A fluid multi-physics field simulation method for an electromagnetic transient simulation environment

Abstract

The application discloses a fluid multi-physical field simulation method for an electromagnetic transient simulation environment. The method expands the existing equivalent circuit model of a water pipe, so that the natural convection of liquid in the pipe and the thermal dynamic process accompanying the natural convection can be simulated when the external driving flow rate is zero, thereby the temperature distribution of the liquid in a central heating or central cooling system with more temperature fluctuation and fluid flow discontinuity can be simulated and analyzed more accurately. Meanwhile, the application models the water pipe by using the equivalent circuit, so that a comprehensive energy system composed of a power system and the central heating or central cooling system can be modeled and simulated in the same electromagnetic transient simulation environment, thereby avoiding the simulation of different systems by using different simulation software, simplifying the computer simulation process, and avoiding the problem of asynchronous data exchange when different software is connected.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromagnetic transient simulation, and particularly relates to multi-physical field transient simulation of fluid natural convection by using an electromagnetic transient simulation method. BACKGROUND

[0002] With the increasing penetration of renewable energy in power systems, the intermittency and volatility of wind power, photovoltaic power and other electric energy have an increasingly non-negligible impact on the reliability and stability of power systems. In order to ensure the safe and reliable operation of power systems, the problem of curtailment of wind power and photovoltaic power often occurs. By using electric heat conversion technologies such as electric heaters and heat pumps, the surplus electric energy can be converted into heat energy for use or storage. Through this conversion, the heat supply system or the cold supply system can help to absorb the excess electric energy in the power system and reduce the curtailment of wind power and photovoltaic power. With the large-scale conversion of renewable electric energy with volatility and intermittency into heat energy in the heat supply system or the cold supply system by using electric heat conversion technologies, compared with traditional heat supply systems, the heat supply system or the cold supply system is likely to exhibit more temperature volatility and fluid flow intermittency. Therefore, to study the characteristics of the heat supply system or the cold supply system, it is necessary to accurately model the thermal dynamic process in the system.

[0003] To study the thermal dynamic process in the heat supply system or the cold supply system, it is necessary to use the dynamic model of such a system. The model based on the finite element method is a useful model. In such a model, the pipe in the system is spatially divided into a plurality of adjacent elements, and the temperature variable of the liquid in the pipe is implicitly included in the differential equation set for the energy conservation of the elements. By numerically solving the differential equation set, the temperature of the liquid in the element can be solved, and the thermal transient process of the liquid in the pipe can be simulated. It is worth noting that using such a model needs to pay attention to the distortion of the calculation results caused by artificial diffusion.

[0004] To avoid the distortion of the calculation results caused by the numerical method, an analytical method can also be used to solve the energy conservation equation set of the finite element. One analytical method is to use the method of characteristics to solve the differential equation. Compared with the numerical method, the calculation amount of the method of characteristics is small and the calculation result is accurate. Another analytical method uses Fourier series and trigonometric function transformation, which uses the lag time of the fluid in the system and the temperature decay degree to describe the temperature dynamic process of the system. The lag time can be estimated by the flow time of the liquid, and the temperature decay degree is mainly determined by the heat insulation performance of the pipe.

[0005] Another dynamic model, so-called nodal model, only considers the inflow and outflow of liquid in the system, and the temperature of the outflow liquid is estimated based on the temperature of the inflow liquid and the flow path, like quasi-dynamic model. Given that the duration of transient process of fluid flow rate change in the system is far shorter than that of temperature change transient process, the model regards the flow rate of liquid in the system as constant. This method can reduce the amount of calculation, but is only applicable to the case where the flow rate in the system is constant, which limits its application range.

[0006] In order to put the integrated energy system into the simulation environment of power circuit for simulation, document 1 (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) proposes an equivalent circuit model of water pipe. The model uses analogy method to use electrical quantities to analog various physical quantities of fluid and temperature, and on this basis, an equivalent circuit model of water pipe is constructed. Document 2 (J. Yang, N. Zhang, A. Botterud, and C. Kang, "On an equivalent representation of the dynamics in district heating networks for combined electricity heat operation", IEEE Transactions on Power Systems, vol. 35, pp. 560-570, 2020) based on Laplace transform, explicitly describes the energy input and output relationship at both ends of the water pipe in the model. Thus, the document simulates the water pipe by means of transmission line model.

