Heat Flux Density Determining at the Pulsating Thermal Pipes Adiabatic Section of the Spacecraft Thermal Control System

Аuthors

Netelev A. V.^*, Reutov A. M.^**, Ivashinenko M. O.^***

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

*e-mail: netelev@mail.ru
**e-mail: reutow.ar@yandex.ru
***e-mail: mari.lauta@mail.ru

Abstract

Pulsating heat pipes represent an effective means for removing heat from the sources with high heat dissipation. In the pulsating heat pipe, heat is being transferred by the two-phase oscillating liquid-gas flow caused by the self-sustaining pressure fluctuations of the gas phase. Widespread application of the heat pipes is hindered due to the complications of this pipe starting conditions realization. This problem may be rectified under condition of detailed and scrupulous studying of the processes running in the pipe. As of today, many research teams are being preoccupied with the issues associated with modeling oscillating processes in the heat pipes. Mathematical models with lumped and distributed parameters in overall and partial derivatives are being used for the thermo-physical computing of the two-phase flow in a pulsating heat pipe. For thermal processes modeling in the pulsating heat pipes, it is important to know how the heat pipe with the environment and structure interaction is being exercised.
Specifically, the information on the heat exchange at the section between the cooler and heater (the adiabatic zone) of the pulsating heat pipe is necessary. The heat flux direct measurement at the heat pipe adiabatic section is impossible since the tube diameter is small, and introduction of changes to its structure would inevitably lead to the measured data distortion. n practice, methods based on the heat transfer inverse problems solving are being used for the heat flux evaluation. These methods allow employing in computations the indirect data on the adiabatic section thermal state such as temperature of the heat pipe outer surface. The problem under consideration employs thermal measurements in several points of the pipe, obtained from the thermal sensors installed there.
When solving the inverse heat transfer problems, a common practice consists in minimizing the functional of the difference between the computed and experimentally measured temperatures. This approach supposes computing the gradient of the functional being minimized. The gradient computing of the functional may be rather complicated for the multi-level mathematical models. The authors propose employing genetic algorithms for the function extreme search while practical realization of the engineering computations. Genetic algorithms are simple to implement and offer several advantages:
- robustness to the local extremums entering;
- no necessity for the goal function derivatives computing;
- suitable for solving the problems with complex models and hierarchies;
- genetic algorithms do not require the function to be well-defined, continuous, and differentiable throughout the entire solution domain.
The method for the thermal flux setting through the adiabatic section wall of the pulsating thermal pipe was developed by the genetic algorithm for minimizing the functional of the difference between the computed and experimental temperatures. The authors evaluated effectiveness of various genetic algorithm development options. The developed method validation was performed with the model experiment data. The method demonstrated good convergence to an exact solution under perturbed conditions. The method effectiveness was confirmed through a comparative analysis with the results obtained by other authors.

Keywords:

pulsating heat pipes, inverse heat transfer problem, local heat flux, genetic optimization

