A numerical study of the effect of a hybrid cooling system on the cooling performance of a large power transformer

A numerical study of the effect of a hybrid cooling system on the cooling performance of a large power transformer

Applied Thermal Engineering 136 (2018) 275–286 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier...

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Applied Thermal Engineering 136 (2018) 275–286

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

A numerical study of the effect of a hybrid cooling system on the cooling performance of a large power transformer Young Joo Kima, Myunggeun Jeonga, Yong Gap Parkb, Man Yeong Haa, a b

T



School of Mechanical Engineering, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Korea Rolls-Royce and Pusan National University Technology Centre in Thermal Management, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Korea

H I GH L IG H T S

study carried to investigate the cooling performance of radiators. • This values of the FOM in the hybrid cooling system depended on the fan position. • The • The values of the FOM in the hybrid cooling system depended on the oil flow rate.

A R T I C LE I N FO

A B S T R A C T

Keywords: Power transformers Cooling fan configuration Factor of merit Numerical analysis Radiators Cooling performance Hybrid cooling

This study analyzed the conjugate heat transfer and fluid flow of radiators used in a power transformer to investigate the cooling performance. The flow and temperature distributions around the radiators were analyzed to investigate the fundamental mechanisms of radiator cooling in the hybrid cooling system. The oil flow rate in the radiators was varied in the range of 44.4 LPM ∼ 309.6 LPM. The cooling fan location was also varied along the bottom and right surfaces of the radiators, and their effects on the cooling performance were evaluated. The computational results using the standard k−ε turbulence model were compared with the measured data, showing the good agreement between them with the difference which is less than 5%. The cooling fans located at the center of the bottom surface and the bottom of the right surface resulted in the best cooling performance regardless of the insulating oil flow rate due to the positive interaction between the vertical and horizontal air flows induced by fans, giving about 22% higher cooling performance than the worst cooling performance at all flow rate.

1. Introduction A power transformer generates heat loss during the process of electricity conversion. If the heat generated in this process is not emitted efficiently to the surroundings, the temperature in the transformer increases significantly, which can compromise the performance of the transformer’s insulators, shorten its lifespan of the transformers, and cause malfunctions or explosions [1,2]. The size and weight of transformers have been significantly reduced with the recent trend towards high efficiency and miniaturization, but this has increased the rate of heat generated per unit volume of windings in the transformer. Therefore, it is essential to develop a high-performance cooling technology to maintain an allowable temperature for stable operation [3]. A power transformer is cooled down by a radiator mounted on the outside, which can also be used in diverse places besides a power transformer. Various studies have examined radiators for air-



conditioners and automobiles. Kim and Cho [4] carried out a study to improve the heat exchange performance and pressure drop using different radiator fin pitches at low Reynolds number. Kim and Bullard [5] used the Colburn j-factor and Fanning friction factor to evaluate the heat exchange performance and pressure drop of various types of radiators according to the factors such as the fin pitch and louver fin angle. Bintoro et al. [6] conducted a study on a cooling method for an electronic device using an impinging jet with deionized water as the working fluid. Other research has looked at improving and optimizing the cooling performance of thermal management systems and heat exchangers [7–14]. Although much research has been done on air conditioners and automotive radiator systems, there is relatively little research on external cooling systems of power transformers. Cooling systems for the power transformer have been designed to have more radiators than required to for cooling. Therefore, there were no big problems with

Corresponding author. E-mail address: [email protected] (M.Y. Ha).

https://doi.org/10.1016/j.applthermaleng.2018.03.019 Received 13 March 2017; Received in revised form 23 February 2018; Accepted 6 March 2018 Available online 07 March 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

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than vertical cooling. Van der Veken et al. [27] developed a full thermohydraulic radiator model to increase the efficiency of thermal calculations. They compared the results with measured data to validate the model. For efficient cooling, a large power transformer uses different external cooling systems depending on its total heat loss. If the total heat loss is low, the cooling is performed using an ONAN cooling system, but above a certain level, ONAF or oil directed–air forced (ODAF) cooling systems are used. In an air-forced (AF) cooling method, cooling fans are generally installed on one of the side surfaces of the radiator (vertical or horizontal) for efficient manufacturing and transportation. However, effective cooling is difficult because the base capacity of the transformer increases, and as a result, over-designing with additional sets of radiators occurs because of the limited space available for fans. Therefore, this study considers a hybrid cooling system based on the OD cooling method, in which cooling fans are installed on the radiator surface along the horizontal and vertical sides simultaneously. A threedimensional numerical analysis was carried out to investigate the fluid flow and heat transfer phenomena inside and outside the radiator. The numerical method was validated by the results with experimental data using four sets of radiators for AN, AF-vertical, and AF-horizontal cooling systems. The cooling mechanisms of the radiator were identified by comparing and analyzing the characteristics as a function of the oil flow rate. The main factors affecting the cooling performance of the radiator were derived, and a method is proposed to install cooling fans effectively for efficient radiator cooling. In addition, the cooling performance factor of merit (FOM) was evaluated for five sets of radiators.

