CN113962131A - Method for efficiently simulating flowing heat transfer of large natural gas pipe network - Google Patents
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Abstract
The invention discloses a method for efficiently simulating flow heat transfer of a large natural gas pipe network, which relates to the field of natural gas pipe network data simulation. The method combines the sparsity of the discrete matrix and the characteristics of the pipe network structure, and utilizes a circular tri-diagonal matrix solving algorithm and an open source vector library to construct a method for separately simulating the pipeline nodes in the pipe network, thereby accelerating the calculation speed.
Description
Technical Field
The invention relates to the field of numerical simulation of natural gas pipe networks, in particular to a method for efficiently simulating flow heat transfer of a large-scale natural gas pipe network.
Background
The oil and gas field is related to the lives of military and civilian in China, and along with the rapid development of economy, the demand of China on petroleum and natural gas energy sources is greater and greater, so that safe and reliable natural gas pipe network construction is one of the key factors related to energy transformation in China. The safe and reliable natural gas pipeline network construction cannot accurately and efficiently simulate the flowing state of gas in the pipeline network, such as pressure, flow, temperature and the like. The conventional pipe network simulation algorithm has the factors of large calculation amount (a Newton iteration method or a linearization method and the like require to calculate a Jacobian matrix, so that the calculation amount is overlarge), low discrete coefficient matrix solving speed (the discrete coefficient matrix is a large irregular sparse matrix and is solved by the iteration method) and the like, so that the overall simulation speed is low, and the simulation requirement of a large natural gas pipe network cannot be applied.
Disclosure of Invention
The invention aims to provide a method for efficiently simulating flow heat transfer of a large natural gas pipe network.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for efficiently simulating flow heat transfer of a large natural gas pipe network comprises the following steps:
acquiring pipe network parameters of a natural gas pipe network, wherein the pipe network parameters comprise time, axial length of a pipeline, diameter of the pipeline, inclination angle of the pipeline, mass source of fluid flowing into or out of the pipeline and total heat exchange coefficient between the fluid and the environment;
establishing a one-dimensional control equation of the natural gas pipe network, including a continuous equation, a momentum equation and an energy equation, and converting the control equation into an integral form by utilizing a Gaussian theorem;
dispersing all pipelines of the natural gas pipe network by constructing a main grid and a staggered grid according to the axial length of the pipelines;
dispersing a control equation in an integral form on each grid by adopting a first-order windward format for the dispersed pipeline, wherein the control equation comprises a momentum equation dispersed on a staggered grid and a continuous equation and an energy equation dispersed on a main grid;
arranging coefficients in the discrete control equations on all grids according to the grid sequence to obtain a coefficient matrix similar to the three opposite angles;
dividing coefficient matrixes corresponding to all pipelines in a natural gas pipeline network into blocks, wherein the coefficient matrix corresponding to each pipeline is divided into one block;
extracting a coefficient matrix corresponding to each pipeline according to the blocks to obtain a circulation-like three-diagonal matrix; fast solving is carried out based on the cyclic tri-diagonal matrix to obtain a function change solution of two end points and an inner point of the pipeline;
deleting all common three-diagonal matrix elements in the coefficient matrix of the block by using function change solution to obtain an irregular sparse matrix; solving the irregular sparse matrix by adopting a stable double-conjugate gradient method to obtain an end point value of each pipeline;
and substituting the endpoint value of each pipeline into the function change solution to obtain the internal point value of each pipeline, and forming a solution of the natural gas pipe network by the endpoint value and the internal point value of each pipeline to realize the flow heat transfer simulation of the natural gas pipe network.
Further, the method for constructing the main grid and the staggered grid comprises the following steps: dividing the whole pipeline by taking a preset length as a unit from the starting point of each pipeline, wherein the divided grids are main grids; and taking the middle points of two adjacent main grids as two boundaries, and taking the area in the two boundaries as a staggered grid.
Further, when main grids and staggered grids are constructed at the pipeline intersection, the main grids are arranged at the pipeline intersection, and the staggered grids are arranged inside the pipeline and staggered with the main grids by half.
Further, based on the vectorization function library, the friction coefficient between the fluid and the pipeline is calculated iteratively.
Further, by utilizing a SIMPLE algorithm, the change data of the fluid speed, the fluid pressure, the fluid speed, the fluid internal energy, the fluid enthalpy and the fluid temperature parameter in the pipe network along with the time are solved through a time propulsion method.
