CN114065484A - Hydropower station regulation guarantee simulation platform with pressure regulating chamber and open-full flow tailwater system - Google Patents

Hydropower station regulation guarantee simulation platform with pressure regulating chamber and open-full flow tailwater system Download PDF

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CN114065484A
CN114065484A CN202111231740.2A CN202111231740A CN114065484A CN 114065484 A CN114065484 A CN 114065484A CN 202111231740 A CN202111231740 A CN 202111231740A CN 114065484 A CN114065484 A CN 114065484A
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桂绍波
李玲
郑涛平
田子勤
邹海青
陈冬波
郭学洋
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Changjiang Institute of Survey Planning Design and Research Co Ltd
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Abstract

本发明公开了一种带调压室和明满流尾水系统水电站调节保证仿真平台。它包括输水发电系统有压段模块、明满交替流段模块、混流式水轮发电机组模块、调速器模块、尾水调压室模块、气体空腔模块和电网模块；输水发电系统有压段模块用于描述有压输水发电系统隧洞或管道的有压瞬变流流体运动；明满交替流段模块用于描述明满流流体运动；混流式水轮发电机组模块用于确定混流式水轮机的参数；尾水调压室模块用于获得尾水调压室涌浪情况；气体空腔模块用于描述隧洞内滞留空气以及隧洞顶部空气渗入和排出对明满流段的影响。本发明具有准确性高的优点。

Figure 202111231740

The invention discloses a regulation assurance simulation platform for a hydropower station with a surge chamber and a full-flow tail water system. It includes the pressure section module of the water transmission power generation system, the open and full alternating flow section module, the Francis turbine generator set module, the governor module, the tail water surge chamber module, the gas cavity module and the power grid module; the water transmission power generation system The pressure section module is used to describe the pressure transient flow fluid movement in the tunnel or pipeline of the pressurized water transmission power generation system; the open and full alternating flow section module is used to describe the open and full flow fluid movement; the Francis turbine generator set module is used to determine The parameters of the Francis turbine; the tail water surge chamber module is used to obtain the surge condition of the tail water surge chamber; the gas cavity module is used to describe the effect of the air trapped in the tunnel and the infiltration and discharge of air at the top of the tunnel on the open flow section. The present invention has the advantage of high accuracy.

Figure 202111231740

Description

Hydropower station regulation guarantee simulation platform with pressure regulating chamber and open-full flow tailwater system
Technical Field
The invention relates to the technical field of water conservancy and hydropower engineering, in particular to a hydropower station regulation guarantee simulation platform with a surge chamber and an open-full-flow tail water system.
Background
The hydraulic unsteady flow and water hammer begin to discuss the transmission of sound waves in water, and with the development of the worldwide electric power industry and the construction of large-scale hydro-junction projects with long water diversion, single-machine capacity and huge machine flow, the hydraulic transition process of hydropower stations draws more and more attention. The research on the hydraulic transition process of the hydropower station mainly comprises two aspects: the method is used for researching the unsteady flow phenomenon of a hydropower station runner and researching the transition process characteristic of a unit. Accurate prediction of characteristic change rules of the hydroelectric generating set in the transient process is always a key point and a difficult point of hydropower station engineering design. Especially in recent years, hydropower engineering often considers the problem of one tunnel with multiple purposes in order to save investment, for example, a construction diversion tunnel is changed into a power generation tail water tunnel in the later stage of the engineering. Obviously, for hydropower stations with longer tail water tunnels, the economic benefit brought by the multiple purposes of one tunnel is very considerable, and the method also has good effects of reducing excavation of the cavern and maintaining better rock mechanical conditions. However, for the hydroelectric engineering similar to changing a diversion tunnel into a tail water power generation tunnel, the tail water tunnel of the power station is often likely to have open-full alternate flow and complex air intake and exhaust processes, and thus, the hydraulic transition process of the water delivery power generation system is likely to generate large pressure pulsation, so that the tail water system of the power station with the open-full alternate flow has complex influence on the stability and the transition process of the power station operation.
At present, a shock wave capture method based on a Preissmann virtual slit method assumption is mainly adopted for numerical simulation research on a hydraulic transition process of a water transport and power generation system with full flow and full flow, although the method can uniformly solve the full flow and full flow, because the method assumes a one-to-one correspondence relationship between water depth and water pressure in a tunnel, influence of air retention in the tunnel and air infiltration and exhaust at the top of the tunnel cannot be well considered, and the method has distortion on simulation of physical phenomena with negative pressure and air sac involved in the tunnel.
Therefore, there is a need to develop a hydropower plant regulation assurance simulation platform that takes into account the full alternating flow, as well as air entrapment within the tunnel and air infiltration and removal from the top of the tunnel.
Disclosure of Invention
The invention aims to provide a hydropower station regulation and guarantee simulation platform with a pressure regulating chamber and a full-flow wake system, which guarantees unconditional stability of an unsteady solving process, can accurately predict the change rules of parameters of the hydroelectric generating set and a water delivery tunnel transition process under various complex working conditions such as start, normal stop, accident stop, emergency stop, refusal action of a main pressure distribution valve, action of an accident pressure distribution valve, runaway and the like of the mixed-flow hydroelectric generating set, can calculate and analyze the influence of disturbance such as air intake, exhaust, pressure fluctuation and the like of the wake pressure regulating chamber and full-flow wake on the stable operation of the mixed-flow hydroelectric generating set, optimizes the start and stop rules of the hydroelectric generating set and the arrangement of the water delivery power generation system, and has high accuracy.
In order to achieve the purpose, the technical scheme of the invention is as follows: take surge-chamber and open full-flow wake system hydropower station to adjust and guarantee simulation platform, its characterized in that: the system comprises a pressure section module, a bright and full alternating flow section module, a mixed flow type hydraulic generator set module, a speed regulator module, a tail water pressure regulating chamber module, a gas cavity module and a power grid module of the water delivery power generation system;
the pressure section module of the water delivery power generation system is used for describing the pressure transient flow fluid movement of a tunnel or a pipeline of the pressure water delivery power generation system;
the open-full alternating flow section module is used for describing the motion of open-full flow fluid, simulating the change rule of the water depth/water pressure and open-full flow interface of the open-full flow section of the water delivery and power generation system, and calculating and analyzing the influence of the air intake and exhaust processes and water pressure fluctuation of the open-full flow section water delivery and power generation system on the stable operation of the water turbine generator set;
the mixed-flow water turbine generator set module is used for determining parameters of the mixed-flow water turbine, and the parameters of the mixed-flow water turbine comprise an effective water head, boundary conditions, flow, shaft output and generator set rotating speed; the speed regulator module is used for optimizing and setting speed regulator parameters;
the tail water surge chamber module is used for substituting the head end characteristic of the tail water tunnel, the tail end characteristic of the tail water branch tunnel and the flow speed head difference into a surge chamber continuous equation to obtain the surge condition of the tail water surge chamber;
the gas cavity module is used for calculating an airbag cavity control body of the open-full flow section and describing the influence of air detained in the tunnel and air permeation and discharge at the top of the tunnel on the open-full flow section;
and the power grid module is used for determining the stability of the power grid frequency modulation working condition unit.
