A Numerical Investigation on bubble formation in Coolant channel with various Ethylene Glycol and water compositions and change in contact angle

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1 2016 IEEE 23rd International Conference on High Performance Computing Workshops A Numerical Investigation on bubble formation in Coolant channel with various Ethylene Glycol and water compositions and change in contact angle Vamshi Krishna Chitikase Global Propulsion Systems Transmission & Electrification CFD General Motors Bangalore, India vamshikrishna.chitikase@gm.com Chih-Cheng Hsu Engineering Propulsion Systems Electrification Thermal General Motors North America Chihcheng.hsu@gm.com Abstract Numerous latest high power electronic circuit systems use an external cooling channel filled with circulating liquid coolant which acts as a heat sink to remove generated heat from surrounding components. While filling the coolant, air in the channel has to be completely removed before the final sealing is applied for good thermal and Noise, Vibration & Harshness (NVH) performance of the heat sink. It is also important from pump durability perspective. A numerical investigation has been conducted to understand the effect of capillary number and contact angle on the bubble formation by using several compositions of Ethylene Glycol and water mixture. The results indicated that bubble formation decreases with increase in Capillary number and increases with increase in contact angle Keywords-Bubble;Ethylene Glycol;Capillary number;contact angle;cfd I. INTRODUCTION Cooling of electronic components has become a sizable challenge due to the improvements in the design of faster and smaller components. Hence various cooling techniques have come into practice for the efficient removal of the heat from heat producing components. One such technique is usage of coolant channel through which liquid is pumped. The heat removing capacity of the coolant is affected by entrapped air in the coolant channel during the coolant fill. Presence of air decreases the heat removal capacity hence decreasing the effectiveness of the coolant system. One of the most common coolants used is Ethylene glycol and water mixture. Several compositions of the Ethylene glycol and water mixtures are used by varying the percentage of Ethylene glycol. Mixture properties such as dynamic viscosity, surface tension and density varies for various compositions. Therefore, a non-dimensional number known as Capillary number is expressed in terms of triple line velocity, dynamic viscosity and surface tension and effect of it is studied on the bubble formation. Apart from capillary number, contact angle between the coolant and the solid surface also influences the bubble formation hence effect of contact angle is also studied in this paper. Contact angle,, is a quantitative measure of wetting of a solid by a liquid. It is defined geometrically as the angle formed by a liquid at the three phase boundary where a liquid, gas and solid intersect. The popular Young equation describes the balance at the three phase contact of solidliquid and gas. sv = sl+ lv cos (1) In equation (1) solid vapor interfacial surface energy is denoted by sv, the solid liquid interfacial surface energy by sl, and the liquid vapor interfacial surface energy is denoted by lv. From Figure 2 it can be seen that the low contact angle values indicate good spreading of liquid on the surface while high contact angle values show poor spreading. If the contact angle is less than 90 it is said that the liquid wets the surface and if the contact angle is greater than 90, the liquid poorly wets or doesn t wet the surface. Figure 1. Contact angle definition[14] Figure 2. Contact angle between coolant and wetting surface for various materials [14] Contact angle can be differentiated as static and dynamic angle. Contact angle measured when droplet is standing on the surface and the three phase boundary is not moving is known as static contact angle. When the three phase boundary is moving, dynamic contact angle is measured in terms of advancing and receding angles (Figure3). The /16 $ IEEE DOI /HiPCW

2 magnitude of the contact angle for a phase interaction depends on the combination of fluids and the solid that are in contact and on the temperature. The contact angle is measured at the triple line, which is the line where the wall and both fluid phases are in mutual contact. Figure 3. Advancing and Receding Contact angle[15] II. GEOMETRIC MODELLING AND MESH GENERATION A. Methodology For Computational Fluid Dynamics (CFD) simulation, first of all a representative geometry of the coolant channel was created using STAR CCM+. Once the geometry is created, it need to be meshed which was also done using STAR CCM+. Physics continuum and boundary type for the surfaces generated were defined. Based on Reynolds number of the flow appropriate model is selected for modelling turbulence. Finally post processing is done for analyzing the results. B. Geometry modelling and meshing of CFD domain Geometry generation is first step for making the CFD domain. In STAR CCM+ any 3D shape can be created. Initially 2D shape is created and using several operations such as Unite, Move, Copy, Sweep etc. 3-D geometry is created out of 2D plane. For applications such as flow of coolant is involved that require a dynamic contact angle ( k), Kistler method [15] is used Here fhoff is the Hoffman function (2) (3) In equation (2) s is static contact angle and how this is used in the equation is discussed in detail in the following sections. Triple line velocity is the common quantity used in many dynamic angle correlations. This quantity is linked to the dimensionless Capillary number as Figure 4. CFD Model Here V is the triple line velocity ; μ is the dynamic viscosity of the primary phase (mostly a liquid phase); is the surface tension force. The triple line velocity can be defined as Where V is the relative velocity of the fluid and the corresponding wall at the triple line. n t is the normalized wall tangent pointing in the same direction as the volume fraction gradient of the primary phase. (4) (5) Figure 5. CFD Model Cross Section ( 22.5mm in Length and 3.2mm in width) After the geometry of the CFD domain is prepared, immediate step is to mesh it. It is mandatory to use good quality mesh to achieve better results. Here meshing was done using STAR CCM+ itself. Poly mesh with prism layers was used for volume meshing of count 0.97 million. Appropriate number of prism layers and the first prism cell height is determined to capture the boundary layer appropriately. A horizontal cross section of mesh is displayed in Figure

