A method for calculating the temperature of a multi-heat source steam network considering intersection nodes

Abstract

The present invention discloses a method for calculating the temperature of a multi-heat source steam network considering intersection nodes, comprising: step 1: using a matrix to represent the relationship between a branch pipe section, a residual tree pipe section, an independent node, and a reference node of a steam network; step 2: dividing the matrix of the steam network into a first-type matrix and a second-type matrix; step 3: calculating the iterative temperature of each node in the first-type matrix according to the steam temperature of the steam source node; step 4: calculating the iterative temperature of each node in the second-type matrix according to the iterative temperature of the intersection node in the first-type matrix; step 5: using the initial pressure and the iterative temperature obtained by joint calculation to repeat steps 2-4 until the iterative difference meets the iteration stop condition; the present invention adopts the Gauss-Seidel iteration method to improve the convergence speed; adopts the idea of ​​a branch pipe network to solve the problem of hydraulic calculation of multiple gas sources in a steam system; adopts the method of dividing the matrix to solve the problem of temperature calculation of intersection nodes in a multi-gas source steam network.

Description

Technical Field

[0001] The invention belongs to the field of steam pipe networks, and in particular relates to a method for calculating the temperature of a multi-heat source steam pipe network taking into account intersection nodes. Background Art

[0002] Steam system is an important public utility that converts primary energy (fuel, water, etc.) into secondary energy (electricity, steam, etc.). Steam, as a good heat transfer medium, has the advantages of high heat capacity, large heat transfer coefficient, and easy access to working fluids. Steam, as a heat source, is widely used in industrial fields such as steel, petrochemical, textile, papermaking, and food processing.

[0003] At present, there have been a lot of research on the hydraulic and thermal calculation of steam systems. The current calculation methods mainly include the ring equation method, the node equation method and the pipe section equation method. These three methods are essentially to solve the basic equations of the pipe network simultaneously, including the pipe network pressure drop / temperature drop equation, the node flow balance equation, and the ring energy equation. However, the current calculation methods all have different shortcomings, including the sensitivity of initial condition setting, the convergence speed problem, the complex input information problem, the applicability of branch-ring mixed pipe networks, the problem of ignoring the effect of steam thermal changes on various properties such as steam density and specific heat, the problem of ignoring the temperature calculation of intersection nodes in multi-heat source steam pipe networks, and the problem of ignoring the calculation of condensate loss. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating the temperature of a multi-heat source steam network taking into account intersection nodes, so as to solve the problems of poor convergence performance of the calculation method and failure to consider intersection nodes in thermal calculations in hydraulic and thermal calculations of multi-heat source steam networks.

[0005] The present invention adopts the following technical solution: a method for calculating the temperature of a multi-heat source steam network considering an intersection node, comprising:

[0006] Step 1: Use a matrix to represent the relationship between the branch pipe section, the remaining branch pipe section, the independent node, and the reference node of the steam pipe network;

[0007] Step 2: Divide the matrix of the steam pipe network into a first type matrix and a second type matrix; the first type matrix is ​​the association matrix of the pipe network between the interconnected gas source nodes and the intersection nodes, and the second type matrix is ​​the association matrix of the pipe network between two interconnected intersection nodes;

[0008] Step 3: Calculate the iterative temperature of each node in the first type matrix according to the steam temperature of the steam source node;

[0009] Step 4: The intersection nodes in the first matrix are used as steam source nodes in the second matrix that intersect with them, and the iterative temperature of each node in the second matrix is ​​calculated according to the iterative temperature of the intersection nodes in the first matrix;

[0010] Step 5: Use the hydraulic iteration method to calculate the initial pressure of the hydraulic iteration calculation according to the matrix, repeat steps 2-4 with the iterative temperature obtained by the joint calculation, and determine the iterative difference of the temperature and pressure of each node until the iterative difference meets the iteration stop condition.

[0011] Furthermore, in step 4, when two steam paths converge into any intersection node, the calculation formula for the node temperature of the intersection node is:

[0012]

[0013] Among them, Q 1 , Q 2 are the steam flow rates of the pipe sections on both sides of the intersection node, T 1 , T 2 are the steam temperatures of the pipe sections on both sides of the intersection.

[0014] Furthermore, the segmentation method in step 2 is specifically as follows: the steam network is divided into multiple parts with each gas source node and each intersection node as breakpoints, wherein the association matrix of the network starting from the steam source node and ending at the first intersection node closest to the steam source node along the network is a first-type matrix; in the network, the association matrix of the network of two connected intersection nodes is a second-type matrix.