In the above technical scheme, in the pressure section module of the water delivery power generation system, the pressure section control equation and the solving method thereof are as follows:
the differential equations describing the motion of pressure transient fluid are shown in equations (1) and (2):
Figure BDA0003316250540000031
Figure BDA0003316250540000032
in the formulas (1) and (2), V is the fluid velocity, m/s; h is water level or pressure, m; a is the water shock wave speed, m/s; g is the acceleration of gravity, m/s2；S0Is a channel bottom slope; sfIs friction slope drop;
the tunnel or pipeline of the pressure water delivery power generation system adopts a characteristic line method to convert a fluid motion partial differential control equation into an ordinary differential equation, and the following can be obtained:
the positive characteristic line equation applicable to the lower end face of the pipeline for describing transient flow is as follows:
Qp1＝Cp-CaHp1 (3)
the negative characteristic line equation applicable to the upper end face of the pipeline for describing transient flow is as follows:
Qp2＝Cn+CaHp2 (4)
in the formulae (3) and (4), Qp1And Qp2Flow rate of the lower and upper end faces, m3/s；Hp1And Hp2Water level or pressure m on the lower end surface and the upper end surface respectively; ca、CpAnd CnAre discrete equation coefficients.
In the above technical solution, in the full-open alternating flow section module, the full-open alternating flow section control equation and the solving method thereof are as follows:
the differential equations describing the motion of the full flow fluid are shown in equations (5) and (6):
Figure BDA0003316250540000033
Figure BDA0003316250540000034
in the formulas (5) and (6), B is the width of the water surface, and m; y is water level or pressure, m; v is the fluid velocity, m/s; g is the acceleration of gravity; a is the area of the water passing section; s0Is a channel bottom slope; sfIs friction slope drop;
and (3) discretizing the equation (5) and the equation (6) by adopting a finite difference method implicit format, and solving by adopting a Sternikov implicit format.
In the technical proposal, in the mixed-flow type hydraulic generator set module,
the calculation equation of the effective water head of the water turbine and the solving method thereof are as follows:
the energy equation of the water turbine is mainly expressed by the effective water head of the water turbine; the effective working head acting on the water turbine under the stable working condition is the total pressure difference of the inlet and outlet measuring sections of the water turbine; however, in the transient process, the additional influence of water hammer on the section of the flow passage inlet and the draft tube of the unit section must be considered, so the invention uses the piezometer tube water head of the tail end section of the equivalent pipe at the upstream of the water turbine, the piezometer tube water head and the flow velocity water head of the head section of the equivalent pipe at the downstream are subtracted by the flow velocity water head to serve as the effective water head of the water turbine, and the result has better approximation, namely, the formula for calculating the water head of the unit is shown as the formula (7):
Figure BDA0003316250540000041
in the formula (7), HtIndicating the effective operating head, Q, of the water turbinetRepresenting the flow of the water turbine; hp4、S4And Hp5、S5Respectively representing the pressure and the flow area of the cross section of the upstream and downstream equivalent measuring pipes of the water turbine;
the boundary condition of the mixed-flow water turbine can utilize the unit flow to the unit rotating speed (Q) formed by the dispersion of the comprehensive characteristic curve of the model water turbine11～n11) Relationship curve (array table) and unit output to unit rotation speed (N)11～n11) The relation curve (array table) and the inertia equation of the unit and the action rule of the guide vane are added to solve the rotating speed n and the flow Q of the water turbine after the load change of the unittThe specific solving method comprises the following steps of:
according to the unit speed n of the water turbine11Opening a of the stator, assuming a unit flow rate Q11Unit speed of rotation n11Satisfy a linear relationship within a certain range, in terms of Q11By the definition of (1), the flow rate Q of the water turbine can be obtainedt；
Figure BDA0003316250540000042
In the formula (8), QtThe flow rate of the water turbine; q11Is unit flow rate; d1Representing the diameter of the inlet runner of the water turbine; htIs a unit water head;
according to unit speed n11And opening degree of guide vane alpha from N11～n11On curves, corresponding values can also be obtained by interpolationN11Value, then by N11By the definition of (1), the shaft output N of the water turbine can be obtainedt：
Figure BDA0003316250540000051
In the formula (9), D1Representing the diameter of the inlet runner of the water turbine; htIs a unit water head; n is a radical of11The unit output is taken as the unit output;
and then, calculating the rotating speed n of the hydroelectric generating set by utilizing a set inertia equation (6) of load shedding:
Nt＝WR2(2π/60)2·n(dn/dt) (10)
in formula (10), WR2Representing the moment of inertia of the hydro-generator set;
the differential equation is integrated within delta t time, and the rotating speed n of the unit at any time t in the middle of the hydraulic transition process can be obtained through simplificationpCan be expressed as:
Figure BDA0003316250540000052
in the formula (11), noRepresenting the instantaneous speed of the turbine, N, at the last moment (t- Δ t)0Representing the instantaneous output of the water turbine at the last moment (t-delta t), wherein delta t represents the time difference between two adjacent calculation nodes; WR (pulse Width modulation)2Representing the moment of inertia of the hydro-generator set; n is a radical oftThe shaft output of the water turbine is obtained.
In the technical scheme, according to a typical PID type regulation rule, a four-order Rugga-Kutta method is used for solving a differential equation set of the speed regulator.
