Mathematical modeling method for operation regulation and control analysis of cold water pipe network

Abstract

The invention relates to a mathematical modeling method for operation regulation and control analysis of a cold water pipe network. And mathematical description of the cold water pipe network is obtained through graph theory knowledge. The whole pipe network is regarded as a set of points connected by directed branches, and the topological structure of the whole pipe network can be determined according to the connection relation between the branches (pipe sections) and the points (nodes). According to the law of mass conservation and energy conservation, a steady-state hydraulic model of a pipe network is established, and the model is solved by using a basic loop method. A thermal dynamic model of a pipe network is established according to related knowledge of heat transfer science, and the thermal dynamic model of the pipe network is solved by using an implicit windward difference method. Hydraulic calculation and thermodynamic calculation are alternately carried out, and hydraulic-thermodynamic coupling simulation is carried out on the cold water pipe network.

Description

Technical Field

[0001] The present invention belongs to the technical field of heating, ventilation and air conditioning, and particularly relates to a mathematical modeling method for operation regulation analysis of a cold water pipe network. Background Art

[0002] The operation characteristics of a cold water pipe network are the basis for operation regulation analysis of the cold water pipe network. The supply water temperature and supply water flow rate at each heat exchange station are closely related to the hydraulic condition and thermal condition during the operation regulation of the cold water pipe network. Moreover, the hydraulic condition and thermal condition in the cold water pipe network are also interconnected and influence each other. The refrigeration unit transports the medium in the pipe network to each heat exchange station through a water pump, and the flow distribution at each part of the pipe network affects the medium temperature and heat distribution; at the same time, the change of the supply and return water temperature at each heat exchange station continuously feeds back to the regulation of the hydraulic condition of the water supply system to ensure the stable and reliable operation of the entire water supply system. Summary of the Invention

[0003] The present invention aims to overcome at least one defect (shortcoming) of the above-mentioned prior art, and provides a mathematical modeling method for operation regulation analysis of a cold water pipe network, which can guide the operation regulation of the cold water pipe network system and lay a foundation for practical engineering applications.

[0004] The present invention solves its technical problems by adopting the following technical solutions:

[0005] Step 1: Establish a mathematical description of the cold water pipe network according to the graph theory method;

[0006] Step 2: Establish a steady-state hydraulic model of the pipe network according to the established mathematical description of the pipe network;

[0007] Step 3: Establish a thermal dynamic model of the pipe network according to the established mathematical description of the pipe network;

[0008] Step 4: Solve the established thermal dynamic model of the pipe network;

[0009] Step 5: Introduce the simulation process of the established steady-state hydraulic-thermal model of the pipe network.

[0010] The specific implementation method of the above Step 1 is as follows:

[0011] For a pipe network containing M nodes and N pipe segments, use an M×N matrix (A=(a ij )) M×N ) to represent the topological structure of the pipe network, where the matrix A is called the incidence matrix, and each row in the matrix A represents the node number, and each column represents the pipe segment number.

[0012] The hydraulic model in the above Step 2 includes: node flow equation and loop pressure balance equation.

[0013] The node flow equation is:

[0014] A·G = Q

[0015] Wherein, A is the basic incidence matrix of the pipe network; G is the pipe segment flow vector in the pipe network, and each element represents the flow of the corresponding pipe segment, kg / s; Q is the node flow vector in the pipe network, and each element represents the sum of the flows of the corresponding nodes, kg / s;

[0016] The loop pressure balance equation is:

[0017] A T ·P = ΔP

[0018] Wherein, P is the node pressure vector in the pipe network, and each element represents the pressure value of each node in the pipe network, Pa; ΔP is the pipe segment pressure drop vector in the pipe network, and each element represents the pressure drop of the fluid flowing through the pipe segment, Pa;

[0019] The thermal dynamic model in step 3 is:

[0020]

[0021] Wherein, T is the fluid temperature of the control volume, °C; T 0 is the ambient temperature, °C; t is the time series, s; u is the flow velocity of the fluid in the pipe, m / s; x is the distance along the pipe, m; A 0 is the cross-sectional area of the pipe, m 2 ; ρ is the density of the fluid in the pipe, kg / m 3 ; c p - is the specific heat capacity of the fluid in the pipe, J / (kg·°C); λ is the thermal conductivity of the fluid in the pipe, W / (m·°C); R is the total thermal resistance between the fluid in the pipe and the surrounding environment, m·°C / W;

[0022] The specific implementation method of step 4 is:

[0023]

[0024] Wherein, i is the i-th control volume; n is the n-th moment; Δt is the time interval.

