1D, 2D and 3D numerical simulations were carried out with the Reynolds-Averaged Navier-Stokes equations (RANS) for horizontal oil-water core-annular flow in which the oil core stays laminar while the water layer is turbulent. The turbulence is described with the Launder-Sharma low-Reynolds number $k-ϵ$ model. The simulation results are compared with experiments carried out in our lab in a 21 mm diameter pipe using oil and water with a viscosity ratio of 1150 and a density ratio of 0.91. The 1D results represent perfect turbulent CAF (i.e. no gravity, no interfacial waves), the 2D results represent axi-symmetric CAF (i.e. no gravity, with interfacial waves), and the 3D results represent eccentric CAF (i.e. with gravity, with interfacial waves). The simulation results typically show a turbulent water annulus in which the structure of the (high-Reynolds number) inertial sublayer can be recognized. The pressure drop reduction factor (which is the ratio between the pressure drop for CAF and the pressure drop for single phase viscous oil flow) for the 2D and 3D results is about the same, but its value is about 35% higher than in the experiment. The hold-up ratio in the 3D model is close to the experimental value, but the 2D prediction is slightly lower. The eccentricity predicted by the 3D simulations is much higher than in the experiment. Most likely, the observed differences between the simulations and the experiments are due to limitations of using a low-Reynolds number $k-ϵ$ model. In particular the water layer at the top in the 3D results shows a relaminarization, which might be absent in the experiment.

使用雷诺-平均纳维-斯托克斯方程 (RANS) 对水平油水芯环流进行 1D、2D 和 3D 数值模拟，其中油芯保持层流而水层是湍流。湍流用 Launder-Sharma 低雷诺数描述$克-\epsilon$模型。将模拟结果与我们实验室在直径为 21 mm 的管道中使用粘度比为 1150 和密度比为 0.91 的油和水进行的实验进行了比较。一维结果代表完美湍流 CAF（即无重力，无界面波），二维结果代表轴对称 CAF（即无重力，有界面波），3D 结果代表偏心 CAF（即有重力，有界面波） ）。模拟结果通常显示湍流水环，其中可以识别（高雷诺数）惯性子层的结构。2D 和 3D 结果的压降减少因子（CAF 的压降与单相粘性油流的压降之比）大致相同，但其值比实验中高出约 35% . 3D 模型中的hold-up 比接近实验值，但 2D 预测略低。3D 模拟预测的偏心率远高于实验。最有可能的是，观察到的模拟和实验之间的差异是由于使用低雷诺数的限制$克-\epsilon$模型。特别是 3D 结果中顶部的水层显示了重新分层，这在实验中可能不存在。