In the above technical solution, in the tail water surge chamber module, the surge chamber continuous equation and the solving method thereof are as follows:
let QbpRepresenting the flow through the bottom of the pressure-regulating chamber, HbpFor the head of the piezometer tube at the bottom of the pressure regulating chamber, Hp3The water surface elevation of the surge chamber (expressed by a piezometer tube water head);
the characteristic line equation of the head end of the tailwater tunnel:
Figure BDA0003316250540000053
in the formula (12), Qp7The flow of the tail water tunnel cross section after passing through the surge chamber; cn7、Ca7Are discrete equation coefficients; hp3The water surface elevation of the surge chamber (expressed by a piezometer tube water head); kbpIs impedance coefficient of impedance hole of voltage regulation chamber; qbpRepresenting the flow through the bottom of the surge chamber;
tail water branch hole tail end characteristic line equation:
Qp6＝Cp6-Ca6·Hp6 (13)
in formula (13), Qp6The flow rate of the tail water branch hole section before passing through the pressure regulating chamber; cp6、Ca6Are discrete equation coefficients; hp6The tail water branch hole is used as the pressure of the cross section of the burette;
pressure regulating chamber continuous equation:
Figure BDA0003316250540000061
in the formula (14), Hp3The water surface elevation of the surge chamber (expressed by a piezometer tube water head); qp6The flow rate of the tail water branch hole section before passing through the pressure regulating chamber; qp7The flow of the tail water tunnel cross section after passing through the surge chamber; sbpIs the section area of the pressure regulating chamber;
considering the gradual change influence of the flow passage at the bottom of the pressure regulating chamber, the front and the rear equivalent measuring tubes of the pressure regulating chamber have a flow speed water head difference:
Figure BDA0003316250540000062
in formula (15), KbpIs impedance coefficient of impedance hole of voltage-regulating chamber, Hp7The pressure of the pressure regulating chamber is used as the pressure of the cross section of the burette; qp7The flow of the tail water tunnel cross section after passing through the surge chamber; s6、S7Are respectively asThe cross-sectional areas of the tailwater branch tunnel and the tailwater tunnel; g is the acceleration of gravity; hp3The water surface elevation of the surge chamber; kbpIs impedance coefficient of impedance hole of voltage regulation chamber; qbpRepresenting the flow through the bottom of the surge chamber; qp7The flow of the tail water tunnel cross section after passing through the surge chamber;
wherein, KbpIs defined as follows:
Figure BDA0003316250540000063
in formula (28): sbpMu is a flow coefficient, which is 0.6-0.8, for the area of the cross section of the pressure regulating chamber. S6、S7The cross section areas of the tailwater branch tunnel and the tailwater tunnel are respectively; g is the acceleration of gravity;
substituting equations (12), (13), (15) and (28) into (14), and solving differential equation (14) by the Runge-Kutta method.
In the technical scheme, the calculation method of the airbag cavity control body at the full flow section in the gas cavity module is as follows,
according to a hydraulic model experiment, the airbag in the tunnel is broken when the power generation tail water tunnel exhausts or intakes for a hydropower station which is similar to a diversion tunnel and is used as a power generation tail water tunnel, so that the airbag at the top of the diversion tunnel can be discretized, namely the airbag is respectively concentrated near the top of the tail end of each calculation section to form a very small cavity, and then the cavities are used as an internal boundary of each calculation section;
basically, the air retained in the tailwater tunnel is assumed to be ideal gas, and the moving process meets the isothermal change process (the temperature of the gas is close to the temperature of the water body in the tunnel); the ideal gas state equation is shown below:
piVpi＝mpiRT (16)
in formula (16): p is a radical ofiDenotes the absolute pressure, V, in the gas cavity ipiAnd mpiRespectively representing the gas volume and mass of the gas cavity i at the end of the time period (time T + deltat), R representing the gas constant, and T representing the absolute temperature of the gas;
wherein the absolute pressure p in the gas cavity iiSolving the pressure H with the position transient flow control equationpiSatisfies the following relationship:
pi＝ρg(Hpi+p0/ρg) (17)
in formula (17): p is a radical ofiRepresents the absolute pressure within the gas cavity i; p0Is the initial pressure within the gas cavity i; ρ is the gas density in the gas cavity i; g is the acceleration of gravity;
as shown in fig. 2, the volume of the gas cavity i satisfies the continuity equation, which is expressed as follows:
Vpi＝Vi+0.5Δt(Qpi+Qi-Qpiout-Qiout) (18)
in formula (18): vpiRepresents the gas volume of gas cavity i at the end of the time period (time t + Δ t); viGas volume of gas cavity i; qiout、QpioutRespectively representing the flow rate of the gas cavity i flowing out at the beginning of the time interval (time t) and at the end of the time interval (time t + delta t), QiAnd QpiRespectively representing the inflow flow of the gas cavity i at the beginning of the time period (time t) and the end of the time period (time t + delta t); Δ t represents the time difference between two adjacent computing nodes;
therefore, at the end of the period (time t + Δ t), the mass m of air in the gas cavity ipiCan be expressed as follows:
Figure BDA0003316250540000071
in formula (19): m isi、mpiRespectively representing the mass of the gas cavity i at the beginning of the time interval (time t) and at the end of the time interval (time t + deltat),
Figure BDA0003316250540000081
and
Figure BDA0003316250540000082
respectively representing the mass flow of the gas cavity i flowing in or out at the beginning (time t) and the end (time t + delta t) of the time period; Δ t represents adjacent twoCalculating the time difference of the nodes;
assuming an inflow and outflow open-full flow water transportation power generation system in the air isentropic change process, the following four situations need to be considered for the gas state in the gas cavity by the aerodynamic principle:
1) when p is0>pi>0.53p0When the gas flow state is subsonic
Figure BDA0003316250540000083
Can be expressed as follows:
Figure BDA0003316250540000084
in formula (20): cinThe flow coefficient of the gas inflow is represented, and the value is 0.75; a. theinRepresenting the area of an air inlet of the air cavity i, and calculating and determining according to the area of the cross section of the open-full flow section of the tunnel; p is a radical of0Representing the absolute pressure of the atmosphere outside the tunnel; rho0Represents the atmospheric density; p is a radical ofiRepresents the absolute pressure within the gas cavity i;
2) when pi<0.53p0Mass flow of air with critical speed of sound
Figure BDA0003316250540000085
Can be expressed as follows:
Figure BDA0003316250540000086
in formula (20): cinThe flow coefficient of the gas inflow is represented, and the value is 0.75; a. theinRepresenting the area of an air inlet of the air cavity i, and calculating and determining according to the area of the cross section of the open-full flow section of the tunnel; p is a radical of0Representing the absolute pressure of the atmosphere outside the tunnel; r represents a gas constant, and T represents an absolute temperature of the gas;
3)
Figure BDA0003316250540000087
when the gas is subMass flow of air out of sonic velocity
Figure BDA0003316250540000088
Can be expressed as follows:
Figure BDA0003316250540000089
in formula (21): coutThe flow coefficient of the gas outflow is expressed, and the value is 0.85; a. theoutRepresenting the area of an exhaust port of the gas cavity i, and calculating and determining according to the cross section area of the open-full flow section of the tunnel; p is a radical of0Representing the absolute pressure of the atmosphere outside the tunnel; p is a radical ofiRepresents the absolute pressure within the gas cavity i;
4)
Figure BDA0003316250540000091
mass flow of air from critical speed of sound
Figure BDA0003316250540000092
Can be expressed as follows:
Figure BDA0003316250540000093
in formula (23): p is a radical of0And T represents the absolute pressure and absolute temperature of the atmosphere outside the tunnel respectively; cinAnd CoutRespectively representing the flow coefficients of gas flowing in and out, and respectively taking the values as 0.75 and 0.85; a. theinAnd AoutRespectively representing the areas of an air inlet and an air outlet of the air cavity i, and calculating and determining according to the area of the cross section of the open-full flow section of the tunnel; rho0Represents the atmospheric density and is defined as follows:
Figure BDA0003316250540000094
in the technical scheme, the hydropower station regulation guarantee simulation calculation method with the pressure regulating chamber and the open-full flow tailwater system comprises the following steps,
the method comprises the following steps: the model starts to run;
step two: reading in a runner and a power station database;
step three: calculating a common time step Δ t;
step four: calculating initial steady state water head, output, guide vane opening, each segmented flow, initial water level of a surge chamber, the depth of the open full flow and air content;
step five: calculating t;
t＝(t+Δt)
step six: setting a water head and a rotation speed iteration initial value of the water turbine;
step seven: calculating the opening degree of the guide vane according to the closing rule of the guide vane;
step eight: calculating a unit instantaneous value;
step nine: calculating instantaneous values of a pressure section and a non-pressure section of the water delivery system;
step ten: determining nw、npThe relationship of t; (n)wRepresenting intermediate values of rotational speed in an iterative process, a method of calculating and a method of calculating npSame)
When | nw-npWhen the/delta t is more than or equal to 0.01, jumping to the sixth step;
when | nw-npIf the/| delta t is less than 0.01 and small fluctuation exists, jumping to the eleventh step;
when | nw-npWhen the/| delta t is less than 0.01, jumping to a step thirteen;
step eleven: solving a speed regulator equation;
step twelve: calculating the angle and performance parameters of the guide vane of the unit corresponding to the predicted output;
step thirteen: calculating the flow and the water head of each section of the flow channel;
fourteen steps: storing the result;
step fifteen: calculating t, and jumping to the fifth step when t is less than Time;
when t is larger than or equal to the Time, jumping to the step sixteen;
sixthly, the steps are as follows: and after the calculation is finished, drawing a chart and outputting a calculation result.
