Pipeline equivalent circuit model considering fluid axial diffusion effect

Abstract

A pipeline equivalent circuit model considering the axial diffusion effect of fluid belongs to the technical field of time domain simulation of an integrated energy system, and is composed of an equivalent circuit model for simulating two sections of water pipes with different lengths; the first section of water pipe is divided into N units with the same length, and the equivalent circuit model for simulating each unit is composed of a branch containing a variable resistor and five branches connected in parallel; the equivalent circuit model for simulating the second section of water pipe and the equivalent circuit model for simulating each unit in the first section of water pipe have the same topological structure, and the equivalent circuit model for simulating the second section of water pipe and the equivalent circuit model for simulating each unit in the first section of water pipe are connected in series to obtain the pipeline equivalent circuit model. The thermal dynamic process of the liquid in the water pipe can be simulated, joint simulation and analysis of a comprehensive energy system covering electric power and thermal power are achieved in the same simulation environment, the simulation precision and efficiency are improved, and the simulation calculation amount is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of time domain simulation of integrated energy systems, and in particular relates to a pipeline equivalent circuit model that takes into account the axial diffusion effect of a fluid. Background Art

[0002] Through electric-to-heat conversion, thermal systems such as district heating systems or district cooling systems can help absorb excess electricity in the power system and reduce wind and solar power curtailment. With the large-scale conversion of fluctuating and intermittent renewable electricity into thermal energy in district heating systems or district cooling systems by electric-to-heat conversion technology, compared with traditional district heating systems, such district heating systems or district cooling systems are likely to show more temperature fluctuations and fluid flow discontinuity. Therefore, in order to study the characteristics of this type of district heating system or district cooling system and better study the energy interaction between the power system and the thermal system, it is necessary to accurately model the thermal dynamic processes in the district heating system or district cooling system.

[0003] At present, the thermal dynamic process in district heating system or district cooling system is mainly studied by using finite element based models. In a finite element based model disclosed in the literature [VD Stevanovic, B. Zivkovic, S. Prica, B. Maslovaric, V. Karamarkovic, and V. Trkulja, "Prediction of thermal transients in district heating systems," Energy Conversion and Management, vol. 50, no. 9, pp. 2167–2173, 2009.], the system pipeline is spatially divided into multiple adjacent finite elements, and the liquid temperature variable in the pipeline is implicit in the differential equations based on the energy conservation of these finite elements. By solving the differential equations by numerical calculation, the liquid temperature in the finite element can be solved, and then the thermal transient process of the liquid in the pipeline can be simulated. When studying the thermal dynamic process in district heating system or district cooling system by using finite element based models, it is necessary to pay attention to the distortion problem caused by false diffusion. In addition, this type of finite element-based model has the problems of large amount of calculation and long simulation time, so it is not suitable for time domain simulation. At the same time, the large amount of calculation also reduces the simulation efficiency.

[0004] In addition to the above-mentioned finite element-based models, node models, i.e., dynamic models, are also used to study the thermal dynamic processes in central heating systems or central cooling systems. The literature [T.Lan and K.Strunz, "Modeling of the enthalpy transfer using electric circuit equivalents: Theory and application to transients of multi-carrier energy systems," IEEE Transactions on Energy Conversion, vol.34, no.4, pp.1720–1730, 2019.] proposed an equivalent circuit model for a water pipe. The equivalent circuit model is a node model. The model has many nodes, and the amount of calculation required for high-precision simulation is large, which will reduce the simulation efficiency. In addition, this type of model only considers the inflow and outflow of liquid in the system. The temperature of the outflowing liquid is estimated based on the temperature of the liquid at the time of inflow and the flow path, ignoring the influence of the axial diffusion of the liquid in the pipe on the temperature distribution. Although this effect can be ignored within a larger time scale, this neglect often causes large errors when it is necessary to analyze the temperature change process of the liquid within a smaller time scale. Summary of the invention

[0005] In order to solve the problems that the existing model using equivalent circuit to simulate the pipeline has many nodes, large calculation amount, long simulation time, low simulation efficiency, and large errors caused by ignoring the influence of axial diffusion of fluid in the pipe on temperature distribution, the present invention provides a pipeline equivalent circuit model taking into account the axial diffusion effect of fluid.

