The mechanical energy balance and energy loss have attracted significant attention in the literature. The general form of the energy equation has been previously presented; however, in most applications the simplified 1-D form without considering the details of turbulent flows has been applied. In this study, a form of the total mechanical energy balance equation for 3-D turbulent flows in open-channels is investigated in which all turbulence parameters involving the effects of the secondary currents can be evaluated by using equalizations that have not previously been applied to the total mechanical energy equation and RANS turbulence models. Based on the equalizations, the existing correlations in the total energy equation are replaced with a combination of mean flow variables and known turbulence parameters from turbulent flow numerical simulations. Therefore, the details of the total mechanical energy balance for 3-D turbulent flows in open-channels with different geometries can be analyzed using the proposed methodology. Then, an explicit relationship for the energy loss, usually determined empirically, is derived from the developed energy equation. In order to investigate the utilization of the analytical relationships, 3-D numerical simulations are performed using OpenFOAM to solve the Navier–Stokes equations with the RSM turbulence model. By applying the analytical relationship and the simulation results, the mechanical energy losses are obtained and compared with the energy losses from the previous energy equations, the effect of the various parameters on the total mechanical energy balance is studied, the role of wall resistance in the mechanical energy is investigated and efforts are made to identify the parameters affecting the local and friction losses of turbulent flows in the irregular open-channels. Finally, a deeper understanding of the details of the energy transformation process and the mechanical energy loss of the complex flows is achieved.

机械能平衡和能量损失在文献中引起了极大的关注。能量方程的一般形式之前已经介绍过；然而，在大多数应用中，应用了简化的一维形式而不考虑湍流的细节。在这项研究中，研究了开放通道中 3-D 湍流的总机械能平衡方程的一种形式，其中所有涉及次级电流影响的湍流参数都可以通过使用以前未应用于的均衡来评估总机械能方程和RANS湍流模型。基于均衡，总能量方程中现有的相关性被平均流动变量和湍流数值模拟中已知的湍流参数的组合所取代。因此，可以使用所提出的方法分析具有不同几何形状的明渠中的 3-D 湍流的总机械能平衡的细节。然后，通常根据经验确定的能量损失的显式关系是从开发的能量方程中得出的。为了研究分析关系的利用，使用 OpenFOAM 进行 3-D 数值模拟，以使用 RSM 湍流模型求解 Navier-Stokes 方程。通过应用解析关系和模拟结果，获得了机械能损失，并与之前的能量方程的能量损失进行了比较，研究了各种参数对总机械能平衡的影响，研究了壁阻力在机械能中的作用，并努力识别影响不规则明渠湍流局部损失和摩擦损失的参数。最后，对能量转换过程的细节和复杂流动的机械能损失有了更深入的了解。研究了壁阻力在机械能中的作用，并努力确定影响不规则明渠中湍流局部和摩擦损失的参数。最后，对能量转换过程的细节和复杂流动的机械能损失有了更深入的了解。研究了壁阻力在机械能中的作用，并努力确定影响不规则明渠中湍流局部和摩擦损失的参数。最后，对能量转换过程的细节和复杂流动的机械能损失有了更深入的了解。