An anaerobic baffled reactor is a system developed in recent decades and has been used as part of the treatment of high-strength wastewater. Since the function of this system is based on its hydrodynamic features, hyd...An anaerobic baffled reactor is a system developed in recent decades and has been used as part of the treatment of high-strength wastewater. Since the function of this system is based on its hydrodynamic features, hydrodynamics and the regime of the flow through the reactor are crucial. In this study, a prototype reactor with eight chambers, which had a total volume of 48 L, and a model reactor, whose dimensions were half of those of the prototype reactor, were used. The Froude dynamic similitude in these reactors was investigated. The results show that the curve dimensionless variances were 0.089 and 0.096 for the prototype and model reactors, respectively, the short-circuiting indices were 0.483 and 0.489 for the prototype and model reactors, respectively, the effective volume and short-circuiting index measurement errors were both 1%, the hydraulic efficiency error was 2%, and the Peclet and dispersion number errors were both 7%. Most of the compared indices were close to one another in value. Therefore, the model reactor can be used based on the Froude dynamic similitude to determine hydrodynamic charac-teristics of a baffled reactor at a full scale.展开更多
Froude similitude and friction similitude are the two crucial similarity conditions that are often used in physical-scale modeling of rivers.However,models often deviate from Froude similitude when dealing with real-w...Froude similitude and friction similitude are the two crucial similarity conditions that are often used in physical-scale modeling of rivers.However,models often deviate from Froude similitude when dealing with real-world situations.This study developed several fixed-bed river models with various curvatures to determine the effect of Froude similitude deviation on curved channel modeling.Models were constructed according to the characteristics of the Middle Yangtze River.Differences in longitudinal slope,transverse slope,and main stream line location were measured by varying Froude similitude deviation.The deviations of longitudinal slope and velocity were negligible because friction similitude was accounted for.The transverse slope varied significantly with the Froude similitude deviation,and the main stream line varied with the curvature and Froude similitude deviation.Formulae were derived to estimate the slope deviation.These analyses helped to clarify the feasibility of the method of Froude similitude deviation for curved channels.展开更多
To investigate the effect of the Froude number(Fr)on solid segregation in a rotating drum,a two dimensional mathematical modelling on solids behaviour in horizontally oriented rotating drums operated in rolling,cascad...To investigate the effect of the Froude number(Fr)on solid segregation in a rotating drum,a two dimensional mathematical modelling on solids behaviour in horizontally oriented rotating drums operated in rolling,cascading and cataracting modes has been carried out by using Euler-Euler multi-fluid model in Fluent6.2 environment.Small particles and big particles are used in the work as binary mixtures to investigate segregation characteristics.The effect of Froude number(rotating velocity)on the flow field is investigated.It is found that the model captures the main features of solids motion and segregation in the drum and numerical results agree well with limited experimental data for solid velocity.展开更多
A mathematically rigorous framework for singular limits of the magnetohydrodynamic rotating shallow water equations with ill-prepared data is developed when the Rossby and Froude numbers tend to zero at different rate...A mathematically rigorous framework for singular limits of the magnetohydrodynamic rotating shallow water equations with ill-prepared data is developed when the Rossby and Froude numbers tend to zero at different rates.The reduced systems are derived,respectively,for the stratification-dominant and the rotation-dominant cases by means of the developed three-scale fast averaging method.展开更多
By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For t...By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics（CFD） results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4？a/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.展开更多
Energy dissipations induced by the hydraulic jump and the trajectory jet are the most widely known as the two dissipation modes at the downstream of flood discharging structures, which are often considered quite diffe...Energy dissipations induced by the hydraulic jump and the trajectory jet are the most widely known as the two dissipation modes at the downstream of flood discharging structures, which are often considered quite different even contradictory. However, such two energy dissipators can be used jointly and harmonically. In this paper, a new type of stilling basin with a shallow-water cushion and a triangular bottom deflector is proposed based on two different scale physical model tests of the flood discharging tunnel No.2 of Luding hydropower project. The experimental results show that the flow regime of the hydraulic jump in the presented stilling basin with bottom deflector enjoys a good and stable performance within a large range of flow rates and the energy dissipation rate is considerably high as compared to the conventional stilling basin even at a low Froude number. The results also indicate that the stilling basin with triangular bottom deflector has a better performance in improving the potential cavitation erosion according to the analysis of the pressure and the cavitation number compared to the trapezoidal one. The proposed new type of shallow-cushion stilling basin with a shallow-water cushion can be applied in similar energy dissipation projects with low Froude number and large range of flow rates.展开更多