cooling. However, in recent years, the number and size of radiators have been reduced to decrease costs due to increasing prices for raw materials. Thus, it is necessary to study radiator design, which is indispensable for the optimal cooling system of a power transformer. Nabati et al. [15] used commercial CFD code to investigate the flow and temperature distribution of insulating oil flowing inside a radiator for cooling a transformer. As the oil flowed farther from the inlet of the radiator, there were decreases in the flow rate of the insulating oil distributed from the distribution manifold at the upper surface of the radiator to each fin. A recirculation region occurs around the radiator fins located farthest from the inlet of the radiator, which causes a sharp decrease in the flow rate of the insulating oil flowing into the radiator fins located farthest from the inlet. Tălu and Tălu [16,17] studied the cooling performance of a 630 kV A transformer radiator using FEM. They examined different temperature conditions of the air outside the radiator. They found that the cooling performance of the radiator improves when the inclination angle between the distribution manifold of the radiator and the transformer is about 20 degrees. Seong et al. [18] carried out a numerical analysis on the fluid flow and heat transfer distribution in the radiator of a transformer using commercial CFD code. They analyzed the cooling performance of the radiator using different cooling methods. They found that increasing the length of the radiator was more effective than increasing the number of radiator fins for improving the cooling performance. Kim et al. [19] numerically predicted the cooling performance of a radiator using commercial CFD code. The cooling performance obtained under the ONAF cooling system condition was 20.1% higher than that under the ONAN conditions. Kim et al. [20] conducted a numerical study to optimize the radiator fin shape for efficient cooling using commercial CFD code. They selected the optimal fin shape of the radiator in the oil directed–air natural (ODAN) cooling system using multiple objective functions. They also evaluated the effect of the optimal fin shape on the thermo-hydraulic design and performance of the radiator. Fdhila et al. [21] numerically analyzed the cooling performance of radiators according to the number and size of the cooling fans using commercial CFD code. They performed a flow analysis on the air side of the radiator using a porous media model and showed that the cooling performance of the radiator improved as the size and number of cooling fans increased. Paramane et al. [22] numerically investigated the effects of the locations of cooling fans on the cooling performance of a radiator. They showed that installing cooling fans on the bottom surface of the radiator provided higher cooling efficiency than installing them on the side surface. In addition, installing the cooling fans on the radiator surface with an offset provided 3% higher cooling efficiency than installing them uniformly. Chandak et al. [23] numerically analyzed the effects of radiation on the heat dissipation of a transformer radiator and observed that radiation needs to be included in the natural convection case. Paramane et al. [24] studied the thermal performance of a radiator in a power transformer with different fan mounting arrangements using commercial CFD code (one-sided mounted, opposite side mounted, staggered mounted, and bottom mounted). They showed that placing fans opposite to each other has a negative impact on the heat transfer dissipation and created a large counter pressure on each fan, resulting in a large leakage of air flow and vertical air flow in the middle radiators of the radiator group. Anishek et al. [25] numerically studied the cooling performance of a power transformer with ONAN cooling. They performed an optimization analysis of the radiator, and the proposed radiator design had 14% better cooling performance than an existing design for the same material cost. Paramane et al. [26] conducted experimental and numerical studies to predict the cooling performance of a transformer radiator. They verified their numerical analysis method by comparing the results with measured data. Horizontal cooling had 6.1% better performance

2. Numerical methodology The conjugate heat transfer and fluid flow were analyzed to determine the flow and temperature fields for the insulating oil flowing inside a radiator, the cooling air flowing outside the radiator, and the temperature fields in the solid portion of the radiator. The temperature on the radiator surface is generally less than 320 K, so the effect of radiative heat transfer is much smaller than that of convective heat transfer and was not considered, similar to the study by Kim et al. [8]. The conservation equations governing the 3-dimensional, incompressible turbulent fluid flow and heat transfer are defined as follows:

∂ (ρui ) =0 ∂x i ∂ (ρui uj ) ∂x i

=−

(1)

