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GASMEMS2010- HT07

Development of a Molecular Dynamics Simulation Model for Heat Transfer in Vapors

JH. Kim, A. J. H. Frijns, A. A. van Steenhoven

Eindhoven University of Technology, Eindhoven, The Netherlands Abstract For many practical cases, such as gas-wall interactions, molecular dynamics simulations are a perfect tool. Here we use such molecular dynamics simulation to study the micro heat transfer of gas in a nanochannel. However, to study larger microchannels molecular dynamics is computationally too expensive. Within the GASMEMS project, firstly an efficient parallel code will be developed and a method for modeling complex wall geometries will be developed. Furthermore, a hybrid method with other particle based methods, like Monte Carlo method or with Continuum methods will be studied. 1 Introduction According to Moore’s law (1965), the power densities in e.g. IC industries is increasing rapidly. However, the limits of air fan cooling for integrated circuit are reached, and new cooling methods are needed. One method is micro channel cooling. In micro channel cooling, the heat is transferred to the fluid, flowing through a micro channel in close contact with the processor. The heat transfer can be even further enhanced by evaporation inside these channels. Inherent in this new technology is the need to develop the fundamental science and engineering of multi phase micro flow, since on micro scale the fluid tends to behave differently than the fluid we are used to handling in our daily life. Low Reynolds and high Knudsen number are typical conditions of a micro fluid. Gas-surface interaction is very important for the proper description of heat transfer at high Knudsen numbers, e.g. in micro-channels or at low pressures. Reliable models are needed to capture the temperature jumps and, related to that, the heat transfer between the walls and the gases in MEMS or in systems at low pressures. Particle based methods, like Molecular Dynamics, are capable to model it correctly, but at the expense of high computational efforts and small time and space domains. To speed up the computations, we will couple it to faster and more efficient algorithms like Direct Simulation Monte Carlo (DSMC) techniques for the gas phase and a continuum approach for the solid and liquid part. The influence on heat transfer of wall structures, like roughness, and wall properties, like wetting behavior, will be investigated. The main goal of this project is the improvement and validation of an existing multi-scale Molecular Dynamics/Direct Simulation Monte Carlo (MD/DSMC) simulation method for heat transfer in gases and vapors, which are developed at the Eindhoven University of Technology. Special attention will be paid to largely increased heat transfer at the solid-liquid-vapor interface. Hereto, the MD/DSMC model will be coupled to a continuum model to form a hybrid MD/DSMC/CFD model. Additional studies, like parallelization, inclusion of complex geometry for wall models, will be carried out by our group. 2 Molecular Dynamics for Micro Heat Transfer Study of heat transfer in microchannel has been studied within our group for the last several years. Behavior of a gas confined between two parallel plates, for gas densities ranging from rarefied gases to very dense gases and for various interaction strengths was carried out using an adapted version of molecular dynamics code PumMa (Nedea 2005).

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The most recent study, including evaporation inside microchannels, has been carried out by van den Akker(2010). In the simulation of evaporation inside microchannels, the treatment of fluid-wall heat transfer is the most important factor. In gases close to walls, density fluctuations occur, which have a large effect on the heat transfer between wall and gas. For heat transfer between a micro channel wall and the coolant, the explicit wall model can be used in MD with great accuracy, but also with great computational costs. Other wall models that are computationally cheaper exist, but they are less accurate, or have parameters that are unknown a priori. To overcome this problem, van den Akker (2008) introduced a new model. The new model is based on a vibrating wall model. As shown in figure 1, all interactions are calculated inside the wall and all particles can have different velocities for an explicit wall model. But in the vibration potential wall model, interactions exist between a particle and part of a wall, seen as a rigid vibrating body. During the collision the other particles (here in light color) are ignored. Vibrating potential wall model cuts back on computation time but has an accuracy comparable to the explicit wall model (van den Akker 2008). 3 Conception of the Research Project of TU Eindhoven (ESR 08) The general idea of the research is to follow up of the work of van den Akker. It is planned to extend his work in following areas:

• Higher simulation speed • Variable channel geometry • Coupling with different simulation methods • Simulation with new molecules

3.1 Higher simulation speed The starting point is a parallelization of an existing molecular dynamics code(based on PumMa) developed by van den Akker (2010). The existing MD code has been developed in sequential mode alone. Parallelization of the code has been carried out and has been tested with 20581 argon particles and given conditions shown in figure 2. In this test simulation, a pressure-induced flow of an Argon gas meets an obstacle with lower temperature. The walls have a temperature of 240K, while the gas enters the simulation at 120K. It can be seen as a gas that is cooling a device. Initially, the gas temperature is set to 120K and equal pressure in the whole domain. In general, the execution time for multi processor simulations is known to show an inverse characteristic function as shown in figure 3.

Figure 1: Explicit wall model and Vibrating potential wall model (van den Akker 2008).

(a) Explicit wall model (b) Vibrating potential wall model

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However, in the test simulation, an execution time for 4 processors is not following the characteristic function (Table 1). It is higher than expected time. This is due to an uneven distribution of particles throughout the domain caused by the boundary conditions. Uneven distribution is caused by the temperature difference along the domain. Temperature of the gas is higher in the right side of the channel due to a heating by the high temperature obstacle, and density becomes lower in the right side compared to the left. In the initial state, the particles are more or less evenly distributed (figure 4, up). In table 2, decline in the performance of 4 processors is clearly shown for the higher iterations. In the higher iterations, particles are distributed more unevenly compared to the early states. In the test simulation with 4 processors (figure 4b), after 150,000 iterations, more than 50% of particles are decomposed on one specific processor alone and other processors have to wait for the “overloaded” processor to finish its task. Compared to the simulation with 2 processors (figure 4a), relative overloading of one specific processor is much high in the simulation with 4 processors (figure 4b).

