{cd}{C}_{pcd}{\displaystyle \frac{\partial T}{\partial t}}=V_{cd}.\nabla \left(k_{cd}\nabla T\right)+P\left(T\right)-Q\left(T\right)$$

(5)

where Q and P denote heat created inside the heat sources and heat transferred by heat sources surface, respectively.

2.4.1. Convection Heat Transfer

The convection heat transfer equation is shown in the following equation [22]:

$$P_{conv}=hA\left(T_S-T_F\right)$$

(6)

$$h={\displaystyle \frac{k}{l}}Nu$$

(7)

The Nusselt number in Equation (7) represents the scale of the changing heat transfer coefficient, which will be examined in detail in the following sections.

Nanoparticles alter certain thermal properties of the liquid, ultimately modifying the Nusselt number equation. By introducing nanoparticles (NPs) into pure LN2, the properties of the LN2 nanofluid can be calculated using the following equations [54]:

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

(8)

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

(9)

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

(10)

$${\mu }_{nf}={\displaystyle \frac{{\mu }_{bf}}{{(1-\phi )}^{2.5}}}$$

(11)

$$k_{nf}=\left[{\displaystyle \frac{K_{np}+\left(m-1\right)k_{bf}-(m-1)(k_{bf}-k_{np})\phi }{K_{np}+\left(m-1\right)k_{bf}+(k_{bf}-k_{np})\phi }}\right]k_{bf}$$

(12)

$${\rho }_{nf}{h}_{fg,nf}=\left(1-\phi \right){\rho }_{bf}{h}_{fg,bf}+\left({\displaystyle \frac{T_{b,bf}}{T_{b,np}}}\right)\phi {\rho }_{np}{h}_{fg,np}$$

(13)

where m = 3/Ψ, in which Ψ is the particle sphericity.

Based on new properties of LN₂ nanofluid, Rayleigh and Nusselt numbers are calculated by the following equations, respectively [55]:

$$Ra={\displaystyle \frac{g{\rho }^2{C}_p\beta ∆T{l}^3}{\alpha \mu }}$$

(14)

$$Nu={\displaystyle \frac{pl}{∆T\alpha }}$$

(15)

The impact of nanoparticles on the Nusselt number is calculated by Equation (16) [56]:

$$Nu=2.14{Re}^{0.025}{Pr}^{0.33}{\phi }^{0.004}({\displaystyle \frac{{\mu }_{nf}}{{\mu }_{bf}}}{)}^{0.192}$$

(16)

$$Pr={\displaystyle \frac{{C_{pnf}\mu }_{nf}}{k_{nf}}}$$

(17)

2.4.2. Nucleated Boiling Heat Transfer

Considering that the operating temperature of HTS transformers is slightly higher than the boiling point of LN2, the boiling of LN2 occurs in almost all fault currents. The Rohsenow correlation, shown in Equation (18), provides the best estimate for calculating the boiling heat transfer rate, with empirical validity for different NPs available in [57].

Rensselaer Polytechnic Institute’s (RPI) heat transfer model, used to calculate the heat transfer coefficient, involves convective, quenching, and evaporative heat transfer, as shown in Equations (19)–(21), respectively [58].

$$P_{nb}=P_c+P_q+P_e$$

(18)

$$P_c=h(T_s-T_f)(A-A_b)$$

(19)

$$P_q={2A}_b{f}_d\sqrt{{\displaystyle \frac{t_w{\lambda }_l{\rho }_l{C}_{pl}}{\pi }}}(T_w-T_s)$$

(20)

$$P_e=V_b{N}_W{\rho }_v{h}_{fv}$$

(21)

From these equations, a parameter changed by nanoparticles is nucleation site density, which is calculated by Equation (22) [59], and other parameters will be explained in the following section.

$$N_W=218.8{Pr}^{1.63}\left({\displaystyle \frac{1}{\gamma }}\right){\Theta }^{-0.4}{\Delta T}_w^3$$

(22)

$$Pr={\displaystyle \frac{{C_{pf}\mu }_f}{k_f}}$$

(23)

$$\gamma =\sqrt{{\displaystyle \frac{k_s{\rho }_s{C}_{ps}}{k_f{\rho }_f{C}_{pf}}}}$$

(24)

where $\Theta$ is the porosity constant of the porous layer resulting from the deposition of NPs on the tape surface.