[0006] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0007] The present invention provides a pipeline equivalent circuit model that takes into account the axial diffusion effect of the fluid, wherein the pipeline equivalent circuit model is composed of equivalent circuit models that simulate two sections of water pipes of different lengths;

[0008] The first section of the water pipe is divided into N units of equal length. The equivalent circuit model of each unit consists of a variable resistor. The variable resistor Analogous to the frictional internal resistance of the water pipe, the variable resistor Voltage at Analogously to the average pressure of the liquid in the section of the water pipe; the first branch of the five parallel branches is a resistor resistance resistance With voltage source in series, the resistor Analogously to the equivalent thermal resistance of heat convection from the liquid in this section of the water pipe to the pipe wall, the resistance Analogously to the heat conduction equivalent thermal resistance of the pipe wall, the resistance Analogously, the insulation layer of this section of water pipe integrates the equivalent thermal resistance of heat conduction within the layer, heat convection with air, and heat radiation. Analogous to the external ambient temperature of this section of water pipe; the second branch has a capacitor Composition, the capacitor Analogous to the heat capacity of the liquid in this section of the water pipe, the capacitor The voltage across Analogously to the average temperature of the liquid in this section of the water pipe; the third branch has a capacitor One end of which is connected to the resistor The midpoint of the capacitor Analogous to the heat capacity of the pipe wall, the capacitor The voltage across Analogously to the average temperature of the pipe wall in this section; the fourth branch has a capacitor One end of which is connected to the resistor The midpoint of the capacitor Analogous to the heat capacity of the insulation layer of this section of water pipe, the capacitance The voltage across Analogously to the average temperature of the insulation layer of the water pipe section; the fifth branch consists of a current-controlled current source;

[0009] The equivalent circuit model simulating the second section of the water pipe has the same topological structure as the equivalent circuit model simulating each unit in the first section of the water pipe. The equivalent circuit model simulating the second section of the water pipe and the equivalent circuit model simulating each unit in the first section of the water pipe are connected in series to obtain the pipeline equivalent circuit model.

[0010] Furthermore, the current flowing through the first branch of the five parallel branches is Analogously, the liquid in this section of the water pipe dissipates heat energy to its surroundings.

[0011] Furthermore, the current flowing through the second branch of the five parallel branches is Analogously, the net increase in heat energy of the liquid entering this section of the water pipe.

[0012] Furthermore, the current flowing through the third branch of the five parallel branches is Analogously, the net increase in heat energy entering the wall of this section of the water pipe.

[0013] Furthermore, the current flowing through the fourth branch of the five parallel branches is Analogously, the net increase in heat energy entering the insulation layer of this section of the water pipe.

[0014] Furthermore, in the fifth branch, the output current of the current-controlled current source of the left half model is By analogy with the mobility of the enthalpy flowing with the liquid in this section of the water pipe, its magnitude is determined by the following formula:

[0015]

[0016] in The liquid is at temperature T fl,dx The specific enthalpy under represents the mass flow rate of the liquid at time t; the output current of the current-controlled current source of the right half of the model The mobility of the enthalpy flowing out of the entire pipe as the liquid flows out of the pipe is determined by the following formula:

[0017]

[0018] Where h(T out ) indicates that the liquid is at temperature T out The specific enthalpy under.

[0019] Furthermore, the equivalent circuit of the second section of the water pipe has the same topological structure as each unit in the first section of the water pipe, and each branch has the same physical meaning. The difference is that the parameters of each branch in the equivalent circuit of the second section of the water pipe are determined by the second section of the water pipe.

[0020] Furthermore, the specific calculation process of the equivalent flow time of the liquid in the water pipe in each unit is as follows:

[0021] When the water pipe is filled with liquid, the total mass M of the liquid is:

[0022] M=ρAL#(8)

[0023] The time it takes for the liquid to flow through the entire water pipe is recorded as τ:

[0024]

[0025] The time for the liquid to flow through the two sections of the water pipe is recorded as τ1 and τ2 respectively:

[0026] τ=τ1+τ2#(10)

[0027] The time τ1 for the liquid to flow through the first section of the water pipe is calculated from the circulation time τ of the liquid in N units. N Sure:

[0028] τ1=Nτ N #(11)

[0029] The circulation time τ of the liquid in N units N for:

[0030]

[0031] Where v represents the axial velocity of the liquid in the water pipe, and D represents the diffusion coefficient related to the axial velocity v of the liquid in the water pipe, which is determined by equations (13) and (14):

[0032]

[0033] Where Re represents the Reynolds number corresponding to the flow of liquid in the water pipe at an axial velocity v; when the flow time of liquid in N units τ N After determination, the time τ1 for the liquid to flow through the first section of the water pipe can be determined, and then the time τ2 for the liquid to flow through the second section of the water pipe can be determined.

