CN115587458A - Modeling simulation method for gas-water transient flow of long-distance water conveying pipeline - Google Patents

Modeling simulation method for gas-water transient flow of long-distance water conveying pipeline Download PDF

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CN115587458A
CN115587458A CN202211370280.6A CN202211370280A CN115587458A CN 115587458 A CN115587458 A CN 115587458A CN 202211370280 A CN202211370280 A CN 202211370280A CN 115587458 A CN115587458 A CN 115587458A
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gas
air mass
water body
pressure
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周领
冯瑞琳
陆燕清
李赟杰
薛子剑
胡垠盈
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Hohai University HHU
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Abstract

The invention discloses a modeling simulation method of a gas-water transient flow of a long-distance water pipeline, which comprises the following steps: constructing a control equation of the fast-charging water body carrying the atmospheric air mass in consideration of the step-like unsteady friction model; constructing a numerical format of the fast-charging water body carrying the atmospheric air mass of the unsteady friction model; and (4) carrying out boundary conditions of the pressurized air and the water body, and calculating to obtain a simulation result. The invention develops a stable numerical method for the rapid charging process carrying the atmospheric air mass, and the proposed Galdanai air-water format is more stable and accurate in reproducing the measured atmospheric air mass pressure fluctuation even under the condition that the coulomb number is less than 1; the second order Galdanai scheme adds unsteady friction in the fast charge simulation to facilitate more accurate simulation of the energy consumption process.

Description

Modeling simulation method for gas-water transient flow of long-distance water conveying pipeline
Technical Field
The invention belongs to the technical field of hydraulic numerical simulation calculation of hydropower stations (pump stations), and particularly relates to a modeling simulation method of gas-water transient flow of a long-distance water pipeline.
Background
Large lumps of air are often present at high points and in cross-sectional unevenness in the water supply network. The pressurized atmosphere in the ductwork can cause significant damage and can even lead to a geyser burst or failure of system components. Accurate numerical simulation of all such gas-water transient events is therefore essential to provide safe operating regulations for the piping system and a better understanding of the relevant gas-water mode mechanisms.
Characterization schemes have been widely used to simulate duct transient flow induced by entrained large gas masses. The rigid column method for carrying the atmospheric air mass in the quick charging process is firstly proposed. To improve the accuracy of the method, other factors are added gradually to the existing model, such as filling length variation, water elasticity and unsteady friction. Elastic water models that take into account the elasticity of the water are often used to simulate a rapid charging process with entrained atmospheric air masses. To date, most existing fast-fill models are feature solutions, and developed and validated in the case of single-feature pipelines, where the coulomb number is adjusted to 1.
Real water piping systems often have sections of various lengths, diameters or even materials, and in these complex piping systems the coulomb number cannot be perfectly equal to 1. Therefore, the signature scheme must employ interpolation or wave speed adjustment in the pipeline, both of which can lead to inaccuracies in the numerical simulation.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problem that the numerical value shown by a characteristic scheme is weakened when the coulomb number is less than 1, a modeling simulation method of the gas-water instantaneous flow of the long-distance water conveying pipeline is provided, a stable numerical method is developed for the rapid charging process carrying the atmospheric mass, and the proposed Galdenafil air-water format is more stable and accurate in the aspect of reproducing the measured atmospheric mass pressure fluctuation even under the condition that the coulomb number is less than 1; the second order Galdanai scheme adds unsteady friction in the fast charge simulation to facilitate more accurate simulation of the energy consumption process.
The technical scheme is as follows: in order to achieve the purpose, the invention provides a modeling simulation method of a gas-water transient flow of a long-distance water conveying pipeline, which comprises the following steps:
s1: constructing a control equation of the fast-charging water body carrying the atmospheric air mass in consideration of the step-like unsteady friction model;
s2: constructing a numerical format of the fast-charging water body carrying the atmospheric air mass of the unsteady friction model based on the constructed control equation;
s3: and combining the constructed control equation and the numerical format to perform boundary conditions of the pressurized air and the water body, and calculating to obtain a simulation result.
Further, the control equations in the step S1 include a non-constant water body control equation considering unsteady friction, a pressurized gas control equation, and a gas mass-water interface control equation.