[0007] However, the above models do not consider the natural convection of the liquid in the water pipe. Generally speaking, when the liquid in the water pipe is driven by an external driving force, the enthalpy transfer of the liquid in the water pipe is basically dependent on the external driving flow rate of the liquid. However, the external driving flow rate may be zero in some cases, such as when a valve in the water pipe is closed. At this time, if there is a temperature gradient in the water pipe, the liquid in the pipe may generate natural convection, and the enthalpy transfer of the liquid also occurs. This natural convection is driven by the buoyancy effect, which changes the distribution of the temperature gradient in the water pipe. Therefore, in order to simulate the change of the temperature distribution of the liquid in the water pipe after the water pipe is closed, it is necessary to simulate the natural convection.

[0008] The electromagnetic transient simulation algorithm is mainly applied to computer modeling and simulation of electronic and electrical systems, and is a mature and widely used method by electronic and electrical engineers. There is no solution to use electromagnetic transient simulation software to model and simulate the mechanical and thermal dynamic processes of natural convection of liquid in central heating or central cooling systems in the electromagnetic transient simulation environment. If the mechanical and thermal dynamic processes of natural convection of liquid in central heating or central cooling systems can be simulated in the electromagnetic transient simulation environment, it will be very helpful for accurately simulating and analyzing the interaction between central heating or central cooling systems and power systems containing renewable energy sources with volatility and discontinuity. SUMMARY

[0009] The purpose of the present application is to provide a fluid multi-physical field simulation method for an electromagnetic transient simulation environment. In order to achieve the above purpose, the present application provides the following technical solution, which comprises the following steps:

[0010] S1, discretizing the continuous fluid motion equation set into a difference equation set of fluid motion, the fluid motion equation set comprising a continuity equation reflecting the law of conservation of mass, a motion equation reflecting Newton's second law, and an energy equation reflecting the law of conservation of energy;

[0011] S2, replacing the fluid mechanics and thermodynamics physical quantities in the difference equation set of fluid motion in step S1 with electrical quantities based on the analogy method;

[0012] S3, constructing an equivalent circuit for simulating the mechanical motion of the liquid based on the equation after replacing the physical quantities in S2;

[0013] S4, constructing an equivalent circuit for simulating the thermal motion of the liquid based on the equation after replacing the physical quantities in S2;

[0014] S5, using the equivalent circuit for simulating the mechanical motion of the liquid in step S3 and the equivalent circuit for simulating the thermal motion of the liquid in step S4 to simulate the mechanical motion and thermal motion of the natural convection of the fluid in the electromagnetic transient simulation software.

[0015] Further, the fluid motion is two-dimensional or three-dimensional motion.

[0016] Taking the two-dimensional fluid motion as an example, in step S1, the continuity equation reflecting the law of conservation of mass is:

[0017]

[0018] The continuous two-dimensional motion equation is:

[0019] x-axis direction:

[0020] y-axis direction:

[0021] Wherein: p is the density of the liquid, p is the liquid pressure, μ is the dynamic viscosity of the liquid, g is the acceleration of gravity;

[0022] The continuous energy equation is:

[0023]

[0024] Wherein: c p is the specific heat capacity of the liquid, T is the liquid temperature, k is the thermal conductivity of the liquid, μΦ represents the viscous dissipation of the liquid, represents the heat generation rate of the heat source in unit volume of the liquid;

[0025] The discrete two-dimensional motion equation is:

[0026] x-axis direction:

[0027]

[0028] In the formula:

[0029]

[0030]

[0031]

[0032] Wherein: the liquid in the water pipe is virtually divided into several segments along the axial direction (x direction) and several layers along the gravity direction (y direction), i represents the ith segment in the x-axis direction, and j represents the jth layer in the y-axis direction; After division, a plurality of control volumes are formed, each control volume has a length of Δx in the x direction and a height of Δy in the y direction; is the liquid mass flow rate flowing through the control volume (i, j) along the x-axis direction; Describes the physical quantity related to fluid inertia; Describes the physical quantity related to fluid flow resistance; is a variable with dimension [Pa]; is the cross-sectional area of the control volume (i, j) perpendicular to the x-axis, is the cross-sectional area of the control volume (i, j) perpendicular to the y-axis;

[0033] y-axis direction:

[0034]

[0035] wherein:

[0036]

[0037]

[0038]

