CN113962131B - Method for efficiently simulating flow heat transfer of large natural gas pipe network - Google Patents
Method for efficiently simulating flow heat transfer of large natural gas pipe network Download PDFInfo
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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 structural characteristics of the pipe network, and utilizes a cyclic tri-diagonal matrix solving algorithm and an open source vector library to construct a method for separately simulating pipeline nodes in the pipe network, so that the calculation speed is increased.
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 natural gas pipe network.
Background
The oil and gas field relates to the life of army and citizens in China, and along with the rapid development of economy, the requirements of China on petroleum and gas energy sources are increasingly greater, so that the construction of a safe and reliable natural gas pipeline network is one of key factors related to the energy source transformation in China. The natural gas pipe network construction which is safe and reliable can not be used for accurately and efficiently simulating the flowing state of gas in the pipe network, such as pressure, flow, temperature and the like. The existing pipe network simulation algorithm has the factors of large calculated amount (a Newton iteration method, a linearization method and the like, the calculated amount is required to be calculated, the calculated amount is too large), the discrete coefficient matrix solving speed is low (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 method cannot be applied to the simulation requirement of a large natural gas pipe network.
Disclosure of Invention
The invention aims to provide a method for efficiently simulating flow heat transfer of a large natural gas pipe network, which combines sparsity of a discrete matrix and pipe network structure characteristics, and utilizes a cyclic tri-diagonal matrix solving algorithm and an open source vector library to construct a method for separately simulating pipeline nodes in the pipe network, thereby accelerating calculation speed.
In order to achieve the above 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, pipe axial length, pipe diameter, pipe inclination angle, fluid mass source flowing into or flowing out of a pipe and total heat exchange coefficient between fluid and environment;
Establishing a one-dimensional control equation of the natural gas pipe network, wherein the one-dimensional control equation comprises 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 the pipelines of the natural gas pipeline network by constructing a main grid and a staggered grid according to the axial length of the pipeline;
The discrete pipeline adopts a first-order windward format, and a control equation in an integral form is discrete on each grid, wherein the discrete control equation comprises a momentum equation which is discrete on an interlaced grid, and a continuous equation and an energy equation which are discrete on a main grid;
Arranging coefficients in discrete control equations on all grids according to the grid sequence to obtain a coefficient matrix similar to three diagonal angles;
dividing coefficient matrixes corresponding to all pipelines in a natural gas pipeline network into blocks, wherein the coefficient matrixes corresponding to each pipeline are divided into one block;
Extracting coefficient matrixes corresponding to each pipeline according to the blocks to obtain quasi-cyclic tri-diagonal matrixes; based on the cyclic tri-diagonal matrix, quick solution is carried out to obtain a function change solution of two end points and an internal point of the pipeline;
Deleting all common tri-diagonal matrix elements in the partitioned coefficient matrix by using a function transformation solution to obtain an irregular sparse matrix; solving the irregular sparse matrix by adopting a stable bi-conjugate gradient method to obtain an endpoint value of each pipeline;
substituting the end point value of each pipeline into the function variation solution to obtain the internal point value of each pipeline, and constructing a solution of the natural gas pipeline network by the end point value and the internal point value of each pipeline to realize flow heat transfer simulation of the natural gas pipeline network.
Further, the method for constructing the main grid and the staggered grid comprises the following steps: starting from the starting point of each pipeline, dividing the whole pipeline by taking a preset length as a unit, wherein the divided grids are the main grids; the middle points of two adjacent main grids are taken as two boundaries, and the areas in the two boundaries are taken as an interlaced grid.
Further, when the main grid and the staggered grid are constructed at the pipe junction, the main grid is disposed at the pipe junction, and the staggered grid is disposed inside the pipe and is staggered from the main grid by half a grid.
Further, based on the vectorization function library, friction coefficient between the fluid and the pipeline is calculated iteratively.
Further, by utilizing a SIMPLE algorithm, the time-advancing method is used for solving the change data of the fluid speed, the fluid pressure, the fluid speed, the fluid internal energy, the fluid enthalpy and the fluid temperature parameters in the pipe network along with time.
