层流单分支管路流量分配的理论分析与CFD模拟

Theoretical analysis and CFD simulation on flow distribution in single-branch pipelines under laminar flow condition

摘要:

为揭示层流状态下单分支管路的流量分配规律，本文采用理论分析与数值模拟相结合的方法，基于并联管路压降平衡假设，结合Darcy-Weisbach公式与层流本构关系，推导得出流量配比理论公式，揭示了流量分配与管径四次方成正比、与管长成反比的定量关系。通过CFD数值模拟对不同几何参数及不同注入流量工况进行验证，结果表明：仿真值与理论值的最大误差小于5%，证实了理论模型具备良好的工程适用性；流量分配比例仅由几何参数决定，与注入流量无关。本研究可为分支井结构优化提供理论依据，所提出的方法亦可扩展至多分支管路系统分析。后续研究将延伸至湍流模型及动态流动过程，以进一步提升模型的适用广度。

Abstract:

To elucidate the governing principles of flow distribution within a single-branch pipe under laminar flow， this paper presents a comprehensive investigation combining theoretical analysis and numerical simulation. Grounded in the principle assumption of pressure drop equilibrium in parallel pipelines， a theoretical expression for the flow rate ratio was deduced by integrating the Darcy-Weisbach equation with the laminar flow constitutive relation. This expression establishes a quantitative correlation， indicating that the flow distribution is proportional to the fourth power of the pipe diameter and inversely proportional to its length. The robustness of the theoretical model was rigorously examined via CFD simulations under diverse geometric parameters and injection flow conditions. The results demonstrated a maximum discrepancy of below 5% between simulated and theoretical values， thereby affirming the model’s practical utility for engineering applications. Furthermore， it was concluded that the flow distribution ratio is an intrinsic property dictated exclusively by geometric parameters， showing insensitivity to the injection flow rate. The findings herein offer a robust theoretical underpinning for the structural optimization of branch wells， and the proposed methodology is extensible to more complex， multi-branch pipeline networks. Subsequent research will be directed towards turbulent models and dynamic flow processes to enhance the model’s universality.