With respect to the crest spillway with large unit discharge and low Froude number, the hydraulics of the slit-type energy dissipater at the outlet should be noticed due to the complicated flow regimes. In the present...With respect to the crest spillway with large unit discharge and low Froude number, the hydraulics of the slit-type energy dissipater at the outlet should be noticed due to the complicated flow regimes. In the present paper, some issues about hydraulic characteristics were experimentally investigated by means of five slit-type outlets and four tetrahedrons, including the flow choking, impact to river banks and jet trajectory. The main findings are as follows. The critical Froude number for the flow choking decreases with increasing outlet width of the slit-type energy dissipater. If the flow Froude number is expressed by the parameters just before this energy dissipater, the tetrahedron placed inside the side wall of the outlet could efficiently avoid the flow impact to the river bank of same side, and compared with the jet trajectory of the slit-type energy dissipater, the outlet with tetrahedron has different trajectory trend, i.e., the distance of the jet trajectory decreases with the increase of the water head due to special form of the outlet tetrahedron.展开更多
In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asym...In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asymmetric trapezoidal flume with a length of 7 m and a width of 0.304 m is considered,with the bottom of the flume transversely inclined at an angle of m=0.296 and vertical lateral sides.The corresponding inflow Froude number is allowed to range in the interval(1.40<F1<6.11).The properties of this jump are compared to those of hydraulic jumps in channels with other types of cross-sections.A relationship for calculating hydraulic jump efficiency is proposed for the considered flume.For F1>5,the hydraulic jump is found to be more effective than that occurring in triangular and symmetric trapezoidal channels.Also,when■mes>8 and■>5,the hydraulic jump in the asymmetrical trapezoidal channel downstream of a parallelogram sluice gate is completely formed as opposed to the situation where a triangular sluice is considered.展开更多
文摘An anaerobic baffled reactor is a system developed in recent decades and has been used as part of the treatment of high-strength wastewater. Since the function of this system is based on its hydrodynamic features, hydrodynamics and the regime of the flow through the reactor are crucial. In this study, a prototype reactor with eight chambers, which had a total volume of 48 L, and a model reactor, whose dimensions were half of those of the prototype reactor, were used. The Froude dynamic similitude in these reactors was investigated. The results show that the curve dimensionless variances were 0.089 and 0.096 for the prototype and model reactors, respectively, the short-circuiting indices were 0.483 and 0.489 for the prototype and model reactors, respectively, the effective volume and short-circuiting index measurement errors were both 1%, the hydraulic efficiency error was 2%, and the Peclet and dispersion number errors were both 7%. Most of the compared indices were close to one another in value. Therefore, the model reactor can be used based on the Froude dynamic similitude to determine hydrodynamic charac-teristics of a baffled reactor at a full scale.
基金supported by the Project of Subsequent Work of the Three Gorges Project(Grant No.SXHXGZ-2020-3).
文摘Froude similitude and friction similitude are the two crucial similarity conditions that are often used in physical-scale modeling of rivers.However,models often deviate from Froude similitude when dealing with real-world situations.This study developed several fixed-bed river models with various curvatures to determine the effect of Froude similitude deviation on curved channel modeling.Models were constructed according to the characteristics of the Middle Yangtze River.Differences in longitudinal slope,transverse slope,and main stream line location were measured by varying Froude similitude deviation.The deviations of longitudinal slope and velocity were negligible because friction similitude was accounted for.The transverse slope varied significantly with the Froude similitude deviation,and the main stream line varied with the curvature and Froude similitude deviation.Formulae were derived to estimate the slope deviation.These analyses helped to clarify the feasibility of the method of Froude similitude deviation for curved channels.