According to the method, the natural gas pipe network control equation is solved by adopting the separation algorithm, so that the problem of overlarge calculated amount caused by the need of calculating the jacobian matrix by the coupling algorithm is avoided. And by combining the characteristic of a discrete equation of the pipe network, decoupling the nodes in the pipe network from the pipes by using a cyclic tri-diagonal matrix rapid solving algorithm, and ensuring the correct connection between the pipes in the pipe network on the basis of fully utilizing the characteristic of rapidly solving by a catch-up method. Finally, the open source vectorization tool is utilized to accelerate the speed of non-four arithmetic, thereby further accelerating the solving speed. By the method, a high-efficiency and rapid large-scale natural gas pipe network simulation method is formed. Experimental results show that the simulation speed of the method can be greatly improved, 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 a large-scale natural gas pipe network, and is used for the aspects of process design, production efficiency improvement, energy conservation, consumption reduction and the like in industry.
Drawings
FIG. 1 is a discrete diagram of pipes in a pipe network using a staggered grid.
Fig. 2 is a diagram of a discrete grid employed by a network node.
Fig. 3 is a three-diagonal-like sparse matrix graph.
Fig. 4 is a block diagram of a sparse matrix.
Fig. 5 is a cyclic-like tri-diagonal matrix diagram.
Fig. 6 is a diagram of a topology of a pipe network.
FIG. 7 is a graph showing the flow trend of pipe network inlet.
FIG. 8 is a graph of the time consumption of commercial software SPS versus the time consumption of the simulation of the present invention under different grids.
Detailed Description
In order to make the technical scheme of the invention more understandable, specific examples are described below in detail with reference to the accompanying drawings.
Because the axial length of the pipeline is far greater than the diameter of the pipeline, a one-dimensional control equation is established, wherein the one-dimensional control equation comprises a continuous equation, a momentum equation and an energy equation:
The continuous equation is: The momentum equation is: /(I) The energy equation is: /(I)Where t represents time, x represents the pipe axial length, ρ represents fluid density, u represents fluid velocity,/>Represents the fluid mass source flowing into or out of the pipe, p represents the fluid pressure, g represents the gravitational acceleration, θ represents the pipe inclination, λ represents the friction coefficient between the fluid and the pipe, D represents the pipe diameter, E represents the internal energy of the fluid, H represents the enthalpy of the fluid, k represents the total heat exchange coefficient between the fluid and the environment, T e represents the ambient temperature, T represents the temperature of the fluid, and A represents the cross-sectional area of the conduit.
The friction coefficient lambda between the fluid and the pipeline adopts Ke Liebo Rock formula:
where K e is the absolute roughness of the pipe and Re is the Reynolds number.
Converting the control equation into an integral form using the Gaussian theorem, i.e /> Where V represents the conduit volume and A represents the conduit cross-sectional area.
According to the axial length of the pipeline, a main grid and an interlaced grid shown in fig. 1 are constructed to discrete all the pipelines in the pipeline network, 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: starting from the starting point of the pipeline, dividing the whole pipeline by adopting a unit with a preset length of 100-1000 m, for example, 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 the midpoints (e.g., P points) in the primary grid as boundaries, every two neighboring midpoints represent an interleaved grid.
The network nodes adopt discrete grids shown in figure 2 in a discrete mode. The main grid is placed at the pipe junction and the staggered grid is placed inside the pipe (i.e., not at the pipe junction) to avoid the problem of speed in more than two directions at the node, i.e., only two forward or backward flow directions. In fig. 2, a solid line box represents a main grid, a broken line box represents an interlaced grid, a numeral represents a grid interface, and a letter represents a center of the main grid.
On the basis of pipeline dispersion, a control equation in an integral form is dispersed on each grid by adopting a first-order windward format (the amount needed at the grid interface but not at the interface but at the node is replaced by a value at the node upstream from the incoming flow direction). Wherein the momentum equations are discrete on an interleaved grid (see fig. 1, solid line grid); the continuous equation and the energy equation are discretized on a main grid (see the dashed grid of fig. 1).