The method solves the natural gas pipeline network control equation by adopting the separation algorithm, thereby avoiding the problem of overlarge calculated amount caused by the fact that the coupling algorithm needs to calculate the Jacobian matrix. And by combining the characteristics of a discrete equation of the pipe network and utilizing a rapid solution algorithm of the cyclic tri-diagonal matrix, the nodes in the pipe network are decoupled from the pipelines, so that the correct relation among the pipelines in the pipe network is ensured on the basis of fully utilizing the rapid solution characteristic of the catch-up method. And finally, accelerating the speed of non-four fundamental operations by using an open source vectorization tool, thereby further accelerating the solving speed. By the method, the efficient and quick large-scale natural gas pipe network simulation method is formed. Experimental results show that the method can greatly improve the simulation speed which is 5-40 times of that of commercial software SPS, and can meet the field requirements. The method can be applied to transient calculation of large natural gas pipe networks, and serves the aspects of process design, production efficiency improvement, energy conservation, consumption reduction and the like in the industry.
Drawings
FIG. 1 is a discretized view of a pipe network pipeline using staggered grids.
Fig. 2 is a discrete grid diagram adopted by the nodes of the pipe network.
Fig. 3 is a class-three diagonal sparse matrix diagram.
Fig. 4 is a block diagram of a sparse matrix.
FIG. 5 is a diagram of a quasi-cyclic tri-diagonal matrix.
Fig. 6 is a pipe network topology structure diagram.
Fig. 7 is a comparison graph of the change trend of the inlet flow of the pipe network.
FIG. 8 is a plot of the SPS elapsed time for commercial software on different grids compared to the simulated elapsed time for the present invention.
Detailed Description
In order to make the technical solution of the present invention more comprehensible, embodiments accompanied with figures are described in detail below.
Because the axial length of the pipeline is far greater than the diameter of the pipeline, a one-dimensional control equation is established, and comprises a continuity equation, a momentum equation and an energy equation:
the continuous equation is:
the momentum equation is:
the energy equation is:
where t represents time, x represents the axial length of the pipe, p represents the fluid density, u represents the fluid velocity,
representing the source of mass of fluid flowing into or out of the pipe, p representing the pressure of the fluid, g representing the acceleration of gravity, theta representing the angle of inclination of the pipe, lambda representing the coefficient of friction between the fluid and the pipe, D representing the diameter of the pipe, E representing the internal energy of the fluid, H representing the enthalpy of the fluid, k representing the overall coefficient of heat transfer between the fluid and the environment, TeRepresenting the ambient temperature, T the fluid temperature, a the conduit cross-sectional area.
The friction coefficient lambda between the fluid and the pipeline adopts the Kohlenberg formula:
wherein KeRe is the Reynolds number for the absolute roughness of the pipe.
Using the Gaussian theorem to convert the governing equation into integral form, i.e.
And
where V represents the conduit volume and a represents the conduit cross-sectional area.
According to the axial length of the pipeline, constructing a main grid and a staggered grid shown in fig. 1 to disperse all the pipelines in the pipe network, wherein in fig. 1, P represents a current node, W represents a west node, E represents an east node, W represents a west interface, and E represents an east interface. The method for constructing the grid comprises the following steps: dividing the whole pipeline by taking a preset length, such as 100-1000 m, as a unit from the starting point of the pipeline to obtain a virtual grid covering the whole pipeline, namely a main grid (a main grid is arranged between two adjacent solid lines in fig. 1); taking midpoints (e.g., points P) in the main mesh as boundaries, every two adjacent midpoints represent an interleaved mesh.
The discrete pipe network nodes adopt discrete grids as shown in figure 2. The main grid is arranged at the pipeline intersection, and the staggered grids are arranged inside the pipeline (namely not arranged at the pipeline intersection), so that the problem that the speed is more than two directions at the node is solved, namely, only two forward or backward flowing directions exist. In fig. 2, the solid line boxes represent the main grid, the dashed line boxes represent the staggered grid, the numbers represent the grid interfaces, and the letters represent the center of the main grid.
