Bernagozzi, Marco

Georgoulas, Anastasios

Malavasi, Ileana

Marengo, Marco

Miche, Nicolas

A one dimensional lumped parameter model has been developed within the general framework of the open source software Octave, in order to describe the physical behaviour of a Loop Heat Pipe. By means of the electro-thermal-hydraulic analogy, this model gives the values of temperature and pressure for every part of the device, in response to varying boundary conditions. Furthermore, a novel approach in describing the phase change at the condenser has been adopted, differentiating the vapour quality variation over time. The code is initially validated against both simulation and experimental data found in literature. Since the present work aims to produce a design tool for the automotive industry, a parametric analysis on the geometrical characteristics of a Loop Heat Pipe is then performed, identifying and quantifying the most influential design parameters

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ID 037 1 A novel lumped parameter model for Loop Heat Pipes – validation and parametric analysis Marco Bernagozzi1,*, Anastasios Georgoulas1, Ileana Malavasi2, Nicolas Michè1, Marco Marengo1* Corresponding author: Email: M.Bernagozzi@brighton.ac.uk1 Advanced Engineering Centre University of Brighton, School of Computing, Engineering and Mathematics, Lewes Road, BN2 4GJ Brighton, UK 2 Department of Engineering and Applied Sciences, University of Bergamo, Viale Marconi 5, 24044 Dalmine, Italy Abstract A one dimensional lumped parameter model has been developed within the general framework of the open source software Octave, in order to describe the physical behaviour of a Loop Heat Pipe. By means of the electro-thermal-hydraulic analogy, this model gives the values of temperature and pressure for every part of the device, in response to varying boundary conditions. Furthermore, a novel approach in describing the phase change at the condenser has been adopted, differentiating the vapour quality variation over time. The code is initially validated against both simulation and experimental data found in literature. Since the present work aims to produce a design tool for the automotive industry, a parametric analysis on the geometrical characteristics of a Loop Heat Pipe is then performed, identifying and quantifying the most influential design parameters.  Keywords: Loop Heat Pipe, One dimensional, Lumped parameters, Numerical analysis. 1. IntroductionA Loop Heat Pipe (LHP) is a special type ofHeat Pipe. It was originally developed in theSoviet Union in the early 1980s and its mostunique feature is that it can transfer heat overlong distances (∿10-20 m), with relativelysmall costs since the wick structure is in theevaporator only [1, 2]. It is composed by anevaporator, a compensation chamber, a vapourline, a condenser and a liquid line, as illustratedin Fig. 1.Fig. 1: LHP schematic. In the present investigation, a 1-D lumped parameter model in Octave programming language (Innovate UK Research Project LOOPER), has been developed by means of the electrical-thermal-hydraulic analogy. 2.Mathematical FrameworkIn the start-up phase this transient condition hasto be treated as an isochoric heating, pressureneeds to be incremented alongside thetemperature in order to get to the point whentemperature is high enough to dissipate therequired amount of heat. The procedure is toupdate the pressure corresponding to the newvalue of internal energy of the liquid-vapourmixture each time.The evaporator was de-coupled from thecompensation chamber and analysed with thethermal network shown in Fig. 2.Fig. 2. Thermal Network schematic. 15th UK HEAT TRANSFER CONFERENCE, UKHTC2017, Brunel University London, 4-5 September 2017  2  The vapour line is adiabatic and in the liquid line the liquid is incompressible and it exchanges heat with the ambient. Combining the equation of energy and mass balance, the following differential equation describing the condenser node as vapour quality variation is derived: 𝑑𝑥𝑑𝑡=𝑇𝑐 − 𝑇𝑖(𝑃𝑖)𝑠𝑎𝑡𝑅𝑡,𝑖𝑚𝑖ℎ𝐿𝑉+?̇?𝑚𝑖(ℎ𝑖−1 − ℎ𝑖)ℎ𝐿𝑉 (1)  where the first right hand term is the difference between the temperature of the fluid and the cold source divided by the thermal resistance, the node mass and the latent heat of vaporisation; the second term is the mass flow rate times the enthalpy difference between two nodes divided by the node mass and the latent heat of vaporisation. This approach, to the author’s best knowledge, is a novelty regarding the description of the condenser behaviour.  3. Validation and Parametric Analysis Satisfactory results were obtained on the numerical validation reproducing the results by Pouzet et al. [3], where the applied heat undergoes a 200/400/200W cycle.  Fig. 3:  Evaporator wall temperatures comparison From Fig. 3,6,7 the comparisons show that the model is able to capture the trends of the temperature with acceptable errors, but is also able to predict the overshoot in the upward variation of external heat, in contradiction to the numerical model of the proposed  paper. The model is also able to predict the opposite behaviour of the evaporator wall and the primary wick (see Fig. 5).  Fig. 4 - Mass flow rate comparison  Fig. 5 - Primary wick and vapour grooves temperatures comparison The parametric analysis gives useful information on the most influencing geometrical parameters such as internal and external radius of the condenser, thickness and length of the evaporator shell.  4. Conclusions A 1-D lumped parameter model has been successfully created and validated against numerical and experimental data found in literature. This model has been used to perform a parametric analysis.  References [1]  Y. Maydanik, “ Loop heat pipes,” Applied Thermal Engineering, no. 25, pp. 635-657, 2005.  [2]  T. T. Hoang and J. Ku, “HEAT AND MASS TRANSFER IN LOOP HEAT PIPES,” in Proceedings of 2003 ASME Summer Heat Transfer Conference, Las Vegas, Nevada, USA, 2003.  [3]  E. Pouzet, J. Joly, V. Platel, J. Grandpeix and C. Butto, “Dynamic response of a capillary pumped loop subjected to various heat load transients,” International Journal of Heat and Mass Transfer, no. 47, pp. 2293-2316, 2004.   301302303304305306307750 1250 1750 2250T (K)time (s)Numerical Experimental LOOPER00.0020.0040.006750 1250 1750 2250mass flow rate (kg/s)time (s)experimental LOOPER285290295300305750 1250 1750 2250T (K)time (s)Tvo Simulation Tpw simulationTvo LOOPER Tpw LOOPER

A novel lumped parameter model for Loop Heat Pipes – validation and parametric analysis

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A novel lumped parameter model for Loop Heat Pipes – validation and parametric analysis

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