As example of two phase cooling, we considered a pulsating heat pipe (PHP). An important advantage of such system is that no external pump is needed and.
Turbulence (2004) Vol. 10, pp. 67-74
MICROCHANNEL COOLING: SIMULATIONS AND EXPERIMENTS Arjan J.H. FRIJNS1, Erik H.E.C. EUMMELEN1, Silvia V. NEDEA1, Céline C.S. NICOLE2, and Anton A. VAN STEENHOVEN1 1 Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, 5600 MB Eindhoven, the Netherlands 2 Philips Electronics Nederland BV, Prof. Holstlaan 4, 5656 AA Eindhoven, the Netherlands
Single and two phase microchannel cooling is studied by models and experiments. For single phase cooling three models are discussed: a molecular dynamics model, a Monte Carlo method and a continuum model (CFD). Also microchannel cooling experiments with water and air as coolant are discussed. The experiments and the simulations show good agreement. A pulsating heat pipe is considered as an example of two phase cooling. A onedimensional model and experiments are compared. The trends are predicted well by the model. However, there is a large difference in absolute values between the model and the experiments. Therefore the model needs some modifications for the threedimensional phenomena that occur in the experiments. Keywords: molecular dynamics, Monte Carlo method, hybrid method, CFD, microchannels, pulsating heat pipe, single phase cooling, two phase cooling.
INTRODUCTION There is a tendency for mechanical and electrical components to become smaller and smaller. Since most components produce heat when operating, it is essential to cool them in order to perform well and to ensure the life span of such a component. In designing micro-electronics for example, it is crucial to consider the thermal performance of sub-micron thin films and composites, the effect of microscale heat sources and the rapid transient energy releases. Furthermore, while the chips are becoming smaller and smaller, their power is increasing [1]. Therefore, the cooling performance has to be increased by new solutions for enhanced cooling of components. In our group, microchannel cooling is considered in two ways: by modelling of the heat transfer and fluid flows in microchannels and by experiments. We consider single phase and two phase cooling.
68 1. SINGLE PHASE COOLING Microchannels of a typical size of 100 µm and smaller are considered. For liquids the CFD approach can be used without any problems. However for gases the limit of the continuum approach is reached. For smaller channel sizes, a particle-based method has to be used for the gases. We consider three models: a molecular dynamics model, a Monte Carlo method and a continuum (CFD) model and compare the simulations with experiments. 1.2 MODELS Molecular dynamics (MD) is a computer simulation technique in which the time evolution of a set of interacting particles is followed. This is done by solving the equations of motion of classical multi-body systems. When the positions, masses and velocities of all particles in the system and the forces on the particles are known, the motion of all particles can be calculated. With the computed particle parameters the pressures and temperatures can be determined. The Monte Carlo (MC) method is based on the Direct Simulation Monte Carlo method (DSMC) developed by Bird [2]. The DSMC method does not calculate the collisions exactly as in molecular dynamics, but generates collisions stochastically with scattering rates and post-collision velocity distributions determined from the kinetic theory of a dilute gas. It is a stochastic method and therefore several molecules can be combined into one artificial particle without disturbing the macroscopic properties of the gas. This method is used successfully to study flow and heat transfer in microchannels for a dilute gas. However, for cooling purposes (high pressure or phase transition) we have also to model a dense gas in a microchannel. Therefore, the DSMC method is modified by using the Enskog equation instead of the Boltzmann equation as governing equation [3,4,5]. The Enskog equation preserves the momentum and energy of the system. We showed that both methods can be used to model the heat transfer in nanochannels [5]. The MD method is accurate but computational expensive, while the MC method, in which an artificial particle represents several molecules, is more efficient. However, the boundary effects are computed less accurate, because the solution closely to the boundaries depends on the (artificial) particle size [6]. Therefore the MC method deviates from the MD method when several molecules are put into one MC particle. In order to get an accurate solution near the walls, a detailed model is needed in which the particle diameter is equal to the molecular diameter. MD is suited for that. In the bulk of the channel, the particle diameter is not so critical. In this region the computations can be sped up by MC with several molecules inside one artificial particle and by using larger time steps. So, a coupling of MD with MC is favourable for a fast and accurate solution. We developed a hybrid algorithm in which the total domain is divided into MD and MC subdomains [5]. In each subdomain a different method is used. The computations in the separate subdomains can be performed in parallel. An interface
