# Numerical And Theoretical Investigation On Cooling Performance Engineering Essay

It is well known that both Joule effect and Foucault currents generate an undesirable heat in the transformers. It is desired to remove this heat efficiently in order to preserve it from destruction. The objective in the current paper is to study the present situation of cooling system and to evaluate a new configuration for oil channels based on pin fin technology to improve the cooling efficiency. In the paper, the heat transfer and fluid flow in a cooling system of a power transformer in the ONAN state is studied with aid of computational methods. Two basic models, based on theoretical correlations and numerical methods have been considered. Results show that there is a good agreement between available data, theoretical model and CFD model in the current configuration. Heat transfer is within acceptable range, but the oil entrance and outlet passages should be redesigned to get better flow behavior. The radiator height has a direct effect on outlet temperature; however the maximum reduction in the outlet temperature would be 7%, when the height is doubling. The radiator equipped with internal pin-fins shows better heat transfer behavior, while the pressure drop through the channels remains in acceptable range.

Keyword: CFD, Power transformer, Pin fin, Oil cooling, Numerical modeling

Nomenclature

A Surface area [m2]

CP Specific heat capacity [kJ/kg.K]

CFD Computational fluid dynamics

D Diameter [m]

Dh Hydraulic Diameter [m]

e Specific internal energy [kJ/kg]

ff Friction coefficient [-]

g Acceleration of gravity [m/s2]

h Convective heat transfer coefficient [W/m2.K]

k Thermal conductivity [W/m.K]

kt Turbulent kinetic energy per unit mass [kJ/kg]

LMTD Logarithmic Mean Temperature Difference

Mass flow rate [kg/s]

NuD Nusselt number based on Dh [-]

OF Oil forced

ON Oil natural

ONAF Oil natural, Air forced

ONAN Oil natural, Air forced

P Pressure [Pa]

Pr Prandtl number [-]

Q Rate of heat transfer [W]

Ra Rayleigh number [-]

ReD Reynolds number based on D [-]

T Temperature [C]

u Velocity [m/s]

U Overall heat transfer coefficient [W/m2.K]

Efficiency

o Overall surface efficiency

Dynamic viscosity [Pa.s]

Kinematic viscosity [m2/s]

Density [kg/m3]

## Subscripts:

in Inlet

m Average

out. Outlet

tot Total

∞ Free stream

## Introduction

Transformers are widely used in the industry especially in the distribution power networks. They are most valuable assets in power systems and it appears worthwhile to pay special attention to this key component to ensure stability in power systems. The energy losses in power transformers are proportional to the load. These losses are transformed into heat which causes a temperature rise that can reach high levels and affects negatively the transformer performance which means an operational load and useful life reduction. The heat dissipation through natural convection and with transformer surface is enough in small transformers, but this heat dissipation level is not enough in higher capacity transformers with average and high electrical powers that require more elaborated methods of cooling to remove generated heat effectively(Liang,2001)( Q. He, 2000).

In such kind of power transformers, the cooling is provided through circulation of oil between ducts in the active parts and heat exchangers outside the transformer tank. The oil circulation is due to free convection (ON stands for oil natural circulation in most texts) or combined free and forced convection (that is referred as OF for forced oil circulation in literatures). In the power transformers designing, it is of interest to minimize the size of heat exchangers and internal cooling ducts, while keeping the high efficiency cooling. In the literature, few studies have been conducted on the heat transfer and the fluid flow outside the transformer and most of them have focused on the internal parts of power transformers. For example recently (Mufuta and Van Den Bulck, 2000) studied the case of a winding disc-type transformer and they showed the influence of Re Gr−1/2 on the flow structure and they give some correlations to calculate the heat transfer inside this kind of transformer. Heat transfer inside the channels and thermal behavior of the flow in a pipe with different boundary conditions are investigated widely in heat transfer texts, but no special paper with focus on radiator were found in literature.

In this paper, a cooling radiator element with natural oil and air flows (ONAN) is studied using both theoretical investigation and numerical method. The present study contains the following issues that have not been investigated in former studies:

(1) Calculation of oil flow considering the buoyancy effect inside the transformer.

(2) Effect of inlet oil temperature on the total heat transfer rate.