2.5. Bubbles Behaviors

Microchannels between two tapes of HTS winding play a crucial role in heat transfer, especially under fault current conditions. Figure 4a shows the schematic structure of the windings of the HTS transformer, and Figure 4b shows the geometry grid and the independent mesh of the model.

While bubbles significantly enhance the heat transfer coefficient, their coalescence can disrupt heat transfer in the microchannels. Bubble coalescence creates a blocked area inside the microchannels, which prevents other bubbles from being conveyed outside. The schematic of bubble creation and their coalescence is shown in Figure 5.

The movement of bubbles is influenced by horizontal and vertical forces, as shown in Figure 6, based on Equations (25) and (26):

$$\sum F_x=F_{sl}+F_h+F_{du,f,x}+F_{du,np,x}+F_{st,x}+F_{cp}$$

(25)

$$\sum F_y=F_{qs}+F_B+F_{du,f,y}+F_{du,np,y}+F_g+F_{st,y}$$

(26)

The calculation of each force component is shown in Equations (27)–(35) [60]:

$$F_{qs}=6\pi {\rho }_l\mathrm{\mu }Ur\left\{{\displaystyle \frac{2}{3}}+{\left[{\displaystyle \frac{12}{{Re}_b}}+0.75\left(1+{\displaystyle \frac{3.315}{{Re}_b^{0.5}}}\right)\right]}^{-1}\right\}$$

(27)

$$F_{du,x}=\rho \pi R^2\left(R\ddot{R}+{\displaystyle \frac{3}{2}}{R}^2\right)sin\mathrm{\varnothing }$$

(28)

$$F_{du,y}=\rho \pi R^2\left(R\ddot{R}+{\displaystyle \frac{3}{2}}{R}^2\right)cos\mathrm{\varnothing }$$

(29)

$$F_{st,x}=-1.25d_B\sigma {\displaystyle \frac{\pi \left({\theta }_{\alpha }-{\theta }_{\beta }\right)}{{\pi }^2-{\left({\theta }_{\alpha }-{\theta }_{\beta }\right)}^2}}\left(sin{\theta }_{\alpha }+sin{\theta }_{\beta }\right)$$

(30)

$$F_{st,y}={-d}_B\sigma {\displaystyle \frac{\pi }{({\theta }_{\alpha }-{\theta }_{\beta })}}\left(cos{\theta }_{\beta }-cos{\theta }_{\alpha }\right)$$

(31)

$$F_B={\displaystyle \frac{4}{3}}\pi r^3\left({\rho }_l-{\rho }_v\right)g$$

(32)

$$F_{sl}={\displaystyle \frac{1}{2}}{U}^2\pi {\rho }_l{R}^2{\Gamma }^{0.5}{\left\{{\left[{\displaystyle \frac{1.146\epsilon }{{Re}_b^{0.5}}}\right]}^2+{\left({{\displaystyle \frac{3}{4}}\Gamma }^{0.5}\right)}^2\right\}}^{0.5}$$

(33)

$$F_h={\displaystyle \frac{9}{8}}{\rho }_l{\Gamma }^2\pi {\displaystyle \frac{d_W^2}{4}}$$

(34)

$$F_{cp}=\pi {\displaystyle \frac{d_W^2}{4}}{\displaystyle \frac{2\sigma }{5R}}$$

(35)

Based on the interaction between F_f and F_s, the stability of bubbles can be determined. The bubbles’ breakup and coalescence frequency are calculated by Equations (36) and (37), respectively [61].

$$f_B=0.25{\displaystyle \frac{\sqrt{8.2{\left(\epsilon d_B\right)}^{\frac{2}{3}}-\frac{12\sigma }{\left({\rho }_L{d}_B\right)}}}{d_B}}$$