[0034] Furthermore, the specific calculation process of the liquid temperature at the outflow end of the water pipe is as follows:

[0035] Assume the length of a control body in the water pipe is dx, and use R amb Simulate the thermal resistance between the fluid in the control body and the water pipe environment:

[0036]

[0037] in, It is used to simulate the heat power dissipated by the liquid in the control body to the environment, T amb The ambient temperature outside the water pipe corresponding to the liquid in the control body is simulated, C amb Used to simulate the heat capacity of the fluid in the control body:

[0038] C amb =ρAc p dx#(16)

[0039] Among them, C amb The voltage drop T across the two ends is used to simulate the average temperature of the liquid in the control body;

[0040] The time constant τ of the first-order linear equivalent circuit of the control body th The mathematical expression is as follows:

[0041]

[0042] The first-order linear equivalent circuit of the control body is a closed loop, which is not connected to the circuit simulating other liquids. When the initial state of the first-order linear equivalent circuit of the control body is known and the ambient temperature T outside the water pipe corresponding to the liquid in the control body is amb When given, its capacitance C ambThe value T(t) of the voltage drop T at any time t is calculated by the following formula:

[0043]

[0044] Where T(0) represents the initial state capacitance C amb The voltage drop at both ends; for the liquid in the control body, the temperature when it just enters the second section of the water pipe is determined by the liquid temperature of the Nth unit of the first section of the water pipe. Approximate substitution, that is:

[0045]

[0046] When the liquid in the control body takes time τ2 to flow out of the water pipe, let t = τ2, and when the ambient temperature T amb When (t) is given, the temperature of the liquid in the control body at the outlet of the water pipe can be calculated by formula (18); the obtained temperature T(t) is the liquid temperature at the outlet of the water pipe:

[0047] T out (t) = T(t) #(20).

[0048] The beneficial effects of the present invention are:

[0049] The present invention uses the analogy method to build an equivalent circuit model for the water pipe. The built equivalent circuit model can simulate the thermal dynamic process of the liquid in the water pipe, and can be simulated with the power system in the same electromagnetic transient simulation software, so that the comprehensive energy system covering the power system and the thermal system can be jointly simulated and analyzed in the same simulation environment. At the same time, the pipeline equivalent circuit model of the present invention fully considers the axial diffusion effect of the liquid in the pipe, and models the pipe wall and the insulation layer at the same time. Therefore, the pipeline equivalent circuit model proposed by the present invention can more accurately simulate the temperature change process of the liquid in the water pipe. In addition, due to the combination of the continuous stirring tank model and the plug flow model, compared with the plug flow model, the pipeline equivalent circuit model proposed by the present invention improves the simulation accuracy, and compared with the plug flow model, the pipeline equivalent circuit model proposed by the present invention reduces the simulation calculation amount and improves the simulation efficiency.

[0050] Compared with the prior art, the pipeline equivalent circuit model considering the axial diffusion of fluid provided by the present invention has the following advantages:

[0051] 1. Without significantly increasing the amount of calculation, the pipeline equivalent circuit model proposed in the present invention can simulate the thermal dynamic process occurring in the water pipe within a smaller time scale. Since the heat capacity of the pipe wall and the insulation layer and the axial diffusion effect of the liquid are taken into account, the simulation results are closer to the experimental measurement results, indicating that the pipeline equivalent circuit model proposed in the present invention can better simulate the thermal dynamic process of the liquid in the water pipe.

[0052] 2. Due to the combination of the continuous stirred tank model and the plug flow model, the pipeline equivalent circuit model proposed in the present invention improves the simulation accuracy compared with the plug flow model; compared with the continuous stirred tank model or the multi-node model, the pipeline equivalent circuit model proposed in the present invention reduces the simulation calculation amount and improves the simulation efficiency.

