CN114186510A - MOC-CFD coupling-based energy change prediction method for circulating pump system - Google Patents

MOC-CFD coupling-based energy change prediction method for circulating pump system Download PDF

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CN114186510A
CN114186510A CN202111495992.6A CN202111495992A CN114186510A CN 114186510 A CN114186510 A CN 114186510A CN 202111495992 A CN202111495992 A CN 202111495992A CN 114186510 A CN114186510 A CN 114186510A
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陈小平
张孝铭
朱祖超
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Zhejiang Sci Tech University ZSTU
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Abstract

The invention discloses a circulating pump system energy change prediction method based on MOC-CFD coupling, which comprises the steps of constructing a circulating pump system consisting of a pipeline, a valve, a water tank and a centrifugal pump, performing three-dimensional computational fluid dynamics of the centrifugal pump and the valve and one-dimensional characteristic line method coupling analysis of the pipeline, and establishing an energy function of a dimensionless field according to the water tank inlet and outlet water head calculation result and the results obtained by the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve and the one-dimensional characteristic line method coupling analysis simulation calculation of the pipeline, so as to predict the energy change of the circulating pump system. The invention avoids the waste of computing resources caused by three-dimensional computation of the whole system, and simultaneously avoids the defect that the detailed condition of the internal flow of the key component is difficult to determine caused by pure one-dimensional computation of the whole system.

Description

MOC-CFD coupling-based energy change prediction method for circulating pump system
Technical Field
The invention relates to energy change prediction of a circulating pump valve pipeline system, in particular to a one-dimensional-three-dimensional coupling and energy gradient-based simulation method of the circulating pump valve pipeline system under a constant working condition or a variable working condition and a prediction method of subsequent energy consumption evaluation.
Background
The circulating pump valve pipeline system is an important component of the process industry, and is widely applied to the fields of electric power, metallurgy, petrifaction, aerospace and the like, and the energy transmitted to working fluid by the pump is far greater than the energy required by the system. At present, a theoretical simulation and analysis method is lacked for a circulating pump system, so a set of more perfect mechanistic simulation method needs to be established, and more effective energy change analysis is carried out on a simulation result.
The following problems exist in the simulation and energy-saving prediction of the circulating pump system at present:
1. the simulation of the circulation pump system mainly adopts pure one-dimensional numerical simulation, but the pure one-dimensional numerical simulation method has difficulty in analyzing the internal detailed flow of some important parts.
2. The pure three-dimensional numerical simulation method is an effective method for obtaining the internal flow of the hydraulic machine, can analyze the internal flow condition of key components in the system in detail, but can occupy a large amount of computing resources and computing time when the pure three-dimensional calculation is carried out on the whole system, and in addition, if different structures of the system are simulated by adopting the pure three-dimensional numerical simulation method, a large amount of modeling time can be consumed.
Disclosure of Invention
The invention aims to provide a circulating pump system energy change prediction Method based on one-dimensional Characteristic line (MOC) and three-dimensional Computational Fluid Dynamics (CFD) coupling, which simplifies a pipeline part in a circulating pump system into one-dimensional flow, calculates through an MOC theory, simulates a pump and a valve in the system by using three-dimensional CFD, realizes the output Of a transient simulation result, the automatic updating Of boundary conditions and the automatic control Of data interaction, finally establishes an energy change formula, and predicts the energy change caused by different structures Of the system.