(36)

$$f_C=5.77{\alpha }^2{\epsilon }^{1/3}{d}_B^{-11/3}exp(-1.29{\epsilon }^{{\displaystyle \frac{1}{3}}}{d}_B^{{\displaystyle \frac{5}{6}}}\sqrt{{\displaystyle \frac{{\rho }_f}{\sigma }}})$$

(37)

where d_B is the diameter of the bubbles calculated by the following equation [59]:

$$d_B={\displaystyle \frac{32({\pi }^2-{\left({\theta }_{\alpha }-{\theta }_{\beta }\right)}^2)}{\pi \left({\theta }_{\alpha }-{\theta }_{\beta }\right)(sin{\theta }_{\alpha }-{sin\theta }_{\beta })}}\times {\displaystyle \frac{{\rho }_l{V}_l^2}{\sigma }}({\displaystyle \frac{\pi }{8}}{C}_D{Re}_b^2-{\displaystyle \frac{2}{\pi }}{\rho }^{\mathrm{*}-4}{Ja}^4{Pr}^{-2}sin\phi )$$

(38)

$${\rho }^{\mathrm{*}}={\displaystyle \frac{{\rho }_{nf}-{\rho }_g}{{\rho }_{nf}}}$$

(39)

Experimental results of the nanoparticle deposition effect on the tape surface show that NPs decrease the contact angle of the bubbles according to the Young–Laplace equation [62]:

$$cos\theta ={\displaystyle \frac{{\gamma }_{sv}-{\gamma }_{sl}}{\sigma }}r$$

(40)

where ${\gamma }_{sv}-{\gamma }_{sl}$ is the adhesion tension, and r is the roughness factor of the nano-porous coating shown in Figure 7, both of which increase by adding NPs to the fluid [63].

Finally, one of the important properties of the liquids related to the NPs and effects on Equations (30), (35)–(38) is the surface tension of the liquid calculated by Equation (41) [64]:

$$\sigma ={\sigma }_f+R_{g}T{\Gamma }_b^{\Sigma }({\displaystyle \frac{{\omega }_p+{\omega }_p{K}_p\left(\phi +K_{\Sigma }\right)-K_p{K}_{\Sigma }}{1+K_p\phi }}\phi -{\displaystyle \frac{{\omega }_p+{\omega }_p{K}_p{K}_{\Sigma }-1}{K_p}}lnln\left(1+K_p\phi \right))$$

(41)

where ${\omega }_p$, $K_p$, and $K_{\Sigma }$ are the number of adsorption sites for one nanoparticle, equilibrium adsorption constant, and ratio surface to bulk preference that is calculated by the following equations, respectively.

$${\omega }_p={\displaystyle \frac{M_p{\rho }_f{L}_f}{M_f{\rho }_p{L}_p}}$$

(42)

$$K_p={\displaystyle \frac{{\delta }_m}{L_p}}\sqrt{{\displaystyle \frac{\pi k_{B}T}{{\Phi }_m}}}{e}^{-{\displaystyle \frac{{\Phi }_m}{k_{B}T}}}$$

(43)

$$K_{\Sigma }={\displaystyle \frac{{\Gamma }_{p,max}^{\Sigma }}{{\Gamma }_b^{\Sigma }}}$$

(44)

$${\Gamma }_b^{\Sigma }={\displaystyle \frac{{\rho }_p}{M_p}}{\displaystyle \frac{L_p^2}{L_f}}$$

(45)

$${\Gamma }_{p,max}^{\Sigma }=0.9L_p{\displaystyle \frac{{\rho }_p}{M_p}}$$

(46)

Other parameters that affect the quenching heat flow and bubble behaviors are the bubble generation frequency and bubble waiting time calculated by Equations (47) and (48) [59].

$$f_d=\sqrt{{\displaystyle \frac{4g({\rho }_f-{\rho }_g)}{3d_w{\rho }_f}}}$$

(47)

$$t_w={\displaystyle \frac{0.8}{f_d}}$$

(48)