[0039] wherein: is the mass flow rate of the liquid flowing through the control volume (i, j) in the y-axis direction; describes a physical quantity related to the fluid inertia; describes a physical quantity related to the fluid flow resistance; is a variable with dimension [Pa];

[0040] The discretized energy equation is:

[0041]

[0042] wherein: describes the rate of change of enthalpy within the control volume; respectively describe the enthalpy fluxes into and out of the control volume (i, j) from the x-axis and the y-axis; describes the heat dissipation of the liquid within the control volume (i, j) to the surrounding environment; respectively represent the heat conduction between the control volume (i, j) and its adjacent control volumes (i, j+1), (i, j-1), (i+1, j) and (i-1, j);

[0043] wherein:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] wherein: represents the heat capacity of the liquid in the control volume (i, j); represents the thermal resistance of the liquid in the control volume (i, j) in the x direction; represents the thermal resistance of the liquid in the control volume (i, j) in the y direction; represents the equivalent thermal resistance between the liquid in the control volume (i, j) and the environment outside the pipe.

[0052] Further, the liquid density p can be calculated by the calculation formula:

[0053] p(T) = p0(1 - β(T - T0))#(21)

[0054] wherein p0 is the density of the liquid at the standard temperature T0 = 298.15 K; β is the thermal expansion coefficient of the liquid.

[0055] Further, in step S2, the electrical quantities such as electric potential, electric current, electric resistance, electric capacity, and electric inductance are respectively used to replace the physical quantities such as liquid pressure, flow rate, friction impedance, capacity, and inductance in the fluid mechanical motion differential equation group in S1; the electrical quantities such as electric potential, electric current, electric resistance, electric capacity, and electric inductance are respectively used to replace the physical quantities such as liquid temperature, enthalpy mobility or thermal conductivity, thermal resistance, and heat capacity in the fluid thermal motion differential equation group in S1.

[0056] Further, the equation group after the physical quantity replacement in step S2 is:

[0057] The x direction motion equation is:

[0058]

[0059] The y direction motion equation is:

[0060]

[0061] wherein, is the inductance, the dimension is [H], and the value is respectively equal to is the resistance, the dimension is [Ω], and the value is respectively equal to p x , p y is the voltage, the dimension is [V], and the value is respectively equal to is the electric potential, the dimension is [V], and the value is equal to p (i，j) ; is the electric current, the dimension is [A], and the value is respectively equal to

[0062] The energy equation is:

[0063]

[0064] wherein, is a capacitance, dimension [F], whose value is equal to is a resistance, dimension [Ω], whose value is equal to is a current, dimension [A]; is a potential, dimension [V].

[0065] Further, in step S3, a two-dimensional equivalent circuit of the mechanical movement of the fluid in the pipe is established according to the calculation formulas (22) and (23), wherein a node (i, j) in the circuit corresponds to a control volume (i, j) in the liquid, the node potential corresponds to the liquid pressure in the control volume, and the current between the nodes corresponds to the liquid volume flow rate between the control volumes; in the circuit, the node (i, j) represents the control volume (i, j), two adjacent nodes in the x direction are connected by a branch composed of a variable resistance with a size equal to , an inductance with a size equal to , and a controlled voltage source with an output voltage equal to ; and two adjacent nodes in the y direction are connected by a branch composed of a variable resistance with a size equal to , an inductance with a size equal to , and a controlled voltage source with an output voltage equal to .

[0066] Further, in step S4, a two-dimensional equivalent circuit of the thermal dynamics of the fluid in the pipe is established according to the calculation formula (24), wherein a node (i, j) in the circuit corresponds to a control volume (i, j) in the liquid, the node potential corresponds to the average temperature of the liquid in the control volume, and the current between the nodes corresponds to the enthalpy mobility or the thermal conductivity between the control volumes; in the circuit, the node (i, j) represents the control volume (i, j), two adjacent nodes in the x direction are connected by a branch containing a resistance R t，x , and two adjacent nodes in the y direction are connected by a branch containing a resistance R t，y ; the node and the ground point are connected in parallel by two branches: one branch contains a capacitance , and the other branch is composed of a resistance and a controlled voltage source with an output voltage of .

[0067] Further, the fluid includes gas and liquid.

[0068] In another aspect, the application also provides an application of the fluid multi-physical field simulation method for an electromagnetic transient simulation environment in simulation of liquid or gas movement.