The coefficients in the discrete control equations on all grids are arranged according to the grid order, and a coefficient matrix similar to the three diagonal angles can be obtained, as shown in fig. 3.
The coefficient matrix shown in fig. 3 is partitioned according to each pipeline, namely, equation coefficients corresponding to each pipeline in the pipe network are partitioned into one block, as shown in fig. 4.
Extracting a coefficient matrix (such as a certain dotted line frame in fig. 4) corresponding to a certain pipeline to obtain a cyclic tri-diagonal matrix (on the basis of a standard tri-diagonal matrix, a first row and a last row have non-zero elements on non-tri-diagonal) as shown in fig. 5. Therefore, based on a quick solving algorithm of the class-cyclic tri-diagonal matrix, the function variation solution of the two end points (the start point and the end point) and the internal point (the points except the start point and the end point) of the pipeline is solved by taking the two end points (the start point and the end point) as unknown quantities. The solving process is as follows: let a certain solution of a certain pipeline be denoted by x 1,x2,…,xn-1,xn and x 1、xn be the solution of two endpoints, then the solution of the internal points can be obtained by solving based on a quasi-cyclic tri-diagonal matrix (solving the internal tri-diagonal equation) as ：x2＝s2+a2x1+b2xn,…,xn-1＝sn-1+an-1x1+bn-1xn, where s represents the solution of x 1＝0、xn =0, a represents the solution of x 1＝1、xn =0 and b represents the solution of x 1＝0、xn =1.
Then, deleting all the common tri-diagonal matrix elements shown in fig. 4 to obtain an irregular sparse matrix with greatly reduced matrix orders, so that the number of matrix conditions is also greatly reduced, and solving the irregular sparse matrix by adopting a stable bi-conjugate gradient method (BiCGStab), so as to finally obtain the endpoint value of each pipeline. And substituting the obtained function change solutions x2＝s2+a2x1+b2xn,…,xn-1＝sn-1+an-1x1+bn-1xn of the two end points and the internal point of the pipeline in the previous step to obtain 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 calculated momentum equation) Implicit equation Ke Liebo Rock's equation/>, is usedAn iterative method is needed to solve, the equation contains time-consuming operations such as logarithm, evolution and the like, and a large number of identical operations exist in the calculation process, therefore, when calculating friction, the solving speed is further accelerated by using an open source vectorization function library (such as Numpy in Python and the like) based on hardware acceleration, for example, a corresponding vectorization function library is introduced, all data needing logarithm and evolution are formed into a new array, and the new array is transferred into a function corresponding to the vectorization function library to calculate the logarithm and evolution of the needed data.
And solving the time-dependent 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 by using a SIMPLE algorithm through a time propulsion method.
The acceleration effect of the present invention is described below by a certain pipe network example: FIG. 6 is a topological structure diagram of a pipe network, and FIG. 7 is a comparison diagram of simulation results, wherein the simulation results are basically the same, and the errors are within an acceptable range; fig. 8 shows that the acceleration effect is very remarkable, about 5 to 40 times. The step size of the grid can be 500m (500 m corresponds to the first point in fig. 8) when the method is combined with the field practical application, and the method is about 40 times faster than commercial software, so that the method can completely meet the industrial requirements.
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and those skilled in the art may modify or substitute the technical solution of the present invention, and the scope of the present invention is defined by the claims.