2.5.1. Void Fraction

The void fraction, defined as the ratio of the gas phase volume to the total volume in a two-phase flow, is crucial in microchannel heat transfer as it directly affects the NBHTC, pressure drop, and flow patterns [65]. During short periods, accurate prediction of void fraction is essential for optimizing thermal performance and ensuring efficient heat transfer. The addition of nanoparticles can significantly impact the void fraction by altering the fluid’s properties, such as thermal conductivity and viscosity, leading to enhanced heat transfer rates and potentially more stable flow patterns [66]. Moreover, the investigation of void fraction patterns can determine the blocked points and areas inside the microchannels. However, the exact effect depends on factors like nanoparticle concentration, size, and material, which can either promote or hinder bubble formation and growth [66,67]. Zuber and Findlay [68] were among the earliest investigators to introduce a general framework for the drift flux model to determine void fraction according to Equation (49):

$$\alpha ={\displaystyle \frac{X}{C\left[X+\frac{{\rho }_g}{{\rho }_f}(1-X)\right]+\frac{{\rho }_g{u}_{gj}}{G}}}$$

(49)

where α is the void fraction, X is a universal parameter depending on heat flux, C is termed the distribution parameter, G is mass velocity, and u_gj is drift velocity.

The impact of NPs on the Zuber equation is obtained by the addition of a function representing the effect of nanoparticles on the void fraction.

2.5.2. Governer Equations

The LN₂ movement inside the cryostat is estimated by momentum, Navier–Stokes, and energy governing equations, which are shown in Equations (50)–(52), respectively, solving two adjacent meshes [22].

$${\displaystyle \frac{\partial {\rho }_l}{\partial t}}+\overrightarrow{\mathit{\nabla }}.{\rho }_l\overrightarrow{v}=0$$

(50)

$${\rho }_l.\nabla \overrightarrow{v}=-\nabla P_e+\rho \overrightarrow{g}+\mu {\nabla }^2\overrightarrow{v}$$

(51)

$${\rho }_l{C}_p.\nabla T-{\displaystyle \frac{D{P}_e}{Dt}}=\mathrm{k}{\nabla }^{2}T+q_w$$

(52)

where $v$ is the fluid velocity, F is the body force vector, P_e is the pressure, and q_w is volumetric heat source inside the transformer.

3. Results

The specifications of the 250 MVA HTS power transformer designed for OS application are detailed in

Table 1. Transformer and its HTS tapes specifications.

Parameter	Value
Capacity	250 MVA
HV/LV voltage	220/33 kV
HV/LV current	655/4182.5 A
Tape material	YBCO
Tape dimension	0.12 × 10 mm2
Critical current	300 A (65 K) 200 A (77 K)
Microchannel width	0.1 mm

and

Table 2. Dimensions and physical properties of transformer.

Element	Dimension	Material
HV winding	10 × 2500 mm	40% Cupper, 50% Hastelloy, 4% silver, 1% YBCO, 5% other materials
LV winding	2 × 5 × 2600 mm	40% Cupper, 50% Hastelloy, 4% silver, 1% YBCO, 5% other materials
Cryostat	1100 × 3000 mm	GFRP with vacuum layer
Windings holders	150 × 2600 mm	GFRP
Core	7500 × 4000 mm	laminated silicon steel

[14,23]. The physical and thermal properties of Al₂O₃ NPs are shown in

Table 3. Al₂O₃ nanoparticle specifications.

Parameter	Value
Density	2719 kg/m3
Specific heat	843 (in 300 k)
Thermal conductivity	0.045 W/m−k
Viscosity	1.72 × 10−5 kg/m−s
Molecular weight	26.98 kg/kmol
Particle size	<100 nm

. This paper utilizes Al₂O₃ nanoparticles of varying diameters and VFs to enhance the heat transfer coefficient. The findings are categorized into four sections: (1) steady-state analysis with AC loss as the heat source, (2) convective and evaporative heat transfer analysis under overload conditions, (3) nucleate boiling heat transfer analysis with fault current loss as the heat source, and (4) bubble behavior analysis under fault conditions.