The hydraulic transition process calculation interface of the water-turbine generator set is established according to the mathematical model and the numerical calculation method, and mixed flow type water-turbine generator set hydraulic transition process calculation software with the tail water pressure regulating chamber and the open-full flow tail water system is compiled by combining a Fortran language and a visual Basic language; the software has the advantages of friendly operation interface, good operability, intuitive, simple and practical output result and the like.
The hydropower station regulation guarantee simulation platform with the pressure regulating chamber and the open-full flow tail water system and the calculation method thereof provided by the invention are suitable for large-scale hydroelectric generating set turbine runner, generator lower frame and other major components to process station foundations on site in the deep mountain canyon region, and have the following beneficial effects:
according to the method, the change rules (including specific values and curves) and the limit values of parameters of the transition process working conditions such as the pressure envelope line of a power station water delivery system, the unit rotation speed rise, the unit section runner inlet/tail end pressure, the draft tube inlet vacuum degree, surge of a surge chamber, the water depth or water pressure of the open-full flow section of the water delivery power generation system, the interface position of the pressure/non-pressure section, air inlet and exhaust of the open-full flow section and the like can be compared intuitively according to the calculated working condition data.
The invention can mainly realize the following functions:
1) calculating the working condition of closing guide vanes by suddenly load shedding of the hydroelectric generating set, outputting parameter extreme values including the rotating speed rise of the hydroelectric generating set, the inlet pressure of a runner of a water turbine section, the inlet vacuum degree of a draft tube, the pressure envelope curve of a water delivery system, surge of a surge chamber, the water depth or water pressure of an open-full flow section of the water delivery power generation system, the interface position of a pressure/non-pressure section and the like, and the change time history thereof, and optimally giving the optimal closing rule of movable guide vanes of the hydraulic turbine;
2) calculating the starting condition of the hydroelectric generating set and the stability of the power grid frequency modulation condition set, and optimizing and setting the parameters of the speed regulator;
3) calculating the main distribution refusal action of sudden load shedding of the hydroelectric generating set and the action working condition of the accident pressure distribution valve, calculating the action setting value of the accident pressure distribution valve, and controlling the control parameters of the transition process such as the maximum rotating speed rise of the hydroelectric generating set to be within a safety range;
4) predicting the time of the unit entering the runaway state and the maximum runaway rotating speed under the runaway working condition;
5) and simulating the change rule of the water depth/water pressure and open-full flow interface of the open-full flow section of the water delivery power generation system, and calculating and analyzing the influence of the air intake and exhaust processes and water pressure fluctuation of the open-full flow section water delivery power generation system on the stable operation of the water turbine generator set.
Drawings
Fig. 1 is a flow chart for calculating the hydraulic transition process of the mixed-flow type hydraulic turbine power generation system with the tail water pressure regulating chamber and the open-full flow tail water system.
FIG. 2 is a schematic diagram of calculation of the air bag cavity control body in the full flow section of the invention.
FIG. 3 is a comparison between the calculation and actual measurement of the rotating speed of the sudden load shedding rated load unit in the embodiment of the invention.
Figure 4 is a comparison of sudden load rejection rated volute inlet pressure in an embodiment of the invention.
FIG. 5 is a comparison of sudden load shedding rated draft tube inlet pressure in an embodiment of the invention.
FIG. 6 is a comparison of top plate pressure against sudden load rejection rated load in an embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be described in detail with reference to the accompanying drawings, which are not intended to limit the present invention, but are merely exemplary. While the advantages of the invention will be clear and readily understood by the description.
The calculation model and the calculation method are used for establishing a mathematical model based on a control equation (comprising a continuity equation and a motion equation) for describing transient variable flow motion and an ideal gas state equation, wherein a pressurized section of a water delivery power generation system is solved by adopting a characteristic line method, a bright full flow section is dispersed by adopting a finite difference method and is solved by adopting a Sternikov implicit format, so that unconditional stability of an unsteady solving process is ensured; the calculation model and the platform provided by the invention can effectively solve the defect that a shock wave capture method based on a Preissmann virtual slit method hypothesis cannot simulate negative pressure and air sac phenomena of an open-full flow system, can accurately predict the change rules of parameters of the transition process of various complex working conditions of the mixed-flow type water turbine generator set and a water delivery tunnel, such as starting, normal stopping, accident stopping, emergency stopping, refusing of a main pressure distribution valve, action of an accident pressure distribution valve, runaway and the like, can calculate and analyze the influence of disturbances of a tail water pressure regulating chamber and open-full alternating flow, such as air inlet, exhaust, pressure fluctuation and the like, on the stable operation of the mixed-flow type water turbine generator set, and optimize the starting, shutdown rules of the set and the arrangement of a water delivery power generation system; meanwhile, the invention can provide comprehensive evaluation for the reliability and safety of the operation mode of the mixed-flow hydropower station with a tail water surge chamber and a full alternating flow, provides a reference for the arrangement design of a water delivery system of a similar power station, and can be widely applied to the technical field of water conservancy and hydropower engineering.
The invention is explained in detail by taking the embodiment of the invention as an example for carrying out the numerical calculation of the hydraulic transition process in the mixed-flow hydropower station of a certain large tailwater system with variable top height, and has the guiding function for the numerical calculation of the hydraulic transition process in the hydropower station of other tailwater pressure regulating chambers with variable top height and the open-full flow tailwater system.