Further, the expression of the non-constant water control equation considering the unsteady friction is as follows:
Figure BDA0003924571120000021
Figure BDA0003924571120000022
in the formula, H is the height of a water head of the piezometer tube; v is the average flow rate; c is the acoustic wave velocity propagating in the water; g is the acceleration of gravity; z is the distance along the pipeline; t is time; f is the Darcy-Visbach coefficient of friction; k is the tile ground friction coefficient; when the flow rate is greater than or equal to zero, sign (V) =1; when the flow rate is less than zero, sign (V) = -1; d is the diameter of the pipeline; the equation of the formula (2) is an unsteady friction term on the right side as a whole.
Further, the expression of the pressurized gas control equation is:
Figure BDA0003924571120000023
in the formula, P a The pressure of the gas after being pressurized; v a The moving speed of the gas under pressure; p a0 And V a0 Is P a And V a An initial value of (d); m is an index of gas state, and may be constant regardless of the transfer of heat.
Further, the expression of the control equation at the air mass-water interface is as follows:
Figure BDA0003924571120000024
in the formula, L W Is the length of the water body, L W0 Is L W The initial value of (1) is obtained by integrating the moving speed delay time when the gas is pressed to obtain the water body change length after a period of time; by solving equations (3) and (4), a method of capturing the pressure and velocity at the boundary between the moving air mass and water is established.
Further, the numerical format in step S2 is a non-constant water body numerical format considering unsteady friction, and specifically includes the following steps:
Figure BDA0003924571120000025
in the formula (I), the compound is shown in the specification,
Figure BDA0003924571120000026
w，
Figure BDA0003924571120000027
s is a matrix converted into a Galdenafil method; f is a solving processFlux; the water body can be divided into N unit bodies, and the integral of the formula (3) along the boundary of each control body i can obtain a result;
for the ith control volume, the integral between control planes i-1/2 and i +1/2 can be expressed as:
Figure BDA0003924571120000028
in the formula, Δ t is time interval, Δ x is space step length, superscripts n and n +1 represent t and t + Δ t time steps, respectively, and W is W at interface [ i-1/2, i +1/2 ] of control body]Is determined by the average value of (a) of (b),
Figure BDA0003924571120000031
and
Figure BDA0003924571120000032
is the ith cell internal cell flux.
Further, the step S3 specifically includes:
when the boundary unit at the junction of the water body and the large-volume air mass is calculated, a Galdenafil method and a characteristic scheme are combined:
Figure BDA0003924571120000033
Figure BDA0003924571120000034
Figure BDA0003924571120000035
Figure BDA0003924571120000036
in the formula, H A ，V A The value of the N-1/2 interface W; h C ，V C Is water body and large volume of airPressure and velocity at the bolus junction; h P ，V P The pressure and velocity determined jointly for equations (7) and (8); h E ，V E Is H P ，V P Pressure and velocity at the previous time; h G ，V G Is H P ，V P The pressure and the speed obtained by interpolation at the current moment and the last moment; h D ，V D The pressure and the speed obtained at the gas interface of the water body; Δ L w The length of the micro water body section is continuously changed along with the compression and expansion of the gas; w N+1 ，W N+2 Is the virtual cell volume value.
The invention provides a second-order finite volume Galdenafil scheme for simulating a fast charging and flowing process of large-volume air entrained by a long-distance water conveying pipeline, which is not used for solving the problem of impacting the large-volume air before. In complex piping systems, when the coulombs are less than 1, the Galdenafil scheme performs better in transient pressure simulation than the signature schemes used in the past, because the numerical format has the advantage of producing less attenuation in numerical format. The Galdanai scheme provided by the invention considers the unsteady friction coefficient in the water filling column simulation, and can more accurately represent the energy dissipation process. The invention provides an air-water boundary processing method based on a second-order Galdenafil scheme, a special mixing strategy is provided at the air-water boundary, and a characteristic scheme and the Galdenafil scheme are combined to solve so as to solve the problem of unit assignment caused by real-time dynamic change of the air-water interface.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1. the Galdenafil format is utilized to simulate the process of the rapid charge of the entrained air mass, the numerical value format improvement is carried out on the process of simulating the rapid charge of the entrained air mass by the prior characteristic scheme, when the coulomb number is less than 1, less numerical value format attenuation is generated due to the advantage of the Galdenafil numerical value format, and the Galdenafil performs better than the prior characteristic scheme in the instantaneous pressure simulation.
2. In contrast to the steady friction term, which is added to the governing equation and the modified Galdenafil numerical format, the steady friction is determined by a constant pressure gradient along the axis of the pipe. In this case, wall shear stress or head loss is generally expressed as a function of average velocity. However, during transients involving cavitation, the pressure gradient of the packed water column is time-varying and therefore the velocity profile can be very complex. The friction force is dominant in the boundary layer region, and the inertial force is dominant near the center of the pipe. Therefore, the wall shear stress is not expressed by an average speed function, and the energy change process of the entrained air mass can be simulated more accurately by adding the step Keno unsteady friction term.