The model includes two adjacent tapes within one of the double-pancake windings (HV winding) to illustrate the impact of nanoparticles on heat transfer within the microchannel between these tapes.

3.1. Steady-State Heat Transfer

Increasing the convective heat transfer coefficient in the steady state of the HTS transformer can optimize the operation of the cooling system of the HTS transformer in order to decrease the temperature of the tapes in the steady state. The heat sources of the tapes in this condition are limited to AC loss, as calculated by Equation (1). According to Equations (7) and (12), the convective heat transfer coefficient of a nanofluid primarily depends on the VF of nanoparticles. The convective heat transfer coefficient for Al₂O₃ nanoparticles with a 40 nm diameter is illustrated in Figure 8.

The temperature distribution on the tapes in a steady state is depicted in Figure 9. Comparing Figure 9a,b reveals that adding nanoparticles to LN2 decreases the natural flow of LN2. This flow is driven by the dependence of LN2 density on temperature and is directed opposite to gravity. This phenomenon can be explained using Equations (8) and (11).

3.2. Overload Thermal Analysis

The flux flow state is a critical mode of HTS transformer operation. In this state, the current in the tapes is near the critical current. When the current exceeds the critical level, the resistance of the HTS layer increases significantly, causing most of the current to be carried by the superconducting layer until the temperature reaches the critical point, leading to quenching. While this state is not ideal for the continuous operation of the transformer, by enhancing the heat transfer coefficient in this mode, the transformer can be used under the overload condition for limited periods. Therefore, by enhancing heat transfer through the addition of nanoparticles in this mode, the HTS power transformer can withstand limited overloads for short periods, which can be further investigated based on future plans for offshore wind farms.

The hotspot temperature of the tapes for different currents is illustrated in Figure 10. In this figure, point (1) represents the critical current point of the YBCO tapes, point (2) indicates the saturated temperature of LN2, and point (3) denotes the critical temperature of YBCO.

In the region between point (a) and point (c), flux flow occurs, and the power transformer can tolerate a fairly long time in the region (a,b) and a very short time in the region (b,c). As the VF (VF) of nanoparticles increases, the hotspot temperature decreases. This decrease in hotspot temperature is more pronounced at higher currents, leading to a reduction of approximately 30% in most cases. It should be noted that the use of NPs with smaller VFs has less impact on reducing the hotspot temperature.

As shown in Figure 10, at points (b) and (c), the tape current increases by about 8% and 10%, respectively, as a result of adding 1% NPs to the liquid nitrogen.

3.3. Fault Current Condition

3.3.1. Bubble Behavior Analysis

The coalescence of bubbles can create blocked areas inside the microchannels, disrupting the cooling performance of LN2. Bubble coalescence depends on several parameters, including bubble diameter, surface tension, and bubble break-up frequency, all of which change when NPs are added. These changes occur due to the forces that bring particles into the bubbles. Figure 11 shows the bubble density inside the microchannel with pure LN2 and LN2 containing 1% Al₂O₃ nanoparticles with a 40 nm diameter. As shown in this figure, the blocked points caused by large bubbles are completely removed in Figure 11b compared with Figure 11a. This results in a reduction in bubble size and bubble coalescence frequency. The effect of the reduction in the VF of bubbles on the temperature distribution is shown in the following section.

3.3.2. Fault Condition Heat Transfer

Heat transfer and cooling systems play a vital role in the fault current condition of the HTS transformer. The weak operation of the cooling system can cause serious damage to the HTS tape such as its burning and melting. In this condition, the main part of heat transfer is related to the bubbles generated by nucleate boiling.