69 between these subdomains is used to exchange data and particles from one subdomain to the other subdomain. Care must be taken for the coupling of the data of the different subdomains, since the time steps in MD and in MC may differ. Preliminary results [5,7] show that the algorithm is working and the CPU-time decreases for the coupled problem compared to pure MD computations. In industry quite often continuum models are used. For microchannels with a typical size of 100 µm, this approach is still valid for liquids. For gases, sometimes modified boundary conditions are needed. We used the commercial CFD-package Flotherm that is often used in microelectronics industry. 1.3 EXPERIMENTS To validate our simulations, experiments on heat transfer in microchannels are needed. We studied single phase cooling with water or air as coolant. These experiments were performed in a silicon device with 75 microchannels with a size of 100µm x 300 µm x 15 mm (width x height x length). At the bottom of the device a heater was attached. The microchannels were sealed on top with a glass plate. The temperatures, the pressures and the fluid flows were measured. We have carried out the experiments for water and air as coolant. The mass flow of water was in the range from 0.07 to 1.07 kg/min at a power dissipation of 105 W/cm2. The mass flow for air was in the range from 10 to 35 g/min. The thermal resistance was determined based on the inlet temperature and the heater temperature. A typical result is shown in Fig 1.
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Fig 1. Thermal resistance as function of the mass flow through the microchannels for water as coolant.
1.4 RESULTS We compared these experiments with CFD simulations (Flotherm). No-slip boundary conditions and a uniform flow at the inlet are used, since at the inlet a relative large revervoir is located. The numerical and experimental results show
70 good agreement [8,9]. The drop in the thermal resistance with increasing flow rate is due to the decreasing capacitive resistance. The measured thermal resistance varies from 0.32 Kcm2/W at a flow of 0.075 kg/min to less than 0.05 Kcm2/W at a flow of 1 kg/min. The corresponding pressure drop ranges from 0.1 to 2.6 bars. It is seen that at flow rates in excess of 0.6 kg/min the experimentally determined pressure drop is larger as the pressure drop calculated. A possible explanation for this phenomenon is the transition from laminar to turbulent flow due to surface roughness. We will perform extra experiments to determine whether this is really the case. For air as coolant the results are similar [8,9]. However, the thermal resistance is much higher in case of air cooling than for water cooling. 2. TWO PHASE COOLING As example of two phase cooling, we considered a pulsating heat pipe (PHP). An important advantage of such system is that no external pump is needed and therefore can be integrated into a device more easily. The concept of pulsating heat pipes is developed in the early 1990’s by H. Akachi [10]. The pulsating heat pipe consists of a closed meandering capillary tube, as shown in Fig 2.
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Fig 2. Schematic overview of a pulsating heat pipe
Unlike a standard heat pipe, a pulsating heat pipe has no internal wick structure. The liquid will have to be transported back to the evaporator in another way. In a PHP the oscillating motion takes care of the fluid transportation. By heating one side and cooling the other, as indicated in Fig 2, oscillations of the working fluid occur in the heat pipe. These oscillations are caused by thermally driven pressure differences within the system. Due to the oscillating motion of the liquid and vapour, heat is transferred. Both latent heat and sensible heat transfer takes place. Latent heat transfer is caused by
71 vapourisation on the hot side and subsequent condensation on the cold side. Sensible heat is transferred by the liquid plugs which can move from the hot to the cold side. Although the pulsating heat pipe has found already some applications in aerospace and electronics cooling, the driving forces are not yet fully understood which complicates the design process of an optimal heat spreading by a PHP. In order to gain more insight into the mechanisms, we studied the thermal resistance.