3. A Galdenafil method and a characteristic scheme are combined at the boundary to track the moving air mass-water boundary, so that the problem of assignment at the boundary is solved by combining the characteristic scheme while the calculation accuracy is improved by using the Galdenafil method. Short water column length Δ L due to compression and expansion of air column w Constantly changing over time. These results indicate that the variable W for the Nth control volume cannot be obtained by integrating the control surface i-1/2 to i +1/2 once. In order to update W from the current time to the next time, detailed boundary processing indicates that Δ t/(Δ L) is required w A) a number of integrations. However, starting from the second integration, the values of the 4 control volumes adjacent to the nth cell are not updated due to lack of suitable methods. The control body updating difficulty determines that a new method is needed to solve the problem, and the method that the values of 4 control bodies adjacent to the Nth unit are verified to be feasible in combination with the characteristic line method.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a Galdenafil grid diagram of a process water body for entrained air mass fast charging according to the present invention;
FIG. 3 is a schematic of the boundary conditions for the entrained mass rapid charging process of the present invention;
FIG. 4 is a graph comparing experimental values of examples with a second order Galidean Pi-formatted simulated air mass pressure considering step like Nono steady rubbing;
FIG. 5 is a graph comparing an embodiment characterization scheme and a second order Galidean Pi-formatted simulated air mass pressure considering step like Nono steady rubbing.
Detailed Description
The present invention is further illustrated by the following figures and specific examples, which are to be understood as illustrative only and not as limiting the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.
The invention provides a modeling simulation method of a gas-water transient flow of a long-distance water conveying pipeline, which comprises the following steps as shown in figure 1:
s1: constructing a control equation of the fast-charging water body carrying the atmospheric air mass in consideration of the step-like unsteady friction model;
s2: constructing a numerical format of the fast-charging water body carrying the atmospheric air mass of the unsteady friction model based on the constructed control equation;
s3: and combining the constructed control equation and the numerical format to perform boundary conditions of the pressurized air and the water body, and calculating to obtain a simulation result.
In this embodiment, the method is applied as an example, which specifically includes:
in order to verify and analyze the simulation effect of the Galdenafil method of the entrained atmosphere fast-charging process considering unsteady friction, a pipeline hydraulic transient experimental device system designed and built by Zhou in 2018 is selected for verifying the effectiveness of the instantaneous flow simulation method in the fast-filling pipeline with the interlayer air bag. Example 1: the pipeline length 8.862m, the diameter 0.04m, the constant water head of the upstream water tank 0.08MPa, the wave speed 850m/s, the initial static state, the initial air mass length 0.3m, the initial air mass pressure 9.794m and the valve opening instantly. Example 2: the pipeline length is 101m, the diameter is 0.04m, the constant water head of an upstream water tank is 1.35MPa, the wave speed is 850m/s, the pipeline is in a static state initially, the length of an initial air mass is 1m, the pressure of the initial air mass is 9.794m, and the valve is opened instantly.
The specific implementation steps are as follows:
s1: constructing a control equation of the fast-charging water body carrying the atmospheric air mass by considering a step-like Nao unsteady friction model:
the control equations include a non-constant water body control equation that accounts for unsteady friction, a pressurized gas control equation, and a gas mass-water interface control equation.
The expression of the non-constant water control equation considering the unsteady friction is as follows:
Figure BDA0003924571120000051
Figure BDA0003924571120000052
in the formula, H is the height of a water head of the piezometer tube; v is the average flow rate; c is the acoustic wave velocity propagating in the water; g is the acceleration of gravity; z is the distance along the pipeline; t is time; f is the Darcy-Visbach coefficient of friction; k is the tile ground friction coefficient; when the flow rate is greater than or equal to zero, sign (V) =1; when the flow rate is less than zero, sign (V) = -1; d is the diameter of the pipeline; the equation of the formula (2) is an unsteady friction term on the right side as a whole.
The expression of the pressurized gas governing equation is:
Figure BDA0003924571120000053
in the formula, P a The pressure of the gas after being pressurized; v a The moving speed of the gas under pressure; p a0 And V a0 Is P a And V a An initial value of (d); m is an index of gas state, and may be constant regardless of the transfer of heat.