∂P ∂ ⎛ ∂uj μ + −ρui′ u′j ⎞ + ρgj β (T −T0) ∂x j ∂x i ⎝ ∂x i ⎠ ⎜



(2)

∂ (ρui T ) ∂ ⎛ kf ∂T = −ρui′ T ′⎞⎟ ⎜ ∂x i ∂x i ⎝ CP,f ∂x i ⎠

(3)

∂ ⎛ ∂T ⎞ kS =0 ∂x i ⎝ ∂x i ⎠

(4)





Eqs. (1)–(3) represent the conservation equations for mass, momentum, and energy of the fluid (oil or air), respectively, inside and outside the radiator. The terms −ρui′ u′j and −ρui′ T ′ in (2) and (3) represent the Reynolds stress and turbulent heat flux. The term ρgj β (T −T0) in (2) represents the buoyancy term for the cooling air outside of the radiator, which is defined by the Boussinesq approximation. The subscripts i and j used in (1)–(4) represent the tensor notation. The numerical solutions for (1)–(4) were obtained using FLUENT. The second-order upwind scheme was used for the numerical integration of the convection terms. The SIMPLE algorithm was used for the velocity–pressure coupling technique, and the conductive heat transfer of the radiator fins was simulated using the shell-conduction method provided by FLUENT. Fig. 1 shows the full model and computational domain for the 276

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Table 1 Boundary conditions used. Boundary Inlet

Mass flow inlet

Outlet

Pressure outlet

∀oil =44.4 Toil,in LPM =348.15 K ∀oil =132.6 LPM ∀oil =221.4 LPM ∀oil =309.6 LPM Gauge pressure = 0 Pa

Air

Inlet Outlet

Pressure inlet Pressure outlet

Atmospheric pressure T∞ = 293.15 K

Radiator fin

Fin

Coupled wall condition

Shell conduction (thickness = 0.001 m)

Cooling fan

Casing

Adiabatic wall condition Fan Condition



Oil

(a) Full model

Condition

Fan

Constant pressure jump = 100 Pa

side was designated as radiator 1, while the radiator located on the farright side was radiator 5, as shown in Fig. 1(b). To prevent the entrance effect and back flow from the wake, the inlet and outlet lengths of the pipes were increased. A total of 30 radiator fins were used for each set of radiators, and the distance between each set of radiators was 60 mm. As shown in Fig. 1(c), the radiator has upper and lower manifolds with diameters (D ) of 76.2 mm, and the length of the manifold (L ) is 2500 mm. The diameter of the radiator fins (d ) is 10 mm, and the length of a fin (Lt ) is 2347.6 mm. The distance between each fin (l ) is 35 mm. Aluminum material properties were used for the radiator. The boundary conditions are summarized in Table 1. A gravitational acceleration of −9.81 m/s2 was applied in the direction of the z -axis to interpret the natural convection. In the hybrid cooling systems considered, cooling fans are installed at different positions along the bottom and right surfaces of the radiators, as shown in Fig. 2. Four cooling fans were installed on the bottom and right surfaces of the radiators with two on the bottom and two on the right surface. Nine different cooling models were considered according to the location of the cooling fans, as shown in Fig. 2(a)–(i). For example, AF-S1B2 is an air-forced cooling method and has cooling fan number 1 located on the side of the radiator and cooling fan number 2 located at the bottom, as shown in Fig. 2(b). In the AF cooling models, radiators are cooled by forced convection. The effects of the fan location were investigated. The diameter and power consumption of each fan used were 600 mm and 122.58 W. These values correspond to the size and capacity of fans that are generally used for radiator cooling. Considering the complex shape of radiators, the full geometry of the radiators would require large computational resources and time in the numerical analysis. To solve these problems and enhance the accuracy, a porous media approach (PMA) was employed. The number of grid cells was approximately 21 million based on the computational resources and time available.