3 In this analysis +/- 10 o is used to define advancing and receding contact angle for a specified equilibrium contact angle e and the range for the equilibrium Capillary number Ca eq used is -0.5 to 0.5. Advancing and receding contacting angle as s is substituted in equation (2) to get kistler dynamic contact angle k which is in turn substituted in equation (6) to calculate dynamic contact angle. Figure 6. Mesh across the crossection of CFD Model C. Multiphase modelling & boundary conditions The Eulerian multiphase flow model in STAR-CCM+ is used to solve the multi-phase flow problem presented in this paper. In the Eulerian multiphase flow model, the phases are treated as interpenetrating continua coexisting in the flow domain. Equations for conservation of mass, momentum and energy are solved for each phase. The part of the flow domain occupied by each phase is specified by its volume fraction and each phase has its own velocity, temperature and physical properties. Interactions between phases due to differences in velocity and temperature are taken into account by means of the inter-phase transfer terms in the transport equations. In this solution method, all the phases share a common pressure field. In this paper flow is assumed to be isothermal, hence the main equations solved are the conservation of mass, and momentum for each phase, the energy equation is not solved. The static contact angle s used here in equation (2) is either the static advancing or receding contact angle. Depending on the sign of the capillary number it is specified as the advancing contact angle or receding contact angle. To enhance the stability of the methodology implemented in STAR-CCM+, a range for the equilibrium capillary number Ca eq is defined. The resulting dynamic contact angle k is blended with the equilibrium contact angle e within the specified range -Ca eq<ca eq<ca eq as a weighted average (6) Here e is a user-specified value, the factor f is determined within the Ca eq range as (7) To calculate the continuous and dispersed phase turbulence stresses, values for k and are required. These are computed using the extended k- equations containing extra source terms that arise from the interphase forces present in the momentum equations. The additional terms account for the effect of particles on the turbulence field. Here the Reynolds number for the flow varies from 500 to 8000 based on the Ethylene Glycol and Water content. Hence for low Reynolds number (< 2000), laminar model is employed and for higher Reynolds number flow condition realizable k- turbulence model is employed. Velocity inlet (Velocity as 1.17m/s computed for 5 liter per min) is used as Inlet boundary condition and Pressure outlet (Atmosphere outlet) is used as Outlet boundary condition. Primary Phase is the Ethylene glycol and secondary phase is air. For primary phase, volume fraction of 1 is used at inlet and 0 at outlet. Volume % ( Ethylene Glycol/Water) Surface Tension (N/m) Density (kg/m 3 ) Dynamic Viscosity (Pa.s) 0/ / / / TABLE I. PROPERTIES OF THE COOLANT MIXTURE [12,13] Capillary Number D. Modelling assumptions In addition to the models and parameters discussed previously, other assumptions involved in the CFD simulations are stated below. The effect of temperature change on the flow has been neglected assuming isothermal conditions. No slip boundary conditions are assumed at the wall of tubing. The effect of wall roughness on the flow and shear stress has not been investigated. E. Solution Strategy & Convergence A calculation of multiphase flow for a geometry such as C shaped channel with 180 o bend requires an appropriate numerical strategy to avoid a divergent solution. A transient solution strategy, with quite small time steps is used to achieve convergent solution. Sufficient number of inner iterations are used to achieve convergence in each time step. The convergence criterion is based on the residual value of the calculated variables, i.e., mass, velocity components, energy, turbulence kinetic energy, turbulence dissipation rate 125

