CN106777557A - A kind of determination method of pumping plant approach channel and forebay water body carrying rate - Google Patents

A kind of determination method of pumping plant approach channel and forebay water body carrying rate Download PDF

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CN106777557A
CN106777557A CN201611070966.8A CN201611070966A CN106777557A CN 106777557 A CN106777557 A CN 106777557A CN 201611070966 A CN201611070966 A CN 201611070966A CN 106777557 A CN106777557 A CN 106777557A
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water
pumping plant
approach channel
formula
rate
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CN106777557B (en
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陈鑫
王福军
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China Agricultural University
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    • G06COMPUTING; CALCULATING; COUNTING
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Abstract

The present invention relates to a kind of pumping plant approach channel and the determination method of forebay water body carrying rate, comprise the following steps:1) relational expression that the flow velocity of pumping plant approach channel and forebay water body is changed over time is determined;2) calculate pumping plant approach channel and the maximum of forebay water body thanks to Wurz number Θm, friction factor f and roughness height kN;3) the ratio Ψ of sedimentation times and flowing cycle of the sediment settlement speed w and silt of calculating pumping plant approach channel and forebay water body in sediment transport layer;4) silt of pumping plant approach channel and forebay water body is calculated to the phase drift ψ of the flow velocity and residual α of silt phase;5) water body carrying rate Δ/D that the nondimensional depth of erosion of calculating pumping plant approach channel and forebay water body is represented.