2.1 MODEL We used a one-dimensional analytical model for the PHP developed by Shafii et al. [11]. Their model consists of a tube filled with vapour plugs and liquid slugs. The oscilatory phenomenon in the PHP is predicted by solving the mass, momentum and energy equations for each liquid slug or vapour plug. They assume that the evaporative and condensation heat transfer coefficients are constant and that the liquid is incompressible and the vapour plugs can be modelled as an ideal gas. On the liquid slugs, the folowing forces act: a force caused by the pressure difference of adjoining vapour plugs, friction forces, the gravity and the capillary force or surface tension. Their results show that the heat transfer is due mainly to the exchange of sensible heat. So, the maximum heat transfer depends on the oscillation frequency. 2.2 EXPERIMENTS The pulsating heat pipe is made from an aluminimum plate in which the channels are milled. The plate is sandwiched between two polycarbonate plates to keep the device transparent. These polycarbonate plates are 10 mm thick. At one side the pulsating heat pipe is heated by electrical film heaters. At the other side it is cooled by a cooling fluid. During the experimenst the heating power, the condensor and evaporator temperatures are measured and the device is filmed. 2.3 RESULTS The thermal resistance of the pulsating heat pipe is seen to depend on several factors. One of them is the oscillation frequency. This frequency depends on the fluid propertis, like viscosity, latent heat and surface tension as shown in Fig 3. The square gives the reference situation in which the properties of water have been used in the model. Water is used as a reference since it is frequently used in PHP’s. It is seen that the effect of surface tension is negligible. The viscosity, and especially the latent heat have a major influence on the oscillation frequency. From these computations follows that the oscillation frequency for water should by about 20 Hz. The amplitude is 1.95 cm. However, from the analysis of the experiments follows that the oscillation frequency is about 10 Hz with an amplitude of 1.0 cm.
72
Fig 3. Oscillation frequency as function of the fluid parameters.
Also the effect of the inclination angle is considered. In horizontal orientation the measured thermal resistance is comparable to the resistance of an unfilled heat pipe, about 5 K/W. When the PHP is operated vertically with the heater on the bottom side, the thermal resistance can become significantly smaller: 3.7 K/W at an input power of 15 W. Further increase in power reduces the thermal resistance even further, which is in line with the observations of Khandekar [12]. Different kinds of working fluid are employed too. It is seen that both ethanol and methanol are better working fluid than water for the working conditions tested. This is also expected since the latent heat for ethanol and methanol is lower than for water. Proper functioning of the PHP starts at lower power for these working fluids. The thermal resistance is lower too. The filling ratio of the PHP does not seem to be a critical paramater for the PHP to function properly. The filling ratio is tested for 20, 45 and 70 % and measured thermal resistances were in 12 % in agreement. 2.4 DISCUSSION The trends are predicted well by the model. However, there is a large difference in absolute values between the model and the experiments. In the experiments it is seen that when the pulsating heat pipe is in vertical position the liquid film on the walls drips down and is collected in the bottom turn. In this way new liquid slugs are formed constantly, which affect the fluid flow. In the model such phenomena do not occur since it is strictly one dimensional. Hence no new liquids slugs can be formed in the model. It is also seen in experiments that vapour plugs can coalesce, which decreases the amount of vapour plugs. In the model the liquid slugs are isolated from each other by the vapour plugs located between them. But in practice two vapour plugs can move towards each other to form one new vapour plug. The liquid slug, which