The invention relates to a MOC-CFD coupling-based energy change prediction method for a circulating pump system, which comprises the following specific steps:
firstly, constructing a circulating pump system consisting of a pipeline, a valve, a water tank and a centrifugal pump; then, the three-dimensional computational fluid dynamics of the centrifugal pump and the valve and the one-dimensional characteristic line method coupling analysis of the pipeline are carried out, and the specific process is as follows: and in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve, transmitting the pressure of the inlet and the outlet into the one-dimensional characteristic line method analysis of the pipeline after each iteration, comparing the volume flow obtained by the one-dimensional characteristic line method analysis with the volume flow of a speed interface in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve, and calculating the next time step when the convergence standard is reached, or fitting new boundary conditions again in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve for iterative calculation according to the volume flow calculation result obtained by the one-dimensional characteristic line method analysis. And finally, establishing an energy function of a dimensionless field according to the calculated results of the water inlet and outlet water heads of the water tank and the results obtained by three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve and one-dimensional characteristic line method coupling analysis simulation calculation of the pipeline, and predicting the energy change of the circulating pump system. The energy function calculation formula is as follows:
Figure BDA0003400084870000021
preferably, the log LGK expression of the energy gradient is established as follows:
LGK＝log10 K
preferably, the one-dimensional characteristic line analysis process of the pipeline is as follows:
the water flow in the pressure water conduit satisfies the equation of motion and the equation of continuity.
Equation of motion:
Figure BDA0003400084870000022
continuity equation:
Figure BDA0003400084870000023
in the formula, V is the instantaneous flow velocity of water flow in the pipeline, t is time, x is the distance along the axis coordinate axis of the pipeline, H is the instantaneous water head, g is the gravity acceleration, D is the diameter of the pipeline, f is the Darcy-Weisbach friction coefficient, c is the water hammer wave velocity, alpha is the included angle between the axis of the micro-pipe section and the horizontal direction, and alpha is positive when the height of the micro-pipe section increases along the direction of the water flow.
Dividing a pipeline with the length of L into N sections, wherein the length of each section is delta x-L/N, the time step length is delta t-delta x/c, converting a motion equation and a continuity equation into a full differential equation form by adopting a one-dimensional characteristic line method, then constructing a time and space network, and further solving by using a finite difference method to obtain the water head of each position of the pipeline at the corresponding moment.
Constructing a differential network of characteristic lines by finite difference method at t0A positive water hammer C is transmitted from the point A at the moment+Propagating x over Δ t timei-xi-1And if the distance of the segment reaches the point P, integrating the positive characteristic line equation from the point A to the point P along the positive water hammer propagation characteristic line, and simplifying the equation to obtain:
Figure BDA0003400084870000031
in the formula, HPHead at P point, QPIs the volume flow at point P, HAHead at A point, QAIs the volume flow at point A, a is the intermediate transition variable, A is the cross-sectional area of the pipe, xi-1Pipe length along path, x, at point AiThe length of the pipe along the way is P.
Is provided at t0A negative water hammer C is transmitted from the point B at the moment-Propagating x over Δ t timei+1-xiThe distance of the segment is reduced to reach the point P,then the negative characteristic line equation from point B to point P is integrated along the negative water hammer propagation characteristic line and simplified to:
Figure BDA0003400084870000032
in the formula, HBHead at point B, QBIs the volume flow at point B, xi+1The length of the pipe along the way is point B.
Finally, the volume flow at the point P when the characteristic line is propagated along the positive water hammer is obtained by the following steps:
QP＝Kp-KaHP (5)
the volume flow at point P when propagating the characteristic line along the negative water hammer is:
QP＝Kn+KaHP (6)
combining the vertical type (5) and the formula (6), and obtaining a final expression of the volume flow and the water head at the position of the P point of the pipeline:
Figure BDA0003400084870000035
Figure BDA0003400084870000033
then the final expression of the volume flow and the water head at any point of the pipeline is recorded as follows:
Figure BDA0003400084870000034
Figure BDA0003400084870000041
wherein,
Kp＝QA+KaHA-KfQA|QA| (9)
Kn＝QB-KaHB-KfQB|QB| (10)
Figure BDA0003400084870000042
Figure BDA0003400084870000043
each parameter on the right side of the equation of the formula (7) and the equation of the formula (8) can be obtained by calculating the parameter at the previous moment, so that a numerical solution of the transient flow in the pressure diversion pipeline is obtained.