[0015] The beneficial effects of the present invention are:

[0016] The present invention does not require input of loop matrix information, has a fast calculation speed, can calculate branch-ring mixed pipe networks, and can completely implement the calculation process by a computer program, thereby improving the problem of convergence failure.

[0017] The present invention adopts Gauss-Seidel iteration method to improve the convergence speed; adopts the idea of ​​tree branch pipe network to solve the problem of multi-gas source hydraulic calculation of steam system; adopts the method of partitioning matrix to solve the problem of intersection node temperature calculation in multi-gas source steam pipe network;

[0018] In the prior art, the calculation of the intersection node temperature is ignored in the usual node equation method, which leads to inaccurate temperature calculation. The present invention solves the problem of ignoring the calculation of the intersection node temperature by using a partition matrix method.

[0019] The present invention improves the stability and convergence accuracy of temperature calculation of a multi-heat source steam pipe network. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the calculation process of the present invention;

[0021] Figure 2 It is a schematic diagram of the steam pipe network of the present invention;

[0022] Figure 3 It is a schematic diagram of the pipe segment node association matrix of the present invention;

[0023] Figure 4 It is a schematic diagram of the structure of the steam pipe network after segmentation of the present invention;

[0024] Figure 5 is a flow chart of a matrix segmentation method of the present invention;

[0025] Figure 6 The flowchart of calculating the node temperature of the intersection node of the present invention is shown in FIG. DETAILED DESCRIPTION

[0026] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] The present invention discloses a method for calculating the temperature of a multi-heat source steam network considering intersection nodes, such as Figure 1 As shown, including:

[0028] Step 1: Use a matrix to represent the relationship between the branch pipe sections, residual pipe sections, independent nodes, and reference nodes of the steam pipe network.

[0029] The steam network can be abstracted as a graph consisting of nodes and pipe segments, such as Figure 2 As shown in Figure 2, the pipe segment node association matrix can be constructed based on the steam network structure, as shown in Figure 2. Figure 3 shown.

[0030] According to the node properties, nodes are divided into independent nodes and reference nodes. According to the pipe network structure, pipe sections are divided into branch pipe sections and residual tree pipe sections. Reference nodes are nodes with known pressure but unknown flow, and independent nodes are nodes with known flow but unknown pressure. Intersection nodes are nodes where two pipe sections intersect.

[0031] The selection of co-tree segments and branch segments is determined based on the relationship between spanning trees and loops in graph theory. A spanning tree is a subgraph that connects all nodes but does not contain any loops. Branch segments are segments in the spanning tree, and segments outside the spanning tree are co-tree segments. The number of branch segments is equal to the number of independent nodes, and the number of co-tree segments is equal to the number of loops in the network (including virtual loops directly formed by two reference nodes).

[0032] The pipe segment node association matrix uses graph theory to represent the relationship between pipe segments and nodes using a matrix, where the rows of the matrix represent nodes and the columns represent pipe segments. ij ] n×m , where n is the number of nodes and m is the number of pipe segments.

[0033] The element of the link node association matrix A in row i and column j is defined as:

[0034]

[0035] To facilitate subsequent calculations, when constructing the matrix row numbering, the independent nodes are on the top and the reference nodes are on the bottom, and when constructing the column numbering, the branch segments are on the left and the residual tree segments are on the right. At this time, the matrix A can be expressed as:

[0036]

[0037] A I =[A 11 |A 12 ], A X =[A 21 |A 22 ]

[0038] Step 2: Divide the matrix of the steam network into a first type matrix and a second type matrix; the first type matrix is ​​the association matrix of the network between interconnected gas source nodes and intersection nodes, and the second type matrix is ​​the association matrix of the network between two interconnected intersection nodes.

[0039] The specific segmentation method is as follows: the steam network is divided into multiple parts with each gas source node and each intersection node as breakpoints, wherein the association matrix of the network starting from the steam source node and ending at the first intersection node closest to the steam source node along the network is a first-type matrix; in the network, the association matrix of the network of two connected intersection nodes is a second-type matrix.