[0069] Compared with the prior art, the present application has the following beneficial effects:

[0070] 1. The fluid multi-physical field simulation method for the electromagnetic transient simulation environment expands the existing equivalent circuit model of the water pipe, so that the natural convection of the liquid in the pipe and the thermal dynamic process accompanying the natural convection can be simulated when the external driving flow rate is zero, and thus the temperature distribution of the central heating or central cooling system with more temperature fluctuation and fluid flow discontinuity characteristics can be simulated and analyzed more accurately.

[0071] 2. The fluid multi-physical field simulation method for the electromagnetic transient simulation environment uses the equivalent circuit to model the water pipe, so that the systems containing different energy forms can be modeled and simulated in the same electromagnetic transient simulation environment, thereby avoiding the simulation of the same system using different simulation software, simplifying the computer simulation process, and avoiding the out-of-sync problem of data exchange between different software interfaces. BRIEF DESCRIPTION OF DRAWINGS

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced. Obviously, the drawings in the following description are only some embodiments described in the present application, and other drawings can also be obtained by those skilled in the art according to these drawings.

[0073] Figure 1 A horizontally placed cylindrical water pipe is provided for the embodiments of the present application.

[0074] Figure 2 A three-dimensional view of the segmentation scheme of the liquid inside the water pipe is provided for the embodiments of the present application.

[0075] Figure 3 A two-dimensional view of the segmentation scheme of the liquid inside the water pipe is provided for the embodiments of the present application.

[0076] Figure 4 A two-dimensional equivalent circuit describing the mechanical movement of the liquid is provided for the embodiments of the present application.

[0077] Figure 5 A two-dimensional equivalent circuit describing the thermal dynamics of the liquid is provided for the embodiments of the present application.

[0078] Figure 6 The temperature response of the liquid in the pipe when the external driving flow rate is not zero is provided for the embodiments of the present application.

[0079] Figure 7Temperature response of the liquid in the upper half of the pipe as a function of the axial length of the control volume (top) and the percentage difference from the ANSYS Fluent simulation results (bottom) provided for the embodiments of the present application.

[0080] Figure 8 Temperature response of the liquid in the upper half of the pipe as a function of the thickness of the control volume in the direction of gravity (top) and the percentage difference from the ANSYS Fluent simulation results (bottom) provided for the embodiments of the present application.

[0081] Figure 9 Distributed heat supply unit schematic provided for the embodiments of the present application.

[0082] Figure 10 Dynamic response of the water temperature of the heat supply unit when the temperature of the main water supply pipe rises provided for the embodiments of the present application.

[0083] Figure 11 Dynamic response of the water temperature of the heat supply unit when the temperature of the main water supply pipe drops provided for the embodiments of the present application. DETAILED DESCRIPTION

[0084] In order to better understand the technical solutions, the method of the present application will be described in detail below with reference to the accompanying drawings.

[0085] The present application provides a fluid multi-physical field simulation method for an electromagnetic transient simulation environment, which uses an analogy method to build an equivalent circuit model for a water pipe, which can simulate the natural convection of the liquid in the water pipe caused by temperature difference without external driving force, and the change of the internal temperature distribution of the water pipe caused thereby. In addition, the model can be simulated with the power system in the same electromagnetic transient simulation environment, and can realize multi-physical field transient simulation and analysis of a comprehensive energy system covering the power system and the central heating system or the central cooling system in the same simulation environment.

[0086] The present model is based on the following basic assumptions:

[0087] 1) The volume of the liquid in the water pipe cannot be compressed, and the liquid in the same control volume has the same physical properties;

[0088] 2) There is no heat source inside the liquid;

[0089] 3) The system is always full of liquid;

[0090] 4) The radiation dissipation and viscous dissipation of the liquid are ignored;

[0091] 5) Gravity is the only volume force acting on the liquid;

[0092] 6) When there is an external driving force, the flow of the liquid in the water pipe is regarded as laminar and fully developed, and the relative motion of different parts inside the liquid is ignored;

[0093] 7) Only natural convection occurs, the liquid motion along the horizontal radial direction in the horizontal tube is ignored, and the convection of the liquid is only considered as two-dimensional motion in a series of vertical planes in the tube.