Preferably, the centrifugal pump and the valves are simulated by three-dimensional computational fluid dynamics without considering temperature changes, the solution domain is discretized into a series of nodes with a limited number by using boundary conditions and given initial conditions of water flow velocity, static pressure and external force, the continuous water flow velocity, static pressure and external force in the solution domain are replaced by the set of the water flow velocity, static pressure and external force on the discrete nodes, the continuous boundary conditions in the solution domain are replaced by the set of the boundary conditions on the discrete nodes, and the numerical solution of the fluid control equation on each discrete node is solved iteratively.
Wherein the fluid control equation for a centrifugal pump or valve comprises:
(1) the continuity equation is expressed in a spatial cartesian coordinate system as:
Figure BDA0003400084870000044
where ρ is the fluid density, t represents time,
Figure BDA0003400084870000045
in order to be a gradient operator, the method comprises the following steps,
Figure BDA0003400084870000049
is a centrifugalFlow velocity vector in the pump or valve.
(2) The conservation of momentum equation is expressed in a spatial cartesian coordinate system as:
Figure BDA0003400084870000046
in the formula,
Figure BDA0003400084870000047
denotes the partial derivative, p denotes the pressure, u, v, w denote the pressure, respectively
Figure BDA0003400084870000048
Component in x, y, z coordinate, τxxIndicating viscous stress
Figure BDA0003400084870000051
Two derivations of the x coordinate, τxyIndicating viscous stress
Figure BDA0003400084870000052
Derivation of the x and y coordinates, respectively, tauxzIndicating viscous stress
Figure BDA0003400084870000053
Derivation of the x and z coordinates, respectively, tauyxIndicating viscous stress
Figure BDA0003400084870000054
Derivation of the y and x coordinates, respectively, tauyyIndicating viscous stress
Figure BDA0003400084870000055
Two derivations of the y coordinate, τyzIndicating viscous stress
Figure BDA0003400084870000056
Derivation of the y and z coordinates, respectively, tauzxIndicating viscous stress
Figure BDA0003400084870000057
Derivation of the z and x coordinates, respectively, tauzyIndicating viscous stress
Figure BDA0003400084870000058
Derivation of the z and y coordinates, respectively, tauzzIndicating viscous stress
Figure BDA0003400084870000059
Two derivatives of the z coordinate, Fx、FyAnd FzThe components of the sum of the external forces acting on the infinitesimal body on the x, y and z coordinates respectively.
Preferably, according to Bernoulli's equation, the inlet and outlet water heads of the water tank satisfy the following relation:
Figure BDA00034000848700000510
in the formula, H1Is the inlet head of the water tank H2Is the outlet head of the water tank, Q1Is the volume flow of the inlet of the water tank, Q2Is the volume flow of the outlet of the water tank, D1Is the diameter of the inlet of the water tank D2Is the diameter of the outlet of the water tank, h1Is the height of the inlet of the water tank, h2Is the height of the outlet of the water tank.
The invention has the following beneficial effects:
the MOC-CFD numerical simulation method for the circulating pump valve pipeline system is established by aiming at the circulating pump valve pipeline system, the MOC characteristic line method can be used for efficiently simulating and predicting the extreme value and the change rule of the flow parameter at each node in the pipeline channel, and the method has the advantages of high calculation speed and low calculation cost; and the three-dimensional distribution condition and the evolution law of flow field parameters in a calculation domain can be visually represented by the key parts of the centrifugal pump and the valve by adopting a CFD (computational fluid dynamics) method, so that the research on the internal flow mechanism of the centrifugal pump and the valve and the optimization of the structure are facilitated. Therefore, the MOC-CFD coupling method only analyzes the transient characteristics of the key components, avoids the waste of computing resources caused by three-dimensional computation of the whole system, and also avoids the defect that the detailed condition of the internal flow of the key components is difficult to determine caused by the adoption of pure one-dimensional computation of the whole system. Furthermore, in the simulation process, three-dimensional and one-dimensional boundaries mutually transmit data, wherein the one-dimensional regions representing two pipelines connected with the inlet and the outlet of the centrifugal pump are connected with the centrifugal pump by using the Bernoulli equation, so that a system with longer time or a water tank with smaller size can be simulated, the problem that the dynamic boundary is difficult to determine when key components are independently analyzed is solved, and then an energy function of a dimensionless field is established according to the water inlet and outlet water head calculation results of the water tank and the results obtained by coupling, analyzing and simulating the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve and the one-dimensional characteristic line method of the pipelines, the energy change of the circulating pump system is predicted, and the accuracy of the prediction result is greatly improved.
