CN114996957A - Step-size self-adaptive steady-state simulation method for hot steam network - Google Patents

Step-size self-adaptive steady-state simulation method for hot steam network Download PDF

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CN114996957A
CN114996957A CN202210684462.4A CN202210684462A CN114996957A CN 114996957 A CN114996957 A CN 114996957A CN 202210684462 A CN202210684462 A CN 202210684462A CN 114996957 A CN114996957 A CN 114996957A
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陈锦怡
周苏洋
顾伟
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Abstract

The invention discloses a step-size self-adaptive steady-state simulation method for a hot steam network in the field of simulation modeling of a heating system, which comprises the following steps: the method comprises the following steps: establishing a hydraulic equation set in a heat steam network algebraic form; step two: establishing a thermodynamic equation set in a heat steam network algebraic form; step three: forming a set of thermal vapor steady state network equations; step four: and establishing a step-size self-adaptive method for the hot steam network. The invention establishes a heat steam steady-state network equation set based on a steady-state motion equation transmitted by heat steam in a pipeline network, and provides a step length self-adaptive equation set solution method, so that the final solution result meets the preset precision, and the problem of manually adjusting the step length in the traditional simulation process is solved.

Description

Step-size self-adaptive steady-state simulation method for hot steam network
Technical Field
The invention belongs to the field of simulation modeling of a heat supply system, and particularly relates to a step-size self-adaptive steady-state simulation method for a hot steam network.
Background
The heating engineering and the heating engineering are one of the very important engineering in the energy field in recent years, and occupy very important positions in light/heavy industrial production and urban resident heating. The hot water heating system and the hot steam heating system are two main flow heat energy transmission systems. Compared with hot water, the hot steam can transmit more heat energy at one time under the condition of the same flow rate, so that the hot steam is mainly widely used for industrial production heat supply at present, such as industrial production in chemical industry, steel, pharmacy, textile and the like. However, compared with hot water, the hot steam has large heat energy transmission loss and poor controllability, so that the steam parameter change is large in the transmission process, and the simulation precision variability is high under the condition of selecting the same step length. At present, for the problem of high simulation precision variability under the same step size, an effective step size adjusting method is still lacked, and the problem needs to be solved in the field of hot steam network simulation at present. For this reason, we propose a step-size adaptive hot steam network steady-state simulation method to solve the above problems.
Disclosure of Invention
In view of the defects of the prior art, the present invention aims to provide a step-size adaptive steady-state simulation method for a thermal steam network, so as to solve the problem of the above background art that proposes a step-size specification mechanism for thermal steam network simulation.
The purpose of the invention can be realized by the following technical scheme:
a step-size adaptive steady-state simulation method for a hot steam network, the method comprising the steps of:
the method comprises the following steps: analyzing the motion state of the hot steam in the transport pipeline when the hot steam flows in a steady state, establishing a hydraulic equation set by mass conservation, momentum conservation and loop pressure drop conservation, and establishing a hydraulic equation set in a hot steam network algebraic form;
step two: analyzing the heat dissipation process of the heat steam when the heat steam flows in a stable state in a transportation pipeline, establishing a thermodynamic equation set in a heat steam network algebraic form by energy conservation and node temperature fusion, and establishing a thermodynamic equation set in a heat steam network algebraic form;
step three: combining the hydraulic equation set and the thermal equation set of the steady-state flow of the hot steam in the pipeline network in the first step and the second step to form a hot steam steady-state network equation set;
step four: and estimating errors by using a self-adaptive step size selection method of a normal differential equation single-step algorithm, and establishing a hot steam network step size self-adaptive method.
Preferably, the hydraulic equation system in the first step is obtained by:
the mass flow of steam in line j is a constant value, namely:
M j,in ＝M j,out ＝M j ,j∈W
conservation of momentum equation under steady state flow of steam:
Figure BDA0003697521330000021
for a hot steam network of I-node, J-pipe, let A, A in 、A out The node-pipeline incidence matrix, the inflow node-pipeline incidence matrix and the outflow node-pipeline incidence matrix of the network are respectively, and the value rules are as follows:
Figure BDA0003697521330000022
Figure BDA0003697521330000031
Figure BDA0003697521330000032
preferably, said A, A in 、A out The following relationships exist among the three correlation matrices:
A＝A in -A out
the inflow steam flow is equal to the outflow steam flow, and a node flow balance equation is obtained:
A·M+q＝0
G jj the values of (A) are as follows:
Figure BDA0003697521330000033