(3) Cooling oil properties are considered to be dependent of temperature.

(4) Effect of using extended cooling surface is studied here as well. Especially, proposed pin fin technology is a new idea in the power transformer cooling industry.

The CFD results are validated by comparing the critical parameters with calculated data from theoretical method and available data from manufacturer. Finally, effects of some radiator geometry parameters such as number of cooling channels, height of radiators, and cooling channels geometry are investigated.

## Radiator technical specifications

Most of the power transformers are equipped with detachable panel radiators, which are connected to top and bottom headers, in order to provide the necessary cooling surface. If factors such as expected future load growth or exposure to prolonged high ambient temperatures have to be taken into account, forced air cooling (ONAF) is used to accelerate the cooling process. Cooling fans are activated in one or more stages by the relay contacts of the top oil temperature sensor. A typical transformer which is assembled in Iran Transfo Company is shown in the Figure 1. However the ONAF case is not considered in the current study. The radiators are steel plate heat exchangers that are installed vertically next to transformers and each of them consists of seven channels for oil flow. Each channel is equipped with two internal throughout wings to increase the heat transfer rate from radiator. Two identical steel plates are pressed and welded to each other to form the radiator.

At the upper and lower parts of radiator, semicircular channels are provided as oil flow entry and exit. Oil comes out from transformer and flows to an upper header which directs the oil to semicircular channel. This channel directs the oil into the provided passages inside the radiator. Finally, oil is collected in lower semicircular channel and sent out. Different aspects and dimension of a typical radiator is illustrated in Figures 2 and 3. Radiators are produced in accordance with DIN 42559 (Iran Transfo Corporation Documents,2005) and steel sheets that are used in their manufacturing are St-37.

At final construction stage, the radiator thickness is approximately 12mm. Cooling capacity of each radiators block is defined according to the number and dimensions of their cooling elements (radiators).

## Theoretical modeling

Referring to Figure 1, it can be seen that radiators are installed parallel to each other in both side of transformer and auxiliary fans are added for ONAF conditions. When natural convective heat transfer is not able to dissipate the heat from radiators, these fans start to run and reduce the oil temperature. Based on the radiators location in the cooling system block, they show different heat transfer behavior. The side radiators possess higher heat transfer efficiency than middle radiators, since the side radiators are in contact with lower temperature air. This property is less important in ONAF state. However in the current study, only the middle condition is considered for radiators and the ONAN state is modeled.

The cooling process of oil through the radiator involves natural convection in both oil and air sides and also the conduction in the radiator body. To predict the performance of the radiator, the log mean temperature difference (LMTD) is used as theoretical method. When the inlet temperatures are only known, this method requires an iterative procedure. However it is implemented here as it is simpler to program and also to apply automatic calculation for different cases. The LMTD method is basically based on overall energy balance for the hot and cold fluids (here oil and air respectively) and it relates the total heat transfer rate to the overall heat transfer coefficient, inlet and outlet temperatures and heat transfer surface area. The basic equation in this method that is used to calculate the heat transfer is:

(1)

Where:

Q = rate of heat transfer

F = temperature correction factor

U = overall heat transfer coefficient

A = heat transfer area

LMTD = log mean temperature difference

Considering radiators configuration (Figure 4), flow directions for air and oil are contrary and counter flow condition exists. Thus F in this case is equal to 1 and LMTD is calculated from following correlation:

(2)

To have a correct set of governing equations, an overall energy balance for oil was written as follow:

(3)

However the oil mass flow rate is not known at first stage and it should be calculated in a repetitive procedure. The overall heat transfer coefficient was calculated based on the following general correlation (Lienhard IV and Lienhard V,2005):

(4)

The first two terms in the right hand side of equation represent the convective resistance to heat transfer and the last one shows the conduction resistance of the radiator body. This last term can be removed without significant effect on U calculation. Calculation of the convective resistances is explained in details later in the text.

By applying these equations on radiator, oil outlet temperature and consequently the equivalent heat transfer are obtained. However the following assumptions are taken into account:

(1) The radiator is considered asymmetrical.

(2) The oil flows are treated as 1-dimensional in the cooling ducts with a constant mass flow rate.

