In the metallurgical industries, it is very important to characterize the flow of molten metals in open channels given that they are transported through these devices to different plant sections. Howeve...In the metallurgical industries, it is very important to characterize the flow of molten metals in open channels given that they are transported through these devices to different plant sections. However, unlike the flow of water which has been studied since ancient times, the flow of molten metals in open channels has received little attention. The unsteady non-uniform flow of blast furnace molten pig iron in a rectangular open channel is analyzed in this work by numerical solution of the Saint-Venant equations. The influence of mesh size on the convergence of molten metal height is studied to determine the proper mesh and time step sizes. A sinusoidal inflow pulse is imposed at the entrance of the channel in order to analyze the propagation of the resulting wave. The influence of the angle of inclination of the channel and the roughness coefficient of the walls on the amplitude and the dynamic behavior of the height of the molten metal are analyzed. Phase portraits of the channel state variables are constructed and interpreted. Numerical simulations show that as the angle of inclination of the channel increases, the amplitude of the formed wave decreases. From 10 degrees onwards, the peak of the wave descends even below the initial height. On the other hand, the roughness coefficient affects the molten pig iron height profiles in an inverse way than the angle of inclination. The amplitude of the formed wave increases as the roughness coefficient increases.展开更多
The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Th...The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.展开更多
Most unsteady channel flows in nature and practical engineering appear as gradually varied ones,and in the free surface,the deformation conforms to the long wave hypothesis.One-dimensional total flow models were usual...Most unsteady channel flows in nature and practical engineering appear as gradually varied ones,and in the free surface,the deformation conforms to the long wave hypothesis.One-dimensional total flow models were usually used to for the numerical simulation of long-term and long-distance reaches to describe the water movements,however,the models lack a clear relationship between the three-dimensional flow field and the total flow field.Moreover,few studies of the variations of the roughness coefficient against the time in unsteady flows were conducted.The following results are obtained through the theoretical analysis and the numerical simulations in this paper.(1) One-dimensional total flow control equations of the unsteady gradually varied flow in open channels are obtained directly from the mathematical model of the viscous fluid motion,and can both reflect the influence of the turbulence and provide an explicit expression of the energy slope term.These equations establish a direct connection between the descriptions of the three-dimensional flow fields and the one-dimensional total flows.(2) Synchronous prototype observation data and planar two-dimensional numerical simulation results are used to extract the one-dimensional total flow information and discuss the total flow characteristics.(3)The orders of magnitude for terms in the total flow motion equation are compared,and the variation of the roughness coefficient against the time is analyzed.展开更多
文摘In the metallurgical industries, it is very important to characterize the flow of molten metals in open channels given that they are transported through these devices to different plant sections. However, unlike the flow of water which has been studied since ancient times, the flow of molten metals in open channels has received little attention. The unsteady non-uniform flow of blast furnace molten pig iron in a rectangular open channel is analyzed in this work by numerical solution of the Saint-Venant equations. The influence of mesh size on the convergence of molten metal height is studied to determine the proper mesh and time step sizes. A sinusoidal inflow pulse is imposed at the entrance of the channel in order to analyze the propagation of the resulting wave. The influence of the angle of inclination of the channel and the roughness coefficient of the walls on the amplitude and the dynamic behavior of the height of the molten metal are analyzed. Phase portraits of the channel state variables are constructed and interpreted. Numerical simulations show that as the angle of inclination of the channel increases, the amplitude of the formed wave decreases. From 10 degrees onwards, the peak of the wave descends even below the initial height. On the other hand, the roughness coefficient affects the molten pig iron height profiles in an inverse way than the angle of inclination. The amplitude of the formed wave increases as the roughness coefficient increases.
文摘The Singular Integral Operators Method (S.I.O.M.) is applied to the determination of the free-surface profile of an un-steady flow over a spillway, which defines a classical hydraulics problem in open channel flow. Thus, with a known flow rate Q, then the velocities and the elevations are computed on the free surface of the spillway flow. For the numerical evaluation of the singular integral equations both constant and linear elements are used. An application is finally given to the determination of the free-surface profile of a special spillway and comparing the numerical results with corresponding results by the Boundary Integral Equation Method (B.I.E.M.) and by using experiments.
文摘Most unsteady channel flows in nature and practical engineering appear as gradually varied ones,and in the free surface,the deformation conforms to the long wave hypothesis.One-dimensional total flow models were usually used to for the numerical simulation of long-term and long-distance reaches to describe the water movements,however,the models lack a clear relationship between the three-dimensional flow field and the total flow field.Moreover,few studies of the variations of the roughness coefficient against the time in unsteady flows were conducted.The following results are obtained through the theoretical analysis and the numerical simulations in this paper.(1) One-dimensional total flow control equations of the unsteady gradually varied flow in open channels are obtained directly from the mathematical model of the viscous fluid motion,and can both reflect the influence of the turbulence and provide an explicit expression of the energy slope term.These equations establish a direct connection between the descriptions of the three-dimensional flow fields and the one-dimensional total flows.(2) Synchronous prototype observation data and planar two-dimensional numerical simulation results are used to extract the one-dimensional total flow information and discuss the total flow characteristics.(3)The orders of magnitude for terms in the total flow motion equation are compared,and the variation of the roughness coefficient against the time is analyzed.
