We study the flow behavior of a Newtonian fluid in a planar 4:1 contraction channel using two numerical methodologies: the two-relaxation time lattice Boltzmann method (TRT-LBM) and the finite element method (FEM). To confirm the validity of the TRT-LBM, hydrodynamic quantities such that velocity, pressure, and vortex are carefully investigated at the wide ranges of Reynolds numbers (Re = 0.1–100). At first, we analyze the velocity along the channel. The results of TRT-LBM look reasonable and also coincide with the analytical solution and FEM results. Richer features are observed in the pressure profile along the flow direction. At low Reynolds numbers, the one-step change of the slope in the pressure profile is observed near the contraction region. The slope gradually grows up with the increase of Reynolds numbers, and eventually, this evolves the two-step change. Non-monotonic behavior is observed in the characteristics of the vortex. The size of the vortex non-linearly decreases as the Reynolds number increases. Also, the center of the vortex gradually moved toward the corner of the channel as an increase of Reynolds numbers with non-linearity. Not only the velocity and the pressure profiles but also the characteristics of the vortex quantitatively coincide in TRT-LBM and FEM results. Through this study, we confirm the robustness of the TRT-LBM as a simulation tool to investigate inertial flow in a planar contraction geometry.

我们使用两种数值方法研究牛顿流体在平面 4:1 收缩通道中的流动行为：双弛豫时间格子玻尔兹曼法 (TRT-LBM) 和有限元法 (FEM)。为了确认 TRT-LBM 的有效性，在广泛的雷诺数 (Re = 0.1–100) 范围内仔细研究了速度、压力和涡流等流体动力学量。首先，我们分析沿通道的速度。TRT-LBM 的结果看起来很合理，也与解析解和 FEM 结果一致。在沿流动方向的压力剖面中观察到更丰富的特征。在低雷诺数下，在收缩区域附近观察到压力剖面斜率的一步变化。随着雷诺数的增加，斜率逐渐增大，最终，这演变了两步变化。在涡流的特征中观察到非单调行为。随着雷诺数的增加，涡流的大小呈非线性减小。随着雷诺数的增加，涡旋中心逐渐向通道拐角移动，呈非线性。在 TRT-LBM 和 FEM 结果中，不仅速度和压力分布，而且涡流的特征在数量上也是一致的。通过这项研究，我们证实了 TRT-LBM 作为研究平面收缩几何中的惯性流的模拟工具的稳健性。随着雷诺数的增加，涡旋中心逐渐向通道拐角移动，呈非线性。在 TRT-LBM 和 FEM 结果中，不仅速度和压力分布，而且涡流的特征在数量上也是一致的。通过这项研究，我们证实了 TRT-LBM 作为研究平面收缩几何中的惯性流的模拟工具的稳健性。随着雷诺数的增加，涡旋中心逐渐向通道拐角移动，呈非线性。在 TRT-LBM 和 FEM 结果中，不仅速度和压力分布，而且涡流的特征在数量上也是一致的。通过这项研究，我们证实了 TRT-LBM 作为研究平面收缩几何中的惯性流的模拟工具的稳健性。