Description

A kind of determination method of pumping plant approach channel and forebay water body carrying rate
Technical field
The present invention relates to a kind of pumping plant approach channel and the determination method of forebay water body carrying rate, belong to hydraulic engineering pumping plant neck Domain.
Background technology
In the Transient Flow of pumping plant approach channel and forebay, water body carrying rate is dynamic change.As shown in figure 1, silt Volumetric concentration S (y) is represented by dashed line, and it changes with flowing velocity U, and wherein y is vertical coordinate, is initial bed surface at y=0, under Mark m represents maximum, and Δ is distance of the depth of erosion i.e. saturation surface containing sand bed to initial bed surface, SmIt is to participate in the product of Δ The silt volume total amount of motion is water body carrying rate.
Precisely know the size of the water body carrying rate comprising phase difference effect, concentration is broken under the conditions of being to determine Transient Flow Face and flow velocity section, the important foundation for calculating water body carrying rate and silt discharge, are also to judge that water pump in pump station denudes the foundation of situation. Widely used water body carrying rate is all based on the theory deduction of constant flow out in existing engineering, makees not comprising phase difference With, it is impossible to react water body and hold sand coarse aggregate ratio under the arm during Transient Flow relative to the time response required for hydrodynamic condition, so Can cannot embody the phase of the phase drift of sediment movement relative velocity and the total volume of silt of motion after flowing velocity reduction residual Stay, also result in and water body carrying rate average is underestimated.
The content of the invention
Regarding to the issue above, Transient Flow is obtained by determining phase difference parameter it is an object of the invention to provide one kind Under the conditions of pumping plant approach channel and forebay water body carrying rate determination method.
To achieve the above object, the present invention uses following technical scheme:A kind of pumping plant approach channel and forebay water body carrying rate Determine method, comprise the following steps:
1) relational expression U (t) that the flow velocity of pumping plant approach channel and forebay water body is changed over time is determined;
2) calculate pumping plant approach channel and the maximum of forebay water body thanks to Wurz number Θm, friction factor f and roughness height kN
3) sedimentation times of the sediment settlement speed w and silt of calculating pumping plant approach channel and forebay water body in sediment transport layer and stream The ratio Ψ in dynamic cycle;
4) silt of pumping plant approach channel and forebay water body is calculated to the phase drift ψ of the flow velocity and residual α of silt phase;
5) water body carrying rate Δ/D that the nondimensional depth of erosion of calculating pumping plant approach channel and forebay water body is represented.
The step 1) in, draw the flow velocity of pumping plant approach channel and forebay water body with the time using 2 rank Stokes wave theories The relational expression of change.
The step 2) in, calculate maximum using following formula (1)~(3) and thank to Wurz number Θm, friction factor f and described Roughness height kNProcess it is as follows:
In formula, U is pumping plant approach channel and forebay water volume flow rate, and subscript m represents maximum;D is sediment grain size;T is flowing week Phase;Θ is to thank to Wurz number, and subscript m represents maximum;F is friction factor;S is the ratio of silt and water density;G is that gravity accelerates Degree;kNIt is bed surface roughness height.
In specific solution, first assume that maximum thanks to Wurz number Θm<1, roughness height k is obtained by formula (3)N=5D, substitutes into formula (2) numerical value substitution formula (1) of the friction factor f that will be obtained obtains maximum and thanks to Wurz number Θm, it is compared with 1, if obtaining Maximum thank to Wurz number ΘmIt is unreasonable more than 1 original hypothesis.
Then thank to Wurz number Θ by maximummHypothesis more than 1 is calculated, the roughness height k obtained by formula (3)N=5 ΘmD substitutes into formula (2), and association type (1), obtains formula (4)
The size of friction factor f is solved from formula (4), formula (1) is substituted into and is obtained maximum and thank to Wurz number ΘmIf, gained knot It is reasonable that fruit is assumed more than 1, and maximum is thanked into Wurz number ΘmSubstitution formula (3) obtains roughness height kNValue.
The step 3) in, the sedimentation of the sediment settlement speed w and silt of pumping plant approach channel and forebay water body in sediment transport layer Time is as follows with the calculating process of the ratio Ψ in flowing cycle:
In formula, ν is the kinematic viscosity coefficient of water.
The step 4) in, the phase drift ψ and silt phase of the silt of pumping plant approach channel and forebay water body to flow velocity Residual α calculating process it is as follows:
α=exp (- 0.2/ Ψ) (8)
The step 5) in, the acquisition of the relational expression that the water body carrying rate that nondimensional depth of erosion is represented is changed over time Process is as follows:
It is to obtain the relational expression that the water body carrying rate that nondimensional depth of erosion represents is changed over time using such as following formula (8)
Wherein F represents the sediment carrying capacity of water body.
Due to taking above technical scheme, it has advantages below to the present invention:1st, the present invention can react water body carrying rate It is corresponding relative to time required for hydrodynamic condition during Transient Flow.2nd, the present invention embodies water body carrying rate and exists The phase drift of phase residual and its relative velocity after flowing velocity reduction.3rd, present invention, avoiding equal to sediment movement amount Value is underestimated.
Brief description of the drawings
Fig. 1 is that the water body carrying rate that face containing sand bed of the invention and depth of erosion are represented defines schematic diagram, and S is abscissa, generation Table silt volumetric concentration, y is vertical coordinate, and subscript m represents maximum, and U is flowing velocity, and Δ is depth of erosion;
The Transient Flow rate process that Fig. 2 courses of work of the present invention are used, U/UmIt is nondimensional flow velocity, t/T is nothing The time of dimension;
Fig. 3 is that the water body carrying rate that the present invention determines with conventional method compares, and Δ/D is that the water body that depth of erosion is represented is held under the arm Husky rate and sediment grain size ratio, solid line represent the present invention, and chain-dotted line represents conventional method.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
A kind of pumping plant approach channel and the determination method of forebay water body carrying rate that the present invention is provided, comprise the following steps:
1) relational expression U (t) that pumping plant approach channel and forebay water volume flow rate are changed over time is calculated, can specifically utilizes 2 ranks Stokes wave theories draw the relational expression that pumping plant approach channel and forebay water volume flow rate are changed over time, and this area is partly belonged to because of this Known method, therefore be not specifically described.