The expression of the control equation at the air mass-water interface is:
Figure BDA0003924571120000054
in the formula, L W Is the length of the water body, L W0 Is L W The initial value of (1) is obtained by integrating the moving speed delay time when the gas is pressed to obtain the change of the water body after a period of timeA length; by solving equations (3) and (4), a method of capturing the pressure and velocity at the boundary between the moving air mass and water is established.
S2: based on the constructed control equation, constructing a numerical format of the fast water-filled body carrying the atmospheric air mass of the unsteady friction model:
Figure BDA0003924571120000055
in the formula (I), the compound is shown in the specification,
Figure BDA0003924571120000061
w，
Figure BDA0003924571120000062
s is a matrix converted into a Galdenafil method; f is the flux of the solving process; the water body can be divided into N unit bodies, and the integration of the formula (5) along the boundary of each control body i can obtain a result.
For the ith control volume, the integral between control planes i-1/2 and i +1/2 can be expressed as:
Figure BDA0003924571120000063
in the formula, Δ t is time interval, Δ x is space step length, superscripts n and n +1 represent t and t + Δ t time steps, respectively, and W is W at interface [ i-1/2, i +1/2 ] of control body]Is determined by the average value of (a) of (b),
Figure BDA0003924571120000064
and
Figure BDA0003924571120000065
is the ith cell internal cell flux.
S3: and (3) combining the constructed control equation and numerical format, carrying out boundary conditions of the pressurized air and the water body, and calculating to obtain a simulation result:
referring to fig. 3, when calculating the boundary unit at the junction of the water body and the large-volume air mass, combining a method and a characteristic scheme of the gadanai pi:
Figure BDA0003924571120000066
Figure BDA0003924571120000067
Figure BDA0003924571120000068
Figure BDA0003924571120000069
in the formula, H A ，V A Is the value of the N-1/2 interface W; h C ，V C The pressure and the speed at the joint of the water body and the large-volume air mass; h P ，V P The pressure and velocity determined jointly for equations (7) and (8); h E ，V E Is H P ，V P Pressure and velocity at the previous time; h G ，V G Is H P ，V P The pressure and the speed obtained by interpolation at the current moment and the last moment; h D ，V D The pressure and the speed obtained at the gas interface of the water body; Δ L w The length of the micro water body section is continuously changed along with the compression and expansion of the gas; w N+1 ，W N+2 Is the virtual cell volume value.
A Galdenafil method and a characteristic scheme are combined at the boundary to track the moving air mass-water boundary, so that the problem of assignment at the boundary is solved by combining the characteristic scheme while the calculation accuracy is improved by using the Galdenafil method. Short water column length Δ L due to compression and expansion of air column w Constantly changing over time. These results indicate that the variable W for the Nth control volume cannot be obtained by integrating the control surface i-1/2 to i +1/2 once. To update W from the current time to the next time, detailed boundary processing, as shown in fig. 2, indicates that Δ t/(Δ L) is required w A) timesAnd (6) integrating. However, starting from the second integration, the values of the 4 control volumes adjacent to the nth cell are not updated due to lack of suitable methods. The control body updating difficulty determines that a new method is needed to solve the problem, and the method of combining the characteristic line method to endow the values of 4 control bodies adjacent to the Nth unit to be feasible is verified.
Through the programmed calculation of the method, in order to show the effect of the method, the calculation result of the Galdenafil method considering the atmosphere entrainment fast-charging process of unsteady friction is compared with the experimental result of the embodiment, and the pressure curve is shown in FIG. 4; the calculation result of the Galdenafil method in the entrained atmosphere fast charging process of mixed format boundary processing is compared with the result of the characteristic scheme of the embodiment, and the pressure curve is shown in FIG. 5.
As can be seen from FIG. 4, compared with a model without considering unsteady friction, the unsteady friction model provided by the invention can accurately describe the transient pipeline pressure amplitude and attenuation.
As can be seen from fig. 5, the result of simulating the pressure of the air mass in the rapid air mass inflation process by the second-order galidenafil method is consistent with the result obtained by the characteristic scheme, and when the coulomb number is less than 1, the numerical value is not weakened, and the calculation result is more accurate and stable.
Therefore, the Galdenafil method for calculating the unsteady friction entrained atmosphere mass rapid charging process can well solve the problem of very difficult accuracy of the characteristic scheme in the entrained atmosphere mass rapid charging process, and the proposed scheme can better reproduce atmospheric mass experimental pressure fluctuation and accurately predict the transient pressure damping of the atmospheric mass pipeline.