[0094] For the convenience of describing the method of the present application, a cylindrical water tube horizontally placed is used as an example, as shown in Figure 1 . Figure 1 The direction of the gravitational acceleration is the same as the negative direction of the y axis. It should be pointed out that the method of the present application is not limited to be applied to this type of water tube.

[0095] Due to the symmetry of the cross section of this type of water tube, and the temperature gradient and density gradient of the liquid generally do not distribute along the z axis direction, the motion of the liquid in the z axis direction can be ignored, and only the natural convection of the liquid in the tube is considered as motion in the xy plane. For the convenience of modeling, the fluid mechanics equation set is mathematically transformed. The method of the present application can be applied to two-dimensional or three-dimensional fluid motion, and here, for the convenience of description, only two-dimensional fluid motion is taken as an example. Since the model only considers the two-dimensional motion of the liquid in the vertical xy plane, the two-dimensional fluid mechanics equation set is in the following form:

[0096] 1) The continuity equation reflecting the law of conservation of mass:

[0097]

[0098] where v x and v y are the flow velocities of the liquid in the x and y directions, respectively.

[0099] 2) The motion equation reflecting Newton's second law:

[0100] x axis direction:

[0101] y axis direction:

[0102] where: p is the density of the liquid, p is the pressure of the liquid, μ is the dynamic viscosity of the liquid, and g is the gravitational acceleration.

[0103] 3) The energy equation reflecting the law of conservation of energy:

[0104]

[0105] where: c p is the specific heat capacity of the liquid, T is the temperature of the liquid, k is the thermal conductivity of the liquid, μΦ represents the viscous dissipation of the liquid, represents the heat generation rate of the heat source in the unit volume of the liquid.

[0106] It is worth noting that the liquid density p in the above fluid motion equations (2), (3) and (4) is a variable, which is different in different control volumes due to the different temperatures and pressures of the liquid in each control volume. In the study of natural convection of fluid, the Boussinesq assumption is often used in engineering. This assumption regards the liquid density in the motion equation as a constant, and only regards it as a variable when it is multiplied by the body force (such as gravity), at which time the liquid density can be approximated by the following formula:

[0107] p(T) = p0(1 - β(T - T0)) (5)

[0108] wherein p0 is the density of the liquid at the standard temperature T0 = 298.15 K; β is the thermal expansion coefficient of the liquid.

[0109] The liquid in the water pipe is equally divided into a plurality of virtual small control volumes along the x-axis and y-axis directions, as shown in Figure 2 . In the x-axis direction, it is divided into N x segments, each of which is represented by the variable i, and the length of each control volume is Δx; in the y-axis direction, it is divided into N y layers, each of which is represented by the variable j, and the height of each control volume is Δy. Due to the symmetry of the cross section of the water pipe, the temperature gradient and the density gradient of the liquid generally do not distribute along the z-axis direction, so the motion of the liquid in the z-axis direction can be ignored, and only the natural convection of the liquid in the pipe is regarded as the motion in the xy plane, so the fluid in the z-axis direction does not need to be divided.

[0110] When viewed along the z-axis direction, the distribution of the divided control volumes in the xy plane is as shown in Figure 3 . Each control unit can be represented by a pair of coordinates (i, j). In the control volume (i, j), the cross-sectional area perpendicular to the x-axis is denoted as , and the cross-sectional area perpendicular to the y-axis is denoted as

[0111] It is worth noting that the is equal everywhere in the same control volume, while the at different positions in the same control volume is not equal. For ease of analysis and calculation, the discussed below refers to the arithmetic mean of all cross-sectional areas perpendicular to the y-axis in the control volume (i, j). Thus, the volume of the control volume (i, j) can be calculated by the following formula:

[0112]

[0113] The x-axis direction motion equation (2) can be discretized into the following form:

[0114]

[0115] where:

[0116]

[0117]

[0118]

[0119] where: is the liquid mass flow rate through the control volume (i, j) in the x-axis direction; represents a physical quantity related to fluid inertia; represents a physical quantity related to fluid flow resistance; is a variable with dimension [Pa]. Similarly, the y-axis direction motion equation (3) can also be discretized into the following form:

[0120]

[0121] where is the liquid mass flow rate through the control volume (i, j) in the y-axis direction, and:

[0122]

[0123]

[0124]

[0125] The energy equation (4) can be discretized into the following form:

[0126]

[0127] where: represents the rate of change of enthalpy within the control volume; respectively represent the enthalpy fluxes into and out of the control volume (i, j) from the x-axis and y-axis directions; represents the heat dissipation of the liquid within the control volume (i, j) to the surrounding environment; respectively represent the heat conduction between the control volume (i, j) and its adjacent control volumes (i, j+1), (i, j-1), (i+1, j), and (i-1, j), where:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] where: represents the heat capacity of the liquid in the control volume (i,j); represents the thermal resistance of the liquid in the control volume (i,j) in the x direction; represents the thermal resistance of the liquid in the control volume (i,j) in the y direction; represents the equivalent thermal resistance between the liquid in the control volume (i,j) and the environment outside the pipe.