References

1.  Maidanik YuF, Fershtater YuG, Goncharov KA. Capillary pumped loop for the systems of thermal regulation of spacecraft. ICES 4th European Symposium on Space Environmental Control Systems (October 21-24, 1991; Florence, Italy). Vol. 1. p. 87-92.
2.  Borschev NO. Mean-integral heat transfer coefficient parametric identification in coaxial heat pipes. Aerospace MAI Journal. 2022;29(3):111-121. (In Russ.). DOI: 10.34759/vst-2022-3-111-121
3.  Antonov VA, Goncharov KA, Tulin DV. Heat pipes in spacecraft temperature control systems: Sbornik nauchnykh trudov NPO im. SA. Lavochkina “Aktual'nye voprosy proektirovaniya kosmicheskikh sistem i kompleksov”. Issue 12. Moscow: Poligraf-Inform; 2011. 22 p. (In Russ.).
4.  Dokuchaev AE, Zinchuk AA. Experimental study of the use of a heat pipe in a gas generator. Aerospace MAI Journal. 2011;18(3):89-96. (In Russ.).
5.  Smirnov GF, Savchenkov GA. Pulsating heat pipe. Patent SU 504065 A1, 25.02.1976. (In Russ.).
6.  Alifanov OM, Vikulov AG, Goncharov KA, et al. Pulsating heat pipes and their application in space technology. High Temperature. 2025;63(1):113–151. (In Russ.). DOI: 10.31857/S0040364425010163
7.  Alifanov OM, Goncarov DA, Goncarov KA, et al. Experimental studies of the thermal characteristics of a pulsating heat pipe. High Temperature. 2025;63(3):401-409. (In Russ.).  DOI: 10.7868/S3034610X25030105
8.  Rittidech S, Terdtoon P., Murakami M., et al. Correlation to Predict Heat Transfer Characteristics of a Closed-End Oscillating Heat Pipe at Normal Operating Condition. Applied Thermal Engineering. 2003;23(4):497-510. DOI: 10.1016/S1359-4311(02)00215-6
9.  Khandekar S, Cui X, Groll M. Thermal Performance Modeling of Pulsating Heat Pipes by Artificial Neural Network. 12th International Heat Pipe Conference (IHPC; May 19–24, 2002; Moscow, Russia).
10.  Bertossi R, Ayel V, Mehta B, et al. Motion of liquid plugs between vapor bubbles in capillary tubes: a comparison between fluids. Heat and Mass Transfer. 2017;53(11):3315–3327. DOI: 10.1007/s00231-017-2052-1
11.  Ma Y, Zhang H, Zhuang J. Investigation on effective thermal conductivity of oscillating heat pipes. 13th International Heat Pipe Conference (IHPC; September 21–25, 2004; Shanghai, China).
12.  Kim JS, Bui NH, Kim JW, et al. Flow visualization of oscillation characteristics of liquid and vapor flow in the oscillating capillary tube heat pipe. KSME International Journal. 2003;17(10):1507-1519. DOI: 10.1007/BF02982330
13.  Alifanov OM, Vikulov AG, Morzhukhina AV, et al. Parametric Identification of Thermodynamic Processes in Unclosed-Loop Pulsating Heat Pipes. Heat Transfer Engineering. 2025, pp. 1–16. DOI: 10.1080/01457632.2025.2511453
14.  Alifanov OM. Inverse problems of heat transfer. Moscow: Mashinostroenie; 1988. 280 p.
15.  Colaço M, Bozzoli F, Cattani L, et al. Local heat flux estimation inside tubes through conjugate gradient method with adjoint operator: application to the pulsating heat pipes case. International Journal of Numerical Methods for Heat & Fluid Flow. 2023;33(5):1754-1774. DOI: 10.1108/HFF-09-2022-0547
16.  Cattani L, Mangini D, Bozzoli F. et al. An original look into pulsating heat pipes: inverse heat conduction approach for assessing the thermal behavior. 19th International Heat Pipe Conference and the 13th heat pipe symposium (June 10-14, 2018; Pisa, Italy). p. 1-11.
17.  Alifanov OM, Artyukhin EA, Rumyantsev SV. Extreme methods for solving ill-posed problems and their applications to inverse heat transfer problems. Moscow: Nauka; 1988. 288 p. (In Russ.).
18.  Koza JR. Genetic Programming. Cambridge: On the Programming of Computers by Means of Natural Selection. A Bradford Book The MIT Press Cambridge, Massachusetts London, England; 1998. 609 p.
19.  Panchenko TV. Genetic algorithms. Astrakhan: Astrakhanskii universitet; 2007. 87 p. (In Russ.).
20.  Batishchev DI, Neymark EA, Starostin NV. Application of genetic algorithms to solving discrete optimization problems. Nizhny Novgorod: NGU im N.I. Lobachevskogo; 2006. 136 p. (In Russ.).
21.  Knuth DE. The Art of Computer Programming. Vol. 4A Combinatorial algorithms. Part 1. Chapter 7.2.1.3 Generating all combinations. Addison-Wesley Professional, 2006.