(b) Upper and front views

3. Validation study To ensure the validity of the present numerical analysis, we conducted experiments on the radiator cooling performance with four sets of radiators for the AN cooling model without cooling fans and for the AF-horizontal and AF-vertical cooling models, in which six cooling fans were attached to the cooling systems. Fig. 3 shows the experimental apparatus and a schematic diagram for testing the cooling performance. The experiment used an oil tank to represent the internal heating generated from the core and windings in the transformer. A heater was installed inside the oil tank, and its temperature was controlled externally to reproduce the conditions of the internal heating generated

(c) Side view of the radiator Fig. 1. Full model and computational domain of the radiator cooling system used in a transformer.

radiator cooling system. The computational domain was 2650 mm, 6400 mm, and 5700 mm in the x , y , and z -directions, respectively Five sets of radiators were considered. The radiator located on the far left 277

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(a) AF-S1B1

(b) AF-S1B2

(c) AF-S1B3

(d) AF-S2B1

(e) AF-S2B2

(f) AF-S2B3

(g) AF-S3B1

(h) AF-S3B2

(i) AF-S3B3

Fig. 2. Schematics of different cooling models in the hybrid cooling system.

because radiators 1 and 4 have larger surface areas exposed to the lowtemperature ambient air for natural convective heat transfer than radiators 2 and 3. Owing to the differences in the oil flow rate, the cooling capacities of radiators 1 and radiator 2 were not symmetric to those of radiators 4 and 3, respectively. The numerical cooling capacities accurately represented the measured data obtained from the experiment using the test facility shown in Fig. 3. Specifically, the difference between the computational results using the standard turbulence model and measured data for the cooling capacity of the radiators had a minimum value of less than 6.1%. The oil flow rates into each radiator in the AF-vertical cooling model are 49.8, 100.2, 150.0, and 199.8 LPM for radiators 1, 2, 3, and 4, respectively. In the AF-vertical cooling model shown in Fig. 4(b), the cooling performances of radiators 2 and 3 were better than those of radiators 1 and 4 because of the six cooling fans along the bottom surfaces of the radiators, unlike in the AN cooling model. The cooling fans were symmetric along the vertical centerline of the model, the cooling capacities of the radiators on the left side were different from those on the right side because of differences in the oil flow rate, similar to the AN cooling model. The oil flow rates into each radiator in the AF-horizontal cooling model are 53.4, 65.4, 72.6, and 79.2 LPM for radiators 1, 2, 3, and 4, respectively. In the AF-horizontal cooling model shown in Fig. 4(c), the cooling capacity of radiator 4 had the maximum value because of the six cooling fans along the right surface of radiator 4. However, the cooling capacity of radiator 1 in the AF-horizontal cooling model had the minimum value because it was the farthest from the six fans. The

from the core and windings in the transformer. An oil pump was attached to the oil tank to control the flow rate of insulating oil from the transformer to the radiator. The radiators are attached to the side of the oil tank, as shown in Fig. 3(a). The insulating oil temperature is increased by the heater in the oil tank, introduced to the radiators, and cooled by passing through the radiators before it is reintroduced to the oil tank. The insulating oil is mineral oil, which is used in actual transformers. Similar to the circulation of insulating oil between an actual transformer and radiators, the experiment considers the oil circulation in the OD cooling mode. In the OD cooling mode, the oil circulation is induced by an oil pump attached to the oil tank. All the experimental apparatuses except the radiators are insulated to prevent heat loss to the surrounding environment when the insulating oil circulates in this system. Temperature sensors are installed at the inlet and outlet of the radiator to measure the oil temperature, as shown in Fig. 3(b). A mass flow sensor is installed at the inlet of the radiator. A data acquisition system is used to control the experimental devices and procedure, to acquire data, and to post-process the data easily. Fig. 4 shows a comparison of the numerical results using different turbulence models with experiment data on the radiator cooling capacity from different cooling modes. The cooling capacity represents the total heat transfer rate from the insulating oil circulating in the radiators to the ambient cooling air. The oil flow rates into each radiator in the AN cooling model are 54.6, 65.4, 62.4, and 57.6 LPM (liters per minute) for radiators 1, 2, 3, and 4, respectively. The cooling performances of radiators 1 and 4 located on the left and right sides of the model were better than those of radiators 2 and 3 model. This occurred 278

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(a) Experimental apparatus

(a) AN model

(b) Schematic diagram for the present experiment Fig. 3. Experimental apparatus and its schematic diagram for the test of radiator cooling performance.

radiator cooling capacity increased almost linearly from radiator 1 to radiator 4 with decreasing distance from the six fans. The cooling capacities obtained from the numerical computations using different turbulence models for the AF-vertical and AF-horizontal cooling models, accurately represented the experiment data, as shown in Fig. 4(b) and (c). Also, the difference between the computational results using the standard k−ε turbulence model and measured data on the cooling capacities of the radiators had minimum values of less than 4.51% and 4.85% for the AF-vertical and AF-horizontal cooling models, respectively. Therefore, we used the standard k−ε turbulence model in the numerical simulations for the hybrid cooling systems.