The large mixed-flow hydropower station with the variable-top high-tail-water system in the embodiment is a mixed-flow hydropower station with a tail-water pressure regulating chamber and an open-full-flow tail-water system; in the hydropower station in the embodiment, the maximum water head of the hydropower station is 113.0m, and the rated water head is 85.0 m.
The numerical calculation model of the hydraulic transition process in the embodiment comprises a pressure section module, a full alternating flow section module, a mixed-flow hydraulic generator set module, a speed regulator module, a tail water pressure regulating chamber module, a gas cavity module and a power grid module of the water delivery power generation system; the pressure section module, the open-full alternating flow section module, the mixed-flow hydraulic generator set module, the speed regulator module, the tail water pressure regulating chamber module, the gas cavity module and the power grid module of the water delivery power generation system are regarded as a unified whole which is mutually associated, and are combined to carry out numerical simulation programming calculation; wherein, the computational mathematical model of the pressure tunnel adopts a characteristic line method to calculate and solve; the computational mathematical model of the full-flow wake tunnel is discretized by adopting a finite difference method and solved by adopting a Sternikov implicit format; substituting the characteristic line equations of the upstream and downstream sections of the pressure regulating chamber into a continuous equation of the pressure regulating chamber by a computational mathematical model of the pressure regulating chamber, and solving a differential equation by a Rugga-Kutta method; the computational mathematical model of the water turbine inputs the characteristic curve of the water turbine in an array form, calculates the characteristic parameters of the water turbine at the current working point by using a linear interpolation method, and solves an upstream and downstream section characteristic line equation, a unit rotation inertia equation and a water turbine energy equation simultaneously; the mathematical calculation model of the speed regulator adopts a Rugga-Kutta method to solve a control differential equation of the speed regulator.
As shown in fig. 1, the electrical algorithm of the present embodiment is performed as follows:
a) calculating the length, the diameter, the water shock wave speed and the equivalent resistance coefficient of the equivalent pipe;
b) setting a calculation working condition, and calculating parameters such as unit rotating speed, unit flow, guide vane opening, initial water level of a surge chamber, initial water depth of an open-full flow section, air volume, quality and the like of the water turbine under the steady-state working condition according to a comprehensive characteristic curve of the water turbine;
the initial condition calculation method comprises the following steps:
1) surface curve at initial condition
In order to calculate the transient state, the water depth and flow rate of the initial constant flow on all sections in the system need to be known; if the condition is incompatible with the transient flow control equation, micro-fluctuation is generated on each section in the process of solving the strip matrix, and the actual solution of the system can be influenced by the interference which does not exist actually; if the obtained initial value is very close to the actual value, the change of the flow state can be converged to a stable value close to the real initial boundary condition as long as a certain number of times is calculated;
the initial conditions are determined by solving the ordinary differential equations of the open channel graded flow:
Figure BDA0003316250540000131
in the above formula, x represents a coordinate, y represents a surge chamber water depth, Q represents a flow rate in an open channel, and m represents3/s；S0Is the bottom slope of the channel SfIs the friction slope, B is the water surface width, m.
Equation (25) is a first order differential equation, running along the flow path from aboveIntegrating the equation downstream to downstream can calculate the water depth along the channel and the tunnel; for this purpose, the water depth of the i-section at the known time t is set to y by the Runge-Kutta methodtThen the water depth y at time (t +1)t+1Comprises the following steps:
Figure BDA0003316250540000141
in the formula:
Figure BDA0003316250540000142
Figure BDA0003316250540000143
Figure BDA0003316250540000144
Δ x denotes the space step, in m.
2) Initial condition of air retention in open and full flow section
The volume and the mass of air detained in the open full flow section under the initial state condition are closely related to the initial working condition (downstream water level) of the hydraulic transition process and the shape and the size of the section of the water delivery tunnel of the open full flow section; calculating the air volume V trapped between section i and section i +1 for the open-full flow sectioni+1The following can be calculated:
Figure BDA0003316250540000145
in the above formula, SiAnd Si+1Respectively representing the section areas of a section i and a section i +1 above the water surface of the tunnel at the open-full flow section, wherein deltax represents the space step length;
c) calculating the closing rule of the selected guide vane;
after the generator is separated from the power grid, the rotating speed of the unit begins to rise, the guide vane servomotor begins to act after 0.05-0.1 s of motionless time, and calculation is carried out according to one-section or two-section closing rules;
d) calculating the performance parameter variable instantaneous values of the water turbine at different guide vane angles;
the energy equation of the water turbine is mainly expressed by the effective water head of the water turbine; the effective working head acting on the water turbine under the stable working condition is the total pressure difference of the inlet and outlet measuring sections of the water turbine; however, in the transient process, the additional influence of water hammer on the section of the flow passage inlet and the draft tube of the unit section must be considered, so the invention uses the piezometer tube water head of the tail end section of the equivalent pipe at the upstream of the water turbine, the piezometer tube water head and the flow velocity water head of the head section of the equivalent pipe at the downstream are subtracted by the flow velocity water head and are used as the effective water head of the water turbine, and the result has better approximation, namely:
Figure BDA0003316250540000146
wherein HtIndicating the effective operating head, Q, of the water turbinetRepresenting the flow of the water turbine; hp4、S4And Hp5、S5Respectively representing the pressure and the flow area of the cross section of the upstream and downstream equivalent measuring pipes of the water turbine;
the boundary condition of the mixed-flow water turbine can utilize the unit flow to the unit rotating speed (Q) formed by the dispersion of the comprehensive characteristic curve of the model water turbine11～n11) Relationship curve (array table) and unit output to unit rotation speed (N)11～n11) The relation curve (array table) and the inertia equation of the unit and the action rule of the guide vane are added to solve the rotating speed n and the flow Q of the water turbine after the load change of the unittThe specific solving method comprises the following steps of:
according to the unit speed n of the water turbine11Opening a of the stator, assuming a unit flow rate Q11Unit speed of rotation n11Satisfy a linear relationship within a certain range, in terms of Q11By the definition of (1), the flow rate Q of the water turbine can be obtainedt；
Figure BDA0003316250540000151
According to unit speed n11And opening degree of guide vane alpha from N11～n11The corresponding N can be interpolated on the curve11Value, then by N11By the formula (2), the shaft output N of the turbine can be obtainedt：
Figure BDA0003316250540000152
Wherein D is1Representing the diameter of the inlet runner of the water turbine;
and then, calculating the rotating speed n of the hydroelectric generating set by utilizing a set inertia equation (6) of load shedding:
Nt＝WR2(2π/60)2·n(dn/dt) (10)
wherein, WR2The inertia moment of the water turbine generator set is expressed, the differential equation is integrated within delta t time, and the rotating speed n of the generator set at any time t in the middle of the hydraulic transition process is obtained through simplificationpCan be expressed as:
Figure BDA0003316250540000153