基金Sponsored by the National Natural Science Foundation of China(Grant No.20606006)China Postdoctoral Science Foundation Funded Projectthe Scientific Research Foundation for the Returned Overseas Chinese Sochlars,State Education Ministry
文摘To investigate the effect of the Froude number(Fr)on solid segregation in a rotating drum,a two dimensional mathematical modelling on solids behaviour in horizontally oriented rotating drums operated in rolling,cascading and cataracting modes has been carried out by using Euler-Euler multi-fluid model in Fluent6.2 environment.Small particles and big particles are used in the work as binary mixtures to investigate segregation characteristics.The effect of Froude number(rotating velocity)on the flow field is investigated.It is found that the model captures the main features of solids motion and segregation in the drum and numerical results agree well with limited experimental data for solid velocity.
基金supported by Natural Science Foundation of China(12001506)the Natural Science Foundation of Shandong Province(ZR2020QA014).
文摘A mathematically rigorous framework for singular limits of the magnetohydrodynamic rotating shallow water equations with ill-prepared data is developed when the Rossby and Froude numbers tend to zero at different rates.The reduced systems are derived,respectively,for the stratification-dominant and the rotation-dominant cases by means of the developed three-scale fast averaging method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11302015,11272034)
文摘By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics（CFD） results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4？a/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.
基金Project supported by the National Science Foundation of China(Grand Nos.51079091,51209154)
文摘Energy dissipations induced by the hydraulic jump and the trajectory jet are the most widely known as the two dissipation modes at the downstream of flood discharging structures, which are often considered quite different even contradictory. However, such two energy dissipators can be used jointly and harmonically. In this paper, a new type of stilling basin with a shallow-water cushion and a triangular bottom deflector is proposed based on two different scale physical model tests of the flood discharging tunnel No.2 of Luding hydropower project. The experimental results show that the flow regime of the hydraulic jump in the presented stilling basin with bottom deflector enjoys a good and stable performance within a large range of flow rates and the energy dissipation rate is considerably high as compared to the conventional stilling basin even at a low Froude number. The results also indicate that the stilling basin with triangular bottom deflector has a better performance in improving the potential cavitation erosion according to the analysis of the pressure and the cavitation number compared to the trapezoidal one. The proposed new type of shallow-cushion stilling basin with a shallow-water cushion can be applied in similar energy dissipation projects with low Froude number and large range of flow rates.
基金Project supported by the National Natural Science Foundation of China(Grant No.51179056)
文摘With respect to the crest spillway with large unit discharge and low Froude number, the hydraulics of the slit-type energy dissipater at the outlet should be noticed due to the complicated flow regimes. In the present paper, some issues about hydraulic characteristics were experimentally investigated by means of five slit-type outlets and four tetrahedrons, including the flow choking, impact to river banks and jet trajectory. The main findings are as follows. The critical Froude number for the flow choking decreases with increasing outlet width of the slit-type energy dissipater. If the flow Froude number is expressed by the parameters just before this energy dissipater, the tetrahedron placed inside the side wall of the outlet could efficiently avoid the flow impact to the river bank of same side, and compared with the jet trajectory of the slit-type energy dissipater, the outlet with tetrahedron has different trajectory trend, i.e., the distance of the jet trajectory decreases with the increase of the water head due to special form of the outlet tetrahedron.
文摘In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asymmetric trapezoidal flume with a length of 7 m and a width of 0.304 m is considered,with the bottom of the flume transversely inclined at an angle of m=0.296 and vertical lateral sides.The corresponding inflow Froude number is allowed to range in the interval(1.40<F1<6.11).The properties of this jump are compared to those of hydraulic jumps in channels with other types of cross-sections.A relationship for calculating hydraulic jump efficiency is proposed for the considered flume.For F1>5,the hydraulic jump is found to be more effective than that occurring in triangular and symmetric trapezoidal channels.Also,when■mes>8 and■>5,the hydraulic jump in the asymmetrical trapezoidal channel downstream of a parallelogram sluice gate is completely formed as opposed to the situation where a triangular sluice is considered.
