The Solely Use of the “Hydraulic-Diameter” Concept Is Not Sufficient to Describe Correctly Non-Symmetric Flow in Conduits

作     者：Christos Krimizis-Tsatsoulis Christos Krimizis-Tsatsoulis

作者机构：Alchimica S.A. R&D department Athens Greece 

出 版 物：《Open Journal of Fluid Dynamics》 (流体动力学（英文）)

年 卷 期：2021年第11卷第4期

页      面：210-250页

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

主　　题：Fluid Mechanics Hydraulic Diameter Flow in Annuli Flow in Ducts Flow of Two Adjacent Immiscible Fluids Eigenvectors-Eigenvalues 

摘      要：A well-known cornerstone in fluid mechanics is the equations that relate the friction factor to the Reynolds number obtained from the measurements in cylindrical cross-sectional tubes. The extension of these equations to different geometries failed to give reliable results. The introduction of the Hydraulic Diameter has fixed this issue particularly for the square ducts. However, for non-symmetric flows, as in concentric annuli, the discrepancies were unacceptable. Several attempts have been made to fix these problems with finally the introduction of a new concept like, “Laminar Equivalent Hydraulic Diameter or “Efficient Hydraulic Diameter provided satisfactory results. This approach seems to have fixed the problem and hence has been widely accepted. Nevertheless, it is based on a non-robust theoretical argument. In the present paper, it has been demonstrated that the solely use of the “Hydraulic Diameter concept is insufficient to describe non-symmetric flows as in concentric annuli. It appears the need to use the Z axis component of the skew driving force for the laminar flow and the parameter λ for the turbulent one. At the same time, instead, it has been shown that in the case of flow in square and rectangular ducts, the “Hydraulic Diameter is sufficient to describe it. In this case, the flow is practically symmetric. Moreover, several new straightforward equations are provided, which simplify a lot dealing with non-cylindrical cross-sectional conduits. In doing so, the concept of “Eigenvectors-Eigenvalues has been implemented. This theoretical approach could help to simplify other non-symmetric cases in fluid dynamics. To mention, “Flow past immersed non-symmetric bodies, “Flow in curved conduits etc.