wherein n isoRepresenting the instantaneous speed of the turbine, N, at the last moment (t- Δ t)0Representing the instantaneous turbine output at the last moment (t- Δ t);
e) calculating parameter variable instantaneous values of the section transition process of each section of water delivery tunnel;
in the water delivery power generation system, the pressure section control equation and the solving method thereof are as follows:
the differential equations describing the motion of pressure transient fluid are shown in equations (1) and (2):
Figure BDA0003316250540000161
Figure BDA0003316250540000162
the tunnel or pipeline of the pressure water delivery power generation system adopts a characteristic line method to convert a fluid motion partial differential control equation into an ordinary differential equation, and the following can be obtained:
the positive characteristic line equation applicable to the lower end face of the pipeline for describing transient flow is as follows:
Qp1＝Cp-CaHp1 (3)
the negative characteristic line equation applicable to the upper end face of the pipeline for describing transient flow is as follows:
Qp2＝Cn+CaHp2 (4)
in the water delivery power generation system, the control equation of the open-full alternating flow section and the solving method thereof are as follows:
the differential equations describing the motion of the full flow fluid are shown in equations (5) and (6):
Figure BDA0003316250540000163
Figure BDA0003316250540000164
adopting a finite difference method implicit format, dispersing the equation (5) and the equation (6), and adopting a Sternikov implicit format to solve;
in the water delivery power generation system, a pressure regulating chamber continuous equation and a solving method thereof are as follows:
let QbpRepresenting the flow through the bottom of the pressure-regulating chamber, HbpFor the head of the piezometer tube at the bottom of the pressure regulating chamber, Hp3The water surface elevation of the surge chamber (expressed by a piezometer tube water head);
the characteristic line equation of the head end of the tailwater tunnel:
Qp7＝Cn7+Ca7(Hp3+Kqb·Qbp|Qbp|) (12)
tail water branch hole tail end characteristic line equation:
Qp6＝Cp6-Ca6·Hp6 (13)
pressure regulating chamber continuous equation:
Figure BDA0003316250540000165
considering the gradual change influence of the flow passage at the bottom of the pressure regulating chamber, the front and the rear equivalent measuring tubes of the pressure regulating chamber have a flow speed water head difference:
Figure BDA0003316250540000171
wherein, KbpFor the impedance hole impedance coefficient of the voltage regulating chamber, the following is defined:
Figure BDA0003316250540000172
in the above formula, SbpMu is a flow coefficient, and is generally 0.6-0.8; s6、S7The cross section areas of the tailwater branch tunnel and the tailwater tunnel are respectively;
substituting equations (12), (13), (15) and (28) into equation (14), and solving a differential equation (14) by a Runge Kutta method;
in the water delivery power generation system, the calculation method of the air bag cavity control body at the full flow section is as follows,
according to a hydraulic model experiment, the airbag in the tunnel is broken when the power generation tail water tunnel exhausts or intakes for a hydropower station which is similar to a diversion tunnel and is used as a power generation tail water tunnel, so that the airbag at the top of the diversion tunnel can be discretized, namely the airbag is respectively concentrated near the top of the tail end of each calculation section to form a very small cavity, and then the cavities are used as an internal boundary of each calculation section;
basically, the air retained in the tailwater tunnel is assumed to be ideal gas, and the moving process meets the isothermal change process (the temperature of the gas is close to the temperature of the water body in the tunnel); the ideal gas state equation is shown below:
piVpi＝mpiRT (16)
in the above formula, piDenotes the absolute pressure, V, in the gas cavity ipiAnd mpiRespectively representing the gas volume and mass of the gas cavity i at the end of the time period (time T + deltat), R representing the gas constant, and T representing the absolute temperature of the gas;
wherein the absolute pressure p in the gas cavity iiSolving the pressure H with the position transient flow control equationpiSatisfies the following relationship:
pi＝ρg(Hpi+p0/ρg) (17)
as shown in fig. 2, the volume of the gas cavity i satisfies the continuity equation, which is expressed as follows:
Vpi＝Vi+0.5Δt(Qpi+Qi-Qpiout-Qiout) (18)
in the above formula, Qiout、QpioutRespectively representing the flow rate of the gas cavity i flowing out at the beginning of the time interval (time t) and at the end of the time interval (time t + delta t), QiAnd QpiRespectively representing the inflow flow of the gas cavity i at the beginning of the time period (time t) and the end of the time period (time t + delta t);
therefore, at the end of the period (time t + Δ t), the mass m of air in the gas cavity ipiCan be expressed as follows:
Figure BDA0003316250540000181
in the above formula, mi、mpiRespectively representing the mass of the gas cavity i at the beginning of the time interval (time t) and at the end of the time interval (time t + deltat),
Figure BDA0003316250540000182
and
Figure BDA0003316250540000183
respectively representing the mass flow of the gas cavity i flowing in or out at the beginning (time t) and the end (time t + delta t) of the time period;
assuming an inflow and outflow open-full flow water transportation power generation system in the air isentropic change process, the following four situations need to be considered for the gas state in the gas cavity by the aerodynamic principle:
1) when p is0>pi>0.53p0When the gas flow state is subsonic
Figure BDA0003316250540000184
Can be expressed as follows:
Figure BDA0003316250540000185
2) when pi<0.53p0Mass flow of air with critical speed of sound
Figure BDA0003316250540000186
Can be expressed as follows:
Figure BDA0003316250540000187
3)
Figure BDA0003316250540000188
when the gas is flowing out at subsonic speed, the mass flow rate of the air
Figure BDA0003316250540000189
Can be expressed as follows:
Figure BDA00033162505400001810
4)
Figure BDA0003316250540000191
mass flow of air from critical speed of sound
Figure BDA0003316250540000192
Can be expressed as follows:
Figure BDA0003316250540000193
in the above formula, p0And T represents the absolute pressure and absolute temperature of the atmosphere outside the tunnel respectively; cinAnd CoutRespectively representing the flow coefficients of gas flowing in and out, and respectively taking the values as 0.75 and 0.85; a. theinAnd AoutRespectively representing the areas of an air inlet and an air outlet of the air cavity i, and calculating and determining according to the area of the cross section of the open-full flow section of the tunnel; rho0Represents the atmospheric density and is defined as follows:
Figure BDA0003316250540000194
and (4) conclusion: in the embodiment, by adopting the hydropower station regulation guarantee simulation platform with the pressure regulating chamber and the open-full flow tail water system, the control working condition of sudden rated load shedding of the rated water head hydroelectric generating set of the hydropower station is simulated and calculated, and the working condition is completely consistent with the working condition of a field test; the hydropower station with the pressure regulating chamber and the open-full flow tail water system is adopted for regulating and ensuring the comparison conditions of the results of the simulation platform calculation and the field actual measurement of the rotating speed of the unit, the inlet pressure of the volute, the inlet pressure of the tail water pipe, the variable-roof pressure and the like are respectively shown in the figures 3, 4, 5 and 6;
as can be seen from comparison between the results of the electric calculation and the actual measurement results of the field test shown in fig. 3, 4, 5 and 6 (in fig. 3 to 6, S1 represents the result of the electric calculation, and S2 represents the actual measurement results of the field test): the two methods (namely, the electric calculation and the field test actual measurement) have better approximation, so that the accuracy of the calculation method provided by the invention is verified to a certain extent; therefore, the hydropower station with the pressure regulating chamber and the open-full flow wake system provided by the invention is adopted for regulating and ensuring that the simulation platform can better obtain the change history and the extreme value of the parameters of the mixed-flow type water-turbine generator set with the pressure regulating chamber and the open-full flow wake system and the water delivery power generation system thereof in the transition process.