(3) The oil is considered fully mixed, so the oil outlet temperature is uniform.

(4) Convective heat transfer in the both oil and air side are considered constant.

Based on the usual working conditions for radiators, the following boundary conditions are considered:

TAir = 20 C

Toil-in = 100 C, 90 C, 80 C, 70 C, 60 C, 50 C

Figure 4 illustrates the cooling mechanism in the radiators block. At the first stage, it is necessary to define hot and cold fluids properties, boundary values, oil channels friction factors, pressure loss coefficients and heat transfer coefficient.

Considering the oil and air flows conditions, the following correlations are used to calculate the overall heat transfer coefficient and other relevant parameters for one radiator located in the block:

## Oil convective heat transfer

The physical properties of mineral oil vary with temperature according to the correlations given by the following equations:

## )

(5)

Where T is representing the oil temperature in C.

In first stage, flow was considered to be laminar, as the oil flow is caused by buoyancy effect in the transformer and there is natural circulation in the cooling circuit. However it was verified later and confirmed in the modeling, since in some conditions like high oil inlet temperature it could change to the turbulent flow regime.

Outlet pressure is considered as the static head due to the oil height in the radiator. Then the inlet pressure would be the difference between this pressure and the pressure loss through the radiator. This pressure drop is compensated by the buoyancy effect in the transformer. Natural circulation of oil occurs whenever the correct conditions exist. Even after natural circulation has begun, removal of any one of these conditions will cause the natural circulation to stop. The conditions for natural circulation are as follows:

1. A temperature difference exists (heat source and heat sink exists).

2. The heat source is at a lower elevation than the heat sink.

3. The fluids must be in contact with each other.

The following correlation is used to calculate the buoyancy force in the transformer (Lienhard IV and Lienhard V,2005):

(6)

Calculated value is added to the outlet pressure of radiator to provide the inlet pressure for oil at the radiator inlet.

Assuming the known pressure loss through the radiator, the average oil velocity is obtained from following general equation:

(7)

In laminar flows, ff is obtained from. This average oil velocity is then used again to calculate the Reynolds number to recheck the flow regime.

Calculation showed that the flow cannot reach the fully developed condition in the current configuration. So the following correlation was used to calculate the oil convective heat transfer coefficient (Lienhard IV and Lienhard V,2005):

(8)

should be evaluated at the average surface temperature and other properties are calculated at the average value of the mean oil temperature.

## Air convective heat transfer

Radiators are located in parallel configuration, thus the free convection mechanism within parallel plate channels was considered in order to calculate the convective heat transfer coefficient. Radiators are actually parallel vertical plate channels which are open to the ambient at opposite ends. (Bar-Cohen and Rohsenow,1984) have proposed the following correlation for free convection between vertical parallel plates:

(9)

Where the constants C1 and C2 are 576 and 2.87 respectively and RaS is defined as:

(10)

Here S considered as the distance between radiators’ plates.

There are some steel plates that connect oil channels in the radiator. These small plates were treated as fins, thus the overall surface efficiency in the air side of radiator was considered as:

(11)

Where fin is the fin efficiency for a straight fin of uniform cross section and an adiabatic tip.

A looping model was developed and all above equations were implemented together. The oil outlet temperature was guessed and calculation started. At the end of first iteration, the oil temperature was calculated again from energy balance and compared with the assumption. The loop repeated until the suitable convergence reached.

## CFD modeling

The CFD model contains a more detailed configuration of radiator including the inlet and outlet channels. In the current study the buoyancy effect is assumed to be negligible inside the radiator and also the radiation heat transfer is not considered.

Considering the steady state, 3-D and incompressible laminar flow, the continuity, momentum and energy equations are given by following correlations (Versteeg and Malalasekra, 1996):

(12)

(13)

(14)

is the modified kinematics pressure (P/) and e is representing the specific internal energy. These two parameters should be modeled to close the system of equations.

The Fluent software was used to perform numerical analysis on the model. The finite volume model and related mesh were constructed using Gambit software and the models data were passed to the Fluent software for various analyses. The governing equations solved by Fluent are the Navier-Stokes equations combined with the continuity equation, the thermal equation, and constitutive property relationships which are described above. Once the analyses are completed, the resulting data can be easily evaluated by the Fluent postprocessor.