taking the square vector P of the node voltage 2 ＝[P 1 2 ,P 2 2 ,…,P I 2 ] T ，A j Representing the jth column of the incidence matrix A, the pipe momentum conservation equation is as follows:
Figure BDA0003697521330000034
taking G as diag 11 ,G 22 ,…,G JJ ]And obtaining a hydraulic equation system of the hot steam network:
AGA T p 2 ＝q。
preferably, the system of thermal equations in the second step is obtained as follows:
obtaining a pipeline energy conservation equation by an energy conservation equation:
M j (h j,out -h j,in )+K j (T j -T 0 )L j ＝0
the node temperature fusion equation of the hot steam network is as follows:
Figure BDA0003697521330000041
preferably, the node temperature fusion equation and the pipeline energy conservation equation together form a thermodynamic calculation equation of the steam pipe network, and the following matrix equation is obtained through sorting:
Figure BDA0003697521330000042
preferably, the system of the hot steam steady-state network equation in the third step is obtained by the following method:
and (3) according to the hydraulic equation set of the hot steam network established in the first step and the thermal equation set of the hot steam network established in the second step, combining the hydraulic equation set and the thermal equation set to obtain a state equation set of the hot steam network under the steady state condition:
Figure BDA0003697521330000043
and solving the equation set through the alternate iteration of the hydraulic equation and the thermal equation.
Preferably, the step-size self-adaptive method of the hot steam network in the fourth step is obtained by the following method
Selected order of s 1 And s 2 The parameters of the tail ends of the pipelines obtained by solving the two methods are respectively omega 1 (T 1 ,P 1 ,M 1 ) And omega 2 (T 2 ,P 2 ,M 2 ) The error is:
Figure BDA0003697521330000051
the allowable error is epsilon, when tau (h) > epsilon, the error is not satisfactory, and when the step length is changed from h to epsilon
Figure BDA0003697521330000052
At this time, the following requirements are met:
Figure BDA0003697521330000053
to obtain the increased number of nodes N add ：
Figure BDA0003697521330000054
And after the alternative iterative solution of the third step is completed, automatically adjusting the step length by using the criterion, and returning to the step for solving again, so that the iteration converges to the required precision.
The invention has the beneficial effects that:
1. the invention establishes a heat steam steady-state network equation set based on a steady-state motion equation transmitted by heat steam in a pipeline network, and provides a step-length self-adaptive equation set solution method, so that a final solution result meets the preset precision, and the problem of manually adjusting the step length in the traditional simulation process is solved.
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In order to more clearly illustrate the embodiments or technical solutions in the prior art of the present invention, the drawings used in the description of the embodiments or prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method of simulation of a hot steam network of the present invention;
FIG. 2 is a radial 15-node hot steam network node parameter diagram of the present invention;
FIG. 3 is a parameter diagram of a radial 15 node thermal steam pipeline of the present invention;
FIG. 4 is a diagram of the results of pipeline parameter simulation according to the present invention;
FIG. 5 is a diagram of the results of the node parameter simulation of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-5, the present embodiment selects a 15-node radial steam network for simulation.
A step-size self-adaptive steady-state simulation method for a hot steam network comprises the following steps:
the method comprises the following steps: analyzing the motion state of the hot steam in the transport pipeline during steady-state flow, establishing a hydraulic equation set by mass conservation, momentum conservation and loop pressure drop conservation, and establishing a hydraulic equation set in a hot steam network algebraic form, wherein the method specifically comprises the following steps:
the traditional hot steam network method has fully proved that the inclination angle of the steam pipeline can be ignored generally, and under the condition that the network has reached a steady state, the mass flow of the steam in the pipeline j is a constant value according to the mass conservation law, namely:
M j,in ＝M j,out ＝M j ,j∈W
wherein W is the set of all the pipes, M j,in And M j,out Respectively represents the known steam flow rate, M, of the head and tail ends of the pipeline j j Represents the steam flow of conduit j;
neglecting the inertia term when the steam flows, the momentum conservation equation under the steady-state flow of the steam can be obtained:
Figure BDA0003697521330000061
in the formula, P j,in And P j,out Respectively representing the steam pressure at the head and the tail end of the pipeline j; lambda [ alpha ] j Representing the coefficient of friction resistance of the pipeline j; z is a linear or branched member j Represents the gas compression factor of the water vapour in the conduit j; r represents the gas constant of water vapor; t is j Represents the steam temperature in the pipeline; l is j Is the length of the pipeline; d j Denotes the inner diameter of the pipe, wherein the steam temperature T of the pipe j j And a gas compression factor Z j Taking the average value of the parameters corresponding to the head and the tail ends of the two;
for a hot steam network of I-node, J-pipe, let A, A in 、A out The node-pipeline incidence matrix, the inflow node-pipeline incidence matrix and the outflow node-pipeline incidence matrix of the network are respectively, and the value rules are as follows:
Figure BDA0003697521330000071