Drawings
FIG. 1 is a schematic view of a circulating pump system of the present invention.
FIG. 2 is a time and space grid diagram in the one-dimensional eigen-line method employed in the present invention.
FIG. 3 is a flow chart of a three-dimensional computational fluid dynamics simulation.
FIG. 4 is a system transmission diagram of MOC-CFD coupling analysis in the present invention.
FIG. 5 is a flow chart of MOC-CFD coupling analysis in the present invention.
FIG. 6 is an overall flow chart of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 6, the method for predicting the energy variation of the circulating pump system based on MOC-CFD coupling includes the following steps:
as shown in fig. 1, first, a circulation pump system composed of a pipe, a valve, a water tank, and a centrifugal pump is constructed;
then, in order to realize the joint simulation of the pipeline one-dimensional characteristic line method analysis and the centrifugal pump and valve three-dimensional computational fluid dynamics analysis, the real-time transmission of data is realized by taking pressure and volume flow as transmission parameters on the interface of the one-dimensional characteristic line method computation region and the three-dimensional computational fluid dynamics computation region, so that the consistency of boundary data is ensured, and the scheme of the coupling simulation is shown in fig. 4.
The three-dimensional computational fluid dynamics of the centrifugal pump and the valve and the one-dimensional characteristic line method coupling analysis of the pipeline comprise the following specific processes: and in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve, transmitting the pressure of the inlet and the outlet into the one-dimensional characteristic line method analysis of the pipeline after each iteration, comparing the volume flow obtained by the one-dimensional characteristic line method analysis with the volume flow of a speed interface in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve, and calculating the next time step when the convergence standard is reached, or fitting new boundary conditions again in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve for iterative calculation according to the volume flow calculation result obtained by the one-dimensional characteristic line method analysis. The detailed process of coupling is shown in fig. 5.
And finally, establishing an energy function of a dimensionless field according to the calculated results of the water inlet and outlet water heads of the water tank and the results obtained by three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve and one-dimensional characteristic line method coupling analysis simulation calculation of the pipeline, and predicting the energy change of the circulating pump system, as shown in fig. 6. In the energy function, the fluid is represented as a pressure driven flow and a shear driven flow. For the case of simultaneous pressure-driven flow and shear-driven flow, the general calculation of the energy function is as follows:
Figure BDA0003400084870000071
on the basis of the definition of the energy function, the value of K is relatively fixed due to its physical meaning. When the K value is 1.0, a balance between energy increase and energy loss is expressed, that is, local energy is self-sustained. When the K value is larger than 1.0, the amplitude of the energy increase is larger than the amplitude of the energy loss, and when the threshold value is smaller than 1.0, the amplitude of the energy loss is smaller than the amplitude of the energy increase.
As a preferred embodiment, to facilitate the study of the prediction of the system energy variation, the log LGK expression of the energy gradient is established as follows:
LGK＝log10 K
as a preferred embodiment, the one-dimensional characteristic line analysis process of the pipeline is as follows:
the water flow in the pressure water conduit satisfies the equation of motion and the equation of continuity.
Equation of motion:
Figure BDA0003400084870000072
continuity equation:
Figure BDA0003400084870000073
v is the instantaneous flow velocity of water flow in the pipeline, and the unit is m/s; t is time, unit s; x is the distance along the axis coordinate axis of the pipeline, and the unit is m; h is the instantaneous head, in m; g is gravity acceleration in m/s2(ii) a D is the diameter of the pipeline in m; f is the Darcy-Weisbach friction coefficient; c is the water hammer wave velocity in m/s; alpha is the included angle between the axis of the micro-pipe section and the horizontal direction, and when the height increases along the positive direction of x, the alpha is positive.