Claims (7)

1. A modeling simulation method for a long-distance water pipeline gas-water transient flow is characterized by comprising the following steps:
s1: constructing a control equation of the fast-charging water body carrying the atmospheric air mass in consideration of the step-like unsteady friction model;
s2: constructing a numerical format of the fast-charging water body carrying the atmospheric air mass of the unsteady friction model based on the constructed control equation;
s3: and combining the constructed control equation and the numerical format to perform boundary conditions of the pressurized air and the water body, and calculating to obtain a simulation result.
2. The modeling simulation method for the gas-water transient flow of the long-distance water conveying pipeline according to claim 1, wherein the control equation in the step S1 comprises a non-constant water body control equation, a pressurized gas control equation and an air mass-water junction control equation which take unsteady friction into consideration.
3. The modeling and simulation method for the gas-water transient flow of the long-distance water conveying pipeline according to claim 2, wherein the expression of the unsteady water body control equation considering the unsteady friction is as follows:
Figure FDA0003924571110000011
Figure FDA0003924571110000012
in the formula, H is the height of a water head of the piezometer tube; v is the average flow rate; c is the acoustic wave velocity propagating in the water; g is the acceleration of gravity; z is the distance along the pipeline; t is time; f is the Darcy-Visbach coefficient of friction; k is the coefficient of friction in watts; when the flow rate is greater than or equal to zero, sign (V) =1; when the flow rate is less than zero, sign (V) = -1; d is the diameter of the pipeline; the equation of formula (2) has the unsteady friction term on the right side as a whole.
4. The modeling and simulation method for the gas-water transient flow of the long-distance water conveying pipeline according to claim 2, wherein the expression of the pressurized gas control equation is as follows:
Figure FDA0003924571110000013
in the formula, P a The pressure of the gas after being pressurized; v a The moving speed of the gas under pressure; p a0 And V a0 Is P a And V a An initial value of (d); m is an index of gas state, and may be constant regardless of the transfer of heat.
5. The modeling simulation method for the gas-water transient flow of the long-distance water conveying pipeline according to claim 2 is characterized in that the expression of the control equation at the air mass-water junction is as follows:
Figure FDA0003924571110000014
in the formula, L W Is the length of the water body, L W0 Is L W The initial value of (1) is obtained by integrating the moving speed delay time when the gas is pressed to obtain the water body change length after a period of time; by solving equations (3) and (4), a method of capturing the pressure and velocity at the boundary between the moving air mass and water is established.
6. The modeling simulation method for the gas-water transient flow of the long-distance water conveying pipeline according to claim 1, wherein the numerical format in the step S2 is a non-constant water numerical format considering unsteady friction, and specifically comprises the following steps:
Figure FDA0003924571110000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003924571110000022
w，
Figure FDA0003924571110000023
s is a matrix converted into a Galdenafil method; f is the flux of the solving process; the water body can be divided into N unit bodies, and the integral of the formula (3) along the boundary of each control body i can obtain a result;
for the ith control volume, the integral between control planes i-1/2 and i +1/2 can be expressed as:
Figure FDA0003924571110000024
in the formula, Δ t is time interval, Δ x is space step length, superscripts n and n +1 represent t and t + Δ t time steps, respectively, and W is W at interface [ i-1/2, i +1/2 ] of control body]Is determined by the average value of (a),
Figure FDA0003924571110000025
and
Figure FDA0003924571110000026
is the ith cell internal cell flux.
7. The modeling simulation method for the gas-water transient flow of the long-distance water pipeline according to claim 1, wherein the step S3 specifically comprises:
when the boundary unit at the junction of the water body and the large-volume air mass is calculated, a Galdenafil method and a characteristic scheme are combined:
Figure FDA0003924571110000027
Figure FDA0003924571110000028
Figure FDA0003924571110000029
Figure FDA00039245711100000210
in the formula, H A ，V A Is the value of the N-1/2 interface W; h C ，V C The pressure and the speed at the joint of the water body and the large-volume air mass; h P ，V P The pressure and velocity determined jointly for equations (7) and (8); h E ，V E Is H P ，V P Pressure and velocity at the previous time; h G ，V G Is H P ，V P The pressure and the speed obtained by interpolation at the current moment and the last moment; h D ，V D The pressure and the speed obtained at the gas interface of the water body; Δ L w The length of the micro water body section is continuously changed along with the compression and expansion of the gas; w is a group of N+1 ，W N+2 Is the virtual cell volume value.
CN202211370280.6A 2022-11-03 2022-11-03 Modeling simulation method for gas-water transient flow of long-distance water conveying pipeline Pending CN115587458A (en)

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