Number of Processors 1 2 4 Execution time for 500,000 Iteration (sec) 5670 3109 2949

Figure 2: Test simulation for parallelization (van den Akker 2010).

Figure 3: General characteristic curve of execution time vs. processor. Execution times of the parallel Sieve of Eratosthenes program. (Quinn 2003)

Table 1: Execution times of the test simulation.

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Iteration Period \ Number of Processors 1 2 4 0 to 10,000 90 41 (2.2) 28 (3.2) 10,000 to 20,000 20,000 to 30,000 30,000 to 40,000 40,000 to 50,000 50,000 to 60,000

101 107 112 114 115

54 (1.9) 60 (1.8) 64 (1.8) 67 (1.7) 65 (1.8)

34 (3.0) 46 (2.3) 51 (2.2) 56 (2.0) 59 (2.0)

So far, most of the MD simulation based on PumMa has been working on the homogeneous system (system with uniform spatial density and negligible over time), thus static load balancer has been used. In the case of Micro Heat Transfer, system is heterogeneous. Dynamic repartitioning of the space, to maintain the acceptable load balance, is proposed for heat transfer MD simulation to improve its performance (Srinivasan 1996). 3.2 Variable channel geometries The next work is an addition of geometries to the wall models. So far, current PumMa wall models are built its shape using grids. Each boundary condition for each grid is inputted manually by hands. Disadvantage of this method lies when you have to draw curved three dimensional objects, as for an example, a cylinder. To solve this problem, new wall models (figure 5b) will be described in radial functions (circular, linear, polynomial functions) rather than being described by a large number of grids. The first preliminary tests are done successfully. Later, the code will be then developed in order to join the geometry blocks together. Various functional geometry blocks and user defined geometry blocks formed by grids will be attached together to build a complex geometry for the wall models in a simulation as shown in figure 6.

(a) Domain decomposition for 2 Processors (b) Domain decomposition for 4 processors Figure 4: Particle distribution for an initial state(up) and after 500,000 iterations(down).

Table 2: Execution times (sec) of the test simulation for different iteration periods. The number in Parentheses indicates the performance factor based on the performance of single processor execution.

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3.3 Coupling with different simulation method Thirdly, hybridization of MD, MC, and CFD codes will be done. Study on Hybrid Molecular Dynamics-Direct Simulation Monte Carlo has been already carried out at the Eindhoven University of Technology (Nedea, 2005, 2009). In her study, MD(Language: C) and the MC(Language: Fortran) codes are coupled via a Python interface (Nedea 2009). Similar approach will be carried out in one C code. Parallel processing of Hybrid Methods will be studied. Research on Hybrid MD-MC will be then extended to coupling with CFD method in cooperation with University of Strathclyde, Glasgow.

(b) Current PumMa grid model (b) New function model

Figure 6: Combination of geometry blocks to form a complex geometry wall model.

Figure 5: The geometry for the wall models

Functional model

User defined geometry

Combined model

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3.4 Simulation with new molecules Finally, new molecular models will be simulated in the future. Simulation of Argon and Oxygen molecules were performed by van der Akker(2010) in our group. New molecules, that are used often in real industry, like nitrogen, air, carbon dioxide and water, will be simulated, and will be compared with available experimental data.

4 Conclusion Due to the rapid development of MEMS devices, a precise simulation of gas flows and heat transfer in micro channels has become a necessity. Particle based methods, like Molecular Dynamics, are capable to model it correctly, but at the expense of high computational efforts and small time and space domains. The present paper deals with some topics to further speed up and advance the Molecular Dynamics simulation of micro heat transfer. New simulation techniques will be applied and tested. Some validation results and comparisons to available experimental and numerical data will be presented in a forthcoming paper. 5 Acknowledgements Appreciation is expressed to van der Akker, for useful suggestions during several discussions. The research leading to these results has received funding from the European Community's Seventh Framework Programme (ITN-FP7/2007-2013) under grant agreement n° 215504. 6 References

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Dynamics Simulations on Computer Clusters: Performance Evaluation and Modeling, Mathematical and Computational Modeling, 42, 783.

Markvoort, A.J., 2006, Toward Hybrid Molecular Simulations, PhD Thesis Eindhoven University of Technology.

Moore, G. E., 1965, “Cramming more component onto integrated circuits”, Electronics, 38, 1965 Nedea, S.V., Markvoort, A.J., Hilbers, P.A.J., 2005, Molecular dynamics study of the influence

of wall-gas interactions on heat flow in nanochannels, Physical Review E, 71. Nedea, S.V., Markvoort, A.J., van Steenhoven, A.A., Hilbers, P.A.J., 2009, Heat Tranfer

Prediction for Micro-/Nanochannels at the Atomistic Level Using Combined Molecular Dynamics and Monte Carlo Techniques, Journal of Heat Transfer, 131, 103-111.

Plimpton, S., 1995, Fast Parallel Algorithms for Short-Range Molecular Dynamics, Journal of Computational Physics, 117, 1-19.

Quinn, M.J., 2003, Parallel Programming in C with MPI and OpenMP, McGrawHill, Singapore Srinivasan, S.G., Ashok, I., Jonsson,H. , Kalonji, K., Zahorjan, J., 1996, Dynamic-domain-

decomposition parallel molecular dynamics, Computer Physics Communications, 102, 44-58.

Van den Akker, E.A.T., 2008, Heat Transfer between Walls and Fluids: MD Simulations with Vibrating Walls, in Proceedings of the 1st European Conference on Microfluidics; editors: Colin, S., Morini, G.L., paper 111.

Van den Akker, E.A.T., 2010, Particle-based Evaporation Models and Wall Interaction for Microchannel Cooling, PhD Thesis Eindhoven University of Technology.