Dividing a pipeline with the length of L into N sections, wherein the length of each section is delta x-L/N, the time step is delta t-delta x/c, converting a motion equation and a continuity equation into a full differential equation form by adopting a one-dimensional characteristic line Method (MOC), then constructing a time and space network, and further solving by using a finite difference method to obtain the water head of each position of the pipeline at the corresponding moment.
After the finite difference method is used, a constructed characteristic line difference network is shown in fig. 2, wherein the abscissa is the length of the pipeline along the way, and the ordinate is time; is provided at t0A positive water hammer C is transmitted from the point A at the moment+Propagating x over Δ t timei-xi-1And if the distance of the segment reaches the point P, integrating the positive characteristic line equation from the point A to the point P along the positive water hammer propagation characteristic line, and simplifying the equation to obtain:
Figure BDA0003400084870000081
in the formula, HPHead at P point, QPIs the volume flow at point P, HAHead at A point, QAIs the volume flow at point A, a is the intermediate transition variable (eliminated during calculation), A is the cross-sectional area of the pipe, xi-1Pipe length along path, x, at point AiThe length of the pipe along the way is P.
Is provided at t0A negative water hammer C is transmitted from the point B at the moment-Propagating x over Δ t timei+1-xiAnd when the distance of the segment reaches the point P, integrating the negative characteristic line equation from the point B to the point P along the propagation characteristic line of the negative water hammer, and simplifying to obtain:
Figure BDA0003400084870000082
in the formula, HBHead at point B, QBIs the volume flow at point B, xi+1The length of the pipe along the way is point B.
Finally, the volume flow at the point P along the positive water hammer propagation characteristic line (namely the water hammer wave propagation direction is the same as the water flow direction) is obtained by the following steps:
QP＝Kp-KaHP (5)
the volume flow at point P along the negative water hammer propagation characteristic line (i.e. the water hammer wave propagation direction is opposite to the water flow direction) is:
QP＝Kn+KaHP (6)
combining the vertical type (5) and the formula (6), and obtaining a final expression of the volume flow and the water head at the position of the P point of the pipeline:
Figure BDA0003400084870000083
Figure BDA0003400084870000084
then the final expression of the volume flow and the water head at any point of the pipeline is recorded as follows:
Figure BDA0003400084870000085
Figure BDA0003400084870000091
wherein,
Kp＝QA+KaHA-KfQA|QA| (9)
Kn＝QB-KaHB-KfQB|QB| (10)
Figure BDA0003400084870000092
Figure BDA0003400084870000093
each parameter on the right side of the equation of the formula (7) and the equation of the formula (8) can be obtained by calculating the parameter at the previous moment, so that iterative calculation can be performed on a computer by using the MOC to obtain a numerical solution of the transient flow in the pressure diversion pipeline.
As a preferred embodiment, for centrifugal pumps and valves, simulation is carried out by adopting three-dimensional Computational Fluid Dynamics (CFD) under the condition of not considering temperature change, a solution domain is discretized into a series of nodes with limited number by using boundary conditions and given initial conditions of water flow velocity, static pressure and external force, the continuous water flow velocity, static pressure and external force in the solution domain are replaced by a set of the water flow velocity, static pressure and external force on the discrete nodes, the continuous boundary conditions in the solution domain are replaced by a set of the boundary conditions on the discrete nodes, and the numerical solution of a fluid control equation on each discrete node is solved iteratively. Therefore, the scale and complexity of solving the problem by using the CFD method are positively correlated with the performance of software and hardware of the computer. The flow of the CFD simulation is shown in fig. 3.
