Proceedings of the Asian Conference on Thermal Sciences 2017, 1st ACTS March 26-30, 2017, Jeju Island, Korea ACTS-P00394 NUMERICAL MODELING OF THE GAS-PARTICLE FLUID FLOW AND HEAT TRANSFER IN THE SLIP REGIME Zhenyu Liu, Huiying Wu * Shanghai Jiao Tong University, 800 Dong Chuan Rd. Minhang District, Shanghai 200240, China Presenting Author: zhenyu.liu@sjtu.edu.cn * Corresponding Author: whysrj@sjtu.edu.cn ABSTRACT The transport characteristic of micro-scale gas-particle two-phase fluid plays an important role in the innovative micro devices, such as solid propellant micro thruster and micro combustor, etc. The micro-scale flow and heat transfer processes in gas-particle fluid have attracted more and more attention in recent years due to its significant difference compared with that in the macro scale. The related fundamental phenomenon was still not clearly understood in the previous studies. In this work, a numerical model of the gas-particle flow in the microchannel was established with the Euler-Lagrange method. The numerical simulation was carried out with the slip boundary applied at the channel wall. The micro-scale effect on the gas-particle flow was studied based on the numerical prediction. The aim of this work is to provide a fundamental understanding of the flow and heat transfer characteristics of gas-particle fluid in the slip regime. KEYWORDS: Gas-particle fluid, Two-phase flow, Heat transfer, Slip regime, Numerical modeling 1. INTRODUCTION The transport characteristic of microscale gas-particle two-phase flow plays an important role in the innovative micro devices, such as solid propellant micro thruster and micro combustor, etc. [1, 2]. Microscale flow and heat processes in gas-particle fluid have attracted more and more attentions in recent years due to its significant difference compared with that in the macro-scale fluid flow. The fundamental phenomenon was still not clearly understood in the previous studies. The flow and heat transfer between gas and micro particles has been investigated [3, 4]. In the work of Barber et al. [5], a formulation of the slip boundary condition was presented, which can be applied to a generalized curved surface. It was accomplished by recasting Maxwell s slip-velocity equation as a function of the local wall shear stress and it can be applied on the micro particle surface. Hosseini et al. [6] applied the velocity slip boundary condition for the gas flow regime to the Navier-Stokes equations to obtain the particle deposition in the micro channel, in which the heat transfer process was not considered in the numerical model. The previous work has proved that the rarefaction effect has significant influence on the fluid properties, flow status and heat transfer process [7]. For the slip flow regime (Knudsen number = 0.001-0.1), the rarefaction effects should be considered in the numerical modeling. The continuum assumption still works but the local thermodynamic equilibrium in the near-wall region is not valid any more (but the linear stress strain relationship is still valid). The no-slip boundary applied on the gas-solid interface is not suitable, which means the gas velocity at the interface is not zero and the gas temperature at the interface is not equal to the solid surface temperature. In this paper, a numerical model of gas-particle two-phase fluid flow in a microchannel has been established. The simulations were carried out under different operating conditions. The influence of the micro scale effects was studied based on the numerical predictions. The aim of this work is to provide a fundamental understanding of flow and heat transfer characteristics of gas-particle fluid in the microchannel and reveal the rarefaction effect of the gasparticle flow in the slip regime. 1
2. NUMERICAL MODEL The numerical modeling has been successfully utilized in the prediction of flow and heat transfer processes [8]. The Navier-Stokes equations were adopted to simulate the gas flow field: U g x + V g y = 0 (1) U ρ g (U g g + V U g x g ) = p g + U g y x μ( 2 + 2 U g ) (2) x 2 y 2 The energy equation can be expressed by: V ρ g (U g g + V V g x g ) = p g + μ V g y y ( 2 + 2 V g ) + ρ x 2 y gg (3) 2 T g t + div(t gv ) = k g ρ g c pg div( grad T g ) (4) As the characteristic dimension of micro device decreases, the collisions between molecules will be dominant in the micro scale fluid flow. The continuum assumption for the gas flow is not valid any more. The gas compressibility and rarefaction effect cannot be neglected in this case. And the fluid properties will be influenced by the Knudsen number, which is a dimensionless parameter (the ratio of gas mean free path to flow characteristic length): Kn = λ/l (5) To consider the parameter l in the expression of Kn, the flow characteristic length can be evaluated as a length scale of the flow geometry. For the gas flow predicted in this work, the equivalent diameter of micro channel was adopted as flow characteristic length in the numerical modeling. For gases, the mean free path λ is the average distance traveled by molecules between collisions. For an idea gas, the mean free path can be expressed as λ = KT 2πσ 2 P (6) in which the Boltzmann constant K = 1.38065 10 23,σ is the collision diameter of the molecules, T and P the temperature and pressure of the gas phase. In this work, the gas flow is in the slip flow regime, which considers the non-continuum temperature and velocity phenomena. For the prediction of the flow and heat transfer of gas flow in the slip flow regime, the N-S equations and the Fourier law were adopted in the predication in gas flow region. The velocity slip and temperature jump boundary conditions were adopted near micro channel wall. It has been proved that the first order velocity slip and temperature jump boundary conditions are accurate enough to predict the gas flow in slip flow regime (10 3 < Kn < 10 1 ) [7]. The Maxwell velocity slip boundary condition can be expressed as: U w U g = 2 α v Kn U α v n (7) where U g is the gas velocity at the solid surface and U w is the velocity of the wall. α v is tangential momentum accommodation coefficient, which is equal to 1 assuming that the wall is fully diffuse surface. (8) The temperature jump boundary condition can be expressed as: 2