[0136] The present application is based on the analogy method, and now uses electrical quantities to analog physical quantities in the fluid, as shown in the following Table 1:

[0137] Table 1 Analogy between electrical quantities and fluid mechanics and thermodynamics physical quantities

[0138]

[0139]

[0140] Based on the above analogy, electrical quantities can be used to simulate mechanical and thermodynamic dynamic processes in the fluid, so that the water pipe can be simulated by means of an equivalent circuit. To complete this step, first, the motion equation and energy equations (7), (11) and (15) of the liquid in the water pipe are replaced according to Table 1. After replacement, the three equations are rewritten as follows:

[0141]

[0142]

[0143]

[0144] The equivalent circuit of the water pipe is constructed based on the above three equations:

[0145] 1) Liquid mechanical motion equivalent circuit

[0146] According to the calculation formulas (23) and (24), a two-dimensional equivalent circuit of the mechanical motion of the liquid in the water pipe can be established, as shown in Figure 4As shown. In the circuit, nodes (i, j) are analogous to control volumes (i, j) in a liquid, the node potential is analogous to the liquid pressure within that control volume, and the current between nodes is analogous to the liquid flow velocity between the control volumes. Nodes (i, j) in the circuit represent control volumes (i, j), and adjacent nodes in the x-direction are connected by a path of magnitude equal to... A variable resistor, a resistor of equal value The inductance and an output voltage equal to The branches are connected by controlled voltage sources; two adjacent nodes in the y direction are connected by a branch consisting of a voltage source of equal size. A variable resistor, a value equal to The inductance and an output voltage equal to The branches are connected together by controlled voltage sources.

[0147] 2) Liquid thermal dynamic equivalent circuit

[0148] According to the calculation formula (25), a two-dimensional equivalent circuit of the thermal dynamics of the liquid inside the water pipe can be established, such as Figure 5 As shown. In the circuit, nodes (i, j) are analogous to control volumes (i, j) in a liquid, node potentials are analogous to the average temperature of the liquid within the control volume, and the currents between nodes are analogous to the enthalpy mobility or thermal conductivity between control volumes. Nodes (i, j) in the circuit represent control volumes (i, j), and adjacent nodes in the x-direction are connected by a line containing a resistor R. t,x The branch connection, in the y-direction, connects two adjacent nodes through a path containing a resistor R. t,y The branch connection; the node and grounding point are formed by two branches connected in parallel: one branch contains a capacitor. Another branch is the resistor and output voltage is It consists of controlled voltage sources connected in series.

[0149] It should be noted that although only four nodes are given in the equivalent circuits for liquid mechanical motion and thermal dynamics in the above embodiments, the equivalent circuits can be expanded according to the size of the water pipe and the specific division of its internal control volume. After completely connecting the nodes representing all control volumes, the equivalent circuit model of the water pipe is completed.

[0150] The model method of the present application is verified as follows. Literature 1 proposes a water pipe model which has been verified by experimental data. In addition, ANSYS Fluent software is an engineering calculation software widely used for simulating and calculating fluid motion. By comparing the simulation results of the embodiment of the present application with the water pipe model in literature 1 and the simulation results of ANSYS Fluent software, the correctness of the water pipe modeling method proposed by the present application has been verified. The water pipe used for verification is DN65, and the specific parameters of the water pipe and the liquid are shown in Table 2.

[0151] Table 2 Water pipe and liquid parameters for verification

[0152]

[0153]

[0154] After modeling the water pipe in ANSYS Fluent and using the method of the present application respectively, the verification is carried out under two working conditions: one is the working condition when the flow rate of the liquid in the pipe under the driving force of the external driving force is not zero, at this time the convection motion of the liquid in the pipe is ignored; the other is the working condition when the external driving force is zero, at this time the natural convection of the liquid in the pipe will affect the temperature distribution of the liquid in the pipe.