In the constructed model, radiator is considered as a separate element with internal oil flow from top to down and convective heat transfer on the outer surfaces. All flows were specified as steady state and incompressible. The standard k-ε turbulence model with standard wall function was set for radiator model. The Segregated 3D solver with an implicit formulation was set to solve the model.

Upon completion of each run, results were carefully examined and analyzed to prove their accuracy. The conservation of mass was verified by comparing the inlet and outlet mass flow rate to ensure that the mass balance is achieved. The energy flow into and out of the radiator at the flow boundaries were ensured to be equal to the total energy dissipated at the outer wall. Computational errors both in pressure drop and heat transfer measurements were commonly encountered. This could result in a diverging solution and was corrected by increasing the reference pressure and/or relaxing the modified inertia criteria.

It should be noticed that only one quarter of the radiator is modeled here, since radiator is symmetric with two symmetry axes. Results can be easily extended for other sections.

## Mesh construction

Based on the technical drawings from radiator manufacturer and collected data in the factory, a 3-D mesh model was generated to simulate one radiator element. All important aspects of radiator including inlet and outlet passages and oil passing channels were simulated accurately. The produced finite volume mesh contained approximately 500000 cells. Figure 5 shows an overall view of generated mesh and the whole simulated section.

Since the inlet and outlet flow affect seriously on flow behavior inside the radiator elements, these section were modeled carefully and all important aspect were included in the model. A close view of inlet section is shown in Figure 6.

## Cases investigated

Two main cases are considered: Simple oil channel and oil channel fitted with pin fins internally. For each case, effect of different inlet oil temperatures are modeled and investigated to study the thermo-hydraulic behavior of radiator. The drop shaped fins are used for this study and they form a bridge between two radiator plates(Nabati and Mahmoudi, 2005). Figure 7 shows the fin configuration in the radiator.

## Validity of models

The iteration-based numerical methods were used to solve the governing non-linear equations. Using the Newton–Raphson iterative procedure for theoretical model and finite volume numerical procedure, these equations were solved to find the oil outlet temperature in different cases. Figure 8 shows the comparison between calculated temperatures values and available experimental data from manufacturer. Even though experimental data and modeling results differ slightly, the presented diagram confirms that the constructed model is sufficiently capable to predict the thermal behavior of studied radiator.

Some reasons for slight differences between modeling and experimental results can be stated as followings:

1. Errors caused by measuring system, especially temperature transmitter (experimental errors).

2. Intrinsic numerical errors due to computational operations such as rounding (modeling errors).

3. Errors due to modeling simplification and assumptions which presented in the section 2 (modeling errors).

To minimize the CFD modeling errors, the mesh dependency of the solution was examined by solving the flow and temperature fields for different mesh configurations made of different cells. These profiles were compared in several sections for all configurations to be sure that the maximum difference in the flow field properties between the coarser and finer meshes are less than 1% and the final mesh lead to mesh-independent solutions.

## Results and discussions

Presented results in the current section include output data obtained from different simulations. The modeling started with a validation of reference case followed by a different case containing pin-fins. The purpose of the first case (reference case was to provide some results that can be compared with available factory test data in order to give an indication of the quality of computation and also to evaluate the current situation of available radiators. The results obtained for this model are presented in Figures 9 to 14. Several checks were performed in order to verify accuracy of the generated results. The contour plots for velocity, temperature and pressure were observed separately to ensure that the results satisfy the boundary conditions and also they are not dependent on grid size.

Referring to Figure 6 it can be seen that at the entrance, oil flows in a larger space and continues toward the narrow oil channels. Figures 9 shows the average oil flow rate in the radiator channels at a horizontal surface placed exactly in the middle of radiator element for reference case. There is nearly a linear relation between oil flow rate and oil temperature at the radiator entrance. 1% increase in temperature will subsequently increase the oil flow rate about 1.6%.

Effect of radiator’s height on the outlet temperature is depicted by Figure 10. Obviously, the radiator height has a positive effect on cooling capacity. However, 100% increase is the height only decrease the radiator outlet temperature about 3 to 7%. Doubling the radiator height means the higher production cost and thus there should be an economical analysis between choosing the longer radiators or switching to the forced convection mode. Figure also shows that at higher inlet temperatures, the benefit of longer radiators decreases.