Deriving a fluid control equation for a centrifugal pump or valve according to the law of conservation of mass and the law of conservation of momentum, the fluid control equation comprising:
(1) continuity equation: according to the law of conservation of mass, the increase in mass per unit time in a infinitesimal body is equal to the net mass entering the infinitesimal body. For the flow problem, the mathematical expression of the law of conservation of mass is the continuity equation, expressed in a spatial cartesian coordinate system as:
Figure BDA0003400084870000094
where ρ is the fluid density, t represents time,
Figure BDA0003400084870000095
in order to be a gradient operator, the method comprises the following steps,
Figure BDA0003400084870000096
is the water flow velocity vector in the centrifugal pump or valve.
(2) Conservation of momentum equation: the sum of the rate of change of the momentum of a elementary body per unit time and the external force acting on the elementary body, i.e. the Navier-Stokes (N-S) equation, is expressed in a spatial cartesian coordinate system as:
Figure BDA0003400084870000101
in the formula,
Figure BDA0003400084870000102
denotes the partial derivative, p denotes the pressure, u, v, w denote the pressure, respectively
Figure BDA0003400084870000103
Component in x, y, z coordinate, τxxIndicating viscous stress
Figure BDA0003400084870000104
Two derivations of the x coordinate, τxyIndicating viscous stress
Figure BDA0003400084870000105
Derivation of the x and y coordinates, respectively, tauxzIndicating viscous stress
Figure BDA0003400084870000106
Derivation of the x and z coordinates, respectively, tauyxIndicating viscous stress
Figure BDA0003400084870000107
Derivation of the y and x coordinates, respectively, tauyyIndicating viscous stress
Figure BDA0003400084870000108
Two derivations of the y coordinate, τyzIndicating viscous stress
Figure BDA0003400084870000109
Derivation of the y and z coordinates, respectively, tauzxIndicating viscous stress
Figure BDA00034000848700001010
Derivation of the z and x coordinates, respectively, tauzyIndicating viscous stress
Figure BDA00034000848700001011
Derivation of the z and y coordinates, respectively, tauzzIndicating viscous stress
Figure BDA00034000848700001012
Two derivatives of the z coordinate, Fx、FyAnd FzThe components of the sum of the external forces acting on the infinitesimal body on the x, y and z coordinates respectively.
As a preferred embodiment, for the water tank, in the normal operation process of the circulating pump system, according to the Bernoulli equation, the water inlet and outlet heads of the water tank satisfy the following relation:
Figure BDA00034000848700001013
in the formula, H1Is the water tank inlet water head, unit m; h2Is the outlet head of the water tank, unit m; q1Is the volume flow of the inlet of the water tank, m3/s；Q2Is the volume flow of the outlet of the water tank, m3/s；D1Is the diameter of the inlet of the water tank, and is unit m; d2Is the diameter of the outlet of the water tank, and is unit m; h is1Is the height of the water tank inlet in m; h is2Is the height of the outlet of the water tank in m; h is1-h2The height difference of the inlet and the outlet of the water tank.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms described in the embodiments but also equivalent technical means which can be conceived by those skilled in the art based on the inventive concept.

Claims (5)

1. The MOC-CFD coupling-based energy change prediction method for the circulating pump system is characterized by comprising the following steps: the method comprises the following specific steps:
firstly, constructing a circulating pump system consisting of a pipeline, a valve, a water tank and a centrifugal pump; then, the three-dimensional computational fluid dynamics of the centrifugal pump and the valve and the one-dimensional characteristic line method coupling analysis of the pipeline are carried out, and the specific process is as follows: transmitting the pressure of an inlet and an outlet to the one-dimensional characteristic line method analysis of the pipeline after each iteration in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve, comparing the volume flow obtained by the one-dimensional characteristic line method analysis with the volume flow of a speed interface in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve, and calculating the next time step when the convergence standard is reached, or fitting new boundary conditions again in the three-dimensional computational fluid dynamics analysis of the centrifugal pump and the valve for iterative calculation according to the volume flow calculation result obtained by the one-dimensional characteristic line method analysis; finally, establishing an energy function of a dimensionless field according to the water tank inlet and outlet water head calculation results and the results obtained by three-dimensional calculation fluid dynamics analysis of the centrifugal pump and the valve and one-dimensional characteristic line method coupling analysis simulation calculation of the pipeline, and predicting the energy change of the circulating pump system; the energy function calculation formula is as follows:
