Identification of thermal conductivity and power of a pulsating heat pipe by iterative regularization method

Аuthors

Vikulov A. G., Sudurov A. A.^*

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: suduroff2012@yandex.ru

Abstract

<p style="text-align: justify;">
     A pulsating heat pipe is a device using a two-phase working fluid, which greatly complicates the development of its mathematical model. Capillary-free pulsating heat pipes do not have a capillary limit to the heat they can transfer, since increasing the thermal power also increases the flow velocity of the working fluid and the pulsation frequency, meaning that the tube's conductivity also increases. This kind of PHPs can also operate in microgravity conditions, and therefore are of interest to the space industry. Experiments conducted on PHPs filled with liquid oxygen and hydrogen have also demon-strated their effectiveness in maintaining cryogenic thermal conditions.<br>
     By conducting an experiment, it is possible to restore the model parameters using empirical data, by solving inverse problem. The purpose of this work is to identify the conductivity of the heat pipe, as well as the heat dissipated on the condenser, taking into account its real conductivity.<br>
     To identify the thermal conductivity of a pulsating heat pipe using the iterative regularization method, it is necessary to calculate the thermal conductivity increment from the solution of a variational problem. The pulsating heat pipe model is a lumped-parameter model consisting of an evaporator and a condenser, interconnected by the thermal resistance of the pipe. We shall assume that in the evaporator a small increase in thermal conductivity causes temperature variation. The measured temperatures of the evaporator and condenser are the initial information for solving inverse problems of heat flow diagnostics in the PHP.<br>
     The identified parameters were affected by thermal inertia, expressed as conductivity jumps: when the heater is turned on, the temperature difference between the nodes is small, therefore the conductivity value tends to infinity, and when the heater is turned off, the power drops to zero, thus dropping the conductivity to zero. As a result, it was found that the residual between the model and the data, the regularized solution corresponding to the minimum of the target functional, were achieved at the first iteration, and the conductivity of the pipe does not change with increasing heat load supplied to the evaporator, and is approximately 1,7 W/K.<br>
</p>

Keywords:

pulsating heat pipes, inverse problems, heat transfer in two-phase flows, lumped parameter model, variational problems, experimental data processing, temperature discrepancy, ill-posed problems, mathematical modeling, iterative-variational method

References

1. Hisateru Akachi. Structure of a Heat Pipe. Patent number: 4,921,041. 01.05.1990.
2. Slobodeniuk M, Bertossi R, Ayel V et al. Effect of non-condensable gases on the flat plate pulsating heat pipe under various gravity conditions. Joint 20th IHPC and 14th IHPS (September 07–10, 2021, Gelendzhik, Russia)
3. Wilson CA, Drolen B, Taft B et al. Advanced structurally embedded thermal spreader II (ASETS-II) oscillating heat pipe flight experiment and database. Joint 21st IHPC and 15th IHPS (5–8 Februry 2023. Melbourne, Australia).
4. Sun X, Han D, Li S et al. Modelling of hydrogen filled pul-sating heat pipes considering Taylor bubble generation. Joint 19th IHPC and 13th IHPS (10–14 June 2018. Pisa, It-aly).
5. Vikulov AG, Nenarokomov AV. Thermal processes in engi-neering. 2016;(5):214–226. (In Russ.).
6. Tikhonov AN, Arsenin VYa. Methods of Solving ill-posed problems. Moscow: Nauka; 1979. 285 p. (In Russ.).
7. Alifanov OM. Inverse problems of heat transfer. Moscow: Mashinostroenie; 1988; 285 p. (In Russ.).
8. Cattani L, Bozzoli F, Mangini D et al. An original look into pulsating heat pipes: inverse heat conduction approach for assessing the thermal behavior. Joint 19th IHPC and 13th IHPS (10–14 June 2018. Pisa, Italy) p. 1–11.