[0025] The solution process in step 5 is:

[0026] Input the basic parameters of the pipe network into the hydraulic and thermal simulation model of the pipe network; perform hydraulic adjustment calculation on the pipe network; perform node and pipe traversal, check whether the water flow is consistent with the default direction, and perform thermal calculation in the order of pipe network traversal; determine whether the time reaches the final moment of a calculation cycle. If not, return to the second step to continue the hydraulic and thermal calculation of the next time step. If it reaches the final moment, the calculation ends.

[0027] The advantages and positive effects of the present invention are:

[0028] The present invention obtains a mathematical description of a cold water pipe network through graph theory knowledge. The entire pipe network is regarded as a collection of points connected by directed branches. According to the connection relationship between branches (pipe segments) and points (nodes), the topological structure of the entire pipe network can be determined. According to the laws of conservation of mass and conservation of energy, a steady-state hydraulic model of the pipe network is established, and the model is solved using the basic loop method. According to the relevant knowledge of heat transfer, a thermal dynamic model of the pipe network is established, and the thermal dynamic model of the pipeline is solved using the implicit upwind difference method. By alternating hydraulic calculations and thermal calculations, a hydraulic-thermal coupling simulation of the cold water pipe network is performed. It can guide the operation and regulation of the cold water pipe network system and lay the foundation for practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Solving the pipeline control volume for the thermal dynamic model of the present invention;

[0030] Figure 2 The figure is a flow chart for solving the hydraulic-thermal model of the present invention. DETAILED DESCRIPTION

[0031] The present invention is further described in detail below with reference to the accompanying drawings.

[0032] A mathematical modeling method for cold water network operation regulation analysis includes the following steps:

[0033] Step 1: For element a in matrix A ij ,have:

[0034]

[0035] For the annular central heating network, the basic loop matrix (B = (b ij ) J×N ), where the row number of the matrix B represents the basic loop number, and the column represents the pipe segment number, which is consistent with the column number of the association matrix. For a pipe network diagram containing J loops, a direction can be pre-set for the basic loop. If a pipe segment is on the loop and its direction is consistent with the loop setting direction, then the pipe segment and the loop are in the same direction, otherwise they are in the opposite direction, that is:

[0036]

[0037] Step 2: The specific calculation method of the pressure difference ΔP is:

[0038] S.G. 2 =ΔP

[0039] Where S is the impedance vector of the pipe section in the pipe network, and each element represents the impedance of the pipe section in the pipe network, Pa / (t / h).

[0040] Step 3. The specific calculation method of the thermal resistance R is as follows:

[0041] R = R ins + R λ + R f

[0042] Wherein: R ins is the thermal resistance of the insulation layer; R λ is the thermal resistance of the pipe wall; R f is the convective heat transfer resistance between the cold water and the pipe wall;

[0043]

[0044] Wherein: λ ins is the thermal conductivity of the insulation layer, W / (m·K); d 1 is the outer diameter of the insulation layer, m; d 2 is the inner diameter of the insulation layer, m;

[0045]

[0046] Wherein: λ p is the thermal conductivity of the pipe wall, W / (m·K); d 3 is the outer diameter of the pipe, m;

[0047]

[0048] Wherein, h is the convective heat transfer coefficient between the pipe wall and the fluid, W / (m 2 ·K); d is the characteristic dimension of the pipe: the inner diameter of the circular pipe, m;

[0049] Step 5. The specific method for solving the thermal dynamic model is as follows:

[0050] Solve the thermal model of the pipe by using the finite volume method. The pipe is divided into several control volumes, as Figure 1 shown. The radial temperature distribution can be ignored, and the temperature model in the pipe is a one-dimensional model;

[0051] The upwind difference format can be adopted for the spatial term to make full use of the temperature of the upstream control volume in the pipe;

[0052] The implicit difference format is adopted for time. The temperature of the control volume at this moment can be calculated through the temperature distribution of the pipe at the previous moment and the temperature of the upstream control volume at this moment. It can be unconditionally stable during the calculation process and has good numerical simulation performance.

[0053] The discrete equation is:

[0054]

[0055]

[0056] According to the discrete equation, the temperature expression of the i-th control volume at the n-th moment is derived as:

[0057]

[0058] Step 5, as Figure 2 shown, the specific process for solving the hydraulic-thermal model is as follows:

[0059] The basic parameters of the pipe network input into the pipe network hydraulic-thermal simulation model include: heat exchange station flow rate, pipe network impedance, pipe network diameter, energy station water supply temperature, operation parameters of the water pump, and pipe network incidence matrix;

[0060] Perform hydraulic adjustment calculation on the pipe network. By simulating the hydraulic conditions of the pipe network, the pressures of each node and the flow rates of each pipe section can be obtained;

[0061] Perform node and pipe traversal, check whether the water flow is consistent with the default direction, and perform thermal calculation in the order of pipe network traversal;

[0062] Judge whether the time has reached the final moment of a calculation period. If not, return to the second step to continue the hydraulic-thermal calculation for the next time step. If the final moment is reached, the calculation ends.

