Abstract: Dispersion and deposition of micro- or nano-scaled particles in a sudden expansion and attraction square pore were investigated, especially in different natural convection cases. Both the flow and temperature fields were simulated by using the lattice Boltzmann method (LBM).A two dimensional D2Q9 BGK model was used in the simulation. In addition to drag force, Saffman force and gravity,Brownian force was also taken into account due to the small size of particles. The trajectories of particles in the vortical flow field in a sudden small expansion and attraction square pore were simulated with the same Reynolds number,different Rayleigh numbers(Ra=10²—10⁵),different Stokes numbers(Stk=0.001,0.01,0.1,1，that was,particle diameters were respectively 5.5 μm,17.4 μm,54.8 μm,174 μm).In addition,the number and the position of deposited particles on the bottom with natural convection were analyzed by comparing with the case without natural convection. Moreover,the total deposition efficiencies were obtained under various Ra and Stk values. The results showed that the trajectories of particles varied with different Stokes numbers,but with the same Reynolds numbers. The Ra number showed a strong influence on deposition efficiency while Stk number was less than 0.1,and the deposition efficiency did not show a monotonic change with a decrease of Stk number. Natural convection in the present configuration could either increase or decrease the total deposition efficiency compared with the isothermal case. An intense natural convection could result in a high deposition efficiency, especially for the case of low Stokes number and high Rayleigh number. The goal of the paper was to give a preliminary explanation for the injectivity reduction of a reinjection well in geothermal uses, and the results also indicated that the blocking due to particle deposition in a pore happened easier while injecting cold water. This is true in many realistic reinjection tests for geothermal uses.Dispersion and deposition of micro- or nano-scaled particles in a sudden expansion and attraction square pore were investigated, especially in different natural convection cases. Both the flow and temperature fields were simulated by using the lattice Boltzmann method (LBM).A two dimensional D2Q9 BGK model was used in the simulation. In addition to drag force, Saffman force and gravity,Brownian force was also taken into account due to the small size of particles. The trajectories of particles in the vortical flow field in a sudden small expansion and attraction square pore were simulated with the same Reynolds number,different Rayleigh numbers(Ra=10²—10⁵),different Stokes numbers(Stk=0.001,0.01,0.1,1，that was,particle diameters were respectively 5.5 μm,17.4 μm,54.8 μm,174 μm).In addition,the number and the position of deposited particles on the bottom with natural convection were analyzed by comparing with the case without natural convection. Moreover,the total deposition efficiencies were obtained under various Ra and Stk values. The results showed that the trajectories of particles varied with different Stokes numbers,but with the same Reynolds numbers. The Ra number showed a strong influence on deposition efficiency while Stk number was less than 0.1,and the deposition efficiency did not show a monotonic change with a decrease of Stk number. Natural convection in the present configuration could either increase or decrease the total deposition efficiency compared with the isothermal case. An intense natural convection could result in a high deposition efficiency, especially for the case of low Stokes number and high Rayleigh number. The goal of the paper was to give a preliminary explanation for the injectivity reduction of a reinjection well in geothermal uses, and the results also indicated that the blocking due to particle deposition in a pore happened easier while injecting cold water. This is true in many realistic reinjection tests for geothermal uses.

Key words: square pore, lattice Boltzmann method, micro/nano particles, deposition, natural convection

关键词: 方形孔隙, 格子Boltzmann方法, 微纳米颗粒, 沉积, 自然对流