Claims (10)
1. The method for efficiently simulating the flow heat transfer of the large natural gas pipe network is characterized by comprising the following steps of:
Acquiring pipe network parameters of a natural gas pipe network, wherein the pipe network parameters comprise time, pipe axial length, pipe diameter, pipe inclination angle, fluid mass source flowing into or flowing out of a pipe and total heat exchange coefficient between fluid and environment;
Establishing a one-dimensional control equation of the natural gas pipe network, wherein the one-dimensional control equation comprises 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 the pipelines of the natural gas pipeline network by constructing a main grid and a staggered grid according to the axial length of the pipeline;
The discrete pipeline adopts a first-order windward format, and a control equation in an integral form is discrete on each grid, wherein the discrete control equation comprises a momentum equation which is discrete on an interlaced grid, and a continuous equation and an energy equation which are discrete on a main grid;
Arranging coefficients in discrete control equations on all grids according to the grid sequence to obtain a coefficient matrix similar to three diagonal angles;
dividing coefficient matrixes corresponding to all pipelines in a natural gas pipeline network into blocks, wherein the coefficient matrixes corresponding to each pipeline are divided into one block;
Extracting coefficient matrixes corresponding to each pipeline according to the blocks to obtain quasi-cyclic tri-diagonal matrixes; based on the cyclic tri-diagonal matrix, quick solution is carried out to obtain a function change solution of two end points and an internal point of the pipeline;
Deleting all common tri-diagonal matrix elements in the partitioned coefficient matrix by using a function transformation solution to obtain an irregular sparse matrix; solving the irregular sparse matrix by adopting a stable bi-conjugate gradient method to obtain an endpoint value of each pipeline;
substituting the end point value of each pipeline into the function variation solution to obtain the internal point value of each pipeline, and constructing a solution of the natural gas pipeline network by the end point value and the internal point value of each pipeline to realize flow heat transfer simulation of the natural gas pipeline network.
2. The method of claim 1, wherein,
The continuous equation is:
The momentum equation is:
the energy equation is:
where t represents time, x represents the axial length of the pipe, ρ represents the fluid density, u represents the fluid velocity, Represents the fluid mass source flowing into or out of the pipe, p represents the fluid pressure, g represents the gravitational acceleration, θ represents the pipe inclination, λ represents the friction coefficient between the fluid and the pipe, D represents the pipe diameter, E represents the internal energy of the fluid, H represents the enthalpy of the fluid, k represents the total heat exchange coefficient between the fluid and the environment, T e represents the ambient temperature, T represents the temperature of the fluid, and A represents the cross-sectional area of the conduit.
3. The method of claim 2, wherein the friction coefficient λ between the fluid and the pipe is calculated using the following Ke Liebo lock equation:
Wherein K e is the absolute roughness of the pipeline, and Re is the Reynolds number.
4. A method according to claim 3, characterized in that the friction coefficient λ between the fluid and the pipe is iteratively calculated based on a library of vectorized functions.
5. The method of claim 2, wherein the control equation in integral form is:
Where V represents the conduit volume and A represents the conduit cross-sectional area.
6. The method of claim 1, wherein the time-lapse data of fluid velocity, fluid pressure, fluid velocity, fluid internal energy, fluid enthalpy, and fluid temperature parameters in the pipe network are solved by a time-lapse method using SIMPLE algorithm.
7. The method of claim 1, wherein the method of constructing the primary grid and the staggered grid is: starting from the starting point of each pipeline, dividing the whole pipeline by taking a preset length as a unit, wherein the divided grids are the main grids; the middle points of two adjacent main grids are taken as two boundaries, and the areas in the two boundaries are taken as an interlaced grid.
8. The method of claim 7, wherein the predetermined length is 100 to 1000m.
9. The method of claim 1 or 8, wherein when constructing the primary grid and the staggered grid at the pipe junction, the primary grid is disposed at the pipe junction, and the staggered grid is disposed inside the pipe and is staggered from the primary grid by half a grid.
10. The method of claim 1, wherein the method of solving for the function variation solutions of the two end points and the internal point of the pipeline is: for a function variation solution [ x 1,x2,…,xn-1,xn ] of a certain pipeline, wherein x 1、xn is a function variation solution of two endpoints, solving a quasi-cyclic tri-diagonal matrix to obtain a function variation solution of an internal point, namely ：x2＝s2+a2x1+b2xn,…,xn-1＝sn-1+an-1x1+bn-1xn,, wherein s represents a solution of x 1＝0,xn =0, a represents a solution of x 1＝1,xn =0, and b represents a solution of x 1＝0,xn =1.
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