T w T g = 2( 2 α T )Kn T α T n (9) Where T g is the gas temperature at the solid surface and T w is the temperature of the wall. α T is the thermal accommodation coefficient. The force balance on the particle in the Lagrangian method is defined as du p dt The drag, Brownian, and lifting force are calculated as = g ρ p ρ y + F ρ D(U U p ) + F B + F L (10) F D = 18μ C C ρ p d p 2 (11) F B = ξ 0 πs 0 Δt (12) F L = 2kV0.5 ρd ij ρ p d p (d ij d ik ) 0.25 (V V p ) (13) A heat balance is established to relate the particle temperature to the convective heat transfer at the particle surface. in which the heat transfer coefficient h is determined by m p C p dt p dt = ha p(t g T p ) (14) Nu = hd p k g = 2.0 + 0.6Re d 1/2 Pr 1/3 (15) The Euler-Lagrange approach is adopted in the numerical modeling. The fluid phase was treated as a continuum solving with the Navier-Stokes equations, while the dispersed phase was solved by tracking a large number of particles. The dispersed phase can exchange momentum and energy with the gas phase. The physical model is shown in Fig.1. The gas flows into a channel with a diameter of 6.8 μm, for which the Kn number is approximately at the value of 0.01. The slip boundary was applied at the micro channel wall to consider the micro effect. Fig. 1 Geometry and boundary condition. 3
3. RESULTS AND DISCUSSION The velocity and temperature distributions of pure gas flow in the microchannel are shown in Fig. 2. The gas temperature decreases rapidly due to the small specific heat of gas and high surface area-volume ratio of the microchannel. Fig. 3 shows clearly that the velocity slip and temperature jump occur at the microchannel wall. And the gas flow velocity and temperature distribution varies as the slip boundaries are applied compared with those as the no slip boundaries are applied. Fig. 2 Velocity and temperature distributions in the pure gas flow. (a) Velocity (b) Tempertaure Fig. 3 Comparison of pure gas flow and heat transfer with/without slip boundaries. Figure 4 shows the velocity and temperature distributions of particle flow in the microchannel. The particle velocity distribution is similar to that of the gas phase. At the inlet, the particle distribution is influenced by the velocity distribution, and the particle will then move randomly due to the effects of drag, Brownian and lifting force. The particle temperature decreases rapidly as it is injected into the gas flow, which is similar to that of gas phase. Fig. 4 Velocity and temperature distributions in the particle flow. 4
Figure 5 shows that the gas velocity distribution varies obviously at X = 4 μm, for which the particles (diameter=0.01 μm) are injected into the gas flow. The temperature difference cannot be clearly observed in Fig. 5(b) as the particles are injected. It can be concluded that the injected particle has an obvious influence on the flow characteristic compared to that on the heat transfer process. (a) Velocity (b) Tempertaure Fig. 5 Comparison of gas velocity and temperature with/without particles. 4. CONCLUSIONS A numerical model was established to predict flow and heat transfer processes of gas-particle flow in the slip regime. The results show that the gas velocity slip and temperature jump occurs at the microchannel wall and the gas temperature decreases rapidly due to the small specific heat of gas and high surface area-volume ratio of the microchannel. As the particles are injected into the flow field, the gas velocity varies obviously but the heat transfer process variation cannot be observed clearly. The gas-particle fluid flow and heat transfer processes in the slip regime are influenced by the discontinuity at the microchannel wall and the interaction between particle and gas phase. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China through grant nos. 51676124, 51536005 & 51521004. REFERENCE [1] A. Chaalane, R. Chemam, M. Houabes, R. Yahiaoui, A. Metatla, B. Ouari, N. Metatla, D. Mahi, A. Dkhissi, D. Esteve, A MEMS-based solid propellant microthruster array for space and military applications, in: 15th International Conference on Micro and Nanotechnology for Power Generation and Energy Conversion Applications, PowerMEMS 2015, December 1, 2015 - December 4, 2015, Institute of Physics Publishing, Boston, MA, United states, 2015, pp. 012137. [2] E. Jiaqiang, Q. Peng, X. Zhao, W. Zuo, Z. Zhang, M. Pham, Numerical investigation on the combustion characteristics of non-premixed hydrogen-air in a novel micro-combustor, Applied Thermal Engineering, 110 (2017) 665-677. [3] R.W. Barber, D.R. Emerson, Numerical Simulation of Low Reynolds Number Slip Flow Past a Confined Microsphere, AIP Conference Proceedings, 663(1) (2003) 808-815. [4] P. Wang, X. Yao, H. Yang, M. Zhang, Impact of particle properties on gas solid flow in the whole circulating fluidized bed system, Powder Technology, 267 (2014) 193-200. [5] R.W. Barber, Y. Sun, X.J. Gu, D.R. Emerson, Isothermal slip flow over curved surfaces, Vacuum, 76(1) (2004) 73-81. [6] S.M.J. Hosseini, A.S. Goharrizi, B. Abolpour, Numerical study of aerosol particle deposition in simple and converging diverging microchannels with a slip boundary condition at the wall, Particuology, 13 (2014) 100-105. [7] Z. Liu, J. Zhou, K. Hu, W. H., Numerical Simulation of Gaseous Flow around Micro-Spherical Particle in the Slip Regime, in: The First International Workshop on Computational Particle Technology and Multiphase Processes, March 9-12, 2016, Suzhou, China, 2016. [8] Z. Liu, H. Wu, Pore-scale study on flow and heat transfer in 3D reconstructed porous media using micro-tomography images, Applied Thermal Engineering, 100 (2016) 602-610. 5