Mathematical Simulation of Conjugate Heat Transfer for Accumulator Batteries

D.V. Fedorchenko, M.A. Khazhmuradov, A.A. Lukhanin, Y.V. Rudychev

Abstract - We consider mathematical simulation of conjugate heat transfer using finite elements method. Vehicle accumulator cooling system is studied and heat transfer is simulated using SolidWorks software. We have shown that air mixing in the air is efficient method to increase the heat transfer without additional air drag.

I. Introduction

Modern environment-friendly electric powered and hybrid vehicles use lithium-ion batteries as power source. During operation such batteries produce a considerable amount of heat. This requires efficient cooling systems capable to provide steady temperature regime. At the same time vehicle appliances have weight and size restrictions, putting forward the demand on heat removal intensification for cooling systems. Numerical simulation is the efficient way to find the necessary technical solutions to optimize the parameters of vehicle cooling systems for further experimental research.

Thermal processes in the battery cooling systems are a case of conjugate heat transfer. The hydro- and thermodynamical characteristics of the system: the fields of temperature, velocity and pressure are determined by the coupled system of differential equations. This system of equations includes the heat transfer equation, describing the processes of heat transfer in a battery cell and a system of equations air flow hydrodynamics and the corresponding processes of forced convection. Analytical solution of the system for cases of practical interest is seldom possible, thus usually equations are sampled on a computational grid using the finite elements method [1]. Implementation of this method requires a solid model of the system, while development of the realistic solid model is a separate and rather challenging problem.

Manuscript received November 3, 2012.

D.V. Fedorchenko is with the National Science Center

Kharkov Institute of Physics and Technology (e-mail: fdima@kipt.kharkov.ua).

M.A. Khazhmuradov is with the National Science Center

Kharkov Institute of Physics and Technology (corresponding author to provide e-mail: khazhm@kipt.kharkov.ua).

A.A. Lukhanin is with the National Science Center

Kharkov Institute of lukhanin@kipt.kharkov.ua). Physics and Technology (e-mail:

Y.V. Rudychev is with the National Science Center

Kharkov Institute of Physics and Technology (e-mail:

rudychev@kipt.kharkov.ua).

Nowadays plenty of commercial software implements the finite elements method for heat transfer and fluid dynamics. In this paper we consider the simulation of heat transfer processes in the accumulator battery using SolidWorks 2011 (used to create a solid model) with SolidWorks Flow Simulation module. The later uses the finite volumes method for simulation of liquid flow and conjugate heat transfer.

II. Solid model of battery cells

Accumulator batteries for electric powered vehicles usually consist of a large number of individual power cells placed in a common housing. Simulation of the entire battery requires considerable computational resources; hence the detailed analysis of heat transfer processes becomes rather difficult. Within this paper we consider in detail heat transfer simulation for two adjacent power cells with air gap between them.

Firstly we consider the simple solid model for the single power cell. The solid model must reproduce the thermal properties of the real cell; in particular it should have anisotropic thermal conductivity [2]. our model power cell is a solid box with geometrical dimensions of 150 x 200 x 12 mm. It has the longitudinal thermal conductivity 60 W/(m-K), lateral 1 W/(m-K) and specific heat of 0.8 kJ/kg. Each power cell is a 15 watts heat source.

Actually, our model contains two such cells with 3 mm air gap. To reduce the computational time we consider only the inner half volume of each power cell. This is possible due to symmetry properties of the simulating system.

The next are the boundary conditions. For the power cell we have adiabatic boundary conditions for outer surface 3Q 0 and convective heat exchange for inner surface :

(q5)| 5^ 0 = 0 (1)

(qn)\ 5Qx = h(Ts - Tair)

where q = -kVTs - heat flow in a power cell, k - thermal conductivity, n - the outer surface normal, h - the coefficient of convective heat transfer, Tair- the air temperature in the gap, Ts - the temperature of the power cell. Also both half volumes are uniform volumetric heat sources with heat power of 7.5 W each.

For air gap we have to specify both temperature and air flow boundary conditions:

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(vairn)| 0 Tair| 5Q;n T0

< (vairn)|5Qin _ —v0 Pair|5Qout _ P0 (2)

(qn)\5Qj = h(Tair - Ts)

where T0 and V0 are inlet air temperature and velocity given on inlet 9Qin , P0 - atmospheric pressure specified at the outlet 5Qout, and the heat flux is given on the inner surface, and outer are assumed to be adiabatic.

For calculations using SolidWorks Flow Simulation we also have to specify initial conditions even for the stationary problem. This is due to the fact that actually the calculation module solves the transient problem. The stationary solution is in fact the steady value of the corresponding calculated parameters.

III. Mathematical simulation

The simple geometry described above is a reference point for further studies on heat transfer increase. The obvious way to do this - to increase the surface where the heat exchange occur through the installation of additional elements such as triangles, pins, etc. At the same time these additional elements increase air drag and the corresponding pressure drop. This, in turn, requires more powerful pumping facility, which degrades the performance of the real system cooling. Thus, the main task of the simulation is to optimize the geometry of the additional elements so that providing high heat transfer rate they still have relatively low air drag.

The cooling system for vehicle accumulator battery has certain limits on the air flow rates. High flow rates imply high performance pumping system and also lead to undesirable acoustic effects. Therefore for simulation we limit the range of air flow velocities to 1 - 4 m/s.