(b) AF-vertical model

4. Results and discussions Fig. 5 shows the distribution of the cooling air temperature on the velocity iso-surfaces corresponding to the velocity values of 5 m/s for the hybrid cooling system when the oil flow rate was 44.4 LPM. Cooling fans were installed along the bottom and right surfaces of the radiators. The main flow direction of the cooling air was dependent on the location of the fans. Thus, before the cooling air collision, the main flow of the cooling air was formed along the vertical surface perpendicular to the bottom surface of the radiators and along the horizontal direction perpendicular to the right surface of the radiators, as shown in Fig. 5. However, after the cooling air collision, the flow direction was dependent on the momentum of the cooling air discharged by the fans. The momentum was determined by the location of the fans and the distance from cooling air collision to the fans. The momentum increased from fan positions S1 to S3. It also increased from fan positions B1 to B3. When the fan position was moved from S1 to S3, the main flow of the cooling air was directed to the vertical direction after the cooling air collision because of the increasing effect of the fans on the

(c) AF-horizontal model Fig. 4. Comparison of present numerical results using different turbulence models with data measured from the present experiment on radiator cooling capacity for AN, AFvertical and AF-horizontal cooling models in the standard cooling system.

flow direction of the air. However, from B1 to B3, the main flow direction of the cooling air was directed to the horizontal direction after the collision with an increasing effect of the fans on the flow direction of the air. When the cooling fans were located at B2 or B3, a region of recirculating air flow formed after the cooling air collision in the opposite 279

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(a) AF-S1B1

(b) AF-S1B2

(c) AF-S1B3

(d) AF-S2B1

(e) AF-S2B2

(f) AF-S2B3

(g) AF-S3B1

(h) AF-S3B2

(i) AF-S3B3

Fig. 5. Distribution of cooling air temperature on the velocity iso-surfaces corresponding to the velocity values of 5 m/s for the hybrid cooling system when the oil the flow rate is 44.4 LPM.

direction of the main air flow, as shown by the dotted lines in Fig. 5. For the AF-S1B3 cooling model shown in Fig. 5(c), after the air discharged by fans at S1 and B3 collided, the airflow was directed again toward the fans located at S1. We observed similar recirculation regions in the AFS1B2, AF-S2B2, AF-S2B3, AF-S3B2, and AF-S3B3 models, and their sizes were dependent on the locations of the fans. The recirculating region had a positive or negative effect on the cooling performance of the radiators. If the fans were located at B2, the fans had a positive effect on the cooling performance of the radiators because the air in the recirculating region was used in the cooling of the radiators. However, if the fans were located at B3, the fans had a negative effect on the performance because most of the cooling air in the recirculating region escaped from the radiators and was not used in cooling. Fig. 6 shows the distribution of the cooling air velocity vectors around the radiators and the temperature distribution at the radiator

surfaces. The values were less than or equal to 320 K for different cooling models when the oil flow rate was 44.4 LPM. The fans along the right surface of the radiator were effective in cooling more radiators. The number of radiators exposed to the cooling air increased from S1 to S3. The fans installed along the bottom surface of the radiators were effective in locally cooling the radiators located near the fans. Thus, the cooling performance was dependent on the hybrid effects of the fan locations, as shown in Fig. 6. Fig. 7 shows the overall heat transfer coefficient at each radiator for radiators 1 through 5 from when the oil flow rate in the radiators was 44.4, 132.6, 221.4, and 309.6 LPM. The overall heat transfer coefficient is

h =

280

Q Ar ,s (Toil,avg−Tair ,∞)

(5)

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(a) AF-S1B1

(b) AF-S1B2

(c) AF-S1B3

(d) AF-S2B1

(e) AF-S2B2

(f) AF-S2B3

(g) AF-S3B1

(h) AF-S3B2

(i) AF-S3B3

Fig. 6. Distribution of cooling air velocity vectors around the radiators and the temperature distribution at the radiator surfaces whose values are equal to 320 K or less than 320 K for different cooling models in the hybrid cooling system considered in this study when the insulating oil flow rate is 44.4 LPM.

where Q and Ar ,s are the heat transfer rate and the total surface area of each radiator, respectively. Tair,∞ represents the ambient air temperature. Toil,avg represents the volume-averaged oil temperature, which is defined as:

Toil,avg =

1 Voil

∫V

oil

Toil dV

fans located at B2 on the cooling of radiator 3, and radiator 1 had the largest distance from the fans located at the right surface of the radiators to radiator 5. When the fans were located at B3, the value of h for radiator 5 was the highest, while that for radiator 1 was the lowest because of the hybrid effect of the fans located at B3 with the fans located at S1, S2, and S3. As the oil flow rate increased, the value of h generally increased. Therefore, the heat transfer rate from the hot oil to the cooling air through the radiators increased. Thus, the value of h for ∀oil = 132.6 LPM was much larger than that for ∀oil = 44.4 LPM. However, the value