[0053] 3. The present invention uses an equivalent circuit to model the water pipe, so that the system containing different energy forms can be modeled and simulated in the same electromagnetic transient simulation environment, thereby avoiding the use of different simulation software to simulate the same system, thereby simplifying the computer simulation process and avoiding the problem of data exchange asynchrony between different software interfaces.

[0054] 4. In addition to simulating liquid flow, the pipeline equivalent circuit model proposed in the present invention can also be used to simulate the movement of other fluids such as gas that can be described using fluid motion equations. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a horizontal cylindrical water pipe.

[0056] Figure 2 Schematic diagram of virtual segmentation of water pipes.

[0057] Figure 3 It is the equivalent circuit model of the water pipe.

[0058] Figure 4 This is the water pipe division and the corresponding equivalent circuit model for each part.

[0059] Figure 5 Equivalent circuit for controlling the thermal dynamics of fluids in vivo.

[0060] Figure 6 Comparison of liquid temperature response curves at the water pipe outlet (v=1.244m / s).

[0061] Figure 7 Comparison of liquid temperature response curves at the water pipe outlet (v=0.312m / s). DETAILED DESCRIPTION

[0062] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0063] The pipeline equivalent circuit model of the present invention taking into account the axial diffusion effect of the fluid is based on the following basic assumptions:

[0064] 1) The volume of the liquid in the water pipe cannot be compressed. The liquid in any control body satisfies the law of conservation of mass, and the liquid in the same control body has the same physical properties;

[0065] 2) There is no heat source inside the liquid, and the kinetic energy, potential energy, radiation dissipation and viscous dissipation of the liquid are ignored;

[0066] 3) The inside of the water pipe is always filled with liquid, ignoring the density difference, relative motion and energy exchange between different parts of the liquid;

[0067] 4) The physical parameters of the pipe wall and possible insulation layer at any point in the water pipe are evenly distributed.

[0068] To facilitate the explanation of the principle of the pipeline equivalent circuit model considering the axial diffusion of fluid in the present invention, the following is an illustration using a horizontally placed cylindrical water pipe. It should be noted that the pipeline equivalent circuit model considering the axial diffusion of fluid in the present invention is not limited to application on this type of water pipe.

[0069] like Figure 1 As shown, a horizontally placed cylindrical water pipe (hereinafter referred to as the water pipe) has a length of L and an inner diameter of D. i , outer diameter is D o The outside of the water pipe is an insulation layer, which is close to the outer wall of the water pipe and has an outer diameter of D ins Consider a virtual cylindrical control body (hereinafter referred to as the control body) in a water pipe, whose two ends are planes perpendicular to the axis of the water pipe, with a spacing of dx, and the cylindrical surface is the inner wall of the water pipe. The temperature of the liquid in the control body is a function of time and the position of the moving liquid, which obeys the law of conservation of energy and is expressed mathematically as follows:

[0070]

[0071] Where H represents enthalpy, x is the coordinate of the control body along the axial direction of the water pipe, represents enthalpy mobility, t represents time, It represents the rate at which the liquid dissipates heat to the environment through the pipe wall and the insulation layer. Therefore, the term on the left side of the equal sign represents the enthalpy change of the liquid in the control body, the first term on the right side of the equal sign represents the enthalpy change caused by the liquid flowing out of the control body along the pipe, and the second term on the right side of the equal sign represents the heat dissipated to the environment due to the liquid passing through the pipe wall and the insulation layer. At the same time, canceling dx on both ends of the equal sign, we have:

[0072]

[0073] If T is used to represent the liquid temperature, T ambrepresents the ambient temperature around the water pipe, A represents the cross-sectional area perpendicular to the axial direction inside the water pipe, and c p represents the specific heat capacity of the liquid, represents the mass flow rate of the liquid, then Equation (2) can be rewritten in the following form:

[0074]

[0075] where ρ represents the liquid density, and G' amb is the equivalent thermal conductivity of the water pipe wall and the insulation layer, and is denoted by G amb represents the equivalent thermal conductance of the entire water pipe wall and the insulation layer, then there is:

[0076]

[0077] The water pipe is virtually divided into two segments along the axial direction for easy modeling. As Figure 2 shown, the liquid in the water pipe flows along the positive x-axis direction. The first segment is at the inlet end of the water pipe and can be divided into N equal-length units, each unit having a length of dx and 0 < dx << L; except for the first segment, the rest is all classified into the second segment, and the length of the second segment is l, then there is:

