Abstract The objectives of the present paper are to accurately determine the modifications to a three-dimensional flow field caused by a bifurcation module, to study the downstream evolution of the generated flow field, and to enhance understanding by establishing the individual and combined roles of five factors (viz. curvature of flow path, flow division at the bifurcation ridge, possible change in flow area from mother to daughter branches, complex shape changes in the bifurcation and inertia of the flow) in giving rise to such a flow field in the bifurcation module. The effects of the aforementioned five factors on the loss production in a bifurcation module and on the potential of further loss in downstream units are also studied, and new correlations are developed. The detailed analysis is systematized here by establishing two novel methods of construction of a bifurcation, viz. “co-joining of two bent pipes” and “splitter in a pipe”, and by formally deriving the equivalence condition for the flow in a bifurcation and its constituent elements. Through this systematization an attempt is made to understand comprehensively the complexity of the fluid dynamics occurring in a single bifurcation, which is often masked in the usual studies of flow in large bifurcating networks. Several bifurcation geometries are studied, and about 500 separate three-dimensional computations are performed to achieve a degree of generalization. Use of fine grid (with up to 20 million computational elements in some simulations), double-precision arithmetic and stringent convergence criteria ( 10 − 8 for each scaled residual) ensures high accuracy of the computed solutions. Both primary and secondary flow fields are investigated. Flow path curvature is responsible for the development of Dean-type secondary motion while flow division at the bifurcation ridge generates secondary motion opposite to that induced by curvature. An increase of flow area from inlet to outlet results in an increase of asymmetry in cross-sectional velocity distribution. Although the loss across a bifurcation may sometimes be smaller than that across its constituent elements, it is shown here through the introduction of two parameters that a greater potential for incurring losses in a following straight section is generated in the bifurcation.

中文翻译：

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分岔的流体动力学

摘要 本文的目的是准确确定由分叉模块引起的三维流场的修改，研究生成的流场的下游演化，并通过建立五个单独和组合的角色来增强理解。在分叉处产生这种流场的因素（即流动路径的曲率、分叉脊处的分流、从母分支到子分支的流动面积可能发生的变化、分叉的复杂形状变化和流动的惯性）模块。还研究了上述五个因素对分叉模块中的损失产生和下游单元进一步损失的可能性的影响，并开发了新的相关性。详细的分析在这里通过建立两种新的分岔构造方法进行系统化，即。“两个弯管的共同连接”和“管道中的分流器”，并通过形式上推导出分叉处的流动及其组成元素的等效条件。通过这种系统化，试图全面了解发生在单个分叉中的流体动力学的复杂性，这通常在大型分叉网络中的流动研究中经常被掩盖。研究了几个分岔几何，并执行了大约 500 个单独的三维计算以实现一定程度的泛化。使用精细网格（在某些模拟中使用多达 2000 万个计算元素），双精度算术和严格的收敛标准（每个缩放残差为 10 - 8）确保计算解决方案的高精度。主要和次要流场都进行了研究。流动路径曲率负责迪安型二次运动的发展，而分叉脊处的分流产生与曲率引起的二次运动相反的二次运动。从入口到出口流动面积的增加导致横截面速度分布的不对称性增加。尽管分叉处的损失有时可能小于其组成元素的损失，但这里通过引入两个参数表明，分叉处产生的后续直线段中发生损失的可能性更大。主要和次要流场都进行了研究。流动路径曲率负责迪安型二次运动的发展，而分叉脊处的分流产生与曲率引起的二次运动相反的二次运动。从入口到出口流动面积的增加导致横截面速度分布的不对称性增加。尽管分叉处的损失有时可能小于其组成元素的损失，但这里通过引入两个参数表明，分叉处产生的后续直线段中发生损失的可能性更大。主要和次要流场都进行了研究。流动路径曲率负责迪安型二次运动的发展，而分叉脊处的分流产生与曲率引起的二次运动相反的二次运动。从入口到出口流动面积的增加导致横截面速度分布的不对称性增加。尽管分叉处的损失有时可能小于其组成元素的损失，但这里通过引入两个参数表明，分叉处产生的后续直线段中发生损失的可能性更大。流动路径曲率负责迪安型二次运动的发展，而分叉脊处的分流产生与曲率引起的二次运动相反的二次运动。从入口到出口流动面积的增加导致横截面速度分布的不对称性增加。尽管分叉处的损失有时可能小于其组成元素的损失，但这里通过引入两个参数表明，分叉处产生的后续直线段中发生损失的可能性更大。流动路径曲率负责迪安型二次运动的发展，而分叉脊处的分流产生与曲率引起的二次运动相反的二次运动。从入口到出口流动面积的增加导致横截面速度分布的不对称性增加。尽管分叉处的损失有时可能小于其组成元素的损失，但这里通过引入两个参数表明，分叉处产生的后续直线段中发生损失的可能性更大。