Figure BDA0003697521330000072
Figure BDA0003697521330000073
the following relationships exist among the three correlation matrices:
A＝A in -A out
for a certain node, the steam flow in should be equal to the steam flow out, i.e. the node flow balance equation:
A·M+q＝0
wherein M is [ M ] 1 ,M 2 ,…,M J ] T For the line flow column vector, q ═ q 1 ,q 2 ,…,q I ] T Injecting flow column vectors for the nodes;
for the convenience of subsequent calculation, record G jj The values of (a) are as follows:
Figure BDA0003697521330000074
taking the square vector P of the node voltage 2 ＝[P 1 2 ,P 2 2 ,…,P I 2 ] T ，A j Representing the jth column of the correlation matrix a, the pipe momentum conservation equation can be organized into the following form:
Figure BDA0003697521330000081
taking G as diag 11 ,G 22 ,…,G JJ ]Then, a hydraulic equation set of the hot steam network can be obtained:
AGA T p 2 ＝q
step two: analyzing the heat dissipation process of the hot steam in the steady-state flowing in the transportation pipeline, establishing a thermodynamic equation set in a hot steam network algebraic form by energy conservation and node temperature fusion, and establishing the thermodynamic equation set in the hot steam network algebraic form, wherein the method specifically comprises the following steps:
for the hot steam which stably flows in the pipeline, the energy conservation equation of the pipeline is obtained by the energy conservation equation under the condition of neglecting the inclination angle of the pipeline and the inertia term of the steam:
M j (h j,out -h j,in )+K j (T j -T 0 )L j ＝0
in the formula, h j,in And h j,out Respectively representing the specific enthalpy of the steam at the head end and the tail end of the pipeline j; k j Is the total heat transfer system, T, of the conduit j 0 Is the ambient temperature of the pipeline;
from the same time, the node temperature fusion equation for the hot steam network is:
Figure BDA0003697521330000082
in the formula, q i,in Representing the steam flow injected by the heat source to the node i; t is n,i Representing the steam temperature of the node i, namely the temperature of the steam after the steam is fused at the node i; w i,in Set of all pipes, W, representing ingress nodes i i,out All pipe sets representing egress nodes i;
the node temperature fusion equation and the pipeline energy conservation equation jointly form a thermodynamic calculation equation of the steam pipe network as follows:
Figure BDA0003697521330000083
further elaboration may yield a matrix equation:
Figure BDA0003697521330000091
wherein K is diag [ K ] 1 ,K 2 ,…,K J ]，L＝diag[L 1 ,L 2 ,…,L J ]，M＝diag[M 1 ,M 2 ,…,M J ]，P＝diag[L 1 ,L 2 ,…,L J ]，q in ＝diag[q in,1 ,q in,2 ,…,q in,I ]。
Step three: a hydraulic equation set and a thermal equation set for the steady-state flow of the hot steam in the pipeline network are combined to form a hot steam steady-state network equation set, and the specific situation is as follows:
the hydraulic equation set of the heat steam network is established in S1, the thermodynamic equation set of the heat steam network is established in S2, and the two equations are combined to obtain the state equation set of the heat steam network under the steady state condition:
Figure BDA0003697521330000092
in the above formula, the demanded quantity is steam flow M, steam pressure P, and steam temperature T. Through the alternate iteration of the hydraulic equation and the thermodynamic equation, the solution of the equation set can be obtained through final convergence.
Step four: the method for self-adapting the step length of the hot steam network is established by estimating errors through a self-adapting step length selection method of a normal differential equation single-step algorithm, and comprises the following specific steps:
by the self-adaptive step length selection method of the ordinary differential equation single-step algorithm, the error of the method with the lower order can be estimated by solving the difference of the results through two different order methods. Now, a fourth-order Rungestota method is selected as an accurate value reference value.
The selected orders are respectively s 1 And s 2 The parameters of the tail ends of the pipelines obtained by solving the two methods are respectively omega 1 (T 1 ,P 1 ,M 1 ) And ω 2 (T 2 ,P 2 ,M 2 ) Then the error is:
Figure BDA0003697521330000101
if the allowable error is epsilon, and if tau (h) > epsilon, the error is not satisfactory. Suppose the step size is changed from h to h
Figure BDA0003697521330000102
At this time, the following requirements are met:
Figure BDA0003697521330000103
the number N of the added nodes can be obtained add ：
Figure BDA0003697521330000104
After the alternative iterative solution of S3 is completed, the step size is automatically adjusted using the above criterion, and the solution is re-performed by returning to S3, whereby the iteration converges to the required accuracy.
This example finally converges to the required accuracy (pressure required to be accurate to 1Pa, temperature required to be accurate to 0.01 ℃) through 1 step adjustment, accumulating 20 iterations. Finally, in the process of adjusting the step length, 1 node is respectively added on the pipeline 4 and the pipeline 6, namely a node 16 is added at the midpoint of the pipeline 4, the step length is changed into the original half, a node 17 is added at the midpoint of the pipeline 6, the step length is also changed into the original half, and the solving result is shown in fig. 4 and 5.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are given by way of illustration of the principles of the present invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, and such changes and modifications are within the scope of the invention as claimed.