[0078] l = L - Ndx#97)

[0079] A pipeline equivalent circuit model considering the axial diffusion effect of the fluid in the present invention is established by using the equivalent circuit method. The equivalent circuit model of the water pipe is as Figure 3 shown. This equivalent circuit model can be divided into two parts by the vertical dotted line. The left and right parts respectively simulate the mass flow and heat movement of the liquid in these two segments of the water pipe with lengths of Ndx and l. Among them, the first segment of the water pipe (with a length of Ndx) is composed of N equal-length units, and the equivalent circuit of each unit is composed of two parts, upper and lower. Taking the kth unit as an example, where k ∈ [1, N]: The first part (upper part) consists of a branch containing a variable resistor , and the variable resistor is used to analogize the frictional internal resistance of this segment of the water pipe. The resistance value of the variable resistor is determined by the frictional internal resistance of this segment of the water pipe and is related to the liquid flow rate in this segment of the water pipe. The voltage at the variable resistor analogizes the average pressure of the liquid in this segment of the water pipe.

[0080] The second part (lower part) consists of five parallel branches, specifically as follows:

[0081] 1) The first branch is composed of a resistor resistor resistor connected in series with a voltage source The resistor Analogously to the equivalent thermal resistance of the heat convection from the liquid in this section of the water pipe to the pipe wall, the resistance Analogous to the heat conduction equivalent thermal resistance of the pipe wall, the resistance Analogously, the insulation layer of this section of water pipe integrates the equivalent thermal resistance of heat conduction within the layer, heat convection with air, and heat radiation. Analogous to the ambient temperature of the water pipe. The current flowing through this branch Analogously, the heat energy dissipated from the liquid in this section of the water pipe to its surroundings.

[0082] 2) The second branch is a capacitor The capacitor Analogous to the heat capacity of the liquid in this section of the water pipe. The current flowing through this branch Analogously, it is the net increase in heat energy entering the liquid in this section of the water pipe. The voltage across Analogously, it is the average temperature of the liquid in this section of the water pipe.

[0083] 3) The third branch has a capacitor One end of the resistor is connected to The midpoint of the capacitor Analogous to the heat capacity of the pipe wall. The current flowing through this branch Analogously, it is the net increase in heat energy entering the wall of this section of the water pipe. The voltage across Analogously, it is the average temperature of the wall of this section of water pipe.

[0084] 4) The fourth branch has a capacitor One end of the resistor is connected to The midpoint of the capacitor Analogous to the heat capacity of the insulation layer of this section of water pipe. The current flowing through this branch Analogously, the net increase in heat energy entering the insulation layer of this section of water pipe. The voltage across Analogously, it is the average temperature of the insulation layer of this section of water pipe.

[0085] 5) The fifth branch consists of a current-controlled current source. The output current of the current-controlled current source in the left half of the model is By analogy with the mobility of the enthalpy flowing with the liquid in this section of the water pipe, its magnitude is determined by the following formula:

[0086]

[0087] in The liquid is at temperature T fl,dx The specific enthalpy under represents the mass flow rate of the liquid at time t. The output current of the current-controlled current source of the right half model is The mobility of the enthalpy flowing out of the entire pipe as the liquid flows out of the pipe is determined by the following formula:

[0088]

[0089] Where h(T out ) indicates that the liquid is at temperature T out The specific enthalpy under.

[0090] The equivalent circuit of the second section of the water pipe (length l) has the same topological structure as each unit in the first section of the water pipe (length Ndx), and each branch has the same physical meaning. The difference is that the parameters of each branch are determined by the second section of the water pipe, for example: the resistance R fl,l It is also analogous to the equivalent thermal resistance of heat convection from the liquid in the second section of the water pipe to the pipe wall, but its resistance is determined by the second section of the water pipe.

[0091] Connect the equivalent circuits of the N+1 units in the second section of the water pipe (length l) and the first section of the water pipe (length Ndx) in series, and you can get the following: Figure 3 The equivalent circuit model of the water pipe shown in Figure 1. The corresponding relationship between the equivalent circuit model and the water pipe segmentation is as follows: Figure 4 shown.