[0040] In actual operation, the matrix A is divided into the pipe segment node association matrix of the pipe network between the gas source node and the intersection node, and the pipe segment node association matrix of the pipe network between the intersection node and the intersection node through retrieval. Figure 5 As shown, specifically: the characteristic of the intersection node in the pipe segment node association matrix A is that there are only two elements +1 in each row. The numbers of all intersection nodes in the pipe network can be obtained through program retrieval; the element -1 in the pipe segment node association matrix A represents the outflow node, and +1 represents the inflow node. The number of the column where the element -1 in the row where the starting node is located is the pipe segment number flowing into the node, and the number of the row where the element +1 in the column is located is the node number flowing into the pipe segment. The above method is used to loop the search from this node until the end node to obtain the pipe segment and node numbers between the start node and all the end nodes. The pipe network structure after the pipe network is divided by the intersection node is as follows: Figure 4 As shown, Figure 4 The overall pipeline network has 2 gas source nodes and 3 intersection nodes, which can be divided into Figure 4 The five parts shown can be classified into two types of matrices, namely, the first type of matrix and the second type of matrix.

[0041] Step 3: Calculate the iterative temperature of each node in the first type of matrix according to the steam temperature of the steam source node.

[0042] Calculate the temperature drop-flow equations of the segmented pipe network represented by the first-class matrix where the steam source node is located The temperature drop ΔT of all pipe sections in this part of the pipe network can be obtained, where each vector can be read from the parameter vector of all pipe sections by the retrieved pipe section number of the split pipe network. x And the corresponding partition matrix A x , which can be determined by And the steam source node temperature is used to obtain the node temperature of the divided pipe network.

[0043] Step 4: The intersection nodes in the first type of matrix are used as steam source nodes in the second type of matrix that intersects with them, and the iterative temperature of each node in the second type of matrix is ​​calculated based on the iterative temperature of the intersection nodes in the first type of matrix.

[0044] like Figure 6 As shown, in step 4, when there are two steam confluences at any intersection node, the calculation formula for the node temperature of the intersection node is:

[0045]

[0046] Among them, Q 1 , Q 2 are the steam flow rates of the pipe sections on both sides of the intersection node, T 1 , T 2 are the steam temperatures of the pipe sections on both sides of the intersection.

[0047] When steam is running, pressure and pipe flow are in a two-way coupling relationship. Changes in node pressure will affect pipe flow. The pressure drop at both ends of the pipe is always consistent with the flow direction. The calculation of pressure and flow is more accurate in the hydraulic calculation of the node equation method. When steam is running, temperature and pipe flow are unidirectionally coupled. The pipe flow affects the heat dissipation and causes changes in node temperature, but the change in node temperature does not directly affect the pipe flow. Since the temperature at the intersection node is the mixed temperature of the steam of the two intersection pipes, the temperature drop of the steam in the pipe is consistent with the flow direction, but the temperature drop at both ends of the pipe may be inconsistent with the flow direction. Since the temperatures at the ends of the two converging pipes at the intersection node are inconsistent, and there are overlapping intersection nodes in the split pipe network where multiple steam source nodes are located, it is necessary to retrieve whether the temperatures at the ends of the pipes at both ends of each intersection node have been calculated. If so, the average temperature is obtained according to the pipe flow, and the node temperature of the split pipe network with the corresponding intersection node as the starting point is obtained based on the intersection node temperature, otherwise it is skipped. By calculating the temperature of each split pipe network in turn, the temperature of each intersection node can be obtained, and finally the temperature of all nodes in the pipe network can be obtained.

[0048] Step 5: Use the hydraulic iteration method to calculate the initial pressure of the hydraulic iteration calculation according to the matrix, repeat steps 2-4 with the iterative temperature obtained by the joint calculation, and determine the iterative difference of the temperature and pressure of each node until the iterative difference meets the iteration stop condition.

[0049] The acquisition and input of the initial information of the pipeline network mainly include the physical parameters of the pipeline network structure and the operating parameters of the steam. The physical parameters of the pipeline network include the length, inner diameter, insulation thickness, outer diameter, roughness, laying scene, etc. of each pipe section of the pipeline network. The operating parameters of steam include the pressure of the reference node, the flow of the independent node, and the temperature of the gas source node. The remaining monitoring operation data can be used as reference values ​​for coefficient correction in the calculation method.

[0050] The hydraulic iterative calculation method of the present invention is essentially a block iterative calculation of the basic equation. X , Independent node traffic G I , find the unknown node pressure P I , node traffic G X .