Figure FDA0003400084860000011
2. the MOC-CFD coupling based energy variation prediction method for a recirculating pump system as claimed in claim 1, wherein: establishing the logarithmic LGK expression for the energy gradient is as follows:
LGK＝log10 K。
3. the MOC-CFD coupling based energy variation prediction method for the circulating pump system according to claim 1 or 2, wherein: the one-dimensional characteristic line method analysis process of the pipeline is as follows:
the water flow in the pressure water conduit meets the equation of motion and the equation of continuity;
equation of motion:
Figure FDA0003400084860000012
continuity equation:
Figure FDA0003400084860000013
in the formula, V is the instantaneous flow velocity of water flow in the pipeline, t is time, x is the distance along the axis coordinate axis of the pipeline, H is the instantaneous water head, g is the gravity acceleration, D is the diameter of the pipeline, f is the Darcy-Weisbach friction coefficient, c is the water hammer wave velocity, alpha is the included angle between the axis of the micro-pipe section and the horizontal direction, and alpha is positive when the height of the micro-pipe section increases along the direction of the water flow;
dividing a pipeline with the length of L into N sections, wherein the length of each section is delta x-L/N, the time step length is delta t-delta x/c, converting a motion equation and a continuity equation into a full differential equation form by adopting a one-dimensional characteristic line method, then constructing a time and space network, and further solving by using a finite difference method to obtain the water head of each position of the pipeline at the corresponding moment;
constructing a differential network of characteristic lines by finite difference method at t0A positive water hammer C is transmitted from the point A at the moment+Propagating x over Δ t timei-xi-1And if the distance of the segment reaches the point P, integrating the positive characteristic line equation from the point A to the point P along the positive water hammer propagation characteristic line, and simplifying the equation to obtain:
Figure FDA0003400084860000021
in the formula, HPHead at P point, QPIs the volume flow at point P, HAHead at A point, QAIs the volume flow at point A, a is the intermediate transition variable, A is the cross-sectional area of the pipe, xi-1Pipe length along path, x, at point AiThe length of the pipeline along the way is P;
is provided at t0A negative water hammer C is transmitted from the point B at the moment-Propagating x over Δ t timei+1-xiAnd when the distance of the segment reaches the point P, integrating the negative characteristic line equation from the point B to the point P along the propagation characteristic line of the negative water hammer, and simplifying to obtain:
Figure FDA0003400084860000022
in the formula, HBHead at point B, QBIs the volume flow at point B, xi+1The length of the pipeline along the way which is the point B;
finally, the volume flow at the point P when the characteristic line is propagated along the positive water hammer is obtained by the following steps:
QP＝Kp-KaHP (5)
the volume flow at point P when propagating the characteristic line along the negative water hammer is:
QP＝Kn+KaHP (6)
combining the vertical type (5) and the formula (6), and obtaining a final expression of the volume flow and the water head at the position of the P point of the pipeline:
Figure FDA0003400084860000031
Figure FDA0003400084860000032
then the final expression of the volume flow and the water head at any point of the pipeline is recorded as follows:
Figure FDA0003400084860000033
Figure FDA0003400084860000034
wherein,
Kp＝QA+KaHA-KfQA|QA| (9)
Kn＝QB-KaHB-KfQB|QB| (10)
Figure FDA0003400084860000035
Figure FDA0003400084860000036
each parameter on the right side of the equation of the formula (7) and the equation of the formula (8) can be obtained by calculating the parameter at the previous moment, so that a numerical solution of the transient flow in the pressure diversion pipeline is obtained.