[0092] According to the pipeline equivalent circuit model established by the present invention, which takes into account the axial diffusion effect of the fluid, the equivalent flow time of the liquid in each unit can be determined. The specific process is as follows:

[0093] When the water pipe is filled with liquid, the total mass M of the liquid is:

[0094] M=ρAL#(10)

[0095] The time it takes for the liquid to flow through the entire water pipe is recorded as τ, which can be determined by the following formula:

[0096]

[0097] In a pipeline equivalent circuit model established by the present invention that takes into account the axial diffusion effect of the fluid, the time for the liquid to flow through the two sections of the water pipe is recorded as τ1 and τ2, respectively, so:

[0098] τ=τ1+τ2#(12)

[0099] The time τ1 for the liquid to flow through the first section of the water pipe can be calculated from the flow time τ of the liquid in N units. N Determine, that is:

[0100] τ1=Nτ N #(13)

[0101] The circulation time τ of the liquid in N units N It can be determined by the following formula:

[0102]

[0103] Where v represents the axial velocity of the liquid in the water pipe, and D represents the diffusion coefficient related to the axial velocity v of the liquid in the water pipe, which can be determined by equations (13) and (14):

[0104]

[0105] Where Re represents the Reynolds number corresponding to the liquid flowing in the water pipe at an axial velocity v. When the liquid flow time τ in N units N After determination, the time τ1 for the liquid to flow through the first section of the water pipe can be determined, and then the time τ2 for the liquid to flow through the second section of the water pipe can also be determined.

[0106] According to the pipeline equivalent circuit model established by the present invention, which takes into account the axial diffusion effect of the fluid, the liquid temperature at the outlet of the water pipe can be determined. The specific process is as follows:

[0107] If we do not consider the existence of heat sources inside the liquid or other heat dissipation except to the environment, ignore the conversion between the mechanical energy and internal energy of the liquid, and do not consider the heat exchange between different parts of the liquid, then the enthalpy change of the liquid when flowing in the water pipe depends only on the heat dissipated to the environment. Taking the liquid in a control body with a length of dx in the water pipe as an example, its thermal dynamic process when flowing in the water pipe can be expressed as Figure 5 The equivalent circuit shown is used for simulation.

[0108] Among them, R amb It is used to simulate the thermal resistance between the liquid in the control body and the water pipe environment. Its mathematical expression is as follows:

[0109]

[0110] in, It is used to simulate the heat power dissipated by the liquid in the control body to the environment, T amb The ambient temperature outside the water pipe corresponding to the liquid in the control body is simulated, C amb The mathematical expression used to simulate the heat capacity of the liquid in the control body is as follows:

[0111] C amb =ρAc p dx#(18)

[0112] Among them, C amb The voltage drop T across the terminals is used to simulate the average temperature of the fluid in the control body.

[0113] Based on the above analysis, the time constant τ of the first-order linear equivalent circuit of the control body is th The mathematical expression is as follows:

[0114]

[0115] From equation (17), we can know that the time constant τ of the first-order linear circuit is th It has nothing to do with the axial length dx of the liquid in the control body along the water pipe, and when the specific heat capacity c of the liquid p and density ρ, cross-sectional area of ​​the water pipe and thermal conductivity per unit length G' amb When both can be regarded as constants, the time constant τ th Can also be considered as a constant.

[0116] The first-order linear equivalent circuit of the control body is a closed loop, which is not connected to the circuit simulating other liquids. When the initial state of the first-order linear equivalent circuit of the control body is known and the ambient temperature T outside the water pipe corresponding to the liquid in the control body is amb When given, its capacitance C amb The value T(t) of the voltage drop T at any time t can be calculated by the following formula:

[0117]

[0118] Where T(0) represents the initial state capacitance C amb For the liquid in the control body, its temperature when it just enters the second section of the water pipe can be obtained from the liquid temperature of the Nth unit of the first section of the water pipe. Approximate substitution can be made:

[0119]

[0120] When the liquid in the control body takes τ2 to flow out of the water pipe, t = τ2, and when the ambient temperature T amb When (t) is given, the temperature of the liquid in the control body at the outlet of the water pipe can be calculated by formula (18). The obtained temperature T(t) is the liquid temperature at the outlet of the water pipe, that is:

[0121] T out (t) = T(t) #(22).

[0122] The pipeline equivalent circuit model of the present invention taking into account the axial diffusion effect of the fluid has been compared and verified by experimental measurement data, and the model simulation results are in good agreement with the measured data. The specific parameters of the water pipe and liquid used for verification are shown in Table 1.