Claims (7)

1. A step-size adaptive steady-state simulation method for a hot steam network is characterized by comprising the following steps of:
the method comprises the following steps: analyzing the motion state of the hot steam in the transport pipeline when the hot steam flows in a steady state, establishing a hydraulic equation set by mass conservation, momentum conservation and loop pressure drop conservation, and establishing a hydraulic equation set in a hot steam network algebraic form;
step two: analyzing the heat dissipation process of the hot steam when the hot steam flows in the transportation pipeline in a steady state, building a thermodynamic equation set in a hot steam network algebraic form by energy conservation and node temperature fusion, and building a thermodynamic equation set in a hot steam network algebraic form;
step three: combining the hydraulic equation set and the thermal equation set of the steady-state flow of the hot steam in the pipeline network in the first step and the second step to form a hot steam steady-state network equation set;
step four: and estimating errors by using a self-adaptive step length selection method of a normal differential equation single-step algorithm, and establishing a hot steam network step length self-adaptive method.
2. The steady-state simulation method of the step-size adaptive hot steam network according to claim 1, wherein the hydraulic equation system in the first step is obtained by:
the mass flow of steam in line j is a constant value, namely:
M j,in ＝M j,out ＝M j ,j∈W
wherein W is the set of all the pipes, M j,in And M j,out Respectively represents the known steam flow rate, M, of the head and tail ends of the pipeline j j Represents the steam flow of conduit j;
conservation of momentum equation under steady state flow of steam:
Figure FDA0003697521320000011
in the formula, P j,in And P j,out Respectively representing the steam pressure at the head and the tail end of the pipeline j; lambda [ alpha ] j Representing the coefficient of friction resistance of the pipeline j; z j Represents the gas compression factor of the water vapour in the conduit j; r represents the gas constant of water vapor; t is j Represents the steam temperature in the pipeline; l is a radical of an alcohol j Is the length of the pipeline; d j Denotes the inner diameter of the pipe, wherein the steam temperature T of the pipe j j And gas compression factor Z j Taking the average value of the parameters corresponding to the head and the tail ends of the two;
for a hot steam network of I-node, J-pipe, let A, A in 、A out The node-pipeline incidence matrix, the inflow node-pipeline incidence matrix and the outflow node-pipeline incidence matrix of the network are respectively, and the value rules are as follows:
Figure FDA0003697521320000021
Figure FDA0003697521320000022
Figure FDA0003697521320000023
3. the method of claim 2, wherein the step size adaptive hot steam network steady state simulation method is A, A in 、A out The following relationships exist among the three correlation matrices:
A＝A in -A out
the inflow steam flow is equal to the outflow steam flow, and a node flow balance equation is obtained:
A·M+q＝0
wherein M is [ M ] 1 ,M 2 ,…,M J ] T Is the column vector of the pipeline flow, q ═ q[q 1 ,q 2 ,…,q I ] T Injecting flow column vectors for the nodes;
G jj the values of (A) are as follows:
Figure FDA0003697521320000031
taking the square vector P of the node voltage 2 ＝[P 1 2 ,P 2 2 ,…,P I 2 ] T ，A j Representing the jth column of the incidence matrix A, the pipe momentum conservation equation is as follows:
Figure FDA0003697521320000032
taking G as diag 11 ,G 22 ,…,G JJ ]And obtaining a hydraulic equation system of the hot steam network:
AGA T p 2 ＝q。
4. the steady-state simulation method of the step-size adaptive hot steam network according to claim 1, wherein the thermodynamic equation set in the second step is obtained by:
obtaining a pipeline energy conservation equation by an energy conservation equation:
M j (h j,out -h j,in )+K j (T j -T 0 )L j ＝0
in the formula, h j,in And h j,out Respectively representing the specific enthalpy of the steam at the head end and the tail end of the pipeline j; k j Is the total heat transfer system, T, of the conduit j 0 Is the ambient temperature of the pipeline;
the node temperature fusion equation of the hot steam network is as follows:
Figure FDA0003697521320000033
in the formula, q i,in Representing the steam flow injected by the heat source to the node i; t is n,i Representing the steam temperature of the node i, namely the temperature of the steam after the steam is fused at the node i; w is a group of i,in Set of all pipes, W, representing ingress nodes i i,out Representing the set of all pipes that flow out of node i.
5. The steady-state simulation method of the step-size adaptive hot steam network according to claim 4, wherein the node temperature fusion equation and the pipeline energy conservation equation together form a thermodynamic calculation equation of the steam pipe network, and the following matrix equation is obtained by sorting:
Figure FDA0003697521320000041
wherein K is diag [ K ] 1 ,K 2 ,…,K J ]，L＝diag[L 1 ,L 2 ,…,L J ]，M＝diag[M 1 ,M 2 ,…,M J ]，P＝diag[L 1 ,L 2 ,…,L J ]，q in ＝diag[q in,1 ,q in,2 ,…,q in,I ]。
6. The method for steady-state simulation of the step size adaptive hot steam network according to claim 1, wherein the system of equations of the steady-state hot steam network in step three is obtained by:
and (3) according to the hydraulic equation set of the hot steam network established in the step one and the thermodynamic equation set of the hot steam network established in the step two, obtaining a state equation set of the hot steam network under the steady state condition by combining the hydraulic equation set and the thermodynamic equation set:
Figure FDA0003697521320000042
in the formula, the to-be-solved quantities are steam flow M, steam pressure P and steam temperature T, and the solution of an equation set is obtained through alternate iteration of a hydraulic equation and a thermodynamic equation.
7. The step-size adaptive hot steam network steady-state simulation method according to claim 1, wherein the step-size adaptive method of the hot steam network in the fourth step is obtained by
The selected orders are respectively s 1 And s 2 The parameters of the tail ends of the pipelines obtained by solving the two methods are respectively omega 1 (T 1 ,P 1 ,M 1 ) And omega 2 (T 2 ,P 2 ,M 2 ) The error is:
Figure FDA0003697521320000051
the allowable error is epsilon, when tau (h) > epsilon, the error is not satisfactory, and when the step length is changed from h to epsilon
Figure FDA0003697521320000052
At this time, the following requirements are met:
Figure FDA0003697521320000053
to obtain the increased number of nodes N add ：
Figure FDA0003697521320000054
And after the alternative iterative solution in the third step is completed, automatically adjusting the step length by using the criterion, and returning to the step for solving again, so that the iteration is converged to the required precision.
CN202210684462.4A 2022-06-16 2022-06-16 Step-size self-adaptive steady-state simulation method for hot steam network Pending CN114996957A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115994661A (en) * 2022-12-19 2023-04-21 天津大学 Steam pipe network adjustment strategy information generation method

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115994661A (en) * 2022-12-19 2023-04-21 天津大学 Steam pipe network adjustment strategy information generation method
CN115994661B (en) * 2022-12-19 2024-01-30 天津大学 Steam pipe network adjustment strategy information generation method

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