On the basis of pipeline dispersion, the integral form of the governing equation is dispersed on each grid using a first order windward format (the quantity required at the grid interface, but not at the interface, but at the node, is replaced with the value at the node upstream in the direction of incoming flow). Where the momentum equations are discretized on a staggered grid (see FIG. 1, solid grid); the continuity equations and energy equations are discretized on a master grid (see dashed grid in fig. 1).
The coefficients in the discrete governing equations on all the grids are arranged according to the grid sequence, so that a coefficient matrix similar to three diagonal pairs can be obtained, as shown in fig. 3.
The coefficient matrix shown in fig. 3 is partitioned according to each pipeline, that is, the equation coefficient corresponding to each pipeline in the pipe network is partitioned into one block, as shown in fig. 4.
Extracting a certain stripA coefficient matrix corresponding to the pipeline (e.g., a dashed box in fig. 4) may obtain a circulation-like tri-diagonal matrix as shown in fig. 5 (based on the standard tri-diagonal matrix, the first row and the last row have non-zero elements on non-tri-diagonals), and is characterized in that the remaining matrix is a normal tri-diagonal matrix except for two end points. Therefore, based on the fast solving algorithm of the quasi-cyclic tri-diagonal matrix, the two end points (the starting point and the end point) are used as unknowns, and the functional change solution of the two end points (the starting point and the end point) and the internal point (the points except the starting point and the end point) of the pipeline is solved. The solving process is as follows: let a certain solution of a certain pipeline use [ x ]1,x2,…,xn-1,xn]Is shown, and x1、xnFor a two-endpoint solution, then by solving (solving the internal tri-diagonal equation) based on the class-circled tri-diagonal matrix, the solution for the interior points can be obtained as: x is the number of2＝s2+a2x1+b2xn,…,xn-1＝sn-1+an-1x1+bn-1xnWherein s represents x1＝0、xnA represents x, a being a solution of 01＝1、xnA solution of 0, b represents x1＝0、xnA solution of 1.
Then, deleting all common tri-diagonal matrix elements shown in fig. 4, obtaining an irregular sparse matrix with a greatly reduced matrix order and a greatly reduced matrix condition number, solving the irregular sparse matrix by adopting a stable bi-conjugate gradient method (bicgsab), and finally obtaining an endpoint value of each pipeline. Then substituting the two end points and the function change solution x of the internal point of the pipeline obtained in the last step2＝s2+a2x1+b2xn,…,xn-1＝sn-1+an-1x1+bn-1xnAnd obtaining the value of the internal point, and finally obtaining the solution of the whole pipe network.
Due to the friction coefficient lambda (friction term) in the calculation of the momentum equation
) The implicit equation of the Collybolok formula is used
An iterative method is needed to solve, the equation also contains time-consuming operations such as logarithm and evolution, and a large number of same operations exist in the calculation process, so that when friction is calculated, an open-source vectorization function library (such as Numpy in Python) based on hardware acceleration is used for further accelerating the solving speed, for example, a corresponding vectorization function library is introduced, and all data needing the logarithm and the evolution are combined into a new array and transmitted into a function corresponding to the vectorization function library to calculate the logarithm and the evolution of the needed data.
And (3) solving the change data of parameters such as fluid speed, fluid pressure, fluid speed, fluid internal energy, fluid enthalpy, fluid temperature and the like in the pipe network along with time by using a SIMPLE algorithm and a time propulsion method.
The acceleration effect of the present invention is described below by a certain pipe network calculation example: FIG. 6 is a diagram of a topology structure of a pipe network, and FIG. 7 is a diagram of a comparison of simulation results, which shows that the simulation results are substantially the same and the error is within an acceptable range; FIG. 8 shows the acceleration ratio, which shows that the acceleration effect is very significant, about 5-40 times. And the grid step length can be 500m (500m corresponds to the first point in the figure 8) in the field practical application, so that the method is about 40 times faster than commercial software, and can completely meet the industrial requirement.
The above embodiments are only intended to illustrate the technical solution of the present invention, but not to limit it, and a person skilled in the art can modify the technical solution of the present invention or substitute it with an equivalent, and the protection scope of the present invention is subject to the claims.