4. The MOC-CFD coupling based energy variation prediction method for the circulating pump system according to claim 1 or 2, wherein: under the condition of not considering temperature change, a centrifugal pump and a valve are simulated by adopting three-dimensional computational fluid dynamics, a solution domain is dispersed into a series of nodes with limited number by utilizing boundary conditions and given initial conditions of water flow velocity, static pressure and external force, the continuous water flow velocity, static pressure and external force in the solution domain are replaced by the water flow velocity, static pressure and external force sets on the discrete nodes, the continuous boundary conditions in the solution domain are replaced by the boundary condition sets on the discrete nodes, and the numerical solution of a fluid control equation on each discrete node is solved in an iterative manner;
wherein the fluid control equation for a centrifugal pump or valve comprises:
(1) the continuity equation is expressed in a spatial cartesian coordinate system as:
Figure FDA0003400084860000037
where ρ is the fluid density, t represents time, and ^ is the gradient operator,
Figure FDA0003400084860000038
is the water flow velocity vector in the centrifugal pump or the valve;
(2) the conservation of momentum equation is expressed in a spatial cartesian coordinate system as:
Figure FDA0003400084860000041
in the formula,
Figure FDA0003400084860000042
denotes the partial derivative, p denotes the pressure, u, v, w denote the pressure, respectively
Figure FDA0003400084860000043
Component in x, y, z coordinate, τxxIndicating viscous stress
Figure FDA0003400084860000044
Two derivations of the x coordinate, τxyIndicating viscous stress
Figure FDA0003400084860000045
Derivation of the x and y coordinates, respectively, tauxzIndicating viscous stress
Figure FDA0003400084860000046
Derivation of the x and z coordinates, respectively, tauyxIndicating viscous stress
Figure FDA0003400084860000047
Derivation of the y and x coordinates, respectively, tauyyIndicating viscous stress
Figure FDA0003400084860000048
Two derivations of the y coordinate, τyzIndicating viscous stress
Figure FDA0003400084860000049
Derivation of the y and z coordinates, respectively, tauzxIndicating viscous stress
Figure FDA00034000848600000410
Derivation of the z and x coordinates, respectively, tauzyIndicating viscous stress
Figure FDA00034000848600000411
Derivation of the z and y coordinates, respectively, tauzzIndicating viscous stress
Figure FDA00034000848600000412
Two derivatives of the z coordinate, Fx、FyAnd FzThe components of the sum of the external forces acting on the infinitesimal body on the x, y and z coordinates respectively.
5. The MOC-CFD coupling based energy variation prediction method for the circulating pump system according to claim 1 or 2, wherein: according to Bernoulli equation, the water tank inlet and outlet water heads satisfy the following relation:
Figure FDA00034000848600000413
in the formula, H1Is the inlet head of the water tank H2Is the outlet head of the water tank, Q1Is the volume flow of the inlet of the water tank, Q2Is the volume flow of the outlet of the water tank, D1Is the diameter of the inlet of the water tank D2Is the diameter of the outlet of the water tank, h1Is the height of the inlet of the water tank, h2Is the height of the outlet of the water tank.
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CN115455850A (en) * 2022-08-29 2022-12-09 北京交通大学 CFD-DEM coupling technology-based distribution calculation method for large-particle-size sandy gravel stratum slurry shield circulation system centrifugal pump
CN116184903A (en) * 2023-02-28 2023-05-30 天津市津安热电有限公司 Early warning system and method applied to abnormal operation of heating system
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115455850A (en) * 2022-08-29 2022-12-09 北京交通大学 CFD-DEM coupling technology-based distribution calculation method for large-particle-size sandy gravel stratum slurry shield circulation system centrifugal pump
CN115455850B (en) * 2022-08-29 2023-08-15 北京交通大学 Method for calculating distribution of centrifugal pumps of slurry shield circulation system of large-particle-size sandy pebble stratum
CN116184903A (en) * 2023-02-28 2023-05-30 天津市津安热电有限公司 Early warning system and method applied to abnormal operation of heating system
CN116305700A (en) * 2023-05-18 2023-06-23 青岛研博数据信息技术有限公司 Water hammer evaluation and elimination model for long-distance water delivery pipe network
CN116305700B (en) * 2023-05-18 2023-08-29 青岛研博数据信息技术有限公司 Water hammer evaluation and elimination model for long-distance water delivery pipe network
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