Other parts not described belong to the prior art.

Claims (7)

1. Take surge-chamber and open full-flow wake system hydropower station to adjust and guarantee simulation platform, its characterized in that: the system comprises a pressure section module, a bright and full alternating flow section module, a mixed flow type hydraulic generator set module, a speed regulator module, a tail water pressure regulating chamber module, a gas cavity module and a power grid module of the water delivery power generation system;
the pressure section module of the water delivery power generation system is used for describing the pressure transient flow fluid movement of a tunnel or a pipeline of the pressure water delivery power generation system;
the open-full alternating flow section module is used for describing the motion of open-full flow fluid, simulating the change rule of the water depth/water pressure and open-full flow interface of the open-full flow section of the water delivery and power generation system, and calculating and analyzing the influence of the air intake and exhaust processes and water pressure fluctuation of the open-full flow section water delivery and power generation system on the stable operation of the water turbine generator set;
the mixed-flow water turbine generator set module is used for determining parameters of the mixed-flow water turbine, and the parameters of the mixed-flow water turbine comprise an effective water head, boundary conditions, flow, shaft output and generator set rotating speed;
the speed regulator module is used for optimizing and setting speed regulator parameters;
the tail water surge chamber module is used for substituting the head end characteristic of the tail water tunnel, the tail end characteristic of the tail water branch tunnel and the flow speed head difference into a surge chamber continuous equation to obtain the surge condition of the tail water surge chamber;
the gas cavity module is used for calculating an airbag cavity control body of the open-full flow section and describing the influence of air detained in the tunnel and air permeation and discharge at the top of the tunnel on the open-full flow section;
and the power grid module is used for determining the stability of the power grid frequency modulation working condition unit.
2. The hydropower station regulation assurance simulation platform with a pressure regulating chamber and an open-full flow tailwater system according to claim 1, wherein: in the pressure section module of the water delivery power generation system, a pressure section control equation and a solving method thereof are as follows:
the differential equations describing the motion of pressure transient fluid are shown in equations (1) and (2):
Figure FDA0003316250530000011
Figure FDA0003316250530000012
wherein V is the fluid velocity, m/s; h is water level or pressure, m; a is the water shock wave speed, m/s; g is the acceleration of gravity, m/s2；S0Is a channel bottom slope; sfIs a friction slope.
The tunnel or pipeline of the pressure water delivery power generation system adopts a characteristic line method to convert a fluid motion partial differential control equation into an ordinary differential equation, and the following can be obtained:
the positive characteristic line equation applicable to the lower end face of the pipeline for describing transient flow is as follows:
Qp1＝Cp-CaHp1 (3)
the negative characteristic line equation applicable to the upper end face of the pipeline for describing transient flow is as follows:
Qp2＝Cn+CaHp2 (4)
in the formula, Qp1And Qp2Flow rate of the lower and upper end faces, m3/s；Hp1And Hp2Water level or pressure m on the lower end surface and the upper end surface respectively; ca、CpAnd CnAre discrete equation coefficients.
3. The hydropower station regulation assurance simulation platform with a pressure regulating chamber and an open-full flow tailwater system according to claim 2, wherein: in the full alternating flow section module, the full alternating flow section control equation and the solving method thereof are as follows:
the differential equations describing the motion of the full flow fluid are shown in equations (5) and (6):
Figure FDA0003316250530000021
Figure FDA0003316250530000022
in the formula, B is the width of the water surface, m; y is water level or pressure, m; v is the fluid velocity, m/s; g is the acceleration of gravity; a is the area of the water passing section; s0Is a channel bottom slope; sfIs friction slope drop;
and (3) discretizing the equation (5) and the equation (6) by adopting a finite difference method implicit format, and solving by adopting a Sternikov implicit format.
4. The hydropower station regulation assurance simulation platform with a pressure regulating chamber and an open-full flow tailwater system according to claim 3, wherein: in the mixed-flow type hydraulic generator set module,
the calculation equation of the effective water head of the water turbine and the solving method thereof are as follows:
the energy equation of the water turbine is mainly expressed by the effective water head of the water turbine; the effective working head acting on the water turbine under the stable working condition is the total pressure difference of the inlet and outlet measuring sections of the water turbine; in the transient process, considering that the section of a flow passage inlet and a draft tube of a unit section are influenced by water hammer, the invention uses a piezometer tube water head of the tail end section of an equivalent pipe at the upstream of a water turbine, a flow velocity water head and a piezometer tube water head of the head section of the equivalent pipe at the downstream of the water turbine to subtract the piezometer tube water head and the flow velocity water head as effective water heads of the water turbine, and the result has better approximation, namely, the formula for calculating the unit water head is shown as the formula (7):
Figure FDA0003316250530000031
wherein HtIndicating the effective operating head, Q, of the water turbinetRepresenting the flow of the water turbine; hp4、S4And Hp5、S5Respectively showing the pressure and the flow area of the cross section of the upstream and downstream equivalent pipes of the water turbine；
The boundary condition of the francis turbine utilizes a unit flow-unit rotating speed relation curve and a unit output-unit rotating speed relation curve which are formed by the dispersion of a model turbine comprehensive characteristic curve, adds a unit inertia equation and a guide vane action rule to solve the load change of a unit, and then the rotating speed n and the flow Q of the turbinetThe specific solving method comprises the following steps of:
according to the unit speed n of the water turbine11Opening a of the stator, assuming a unit flow rate Q11Unit speed of rotation n11Satisfy a linear relationship within a certain range, in terms of Q11To find the flow rate Q of the water turbinet；
Figure FDA0003316250530000032
According to unit speed n11And opening degree of guide vane alpha from N11～n11Interpolating on the curve to find the corresponding N11Value, then by N11Determining the shaft output N of the water turbinet：
Figure FDA0003316250530000033
Wherein D is1Representing the diameter of the inlet runner of the water turbine;
and then, calculating the rotating speed n of the hydroelectric generating set by utilizing a set inertia equation of load shedding:
Nt＝WR2(2π/60)2·n(dn/dt) (10)
wherein, WR2The inertia moment of the water turbine generator set is expressed, the differential equation is integrated within delta t time, and the rotating speed n of the generator set at any time t in the middle of the hydraulic transition process is simplifiedpExpressed as:
Figure FDA0003316250530000034
wherein n isoRepresenting instantaneous speed of water turbine at last moment, N0And the instantaneous output of the water turbine at the last moment is shown, and delta t represents the time difference between two adjacent calculation nodes.