[0051] 1) Node flow balance equation group A·Q=G, where Q is the pipe flow and G is the node flow;

[0052] 2) Pipe pressure drop equation group A T P = -ΔP, where P is the node pressure and ΔP is the pressure drop in the pipe section;

[0053] 3) Pipeline flow equations Equivalent to

[0054]

[0055] Where: R is the specific friction resistance, i.e. the loss along the pipe per meter, Pa / m; L is the length of pipe section j, m; ζ is the local resistance coefficient of each resistance component on the pipe section; ρ is the density of the steam in the pipe, kg / m 3 ; u is the flow rate of steam in the pipe section, m / s; f is the friction resistance coefficient of the pipe section; d is the inner diameter of the pipe section, m.

[0056] The above three equations can be combined to obtain the equation group of node pressure and node flow:

[0057] [-A·C * ·A T ]·P=G

[0058] The initial temperature, initial pressure, initial density, dynamic viscosity, constant pressure specific volume, and thermal conductivity of the steam in each pipe section are obtained from the IAPWS_IF97 water vapor state calculation model based on the temperature and pressure of the steam source node. The average steam temperature of the pipe section can be obtained by the formula T j =|A T|·T i / 2 to obtain, where T i is the steam temperature at the two end nodes of the pipe section, T j is the average temperature of the steam in the pipe section; A is the relationship matrix of the branch pipe section, residual pipe section, independent node and reference node of the steam pipe network; the initial node temperature of the pipe network can be selected as the steam temperature of the steam source node.

[0059] The selection of the initial pressure of the hydraulic iterative calculation is related to whether the calculation can converge. The calculation method of the initial pressure of the present invention is as follows:

[0060] Given the initial flow value Q of the Yushu pipe section y , can be uniformly taken as a small value of 0.1kg / s. s =A 11 \(G I -A 12 Q y ) to obtain the initial flow vector Q of the branch pipe section s , where G I is the traffic vector of an independent node.

[0061] From the formula u=4·Q / ρπd 2 Obtain the steam velocity vector u of all pipe sections, where is the flow vector of all pipe sections. The Colebrook-White formula for calculating the friction coefficient in the turbulent zone is The friction coefficient vector f of the pipe section is obtained, where ε is the roughness of the pipe section, d is the inner diameter of the pipe section, Re=ρud / μ is the Reynolds number of the steam in the pipe section, ρ is the steam density of the pipe section, and μ is the dynamic viscosity of the steam in the pipe section.

[0062] Depend on The resistance coefficient vector s of the steam in the pipe section is obtained, where L is the length of the pipe section and ζ is the local resistance coefficient.

[0063] From ΔP = s·Q 2 Calculate the pressure drop vector ΔP of the pipe section, where ΔP s is the pressure drop vector of the branch pipe section, ΔP y is the pressure drop vector of the Yushu pipe section.

[0064] Depend on Obtain the initial value of independent node pressure P I , where P X is the reference node pressure value, and finally the initial pressure of hydraulic iteration calculation is obtained The specific calculation iteration process of the Gauss-Seidel iterative method is as follows:

[0065] For a given system of linear equations

[0066] Ax=b

[0067] Where: A is the coefficient matrix; x is the unknown vector; b is the constant vector.

[0068] First, determine the initial guess value x (0) , for each i=1,2,...,n, update x i :

[0069]

[0070] Complete x i After the update, check the convergence conditions, that is, If it is satisfied, the iteration is stopped; otherwise, the iteration is continued until the iteration result satisfies the given convergence condition.

[0071] When using matrices for calculation, the coefficient matrix A is decomposed into A = DLU, where D is a diagonal matrix, L is the negative value of the lower triangular matrix, and U is the negative value of the upper triangular matrix. The update formula for the unknown vector x is as follows:

[0072] x (k+1) =(DL) -1 (b+Ux (k) )

[0073] First build P I is a set of equations with unknown quantities, [-A·C * ·A T ]·P=G, then [-A I ·C * ·A T ]·P=G I ; Let the matrix [-A I ·C * ·A T ] is H I , H I Divided into two matrices, the left matrix H 1 The number of columns is the number of independent nodes, and the matrix H on the right is 2 The number of columns is the number of reference nodes, and H I =[H 1 |H 2 ];

[0074] Then H 1 ·P I +H 2 ·P X =G I , there is H 1 ·P I =G I -H 2 ·P X =G Im ;PI The system of equations with unknown variables is H 1 ·P I =G Im .