Fluid movement in the air gap is in general governed by Reynolds number

Re = ^, (3)

V

where v is fluid velocity, d is gap width and v is kinematic viscosity. For our model the maximum air flow velocity is 4 m/s, gap width is 3 mm and hence the maximum Reynolds number is 700. The corresponding air flow is laminar. In this case installation of the additional elements in the gap does not lead to the onset of turbulence, even for sharp edges, steps, and similar elements. The only possible effects are higher convection rate due to overall surface increase and mixing of air flow due to these additional elements.

To analyze the effect of air flow mixing we consider the temperature profile in the air gap obtained from numerical simulations for the simple geometry. Figure 1 shows a typical temperature profile in the cross section of the air gap. It follows there is an overheated boundary layer, while central part of the airflow has lower temperature due to the low air thermal conductivity. This effect reduces the cooling efficiency for the case of simple geometry with smooth surfaces. In the case of cooling elements placed in the air

gap the additional cooling effect could be achieved from the mixing of boundary and central parts of air flow.

31.01

30.34 29.63

29.01

28.34 _

27.67 Hj

27.00 И 26.33

25.67

25.00

Fluid Temperature ["C]

Fig. 1 Temperature distribution in the air gap

To analyze the contribution of convection and layer mixing to the heat transfer we perform simulation of cooling process with additional elements having zero thermal conductivity. In this case, increase the heat transfer takes place only due to the mixing of the air layers. Figure 2 shows comparison of calculated average surface temperature for cooling pins made from aluminum, the same pins made from thermal insulator and simple smooth surfaces. Obviously, there is no air mixing for the smooth surfaces - it is the reference point for comparison. From our simulation it follows that pins with zero thermal conductivity provide noticeable lower average surface temperature than smooth surfaces. This proofs that air mixing makes essential contribution to the heat exchange.

It is possible to create cooling element that provides solely the airflow mixing. As such element we consider is twisted ribbon with twist pitch comparable to the width of the air gap. The ribbon width is slightly smaller than gap width. Figure 3 shows solid model that contains such elements. Cooling properties of such elements are insensitive to the ribbon material, as convection cooling in this case is negligible.

In order to compare the cooling efficiency we also developed the solid models with pins (Fig.4) and open pyramids (Fig. 5) as cooling elements. The parameters of solid model are given in the Table I.

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Table I

IV. Results and Discussions

Model Twisted ribbons

Width 3 mm

Thickness 0.2 mm

Twist step 10 mm

Row pitch 2.5 mm

Twist direction alternating

Material Aluminum

Model Pins

Diameter 2.5 mm

Height 1.5 mm

Material Aluminum

Row pitch 5 mm

Step 5 mm

Model Open pyramids

Height 1 mm

Width 4 mm

Depth 2 mm

Vertex angle о О VO

Row pitch 4 mm

Fig. 3. Solid model of the power cell with twisted ribbons

Fig. 5. Solid model of the power cell with open pyramids

We performed the detailed simulation of heat transfer processes using SolidWorks Flow Simulation. The main parameters that characterize cooling efficiency are average surface temperature of the power cell and pressure drop in the air gap. Another parameter that should be controlled is temperature drop along the power cell surface. For the real Li-Ion accumulator batteries this parameter should be less than 10oC.

Figures 6 and 7 show the calculated surface temperatures and pressure drops in the air gap. As expected additional cooling elements increase heat transfer, but pressure drop in the air gap also increases. In all cases the temperature drop along the surface was within the 10DC limit.

From Fig. 6 one can see that for all cooling elements average surface temperature is almost the same and lower than for smooth surfaces. If we consider pressure drop we will find out that the twisted ribbon elements have the lowest (but still higher than for smooth surfaces).

Fig 6. Average surface temperature for various surfaces

The effect of twisted ribbons on the cooling airflow could be easily understood from figures 8 and 9. In the figure 9 the flow trajectories for twisted ribbons exhibit the high degree of rotation compared to essentially more straight

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trajectories for pins (Fig 8.). This rotational movement causes the intensive air mixing and higher heat transfer from the power cell surface.

Fig. 8. Flow trajectories for pins

We performed the additional simulations to compare performance of twisted ribbons made from aluminum and thermal insulator. The both cases gave the similar results. This is additional proof that for twisted ribbons we have only intensive air mixing that leads to more efficient utilization of air heat capacity. From practical point of view this means that the different kinds of plastics and composite materials are suitable to manufacture these elements. This will reduce the overall weight of the battery compared to traditional metal cooling elements.

Fig. 9. Flow trajectories for twisted ribbons

V. Conclusion

The conclusions of the study reveal that cooling efficiency of the narrow air gap could be significantly increased by mixing of boundary and central parts of the air flow. Using mathematical simulation we have showed that this approach is more efficient than traditional methods utilizing pins or wing-like elements. These findings must be of considerable practical value for improving the cooling system design for electric vehicles accumulator batteries.

References

[1] Gallagher R. The finite element method. Basis. Academic Press, 1984, 428 p.

[2] Zhang Jiangyun, Zhang Guoqing, Zhang Lei, Rao Zhonghao. Simulation and Experiment on Air-Cooled Thermal Energy Management of Lithium-Ion Power Batteries. // J. Automotive Safety and Energy, 2011, Vol. 2, No.2. pp.181-184.

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