Numerical investigation of heat transfer in thermosyphon under the emergency mode of operation of lithium-ion batteries of aircraft

. Numerical study of heat transfer in a closed two-phase thermosyphon using the software package ANSYS FLUENT is carried out. Characteristic temperature distributions, current lines and velocity vectors are obtained at critical thermal loads. The temperature difference in the investigated region decreases with increasing heat load was obtained.


Introduction
Rechargeable batteries are one of the main parts of the emergency power supply system for aircraft [1,2]. Their resource characteristics determine the efficiency and safety of the entire power supply system. Nowadays, lithium-ion batteries are attracting the attention of researchers of power sources [3]. But the use of these batteries in aviation technology is associated with the danger of an emergency. This is confirmed by a number of firehazardous accidents on board the aircraft model Boeing 787 [4,5]. The cause of the emergency situation is overheating of the battery.
During the operation of lithium-ion batteries, the thermal runaway effect [6] occurs, followed by a short circuit of the electrical circuit, when the temperature of the individual parts of the battery increases significantly from 10 C to 150 C in a short period of time (2 min) [3]. The main cause of thermal runaway of the battery is its overheating as a result of insufficient heat emission from the battery surface.
It should be noted that the system for removing heat from accumulator batteries based on two-phase closed thermosyphons has not been developed, since the theory of processes in the steam channel and the flowing fluid film has not been formulated. The models described in [7,8] do not take into account the entire complex of heat transfer processes in the vapor and liquid phases of the working fluid.
Purpose of the work: mathematical modeling of the heat transfer process in two-phase closed thermosyphons at critical temperatures of rechargeable batteries of aircraft.
When setting the task, a number of assumptions are adopted. Steam was considered an ideal gas. It was assumed that the thickness of the liquid film does not vary in height.
A schematic diagram of the thermosyphon is shown in Fig.1. Mathematical modeling of heat transfer in a two-phase thermosyphon of a rectangular cross-section was performed using the ANSYS FLUENT package [9].
where u, the velocity components in the projection on the axis х, у, respectively; P -  where P нsaturation pressure; T нsaturation temperature; Runiversal gas constant; Mmolar weight; accommodation coefficient.
To verify the solution method used, the results of mathematical modeling were compared with experimental studies.
An experimental study [10] was carried out for different values of the heat flux. To compare the results of numerical simulation with experimental data, two typical values of the heat flux to the outer walls of the thermosyphon body in the evaporation zone (100 W, 261 W) were chosen. Figure 2 shows that the results of mathematical modeling are in good agreement with the experimental data [10]. Numerical modeling of heat and mass transfer processes in a two-phase closed thermosyphon of a rectangular shape is performed in the emergency mode of operation ( Fig.1) with dimensions: height H = 200 mm, transverse dimension L = 100 mm. The choice of geometric dimensions is due to the characteristic dimensions of a typical lithiumion battery of the Boeing 787 aircraft. The following variants of the heat flux densities on the bottom cover of the thermosyphon in the section y = 0: 0.82·10 3 W/m 2 ; 1.76·10 3 W/m 2 in accordance with the critical temperatures obtained in [3]. Figure 3a shows the temperature distributions, current lines, and velocity vectors that characterize the main regularities of the processes under consideration in the region under study at a thermal load q h =0.  It should be noted that with the increase of q h to 1.76·10 3 W/m 2 (Fig. 3b), the configuration of the lines corresponding to the main characteristics of the steam flow does not change significantly. The temperature difference along the height of the steam channel decreases by approximately 2 °K due to the intensification of heat transfer in the direction of y due to the more intensive evaporation of the coolant on the lower lid.

Conclusion
As a result of numerical investigation, characteristic lines of constant temperatures, current and velocity vectors were obtained.
In the practice of using closed two-phase thermosyphons, the temperature drop from the evaporation zone to the condensation zone is one of the main parameters characterizing the efficiency of its operation. It was found that the increase in the thermal load on the lower cover from 0.82·10 3 W/m 2 to 1.76·10 3 W/m 2 leads to a decrease in the temperature difference in the investigated region by 2 °K. This is probably due to the intensification of heat transfer and the increase in the vapor velocity in the device under study.
The reported research was supported by Russian Federation President Grant for state support of the Russian Federation leading scientific schools SS-7538.2016.8 (No.14.Y31.16.7538-SS).