73 was positioned between the plugs, is thus ”squeezed away” through the liquid film. This may also affect the ratio of the forces acting on a liquid slug. In the model a pressure difference between the adjoining vapour plugs can only be leveled by a movement of the complete liquid slug. In practice the vapour plug at higher pressure may also squeeze liquid away as described above. 3.FUTURE RESEARCH At this moment a first step is made with the development of a hybrid model for heat transfer and fluid flow in microchannel and nanochannels. It is shown that the hybrid method is working for nanochannels in which the MD and MC particles have the same dimensions. However, a sped up is expected when the number of MD particles in a MC particle is increased. Furthermore we want to extend the hybrid method such that evaporation in microchannels can be modelled by coupling the method with a continuum model for the liquid phase. In single phase cooling, the geometry has an important influence on the flow and heat transfer in microchannels. Therefore, we will investigate the behaviour for several geometries and investigate the flow inside the microchannels by microPIV. In two phase cooling we want to extend the one-dimensional model to two- or three dimensions to include the effects of the liquid film and the separation or coalescence of the liquid slugs. ACKNOWLEDGEMENTS The authors would like to thank A.J. Markvoort and P.A.J. Hilbers for their support, their valuable discussions on the development of the hybrid code, and the use of their MD-code PumMa. We also like to thank R. Dekker and R. Pijnenburg for their support with the manufacturing of the microchannels. REFERENCES 1. R.R. Schmidt and B.D. Notohardjono, High end server low temperature cooling, IBM Journal of Research and Development, Vol. 46, pp.739-751, 2002 2. G.A. Bird, Molecular gas dynamics and the direct simulation of gas flows, Clarendon Press, Oxford, 1994. 3. A. Frezzotti, A particle scheme for the numerical solution of the Enskog equation, Phys. Fluids, 9, 1329-1335, 1997. 4. A Frezzotti, Monte Carlo simulation of the heat in a dense sphere gas, European journal of mechanics, 18, 103-119, 1999. 5. A.J.H. Frijns, S.V. Nedea, A.J. Markvoort, A.A. van Steenhoven, and P.A.J. Hilbers, Molecular Dynamics and Monte Carlo Simulations for Heat Transfer in Micro and Nano-channels, in: ICCS 2004; Marian Bubak, G. Dick van Albada, Peter M.A. Sloot, Jack J. Dongarra (editors), Krakow, Poland, 2004.
74 6. S.V. Nedea, A.J.H. Frijns, A.A. van Steenhoven, A.P.J. Jansen, Properties of a dense hard-sphere gas near the walls of a microchannel, in: Second International Conference on Microchannels and Minichannels; Editors: S.G. Kandlikar, Rochester, NY, United States, pp. 289-296, 2004 7. S.V. Nedea, A.J.H. Frijns, and A.A. van Steenhoven, A.J. Markvoort, and P.A.J. Hilbers, Hybrid Molecular Dynamics-Monte Carlo Simulations for the properties of a dense and dilute hard-sphere gas in a microchannel, in: 24th international Symposium on Rarefied Gas Dynamics, Bari, Italy, 2004 8. A.J.H. Frijns, E.H.E.C. Eummelen, C.C.S. Nicole, S.V. Nedea, and A.A. van Steenhoven, Integrated microchannel cooling with water and air: experiments and model simulations, submitted to Microscale Thermophysical Engineering. 9. C.C.S. Nicole, R. Dekker, A. Aubry, R. Pijnenburg, Integrated Micro-Channel Cooling in Industrial Applications, in: Second International Conference on Microchannels and Minichannels; S.G. Kandlikar (editor), Rochester, NY, USA, 2004. 10. H. Akachi, Looped Capillary heat pipe, Japanese Patent, No. 697147, 1994. 11. M.B. Shafii, A. Faghri, and Y, Zhang, Thermal modeling of unlooped and looped pulsating heat pipes, Journal of heat transfer, vol.123, pp. 1159-1172, 2001. 12. S. Khanderkar, N. Dollinger, and M. Groll, Understanding operational regimes of closed loop pulsating heat pipes, Applied Thermal Engineering, vol.23, pp.707-719, 2003.