[0155] 1) Working condition of non-zero external driving flow rate

[0156] Under this working condition, the liquid in the water pipe is virtually divided into 10 segments along the axial direction by using the method of the present application, and each segment has a length of 1 m; it is virtually divided into 4 layers along the direction of gravitational acceleration, and each layer has a thickness of 0.01625 m. The initial temperature of the liquid in the pipe is set to 353K, and the mass flow rate of the liquid is constant at 1kg·s -1 When t = 100s, the temperature of the liquid at the outlet of the water pipe drops to 303K. The average temperature response of the liquid in each segment in the water pipe in the two models is shown in Figure 6 , in which the dashed line is the computer simulation result of the water pipe model in literature 1, and the solid line is the computer simulation result of the model of the present application. It can be seen from Figure 6 that under this working condition, the computer simulation results of the model of the present application and the water pipe model in literature 1 are highly consistent.

[0157] 2) Working condition of zero external driving flow rate

[0158] When the external driving flow rate is zero, the half of the water pipe from x = 0m to x = 5m is regarded as the upper half, and the half of the water pipe from x = 5m to x = 10m is regarded as the lower half. It is assumed that the initial temperature of the upper half is 353K and the initial temperature of the lower half is 303K at t = 0. The average temperature of the liquid in the pipe changes with time as Figure 7 , Figure 8As shown, for simplicity, only the upper half of the temperature response is displayed here. The red solid line in the figure represents the computer simulation result from ANSYS Fluent, while the remaining black lines represent the computer simulation result of the model of this invention.

[0159] Figure 7 This demonstrates the temperature response of the liquid in the upper half of the pipe when it is virtually cut into four layers in the direction of gravity and into different numbers of segments in the horizontal axis. Figure 7 It is evident that the smaller the horizontal axial length of the control volume, the closer its temperature response is to the results of ANSYS Fluent. When this length is 0.1m, the difference between the two is within 2%.

[0160] Depend on Figure 7 It is evident that even when the external driving flow velocity is zero, the liquid temperature inside the pipe will change. This is because, under the influence of natural convection, the warmer liquid inside the pipe will mix with the cooler liquid. Therefore, the average temperature of the liquid in the upper half of the pipe, which initially has a higher temperature, will gradually decrease as natural convection occurs; similarly, the average temperature of the liquid in the lower half of the pipe, which initially has a lower temperature, will gradually increase as natural convection occurs.

[0161] Figure 8 The figure shows the temperature response of the liquid in the upper half of the pipe when the liquid inside the pipe is virtually cut into 4 layers in the horizontal axis and into different numbers of segments in the gravity direction. Similarly, as can be seen from the figure, the smaller the thickness of the control volume in the gravity direction, the closer its temperature response is to the result of ANSYS Fluent, and the difference between the two is within 2%.

[0162] In summary, through analysis and comparison of the results of specific embodiments, it can be seen that the water pipe model proposed by the method of the present invention simulates the dynamic temperature response of the liquid in the pipe under two working conditions: the external driving flow velocity is not zero and the external driving flow velocity is zero. This closely approximates the existing methods for verification, thus verifying the correctness and accuracy of the method of the present invention.

[0163] The method of the present invention will be described below with reference to specific application examples.

[0164] Consider as Figure 9 The diagram shows a distributed heating unit within a centralized heating system. This unit comprises: an electrothermal conversion unit that converts electrical energy into heat energy to supply the centralized heating system; a hot water storage tank that stores excess heat energy within the unit and provides it to the system when needed; and an auxiliary heating device that provides supplementary power when the system's heat load is high and the power supplied by the electrothermal conversion unit and the hot water storage tank is insufficient. The flow rate of the liquid flowing through these three devices can be controlled by water pumps and valves. The power of the hot water storage tank... The droop control has the following characteristics:

[0165]

[0166] where R droop is the droop coefficient, T m,s is the temperature at the end of the heat supply unit, are the upper and lower limit temperatures of the droop control, respectively. When the temperature T m,s at the end of the heat supply unit is greater than the set upper limit temperature , the water tank absorbs the excess heat in the system with a power ; when the temperature T m,s at the end of the heat supply unit is less than the set lower limit temperature , the water tank releases the excess heat in the system with a power ; when the temperature T m,s at the end of the heat supply unit is between the set upper limit temperature and the set lower limit temperature , the water tank valve and the water pump are closed, neither absorbing nor releasing power.