[0123] Table 1 Calibration water pipe and liquid parameters

[0124]

[0125]

[0126] In this verification, a water pipe with a length of 10.52m is used as the simulation object. The water pipe is divided into two sections with lengths of 3.2m and 7.32m, of which the first section of the water pipe is divided into 16 units, each of which is 0.2m long. Water is used as the liquid in the water pipe, the initial water temperature is set to 293.15K, and the water flow velocity is constant at 1.244m / s. When t=0s, the water flow temperature at the inlet end of the water pipe suddenly rises to 353.15K. The simulation results using the model of the present invention are consistent with the dimensionless outlet liquid temperature T measured experimentally in the literature [Saleh Salavati Meibodi, Simon Rees, Dynamic thermal response modelling of turbulent fluid flow through pipelines with heat losses, International Journal of Heat and Mass Transfer, Volume 151, 2020, 119440, ISSN 0017-9310]. 无量纲 (t) data are compared, where the dimensionless outlet liquid temperature is converted by the following formula:

[0127]

[0128] Among them, T 出口 Indicates the liquid temperature at the outlet of the water pipe, T 入口 Indicates the liquid temperature at the water pipe inlet, T 初始 Indicates the initial temperature of each part of the water pipe.

[0129] The temperature response curve of the liquid at the water pipe outlet is as follows: Figure 6 As shown in the figure, the black circles represent the measured results, and the solid line is the computer simulation result of the model of the present invention. Figure 6 It can be seen that the simulation results of the model of the present invention are highly consistent with the measured results. By changing the flow rate of the water pipe, such as reducing the liquid flow rate to 0.312m / s, and keeping other conditions unchanged, the simulation results are also consistent with the measured results. Figure 7 shown.

[0130] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A pipeline equivalent circuit model considering the axial diffusion of fluid, characterized in that: The pipeline equivalent circuit model is composed of equivalent circuit models simulating two sections of water pipes with different lengths; The first section of the water pipe is divided into N units of equal length. The equivalent circuit model of each unit consists of a variable resistor. The variable resistor Analogous to the frictional internal resistance of the water pipe, the variable resistor Voltage at Analogously to the average pressure of the liquid in the section of the water pipe; the first branch of the five parallel branches is a resistor resistance resistance With voltage source in series, the resistor Analogously to the equivalent thermal resistance of heat convection from the liquid in this section of the water pipe to the pipe wall, the resistance Analogously to the heat conduction equivalent thermal resistance of the pipe wall, the resistance Analogously, the insulation layer of this section of water pipe integrates the equivalent thermal resistance of heat conduction within the layer, heat convection with air, and heat radiation. Analogous to the external ambient temperature of this section of water pipe; the second branch has a capacitor Composition, the capacitor Analogous to the heat capacity of the liquid in this section of the water pipe, the capacitor The voltage across Analogously to the average temperature of the liquid in this section of the water pipe; the third branch has a capacitor One end of which is connected to the resistor The midpoint of the capacitor Analogous to the heat capacity of the pipe wall, the capacitor The voltage across Analogously to the average temperature of the pipe wall in this section; the fourth branch has a capacitor One end of which is connected to the resistor The midpoint of the capacitor Analogous to the heat capacity of the insulation layer of this section of water pipe, the capacitance The voltage across Analogously to the average temperature of the insulation layer of the water pipe section; the fifth branch consists of a current-controlled current source; The equivalent circuit model simulating the second section of the water pipe has the same topological structure as the equivalent circuit model simulating each unit in the first section of the water pipe. The equivalent circuit model simulating the second section of the water pipe and the equivalent circuit model simulating each unit in the first section of the water pipe are connected in series to obtain the pipeline equivalent circuit model.

2. A pipeline equivalent circuit model considering the axial diffusion effect of fluid according to claim 1, characterized in that: The current flowing through the first branch of the five parallel branches Analogously, the liquid in this section of the water pipe dissipates heat energy to its surroundings.

3. The pipeline equivalent circuit model considering the axial diffusion effect of the fluid according to claim 1 is characterized in that: The current flowing through the second branch of the five parallel branches Analogously, the net increase in liquid heat energy entering this section of the water pipe.