[0075] The updated value of pressure can be obtained by using the Gauss-Seidel iteration method on this set of equations. 1 Decomposed into upper triangular matrix-L, lower triangular matrix-U, diagonal matrix D, then there are independent node pressure update values ​​P I * =(DL)\(G Im +U·P I ). Node pressure update value P I * The difference between the node pressure P and the node pressure P is used as the end condition of the iteration. The iteration ends when it is less than the set minimum value, and the node pressure calculation result under the current initial steam temperature condition is obtained.

[0076] The basic equations for temperature calculation are:

[0077] Pipe temperature drop equation group: A T T = -ΔT, where T is the node temperature and ΔT is the temperature drop of the pipe section

[0078] Pipe temperature drop-flow equations:

[0079] Among them, q l is the heat dissipation per unit length of the pipe section, C p is the constant pressure specific heat of steam in the pipe section, η is the local heat dissipation loss coefficient, which is the heat dissipation loss coefficient of pipeline accessories, valves, brackets and other structural parts.

[0080] Determine the iterative difference of node temperature, update steam property parameters, and re-perform hydraulic iterative calculation and thermal calculation until steam pressure and temperature reach equilibrium. In subsequent iterative calculations, the pressure drop vector of the pipe section is obtained from the initial pressure, ΔP = -A T P. The flow rate of the pipe section is obtained from the pressure drop of the pipe section. Where δ(ΔP) represents the sign of ΔP, making the flow direction consistent with the pressure drop. Calculate the ratio of the pressure pipe section flow to the pressure drop of the pipe section C * , C * =Q / ΔP; Gaussian iteration method is used to obtain the updated value of the node pressure.

[0081] The intermediate property parameters of steam are calculated based on the average temperature and average pressure of the steam in the pipe section. The calculation formula for the average temperature and average pressure of the steam in the pipe section is:

[0082] T j =|A T |·T i / 2;

[0083] Where, T j is the average temperature of the steam in the pipe section; A is the relationship matrix of the branch pipe section, the remaining tree pipe section, the independent node, and the reference node of the steam pipe network; Ti is the steam temperature of the nodes at both ends of the pipe section;

[0084] P j =|A T |·P i / 2;

[0085] Where P j is the average pressure of the steam in the pipe section, P i is the node steam pressure.

[0086] Update the physical properties of the network nodes and pipe sections according to the obtained network node pressure and network node temperature, including density, dynamic viscosity, constant pressure specific volume, thermal conductivity, and pipe section resistance coefficient s. Determine whether the difference between the updated network node temperature value and the previous network node temperature value reaches the set minimum value, otherwise continue the cycle, perform hydraulic calculations and thermal calculations, and output the calculation results if yes.

[0087] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the temperature of a multi-heat source steam network considering intersection nodes, characterized in that: include: Step 1: Use a matrix to represent the relationship between the branch pipe section, the remaining branch pipe section, the independent node, and the reference node of the steam pipe network; Step 2: Divide the matrix of the steam pipe network into a first type matrix and a second type matrix; the first type matrix is ​​the association matrix of the pipe network between the interconnected gas source nodes and the intersection nodes, and the second type matrix is ​​the association matrix of the pipe network between two interconnected intersection nodes; Step 3: Calculate the iterative temperature of each node in the first type matrix according to the steam temperature of the steam source node; Step 4: The intersection nodes in the first matrix are used as steam source nodes in the second matrix that intersect with them, and the iterative temperature of each node in the second matrix is ​​calculated according to the iterative temperature of the intersection nodes in the first matrix; Step 5: Use the hydraulic iteration method to calculate the initial pressure of the hydraulic iteration calculation according to the matrix, repeat steps 2-4 with the iterative temperature obtained by the joint calculation, and determine the iterative difference of the temperature and pressure of each node until the iterative difference meets the iteration stop condition.

2. A method for calculating the temperature of a multi-heat source steam network considering intersection nodes according to claim 1, characterized in that: In step 4, when two steam flows converge into any intersection node, the calculation formula for the node temperature of the intersection node is: Among them, Q1 and Q2 are the steam flow rates of the pipe sections on both sides of the intersection node, and T1 and T2 are the steam temperatures of the pipe sections on both sides of the intersection node.

3. A method for calculating the temperature of a multi-heat source steam network considering intersection nodes according to claim 1, characterized in that: The segmentation method in step 2 is specifically as follows: the steam network is divided into multiple parts with each gas source node and each intersection node as breakpoints, wherein the association matrix of the network starting from the steam source node and ending at the first intersection node closest to the steam source node along the network is a first-type matrix; in the network, the association matrix of the network of two connected intersection nodes is a second-type matrix.

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