(6)

where Voil represents the oil volume. When the fans were located at B1, the value of h at radiator 3 was the lowest. However, when the fans were located at B2, the value of h at radiator 3 was the highest and the value of h at radiator 1 was the lowest because of the direct effect of the 281

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(a) AF-S1B1

(b) AF-S1B2

(c) AF-S1B3

(d) AF-S2B1

(e) AF-S2B2

(f) AF-S2B3

(g) AF-S3B1

(h) AF-S3B2

(i) AF-S3B3

Fig. 7. Overall heat transfer coefficient (h ) at each radiator from No. 1 to No. 5 for different cooling models in the standard cooling system when the oil flow rate is 44.4, 132.6, 221.4, and 309.6 LPM.

rates of 44.4, 132.6, 221.4, and 309.6 LPM. Regardless of the oil flow rate and fan positions along the bottom surface, the cooling performance of the radiators was highest when the fans were located at S3 due to the hybrid effect of the fans located at the right and bottom surfaces, as shown in Figs. 5 and 6. However, when the fans were located at S1, the cooling performance was the lowest. Table 3(b) lists the total heat transfer rate and cooling capacity ranks according to the fan position s along the bottom surface of the radiators with fixed positions on the right surface and oil flow rates of 44.4, 132.6, 221.4, and 309.6 LPM. The cooling capacity was highest when the fans on the bottom were located at B2, regardless of the oil flow rate and fan positions on the right surface. However, the middle and lowest ranks in the cooling capacity were dependent on the fans along the bottom and right surfaces as well as the oil flow rate. When the fans were located at S1 at 132.6 LPM, the cooling capacity of the radiators was lowest when the fans were located at B1. However, when the fans were located at S1 at ∀oil ⩾ 132.6 LPM, the cooling capacity of the radiators was lowest when the cooling fans were located at the position of B1. However, when the fans were located at S1 at ∀oil = 44.4 LPM, the cooling capacity of the radiators was lowest when the fans were located at B3. When the fans were located at S2 and S3, the cooling capacity was lowest at B3, regardless of the oil flow rate. This low cooling capacity occurred because the amount of cooling air

of h increased very slowly as the oil flow rate increased from 132.6 to 309.6 LPM. Table 2 lists the total heat transfer rate (Qtot ), total-overall heat transfer coefficient (havg ), and cooling capacity ranks for the models from when the oil flow rate was 44.4, 132.6, 221.4, and 309.6 LPM. The values of Qtot and havg increased with the oil flow rate, similar to the variation of h according to the variation in the oil flow rate, as shown in Fig. 7. However, the rates of increase of Qtot and havg decreased as the oil flow rate increased. When ∀oil = 44.4 LPM, the values of Qtot and havg for the AF-S3B2 model were the highest with the best cooling performance, while those for the AF-S1B3 model were the lowest with the worst cooling performance. Therefore, at this flow rate, the AF-S3B2 model showed 22.26% better cooling performance than the AF-S1B3 model. The ranking of cooling performance when ∀oil ⩾ 132.6 LPM was different from that at 44.4 LPM. When ∀oil ⩾ 132.6 LPM, the AF-S3B2 model had the highest cooling performance with the highest values of Qtot and havg , while the AF-S1B1 model had the lowest cooling performance with the lowest values of Qtot and havg . Therefore, the total cooling amounts of the AF-S3B2 model when the oil flow rate was 309.6 LPM show 22.28% better performance than the AF-S1B1 model. Table 3(a) lists the total heat transfer rate and the cooling capacity ranks according to the fan positions along the right surface of the radiator with fixed fan positions of the at the bottom surface and oil flow 282