4. The pipeline equivalent circuit model considering the axial diffusion effect of the fluid according to claim 1 is characterized in that: The current flowing through the third branch of the five parallel branches Analogously, the net increase in heat energy entering the wall of this section of the water pipe.

5. The pipeline equivalent circuit model considering the axial diffusion effect of fluid according to claim 1 is characterized in that: The current flowing through the fourth branch of the five parallel branches Analogously, the net increase in heat energy entering the insulation layer of this section of the water pipe.

6. The pipeline equivalent circuit model considering the axial diffusion effect of the fluid according to claim 1 is characterized in that: In the fifth branch, the output current of the current-controlled current source of the left half model is By analogy with the mobility of the enthalpy flowing with the liquid in this section of the water pipe, its magnitude is determined by the following formula: in The liquid is at temperature T fl,dx The specific enthalpy under represents the mass flow rate of the liquid at time t; the output current of the current-controlled current source of the right half of the model The mobility of the enthalpy flowing out of the entire pipe as the liquid flows out of the pipe is determined by the following formula: Where h(T out ) indicates that the liquid is at temperature T out The specific enthalpy under.

7. The pipeline equivalent circuit model considering the axial diffusion effect of fluid according to claim 1 is characterized in that: The equivalent circuit of the second section of the water pipe has the same topological structure as each unit in the first section of the water pipe, and each branch has the same physical meaning. The difference is that the parameters of each branch in the equivalent circuit of the second section of the water pipe are determined by the second section of the water pipe.

8. The pipeline equivalent circuit model considering the axial diffusion effect of fluid according to claim 1 is characterized in that: The specific calculation process of the equivalent circulation time of liquid in each unit in the water pipe is as follows: When the water pipe is filled with liquid, the total mass M of the liquid is: M=pAL#(8) The time it takes for the liquid to flow through the entire pipe is τ: The time for the liquid to flow through the two sections of the water pipe is recorded as τ1 and τ2 respectively: τ=τ1+τ2#(10) The time τ1 for the liquid to flow through the first section of the water pipe is calculated from the circulation time τ of the liquid in N units. N Sure: τ1=Nτ N #(11) The circulation time τ of the liquid in N units N for: Where v represents the axial velocity of the liquid in the water pipe, and D represents the diffusion coefficient related to the axial velocity v of the liquid in the water pipe, which is determined by equations (13) and (14): Where Re represents the Reynolds number corresponding to the flow of liquid in the water pipe at an axial velocity v; when the flow time of liquid in N units τ N After determination, the time τ1 for the liquid to flow through the first section of the water pipe can be determined, and then the time τ2 for the liquid to flow through the second section of the water pipe can be determined.

9. The pipeline equivalent circuit model considering the axial diffusion effect of fluid according to claim 1 is characterized in that: The specific calculation process of the liquid temperature at the outflow end of the water pipe is as follows: Assume the length of a control body in the water pipe is dx, and use R amb Simulate the thermal resistance between the fluid in the control body and the water pipe environment: in, It is used to simulate the heat power dissipated by the liquid in the control body to the environment, T amb The ambient temperature outside the water pipe corresponding to the liquid in the control body is simulated, C amb Used to simulate the heat capacity of the fluid in the control body: C amb =pAc p dx#(16) Among them, C amb The voltage drop T across the two ends is used to simulate the average temperature of the liquid in the control body; The time constant τ of the first-order linear equivalent circuit of the control body th The mathematical expression is as follows: The first-order linear equivalent circuit of the control body is a closed loop, which is not connected to the circuit simulating other liquids. When the initial state of the first-order linear equivalent circuit of the control body is known and the ambient temperature T outside the water pipe corresponding to the liquid in the control body is amb When given, its capacitance C amb The value T(t) of the voltage drop T at any time t is calculated by the following formula: Where T(0) represents the initial state capacitance C amb The voltage drop at both ends; for the liquid in the control body, the temperature when it just enters the second section of the water pipe is determined by the liquid temperature of the Nth unit of the first section of the water pipe. Approximate substitution, that is: When the liquid in the control body takes time τ2 to flow out of the water pipe, let t = τ2, and when the ambient temperature T amb When (t) is given, the temperature of the liquid in the control body at the outlet of the water pipe can be calculated by formula (18); the obtained temperature T(t) is the liquid temperature at the outlet of the water pipe: T out (t)=T(t)#(20)。

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