4 and volume fraction of the coolant. In this analysis, the effect of temperature change on the flow has been neglected assuming isothermal conditions. No slip boundary conditions are assumed at the wall of tubing. The effect of wall roughness on the flow and shear stress has not been investigated. Default under relaxation factors of volume fraction of coolant, velocity, pressure and turbulent parameters are used. F. Computational Cost In this analysis grid size of the model is 0.97 million. Transient analysis is run using 144 nodes in a high performance computing cluster. Total CPU time consumed for 3 seconds of solution time is sec. III. CFD ANALYSIS & RESULTS Analyses are performed for total twelve different combinations of Ethylene/Water glycol and contact angle for 3 sec of time duration. Ethylene glycol/water composition is varied from 0/100 to 100/0 and equilibrium contact angle e is varied from 30deg to 90deg. By varying the Ethylene glycol content we indirectly varied the capillary number from 0.01 to Figure 8. Contours of volume fraction of coolant at 0.2 sec. As the coolant flows through the channel, bubble starts forming at the end of 180 o bend of the channel at 0.4 sec. Figure 9 shows the regions of bubbles after the bend in the channel. Bubble is the region where air gets suspended or trapped in the liquid continuum. CFD analyses results are presented as volume fraction of coolant across the horizontal cross section of the channel at different times to show how the bubble formation is occurring for various combinations. Blue and red colors in the Figures (7, 8, 9, 10, 11 & 12) indicate the volume fraction of coolant as zero and 1 respectively. Red color region can be treated as coolant and blue color region as air. Figure 9. Contours of volume fraction of coolant at 0.4 sec. Figure 7. Contours of volume fraction of coolant at 0.1 sec. Figure 10. Contours of volume fraction of coolant at 1 sec. 126

5 contact angle increases the bubble formation. It can be concluded that for a given contact angle as capillary number increases the tendency for the bubble formation decreases and for a given capillary number as the contact angle increases the tendency for the bubble formation increases. Hence it can also be concluded that for lower bubble formation and bubble stability, proportion of ethylene glycol content in the coolant should be increased and coolant tube material should be selected in such way that the coolantcoolant tube contact angle is less than 60 o for good wetting of the surface. This will finally lead to a lower air content in the channel and high thermal and NVH performance. Figure 11. Contours of volume fraction of coolant at 2 sec. Figure 12. Contours of volume fraction of coolant at 3 sec. It is observed that even at the end of 3 sec, the bubbles formed after the channel bend are sustained and become stagnant for few cases. For pure water which is the least capillary number case, bubble formation has occurred for both 60 o and 90 o contact angles. For Ethylene glycol/water mixture of 25/75 whose capillary number is 0.03 which is thrice that of the pure water case, smaller bubbles are formed for 60 o contact angle but bigger bubbles are formed for 90 o contact angle. For Ethylene glycol/water mixtue of 50/50 whose capillary number is 0.06 which is 6 times that of the pure water case, smaller bubbles are formed only for 90 o contact angle. But for pure Ethylene glycol whose capillary number is 0.34 which is 34 times that of pure water case, bubbles are not formed for any of the contact angles. REFERENCES [1] Y. Gao, Y. Zheng, Flow Analysis of Circular Bent Pipe Based On Numerical Simulation,Electrical and Control Engineering (ICECE), Sept. 2011, pp [2] Michael Renardy, Yuriko Renardy and Jie Li, Numerical Simulation of Moving Contact Line Problems Using a Volume-of-Fluid Method, Journal of Computational Physics 171, (2001) [3] R. G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, J. Fluid Mech. 168, 169 (1986). [4] R. W. Lockhart and R. C. Martinelli, Proposed Correlation of Data for Isothermal Two-Phase Two-Component Flow in Pipes, Chemical Engineering Progress, Vol. 45, No. 1, 1949, pp [5] J. A. C. Humphrey, J. H. Whitelaw and G. Yee, Turbulent Flow in a Square Duct with Strong Curvature, Journal of Fluid Mechanics, Vol. 103, 1981, pp [6] G. R. Rippel, C. M. Eidt Jr. and H. B. Jordan, Two Phase Flow in a Coiled Tube, Pressure Drop, Holdup, and Liquid Phase Axial Mixing, Industry & Engineering Chemistry Process Design and Development, Vol. 5, No. 1, 1966, pp [7] J. M. Chenoweth and M. W. Martin, Turbulent TwoPhase Flow, Petroleum Refiner, Vol. 34, No. 10, 1955, pp [8] G. R. Rippel, C. M. Eidt Jr. and H. B. Jordan, Two Phase Flow in a Coiled Tube, Pressure Drop, Holdup, and Liquid Phase Axial Mixing, Industry & Engineering Chemistry Process Design and Development, Vol. 5, No. 1, 1966, pp [9] Yuehua Yuan and T. Randall Lee, Contact angle and wetting properties [10] M. Renardy, Y. Renardy, and J. Li, Numerical simulation of moving contact line problems using a volume-of-fluid method, J. Comput. Phys. 171, [11] E. B. Dussan V, On the spreading of liquids on solid surfaces: static and dynamic contact lines, Ann. Rev. Fluid Mech. 11, 371 (1979). [12] [13] [14] [15] STAR CCM User Guide IV. CONCLUSIONS For all combinations, analyses are performed and based on the contours of volume fraction of the coolant it is found that for a given contact angle, increase in Ethylene glycol percentage decreases the bubble formation. As well for a given Ethylene glycol and water composition increase in 127