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escaping from the right bottom portion of the radiators became larger than that when the fans were located at B1 and B2, as shown in Fig. 5. The total heat transfer rate was dependent on the location of the fans along the bottom and right surfaces of the radiators and the oil flow rate, as listed in Tables 2 and 3. The reciprocal action of these factors affects the cooling capacity and was analyzed using Minitab 16.1, as shown in Fig. 8. The dotted line represents the mean value. Fig. 8(a) shows the analysis results for the reciprocal action on the fans installed along the right surface of the radiators (S1, S2, and S3) according to the fan position along the bottom surface of the radiators (B1, B2, and B3). The highest cooling performance occurred when the fans were located at S3 and B2. Fig. 8(b) shows the analysis results for the reciprocal action of the fans installed along the bottom surface of the radiators (B1, B2, and B3) according to the oil flow rate. When the fans were installed at the B1 and B3, reciprocal action occurred as the oil flow rate increased. Fig. 8(c) shows the analysis results for the reciprocal action of the fans installed along the right surface of the radiators (S1, S2, and S3) according to the oil flow rate. The cooling performance increased as the fans moved from S1 to S3, regardless of the flow rate. Fig. 9 shows the main effect of the fan location along the bottom and right surfaces of the radiators and the oil flow rate on the cooling capacity, which was obtained using Minitab 16.1. The dotted lines represent the total-overall heat transfer rate for all cases listed in Table 2. Fig. 9(a) shows the effect on the cooling capacity of the fan positions along the bottom surface of the radiators (B1, B2, and B3). The cooling performance at B2 was higher than that at B1 and B3. When the fans were located at B3, the cooling capacity was the lowest. When the fans were located B1 and B3, the cooling capacity was lower than the total average cooling capacity represented by the dotted line in Fig. 9(a). Fig. 9(b) shows the effect on the cooling capacity of the fan positions along the right surface of the radiators (S1, S2, and S3). The cooling capacity increased from S1 to S3, with the highest cooling performance occurring at S3 and the lowest cooling performance at S1. The cooling capacity at S2 and S3 was larger than the total average cooling capacity of the radiators denoted by the dotted line in Fig. 9(b). At S1, the capacity was smaller than the total average. Fig. 9(c) shows the effect of the oil flow rate on the cooling capacity. The cooling capacity increased with the oil flow rate. The cooling capacity at ∀oil = 44.4 LPM was smaller than the total average capacity of the radiators denoted by the

Table 2 Total heat transfer rate (Qtot ), total-overall heat transfer coefficient (havg ) and cooling capacity ranks for different hybrid cooling models considered when the oil flow rate is 44.4, 132.6, 221.4, and 309.6 LPM.

∀oil (LPM)

Model

Qtot (kW)

havg (W/m2 K)

Rank

44.4

AF-S1B1 AF-S2B1 AF-S3B1 AF-S1B2 AF-S2B2 AF-S3B2 AF-S1B3 AF-S2B3 AF-S3B3

165.27 189.32 195.76 183.26 194.10 201.29 164.64 181.36 190.16

8.11 9.21 9.49 8.92 9.48 9.79 8.01 8.82 9.25

8 5 2 6 3 1 9 7 4

132.6

AF-S1B1 AF-S2B1 AF-S3B1 AF-S1B2 AF-S2B2 AF-S3B2 AF-S1B3 AF-S2B3 AF-S3B3

216.22 250.20 257.73 242.52 259.60 263.73 222.04 243.52 253.26

10.52 12.17 12.53 11.80 12.63 12.83 10.80 11.85 12.32

9 5 3 7 2 1 8 6 4

221.4

AF-S1B1 AF-S2B1 AF-S3B1 AF-S1B2 AF-S2B2 AF-S3B2 AF-S1B3 AF-S2B3 AF-S3B3

225.44 261.60 269.77 254.91 273.53 278.81 234.38 259.06 267.50

10.97 12.73 13.12 12.40 13.31 13.57 11.40 12.60 13.02

9 5 3 7 2 1 8 6 4

309.6

AF-S1B1 AF-S2B1 AF-S3B1 AF-S1B2 AF-S2B2 AF-S3B2 AF-S1B3 AF-S2B3 AF-S3B3

228.68 265.10 273.55 258.85 278.07 279.64 238.69 263.46 271.79

11.13 12.92 13.40 12.59 13.53 13.65 11.61 12.82 13.22

9 5 3 7 2 1 8 6 4

Table 3 Total heat transfer rate and the cooling capacity ranks when the oil flow rate is 44.4, 132.6, 221.4, and 309.6 LPM. Model

∀oil = 44.4 LPM

Qtot (kW)

∀oil = 132.6 LPM Rank

∀oil = 221.4 LPM

∀oil = 309.6 LPM

Qtot (kW)

Rank

Qtot (kW)

Rank

Qtot (kW)

Rank

(a) Effect of cooling fan location along the right surface of radiator S1 B1 165.27 3 S2 189.32 2 S3 195.76 1