Based on Equation (18), nucleate boiling heat transfer is related to the NPs’ diameters and VF. The impact of Al₂O₃ NPs’ VF on the HSPT of the HTS tapes at different fault currents is shown in Figure 12. In this figure, region 1 is the full load and overload operation, region 2 shows the quenching condition, and region 3 shows a state in which the cooling performance of the microchannel is disrupted. The HSPT of the tape in region (2) is decreased between 34 and 37% in different fault currents by adding 1% nanoparticles into the LN2. This factor of HSPT reduction is increased to 58% in region (3) as a result of changing the pool-boiling mode of heat transfer to the nucleated boiling mode. Figure 13 shows the temperature distribution on the tapes and surrounding liquid in 7 PU fault current and poor liquid nitrogen and 1% concentration nanofluid.

By increasing the bubble breakup rate and bubbles’ departure frequency, the quenching heat transfer is increased based on Equation (20). The results of Figure 13 show the increasing quenching heat transfer since the isotherms in Figure 13b are expanded compared with Figure 13a.

The Nusselt number distribution around the tape in pure LN₂ and nanofluid LN₂ is shown in Figure 14a,b, respectively. This comparison demonstrates the direct effect of adding nanoparticles on the heat transfer coefficient. The higher density scattering of the Nusselt number in Figure 14b compared to Figure 14a results from the increased density of nucleation sites, as described by Equation (22).

Comparison

Table 4. Comparison of results relevant to boiling heat transfer increase by adding NPs to cooling fluids.

Paper	Impact of Nanoparticle Conditions on Heat Transfer Coefficient Change (%)
Qi et al. [58]	Improved up to 77.7% in low concentrations and decreased 30.3% in high concentrations
You et al. [60]	Increased up to 200%
Mohebali et al. [61]	Reduced to 31% due to the sedimentation
Wang et al. [69]	Improved about 64%, 61% compared to water for AlN and c-Al2O3, respectively
Wang et al. [70]	Enhanced about 86% using nanofluid compared to water
Wang et al. [71]	Improved about 64%, 61% compared to water for AlN and c-Al2O3, respectively
Choi et al. [72]	Enhanced up to 40% for nanofluid compared to water
Sarafraz et al. [73]	Increased about 23.7% for 0.1 mass%
Balasubramanian et al. [74]	Enhanced during the transient state/improved up to 15% for moderate volume concentration
Our study	Improved up to 52% for various NP concentrations

provides a comparison between the results of this paper and those of other similar studies. The comparison indicates that the increase in the heat transfer coefficient depends on various factors, such as the base fluid, NP concentration, NP shape and size, heat flux, and ambient conditions. However, the logical range of this increase is between 30% and 60%. This paper achieved a 52% improvement of the NBHTC. The results of this study are in the upper-average range of NBHTC improvements achieved by adding nanoparticles.

4. Conclusions

Due to the properties of superconducting materials, the heat transfer coefficient is more important compared with conventional transformers. Microchannels among the tapes of the HTS transformer coil have an important cooling performance during the fault current and overload condition. The blocking of these channels by bubbles created in the boiling process disrupts the heat transfer between tapes and fluid.

The results of this paper show several achievements, including the following:

• Adding nanoparticles to fluids increases the heat transfer coefficient both in convection and nucleated boiling mode.
• Nanoparticles can decrease the coalescence rate between the bubbles and reduce the bubbles’ size. These results improve the cooling performance of the cooling system described in this paper.
• The results have shown that nanoparticles with a VF of 1% had the greatest effect on heat transfer and temperature distribution in microchannels.
• By adding nanoparticles, the blocked area inside the microchannels disappears. This result prevents the tapes from burning during the intense fault currents.

In summary, by adding Al₂O₃ NPs into the LN₂ heat transfer coefficient, it is increased by about 60%, which decreases the HSPT of the tapes by 29%. The heat transfer coefficient is improved by adding NPs in fault conditions. In different fault current amplitudes, both increasing the NBHTC and opening blocked areas have a good effect on the HSPT reduction. In these conditions, the HSPT of tapes is decreased by about 34% in low fault currents (7 PU) and 54% in intense (32 PU) fault currents.