5. The hydropower station regulation assurance simulation platform with a pressure regulating chamber and an open-full flow tailwater system according to claim 4, wherein: in the tail water pressure regulating chamber module, a pressure regulating chamber continuous equation and a solving method thereof are as follows:
let QbpRepresenting the flow through the bottom of the pressure-regulating chamber, HbpFor the head of the piezometer tube at the bottom of the pressure regulating chamber, Hp3The water surface elevation of the surge chamber; qp6Representing the flow of the tail water branch hole section before passing through the pressure regulating chamber; qp7Representing the flow of the tail water tunnel cross section after passing through the surge chamber;
the characteristic line equation of the head end of the tailwater tunnel:
Figure FDA0003316250530000044
tail water branch hole tail end characteristic line equation:
Qp6＝Cp6-Ca6·Hp6 (13)
pressure regulating chamber continuous equation:
Figure FDA0003316250530000041
considering the gradual change influence of the flow passage at the bottom of the pressure regulating chamber, the front and the rear equivalent measuring tubes of the pressure regulating chamber have a flow speed water head difference:
Figure FDA0003316250530000042
wherein, KbpFor the impedance hole impedance coefficient of the voltage regulating chamber, the following is defined:
Figure FDA0003316250530000043
Sbpmu is a flow coefficient, and is generally 0.6-0.8; s6、S7The cross section areas of the tailwater branch tunnel and the tailwater tunnel are respectively;
substituting equations (12), (13) and (15) into (14), and solving differential equation (14) by the Runge Kutta method.
6. The hydropower station regulation assurance simulation platform with a pressure regulating chamber and an open-full flow tailwater system according to claim 5, wherein: in the gas cavity module, the calculation method of the air bag cavity control body at the full flow section is as follows,
according to a hydraulic model experiment, the airbag in the tunnel is broken when the power generation tail water tunnel exhausts or intakes for a hydropower station which is similar to a diversion tunnel and is used as a power generation tail water tunnel, so that the airbag at the top of the diversion tunnel is discretized, namely the airbag is respectively concentrated near the top of the tail end of each calculation section to form small cavities, and the cavities are used as an internal boundary of each calculation section;
basically assuming that air retained in the tailwater tunnel is ideal gas, and the moving process meets the isothermal change process; the ideal gas state equation is shown below:
piVpi＝mpiRT (16)
in the above formula, piDenotes the absolute pressure, V, in the gas cavity ipiAnd mpiRespectively representing the gas volume and mass of the gas cavity i at the end of the time period, R representing the gas constant, and T representing the absolute temperature of the gas;
wherein the absolute pressure p in the gas cavity iiSolving the pressure H with the position transient flow control equationpiSatisfies the following relationship:
pi＝ρg(Hpi+p0/ρg) (17)
the volume of the gas cavity i satisfies the continuity equation, expressed as follows:
Vpi＝Vi+0.5Δt(Qpi+Qi-Qpiout-Qiout) (18)
in the above formula, Qiout、QpioutRespectively representing the flow rate of the gas cavity i at the beginning and at the end of the time interval, QiAnd QpiRespectively representing the inflow flow of the gas cavity i at the beginning and the end of the time interval;
thus, the mass m of air in the gas cavity i at the end of the time periodpiIs represented as follows:
Figure FDA0003316250530000051
in the above formula, mi、mpiRespectively representing the mass of the gas cavity i at the beginning and at the end of the time period,
Figure FDA0003316250530000052
and
Figure FDA0003316250530000053
respectively representing the mass flow of the gas cavity i flowing in or out at the beginning and the end of the time period;
assuming an inflow and outflow open-full flow water transportation power generation system in the air isentropic change process, the following four situations need to be considered for the gas state in the gas cavity by the aerodynamic principle:
1) when p is0>pi>0.53p0When the gas flow state is subsonic
Figure FDA0003316250530000054
Can be expressed as follows:
Figure FDA0003316250530000061
2) when pi<0.53p0Mass flow of air with critical speed of sound
Figure FDA0003316250530000062
Can be expressed as follows:
Figure FDA0003316250530000063
3)
Figure FDA0003316250530000064
when the gas is flowing out at subsonic speed, the mass flow rate of the air
Figure FDA0003316250530000065
Can be expressed as follows:
Figure FDA0003316250530000066
4)
Figure FDA0003316250530000067
mass flow of air from critical speed of sound
Figure FDA0003316250530000068
Can be expressed as follows:
Figure FDA0003316250530000069
in the above formula, p0And T represents the absolute pressure and absolute temperature of the atmosphere outside the tunnel respectively; cinAnd CoutRespectively representing the flow coefficients of gas flowing in and out, and respectively taking the values as 0.75 and 0.85; a. theinAnd AoutRespectively representing the areas of an air inlet and an air outlet of the air cavity i, and calculating and determining according to the area of the cross section of the open-full flow section of the tunnel; rho0Represents the atmospheric density and is defined as follows:
Figure FDA00033162505300000610
7. the hydropower station regulation assurance simulation platform with a pressure regulating chamber and an open-full flow tailwater system according to claim 6, wherein: the hydropower station regulation guarantee simulation calculation method with the pressure regulating chamber and the open-full flow tail water system comprises the following steps,
the method comprises the following steps: the model starts to run;
step two: reading in a runner and a power station database;
step three: calculating a common time step Δ t;
step four: calculating initial steady state water head, output, guide vane opening, each segmented flow, initial water level of a surge chamber, the depth of the open full flow and air content;
step five: calculating time t;
t＝(t+Δt)
step six: setting a water head and a rotation speed iteration initial value of the water turbine;
step seven: calculating the opening degree of the guide vane according to the closing rule of the guide vane;
step eight: calculating a unit instantaneous value;
step nine: calculating instantaneous values of a pressure section and a non-pressure section of the water delivery system;
step ten: determining nw、npThe relationship of t;
when | nw-npWhen the/delta t is more than or equal to 0.01, jumping to the sixth step;
when | nw-npIf the/| delta t is less than 0.01 and small fluctuation exists, jumping to the eleventh step;
when | nw-npWhen the/| delta t is less than 0.01, jumping to a step thirteen;
step eleven: solving a speed regulator equation;
step twelve: calculating the angle and performance parameters of the guide vane of the unit corresponding to the predicted output;
step thirteen: calculating the flow and the water head of each section of the flow channel;
fourteen steps: storing the result;
step fifteen: calculating t, and jumping to the fifth step when t is less than Time;
when t is larger than or equal to the Time, jumping to the step sixteen;
sixthly, the steps are as follows: and after the calculation is finished, drawing a chart and outputting a calculation result.
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CN104179159A (en) * 2014-09-11 2014-12-03 武汉大学 Hydropower station free-surface-pressurized flow tail water system
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