The calculation of mechanical energy loss for incompressible steady pipe flow of homogeneous fluid

The calculation of the mechanical energy loss is one of the fundamental problems in the field of Hydraulics and Engineering Fluid Mechanics. However, for a non-uniform flow the relation between the mechanical energy loss in a volume of fluid and the kinematical and dynamical characteristics of the flow field is not clearly established. In this paper a new mechanical energy equation for the incompressible steady non-uniform pipe flow of homogeneous fluid is derived, which includes the variation of the mean turbulent kinetic energy, and the formula for the calculation of the mechanical energy transformation loss for the non-uniform flow between two cross sections is obtained based on this equation. This formula can be simplified to the Darcy-Weisbach formula for the uniform flow as widely used in Hydraulics. Furthermore, the contributions of the mechanical energy loss relative to the time averaged velocity gradient and the dissipation of the turbulent kinetic energy in the turbulent uniform pipe flow are discussed, and the contributions of the mechanical energy loss in the viscous sublayer, the buffer layer and the region above the buffer layer for the turbulent uniform flow are also analyzed.

Theoretical analysis and numerical simulation of mechanical energy loss and wall resistance of steady open channel flow

The mechanical energy loss and the wall resistance are very important in practical engineering. These problems are investigated through theoretical analysis and numerical simulation in this paper, The results are as follows. （1） A new mechanical energy equation for the total flow is obtained, and a general formula for the calculation of the mechanical energy loss is proposed. （2） The general relationship between the wall resistance and the mechanical energy loss for the steady channel flow is obtained, the simplified form of which for the steady uniform channel flow is in consistent with the formula used in Hydraulics deduced by 7r theorem and dimensional analysis. （3） The steady channel flow over a backward facing step with a small expansion ratio is numerica- lly simulated, and the mechanical energy loss, the wall resistance as well as the relationship between the wall resistance and the mechanical energy loss are calculated and analyzed.

Numerical simulation of turbulent flow behind sluice gate under submerged discharge conditions

The turbulent flow discharging under a sluice gate is one kind of typical flows with complicated boundaries in hydraulic and hydroelectric engineering, and the characteristics of its flow field and flow evolution are important in engineering hydraulics. Although there were many studies in this regard, which mainly focus on the discharge capacity, the local scour and the mean flow field, some issues remain to be further investigated, for example, the variation of the mechanical energy during the scouring process, and the adjustment of the unsteady turbulent flow after the local scour with the downstream steady uniform flow. In this paper, the turbulent flow behind a sluice gate is divided into a rapidly varied flow region and a gradually varied flow region, and the above problems are investigated by theoretical analysis and numerical simulation. The main conclusions are as follows：（1） In the discharging process of the turbulent flow under a sluice gate, the river bed would be scoured continuously and the water–air interface is adjusted accordingly, which leads to a decrease of the mechanical energy of the total flow in the rapidly varied flow region, and the mechanical energy loss would also decrease with the increase of the time, yet the variation of the flow discharge under the sluice gate is very small.（2） In the link between the rapidly varied flow and the uniform flow downstream, the mean wall shear stress and the coefficient for the mechanical energy loss would decrease in the longitudinal direction, the decay of the turbulent kinetic energy near the free surface is much more significant than that near the bed in the longitudinal direction, and the mean turbulent kinetic energy in the section would decrease in the longitudinal direction and the decreasing rate is smaller than that of the mean wall shear stress.