Similar to the oil mass flow rate, the average oil velocity through the radiator channels has a direct relation to the inlet temperature. At higher temperatures there are corresponding higher oil velocities which is a subsequence of superior buoyancy forces (Figure 11). It is to be noted that this is an average velocity graph and depend on the channel position in the radiator, there are different velocities. As a result of pressure at the entrance, the oil searches for the nearest channel to evacuate and therefore the middle channels have the higher velocity profile than the side ones. Also one result from numerical modeling was that the highest wall (or oil) temperatures are located in the middle channels. This is justified with oil velocity; since oil velocity is higher in middle section, the circulation rate is also higher. Thus the warmer oil passes from this section and makes the walls warmer. The side channels are cooler, since the oil velocity is lower there.

Cooling capacity of one radiator is shown in Figure 12. As a result of linear behavior of other parameters, the heat transfer rate from radiator is proportional to the inlet temperature, considering the constant ambient temperature and radiator height. This result could be a good guide for designer to choose the appropriate number of radiators in order to dissipate the heat from oil in the transformers.

Figure 13 shows the comparison of oil flows in the simple oil channels and channels with pin fins. The oil flow has lower values in the pin finned channels due to the resistance that fins insert against the flow. It means that the pressure loss through the channels with pin fin is higher. The reason is that the flow passage cross section area decreases in the sections that fins are inserted. This is a positive effect, as oil has more time to exchange heat with ambient. However this effect decreases, when the inlet temperature increases. Figure 14 depicts the comparison between two different channels. It can be seen that the temperature level is lower in the pin fin case. However the maximum temperature drop in comparison to simple case is 5%. Since the other cooling media in the outside of radiator is air, any attempt inside the oil channels has a minor effect on the heat transfer. In the case studied here, fins also provide a bridge between radiator plates and heat is dissipated through the fins by conduction mechanism. Effect of fins on the internal convective heat transfer is not an effective parameter in the whole heat transfer. Heat transfer in both cases is compared in the Figure 15. The highest cooling capacity of radiators occurs whenever the inlet oil temperature has the highest value. This is due to the maximum temperature difference between oil and surrounding ambient. It can be seen that installation of pin fin increases the cooling capacity about 5 to 10% in respect of the simple radiator.

## CONCLUSIONS

Simulating results have been presented for the buoyancy-driven flow of oil through a radiator with uniform convection heat transfer in the air side including two different channel geometries. The physics of the problem and the heat transfer characteristics have been discussed for these geometries at a wide range of inlet oil temperatures. First, the flow and the heat transfer characteristics of the simple oil channel case is analyzed numerically and validated with the available correlations and data from manufacturer. With the help of verified model, the influences of internal fins on thermo hydraulic behavior of radiator are evaluated. Doubling the radiator height decreases the outlet temperature about 3 to 7%. Using pin fins in the channels decreases the outlet temperature about 5%. Thus that is an economical decision which shows which configuration is justifiable.

The simulation results show that the heat transfer in ONAN state is within acceptable level, but the oil flowing passage needs some correction and optimization. The oil mass flow distribution is not homogenous which affects the heat transfer rate inversely.

It is noticed during the different simulation that increasing the number of fins in front of oil flow after a certain limit would result in an undesired increase in the pressure loss and buoyancy effect is not able to circulate the oil through the radiator. So depend on the case, this issue should be evaluated beside the other parameters to attain the optimized design.

Finally, as a general conclusion it can be said that the uniform shape of oil passages causes unbalanced distribution of oil velocity and flow and directly affects the cooling efficiency. Considering the different calculated velocities, a new diameter design could guarantee the uniform oil flow inside all passages. A combination of this new design with pin fins could be an optimized design for cooling system of power transformers.

Acknowledgments

We would like to acknowledge the use of Fluent Inc.'s solver Fluent 6.2, and its mesh generator Gambit in the current work. The authors also would like to acknowledge technical office staff in Iran Transfo Company, for their technical support and guides and also the managers for providing the useful experimental data.

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