216.22 250.20 257.73

3 2 1

225.44 261.60 269.77

3 2 1

228.68 265.10 273.55

3 2 1

S1 S2 S3

B2

183.26 194.10 201.29

3 2 1

242.52 259.60 263.73

3 2 1

254.91 273.53 278.81

3 2 1

258.85 278.07 279.64

3 2 1

S1 S2 S3

B3

164.64 181.36 190.16

3 2 1

222.04 243.52 253.26

3 2 1

234.38 259.06 267.50

3 2 1

238.69 263.46 271.79

3 2 1

216.22 242.52 222.04

3 1 2

225.44 254.91 234.38

3 1 2

228.68 258.85 238.69

3 1 2

(b) Effect of cooling fan location along the bottom surface of radiator S1 B1 165.27 2 B2 183.26 1 B3 164.64 3 S2

B1 B2 B3

189.32 194.10 181.36

2 1 3

250.20 259.60 243.52

2 1 3

261.60 273.53 259.06

2 1 3

265.10 278.07 263.46

2 1 3

S3

B1 B2 B3

195.76 201.28 190.16

2 1 3

257.73 263.73 253.26

2 1 3

269.77 278.81 267.50

2 1 3

273.55 279.64 271.79

2 1 3

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Fig. 8. Effect of the interaction between the fan position and the oil flow rate on the cooling performance in the hybrid cooling system.

Fig. 9. Effect of various parameters on the cooling performance in the hybrid cooling system.

dotted line. Fig. 10 shows the FOM for different oil flow rates. The FOM was used to evaluate the cooling efficiency of the AF cooling models and is defined as:

FOM = (Q AF −Q AN )/ PAF

(7)

where Q AF and Q AN represent the total heat transfer rate from the oil to the cooling air through the radiators in the AF and AN cooling models, respectively, and refers to the total amount of power used by the fans. 284

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Fig. 10. Factor of Merit for different oil flow rates in the standard and hybrid cooling systems.

The numerator represents the difference in the total heat transfer rate between the AF and AN cooling models, and the denominator represents the total power required by the fans depending on the number of fans used. The FOM of the hybrid cooling system was dependent on the oil flow rate. As shown in Fig. 10, the cooling performance of the radiators decreased when the fans were located at S1. FOM was highest for the AFS3B2 model, regardless of the oil flow rate. When the oil flow rate increased to 132.6 LPM from 44.4 LPM, FOM increased. However, when the oil flow rate increased further to 221.4 LPM and 309.6 LPM, the change in FOM was very small due to the high heating load required.

horizontally induced by fans at S3. When ∀oil = 44.4 LPM, the values of Qtot and havg for the AF-S3B2 model were the highest with the best cooling performance, while those for the AF-S1B3 model were the lowest with the worst cooling performance. Therefore, at this flow rate, the cooling performance of the AFS3B2 model is about 22% higher than that of the AF-S1B3 model. However, when ∀oil ⩾ 132.6 LPM, the AF-S3B2 model had the highest cooling performance with the highest values of Qtot and havg , while the AF-S1B1 model had the lowest cooling performance with the lowest values of Qtot and havg . Therefore, when ∀oil ⩾ 132.6 LPM, the cooling performance of the AF-S3B2 model is about 22% higher than that of the AF-S1B1 model.

5. Conclusions

Acknowledgements

This study analyzed the conjugate heat transfer and fluid flow to investigate the cooling performance of radiators for different cooling models in hybrid cooling systems. A numerical analysis determined the flow and temperature fields for the oil flowing inside the radiator, the cooling air flowing outside the radiator, and the temperature fields in the solid portion of the radiator. The cooling capacity obtained from the computations was compared with measured data. There was good agreement between the computational and measured data with less than 5% difference, particularly when the standard k−ε turbulence model was used. The cooling performance of the radiators was strongly dependent on the location of the fans along the bottom and right surfaces of the radiators. The cooling performance at B2 was higher than that at B1 and B3. If the fans were located at B2, the fans had a positive effect on the cooling performance of the radiators because the air in the recirculating region was used in the cooling of the radiators. However, if the fans were located at B3, the fans had a negative effect on the performance because most of the cooling air in the recirculating region escaped from the radiators and was not used in cooling. When the fan position was moved from S1 to S3, the main flow of the cooling air was directed to the vertical direction after the cooling air collision because of the increasing effect of the fans on the flow direction of the air. Thus, regardless of the oil flow rate and fan positions along the bottom surface, the fan positions B2 and S3 resulted in the best cooling performance due to the positive interaction between the air flow moving vertically induced by fans at B2 and the air flow moving

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