2) calculate pumping plant approach channel and the maximum of forebay water body thanks to Wurz number Θm, friction factor f and roughness height kN, specifically may be used Calculated by following formula (1)~(3):
In formula, U is pumping plant approach channel and forebay water volume flow rate, and subscript m represents maximum;D is sediment grain size;T is flowing week Phase;Θ is to thank to Wurz number, and subscript m represents maximum;F is friction factor;S is the ratio of silt and water density;G is that gravity accelerates Degree;kNIt is bed surface roughness height.
In specific solution, first assume that maximum thanks to Wurz number Θm<1, roughness height k is obtained by formula (3)N=5D, substitutes into formula (2) numerical value substitution formula (1) of the friction factor f that will be obtained obtains maximum and thanks to Wurz number Θm, it is compared with 1, if obtaining Maximum thank to Wurz number ΘmIt is unreasonable more than 1 original hypothesis.
Then thank to Wurz number Θ by maximummHypothesis more than 1 is calculated, the roughness height k obtained by formula (3)N=5 ΘmD substitutes into formula (2), and association type (1), obtains formula (4)
The size of friction factor f is solved from formula (4), formula (1) is substituted into and is obtained maximum and thank to Wurz number ΘmIf, gained knot It is reasonable that fruit is assumed more than 1, and maximum is thanked into Wurz number ΘmSubstitution formula (3) obtains roughness height kNValue.
3) sedimentation times of the sediment settlement speed w and silt of calculating pumping plant approach channel and forebay water body in sediment transport layer and stream The ratio Ψ of dynamic cycle T, specific calculating process is as follows:
The sediment settlement speed w of Forebay of Pumping Station is calculated by following formula (5), by the sediment settlement speed w of Forebay of Pumping Station Value substitute into formula following formula (6) silt sediment transport layer in sedimentation time with flowing the cycle ratio Ψ, the formula (5) of utilization and Formula (6) is as follows:
In formula, ν is the kinematic viscosity coefficient of water.
4) silt of pumping plant approach channel and forebay water body is calculated to the phase drift ψ of the flow velocity and residual α of silt phase, Detailed process is as follows:
Phase drift ψ of the silt to flow velocity is obtained using following formulas (7), silt phase is obtained by following formulas (8) Remain the value of α:
α=exp (- 0.2/ Ψ) (8)
5) water body carrying rate Δ/D that the nondimensional depth of erosion of calculating pumping plant approach channel and forebay water body is represented.
Silt is substituted into following equations to the phase drift ψ of flow velocity, the residual α of silt phase and sediment settlement speed w Group (9) obtains the relational expression that the water body carrying rate that nondimensional depth of erosion represents is changed over time
Wherein F represents the sediment carrying capacity of water body.
Below effect of the invention is illustrated with a specific embodiment.
1) relation that the flow velocity of pumping plant approach channel and forebay water body is changed over time is drawn using 2 rank Stokes wave theories Formula.
The ambient pressure of known embodiments is a standard atmospheric pressure, and water temperature is 20 DEG C.Maximum fluidity speed Um=1.0m/ S, flows cycle T=5s, sediment grain size D=1.0 × 10-4The ratio s=2.65 of m, silt and water density, gravity acceleration g= 9.8m/s2, kinematic viscosity coefficient ν=1.0 × 10 of water-6m2/s.Flow velocity anaplasia at any time is understood using 2 rank Stokes wave theories Turn to:U (t)=0.8cos [2 π (t/T-0.214)]+0.2cos [4 π (t/T-0.214)], drawing image is shown in Fig. 2.
2) calculate pumping plant approach channel and the maximum of forebay water body thanks to Wurz number Θm, friction factor f and roughness height kN
First assume that maximum thanks to Wurz number Θm<1, roughness height k is obtained by formula (3)N=5D;Substitution formula (2), obtain friction because Sub- f=7.0 × 10-3;Substitution formula (1) obtains maximum and thanks to Wurz number Θm=2.16>1, it is known that it is assumed that invalid.
Wurz number Θ is thanked according to maximumm>1, roughness height k is obtained by formula (3)N=5 ΘmD;Substitution formula (2), and association type (1) formula (4), is obtained
Friction factor f=9.3 × 10 are solved from formula (4)-3, substitute into formula (1) and obtain maximum and thank to Wurz number Θm=2.86, generation Enter formula (3) and obtain roughness height kN=1.43 × 10-3m。
3) sedimentation times of the sediment settlement speed w and silt of calculating pumping plant approach channel and forebay water body in sediment transport layer and stream The ratio Ψ in dynamic cycle.
Sediment settlement speed w=8.4 × 10 are obtained from formula (5)-3M/s, substitutes into formula (6) and obtains sedimentation of the silt in sediment transport layer Time and ratio Ψ=6.3 × 10 in flowing cycle-1
4) silt of pumping plant approach channel and forebay water body is calculated to the phase drift ψ of the flow velocity and residual α of silt phase.
Phase drift ψ=5.0 × 10 of the silt to flow velocity are obtained from formula (7)-1S, from formula (8) silt phase residual α= 0.73。
5) water body carrying rate Δ/D that the nondimensional depth of erosion of calculating pumping plant approach channel and forebay water body is represented.
By step 3) and step 4) in the silt that obtains it is heavy to the phase drift ψ of flow velocity, the residual α of silt phase and silt Reduction of speed degree w substitutes into formula (9) and obtains formula (10)
Calculated using formula (1) and thank to Wurz number Θ, that is, obtain Fig. 3.
The present invention takes the Figure of description that above technical scheme is drawn to be able to more intuitively embody of the invention following special Levy:
1. the phase drift of sediment movement relative velocity is embodied.
Fig. 3 solid lines of the invention lag behind the phase of the flow rate process t/T=0.1 of Fig. 2.Such as U/U in Fig. 2m=0 is t/T =0 and t/T=0.42 moment, maximum U/Um=1 is the t/T=0.21 moment;Due to phase drift, in Fig. 3, solid line Δ/D is most Small value appears in t/T=0+0.1 the and t/T=0.42+0.1 moment, and Δ/D maximums appear in the t/T=0.21+0.1 moment.And Fig. 3 represent the chain-dotted line of conventional method then with the flow velocity same-phase of Fig. 2.
2. there is phase residual of the total volume of silt of motion after flowing velocity reduction.
In Transient Flow, even if instantaneous flow velocity is kept to 0, the presence of phase residual causes the total volume of silt of motion also not 0 can be kept to.It is 15.1 that Fig. 3 represents solid line minimum value of the invention, and the chain-dotted line minimum value for representing conventional method is 0.
3. avoid and sediment movement amount average is underestimated.
Due to the presence of phase difference, the residual silt that the positive flow phase (t/T=0-0.42) in part is kicked up is in negative flow Fast stage (t/T=0.42-1) transports so that negative sense flow phase Δ/D relatively forward flow stages, such as Fig. 3 of the present invention It is shown in solid.This conventional method for avoiding chain-dotted line representative is underestimated in negative sense flow phase to Δ/D.
It is as follows advantages of the present invention to be illustrated with reference to Figure of description:
The various embodiments described above are only used for having carried out further specifically the purpose of the present invention, technical scheme and beneficial effect It is bright, it is not intended to limit the invention, all any modification, equivalent substitution and improvements within the spirit and principles in the present invention, done Deng should be included within the scope of the present invention.