[0063] It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive. Therefore, the present invention includes, but is not limited to, the embodiments described in the specific implementation manners. Any other implementation manners obtained by those skilled in the art based on the technical solutions of the present invention also fall within the protection scope of the present invention.

Claims

1. A mathematical modeling method for the operation regulation and analysis of cold water pipe networks, characterized in that: It includes the following steps: Step 1: Establish a mathematical description of the cold water pipe network according to the graph theory method; Step 2: Establish a steady-state hydraulic model of the pipe network according to the established mathematical description of the pipe network; Step 3: Establish a thermal dynamic model of the pipe network according to the established mathematical description of the pipe network; Step 4: Solve the established thermal dynamic model of the pipe network; Step 5: Introduce the simulation process of the established steady-state hydraulic-thermal model of the pipe network.

2. The mathematical modeling method for the operation regulation and analysis of cold water pipe networks according to claim 1, characterized in that: The specific implementation method of step 1 is: For the cold water pipe network, for a pipe network with M nodes and N pipe segments, a M×N matrix (A=(a ij )) M×N ) is used to represent the topological structure of the pipe network. Among them, the matrix A is called the incidence matrix. Each row in the matrix A represents the node number, and each column represents the pipe segment number; For a ring-shaped district heating pipe network, introduce the fundamental circuit matrix (B = (b ij )) J×N ), where the row numbers of matrix B represent the fundamental circuit numbers, and the columns represent the pipe section numbers, which are consistent with the column numbers of the incidence matrix. For a pipe network diagram with J loops, a direction can be preset for the fundamental circuits. If a certain pipe section is on the loop and its direction is consistent with the preset direction of the loop, then the pipe section and the loop are in the same direction; otherwise, they are in the opposite direction.

3. The mathematical modeling method for the operation regulation and analysis of cold water pipe networks according to claim 1, characterized in that: The hydraulic model in step 2 includes: node flow equations and loop pressure balance equations. The node flow equation is: A·G=Q Where, A is the basic incidence matrix of the pipe network; G is the pipe segment flow vector in the pipe network, each element represents the flow of the corresponding pipe segment, kg / s; Q is the node flow vector in the pipe network, each element represents the sum of the flows of the corresponding nodes, kg / s; The loop pressure balance equation is: A T ·P = ΔP Where, P is the node pressure vector in the pipe network, each element represents the pressure value of each node in the pipe network, Pa; ΔP is the pipe segment pressure drop vector in the pipe network, each element represents the pressure drop of the fluid flowing through the pipe segment, Pa.

4. The mathematical modeling method for the operation regulation and analysis of cold water pipe networks according to claim 1, characterized in that: The thermal dynamic model in step 3 is: Among them, T is the fluid temperature of the control volume, °C; T 0 is the ambient temperature, °C; t is the time series, s; u is the flow velocity of the fluid in the pipeline, m / s; x is the distance along the pipeline, m; A 0 is the cross-sectional area of the pipeline, m 2 ; ρ is the density of the fluid in the pipeline, kg / m 3 ; c p - is the specific heat capacity of the fluid in the pipeline, J / (kg·°C); λ is the thermal conductivity of the fluid in the pipeline, W / (m·°C); R is the total thermal resistance between the fluid in the pipeline and the surrounding environment, m·°C / W.

5. The mathematical modeling method for the operation regulation and analysis of cold water pipe networks according to claim 1, characterized in that, The specific implementation method of step 4 is: Where, i is the i-th control volume; n is the n-th moment; Δt is the time interval.

6. The mathematical modeling method for the operation regulation and analysis of cold water pipe networks according to claim 1, characterized in that: The solution process in step 5 is: Input the basic parameters of the pipe network into the hydraulic-thermal simulation model of the pipe network; perform hydraulic adjustment calculation on the pipe network; perform node and pipe traversal, check whether the water flow is consistent with the default direction, and perform thermal calculation in the order of pipe network traversal; judge whether the time reaches the final moment of a calculation cycle. If not, return to the second step to continue the hydraulic-thermal calculation of the next time step. If it reaches the final moment, the calculation ends.

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