Claims (10)
1. A method for efficiently simulating flow heat transfer of a large natural gas pipe network is characterized by comprising the following steps:
acquiring pipe network parameters of a natural gas pipe network, wherein the pipe network parameters comprise time, axial length of a pipeline, diameter of the pipeline, inclination angle of the pipeline, mass source of fluid flowing into or out of the pipeline and total heat exchange coefficient between the fluid and the environment;
establishing a one-dimensional control equation of the natural gas pipe network, including a continuous equation, a momentum equation and an energy equation, and converting the control equation into an integral form by utilizing a Gaussian theorem;
dispersing all pipelines of the natural gas pipe network by constructing a main grid and a staggered grid according to the axial length of the pipelines;
dispersing a control equation in an integral form on each grid by adopting a first-order windward format for the dispersed pipeline, wherein the control equation comprises a momentum equation dispersed on a staggered grid and a continuous equation and an energy equation dispersed on a main grid;
arranging coefficients in the discrete control equations on all grids according to the grid sequence to obtain a coefficient matrix similar to the three opposite angles;
dividing coefficient matrixes corresponding to all pipelines in a natural gas pipeline network into blocks, wherein the coefficient matrix corresponding to each pipeline is divided into one block;
extracting a coefficient matrix corresponding to each pipeline according to the blocks to obtain a circulation-like three-diagonal matrix; fast solving is carried out based on the cyclic tri-diagonal matrix to obtain a function change solution of two end points and an inner point of the pipeline;
deleting all common three-diagonal matrix elements in the coefficient matrix of the block by using function change solution to obtain an irregular sparse matrix; solving the irregular sparse matrix by adopting a stable double-conjugate gradient method to obtain an end point value of each pipeline;
and substituting the endpoint value of each pipeline into the function change solution to obtain the internal point value of each pipeline, and forming a solution of the natural gas pipe network by the endpoint value and the internal point value of each pipeline to realize the flow heat transfer simulation of the natural gas pipe network.
2. The method of claim 1,
the continuous equation is:
the momentum equation is:
the energy equation is:
where t represents time, x represents the axial length of the pipe, p represents the fluid density, u represents the fluid velocity,
representing the source of mass of fluid flowing into or out of the pipe, p representing the pressure of the fluid, g representing the acceleration of gravity, theta representing the angle of inclination of the pipe, lambda representing the coefficient of friction between the fluid and the pipe, D representing the diameter of the pipe, E representing the internal energy of the fluid, H representing the enthalpy of the fluid, k representing the overall coefficient of heat transfer between the fluid and the environment, TeRepresenting the ambient temperature, T the fluid temperature, a the conduit cross-sectional area.
3. A method according to claim 2, wherein the coefficient of friction λ between the fluid and the pipe is calculated using the formula kolebox:
wherein, KeRe is the Reynolds number for the absolute roughness of the pipe.
4. The method of claim 3, wherein the friction coefficient λ between the fluid and the pipe is iteratively calculated based on a vectorized library of functions.
5. The method of claim 2, wherein the control equation in integrated form is:
wherein V represents the pipe volume and a represents the pipe cross-sectional area.
6. The method of claim 1, wherein the change data of the fluid velocity, the fluid pressure, the fluid velocity, the fluid internal energy, the fluid enthalpy and the fluid temperature parameter with time in the pipe network are solved by a time-marching method by using a SIMPLE algorithm.
7. The method of claim 1, wherein the method of constructing the master grid and the staggered grid is: dividing the whole pipeline by taking a preset length as a unit from the starting point of each pipeline, wherein the divided grids are main grids; and taking the middle points of two adjacent main grids as two boundaries, and taking the area in the two boundaries as a staggered grid.
8. The method of claim 7, wherein the predetermined length is 100 to 1000 m.
9. The method of claim 1 or 8, wherein the main grid is disposed at the pipeline intersection when the main grid and the staggered grid are constructed at the pipeline intersection, and the staggered grid is disposed inside the pipeline and staggered by half a grid from the main grid.
10. The method of claim 1, wherein the solution to the functional change of the two end points and the interior point of the pipe is obtained by: function change solution [ x ] for a certain pipeline1,x2,…,xn-1,xn]Wherein x is1、xnFor the function change solution of two end points, solving the class cycle tri-diagonal matrix to obtain the function change solution of the inner point, namely: x is the number of2＝s2+a2x1+b2xn,…,xn-1＝sn-1+an-1x1+bn-1xnWherein s represents x1＝0，xnA represents x as a solution of 01＝1，xnA solution of 0, b denotes x1＝0，xnA solution of 1.
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