Claims (6)

1. a kind of determination method of pumping plant approach channel and forebay water body carrying rate, comprises the following steps:
1) relational expression U (t) that the flow velocity of pumping plant approach channel and forebay water body is changed over time is determined;
2) calculate pumping plant approach channel and the maximum of forebay water body thanks to Wurz number Θm, friction factor f and roughness height kN
3) sedimentation times of the sediment settlement speed w and silt of calculating pumping plant approach channel and forebay water body in sediment transport layer and flowing week The ratio Ψ of phase;
4) silt of pumping plant approach channel and forebay water body is calculated to the phase drift ψ of the flow velocity and residual α of silt phase;
5) water body carrying rate Δ/D that the nondimensional depth of erosion of calculating pumping plant approach channel and forebay water body is represented.
2. the determination method of a kind of pumping plant approach channel as claimed in claim 1 and forebay water body carrying rate, it is characterised in that:It is described Step 1) in, draw the relational expression that the flow velocity of pumping plant approach channel and forebay water body is changed over time using 2 rank Stokes wave theories.
3. the determination method of a kind of pumping plant approach channel as claimed in claim 2 and forebay water body carrying rate, it is characterised in that:It is described Step 2) in, calculate maximum using following formula (1)~(3) and thank to Wurz number Θm, the friction factor f and roughness height kNMistake Journey is as follows:
In formula, U is pumping plant approach channel and forebay water volume flow rate, and subscript m represents maximum;D is sediment grain size;T is the flowing cycle; Θ is to thank to Wurz number, and subscript m represents maximum;F is friction factor;S is the ratio of silt and water density;G is acceleration of gravity; kNIt is bed surface roughness height;
In specific solution, first assume that maximum thanks to Wurz number Θm<1, roughness height k is obtained by formula (3)N=5D, substituting into formula (2) will Numerical value substitution formula (1) of the friction factor f for obtaining obtains maximum and thanks to Wurz number Θm, it is compared with 1, if obtaining most Great Xie Wurz numbers ΘmIt is unreasonable more than 1 original hypothesis;
Then thank to Wurz number Θ by maximummHypothesis more than 1 is calculated, the roughness height k obtained by formula (3)N=5 ΘmD Substitution formula (2), and association type (1), obtain formula (4)
The size of friction factor f is solved from formula (4), formula (1) is substituted into and is obtained maximum and thank to Wurz number ΘmIf acquired results are more than 1 is assumed reasonable, and maximum is thanked into Wurz number ΘmSubstitution formula (3) obtains roughness height kNValue.
4. the determination method of a kind of pumping plant approach channel as claimed in claim 3 and forebay water body carrying rate, it is characterised in that:It is described Step 3) in, the sedimentation time of the sediment settlement speed w and silt of pumping plant approach channel and forebay water body in sediment transport layer and flowing week The calculating process of the ratio Ψ of phase is as follows:
In formula, ν is the kinematic viscosity coefficient of water.
5. the determination method of a kind of pumping plant approach channel as claimed in claim 4 and forebay water body carrying rate, it is characterised in that:It is described Step 4) in, the depth of erosion of pumping plant approach channel and forebay water body is to the residual α's of the phase drift ψ of flow velocity and silt phase Calculating process is as follows:
α=exp (- 0.2/ Ψ).(8).
6. the determination method of a kind of pumping plant approach channel as claimed in claim 5 and forebay water body carrying rate, it is characterised in that:It is described Step 5) in, the acquisition process of the relational expression that the water body carrying rate that nondimensional depth of erosion is represented is changed over time is as follows:
It is to obtain the relational expression that the water body carrying rate that nondimensional depth of erosion represents is changed over time using such as following formula (8)
Wherein F represents the sediment carrying capacity of water body.
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