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

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.