[0167] In the application example, are set to 336 K and 330 K, respectively, and the initial value of T m,s is set to 333 K. At this time, T m,s is exactly between and , the water tank neither absorbs nor releases heat power, the auxiliary heating device is also in the closed state, and the liquid flow rate through both is zero. If the electric heat conversion device is closed at this time, for example, when the connected new energy power generation device output drops to zero, the liquid flow rate through the electric heat conversion device also drops to zero. In this case, the liquid flow rate through the entire heat supply unit and the water supply pipe branch is zero. The benefits brought by the present application are demonstrated by comparing two application scenarios.

[0168] Scenario 1: The water temperature in the system main water supply pipe rises. At this time, if the natural convection of the liquid in the pipe due to temperature difference is not considered, the change in water temperature distribution in the water supply pipe branch will not be reflected. Therefore, in the simulation, the heat supply unit terminal temperature T m,s also does not change, and the droop controller does not act, as shown by the dashed line in Figure 10 . The black line in the figure represents the water temperature, and the blue line represents the heat power absorbed or released by the heat storage water tank. If the water pipe model of the present application is used, the natural convection of the liquid in the pipe can be simulated, so in the simulation, the heat supply unit terminal temperature T m,s will rise due to natural convection, as shown by the black solid line in Figure 10 . As the temperature T m,sThe droop controller will also operate according to equation (26) as the temperature changes. At this time, the hot water storage tank will start up and absorb heat from the main water supply pipe and store it for future use. Thus, the hot water storage tank can play its role as a distributed energy storage device.

[0169] Scenario 2: The water temperature in the main water supply pipe of the system drops. In this case, if natural convection caused by the temperature difference in the liquid within the pipe is not considered, the change in water temperature distribution within the branch water supply pipes will not be reflected. Therefore, in the simulation, the terminal temperature T of the heating unit... m,s Nothing will change, and the droop controller will not activate. Figure 11 The figure shows the water temperature (black line) and the heat power absorbed or emitted by the hot water storage tank (blue line). Using the water pipe model of this invention, the natural convection of the liquid inside the pipe can be simulated; therefore, the terminal temperature T of the heating unit is shown in the simulation. m,s It will decrease with convection, such as Figure 11 The solid black line in the middle shows the change with temperature T. m,s The droop controller will also operate according to equation (26) as the temperature changes. At this time, the hot water storage tank will start and supply heat to the main water supply pipe.

[0170] In summary, this invention proposes a modeling and calculation method for the mechanical and thermal motion of fluids during natural convection in an electromagnetic transient simulation environment. Using this method, the mechanical and thermal transient processes of natural convection within a fluid can be simulated alongside the electrical system within the same electromagnetic transient simulation environment. This eliminates the need for separate modeling and simulation using other simulation software for centralized heating or cooling systems, thus avoiding the problems of connecting two different simulation software programs and synchronizing their data. This invention provides a practical method for conducting multiphysics transient simulations within integrated energy systems in an electromagnetic transient simulation environment. The water pipe model using this invention can more accurately reflect the dynamic processes of liquid flow and temperature in centralized heating systems.

[0171] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fluid multi-physics simulation method for an electromagnetic transient simulation environment, characterized by, The method comprises the following steps: S1, discretizing continuous fluid motion equations into difference equations of fluid motion, the fluid motion equations comprising a continuity equation reflecting the law of conservation of mass, a motion equation reflecting Newton's second law, and an energy equation reflecting the law of conservation of energy; S2, replacing physical quantities of fluid mechanics and thermodynamics in the difference equations of fluid motion in step S1 with electrical quantities based on an analogy method; S3, constructing an equivalent circuit simulating mechanical motion of liquid based on the equations after replacing the physical quantities in S2; S4, constructing an equivalent circuit simulating thermal motion of liquid based on the equations after replacing the physical quantities in S2; S5, simulating mechanical motion and thermal motion of natural convection of fluid in electromagnetic transient simulation software by using the equivalent circuit simulating mechanical motion of liquid in step S3 and the equivalent circuit simulating thermal motion of liquid in step S4; The equation group after replacing the physical quantities in step S2 is: The motion equation in the x direction is: The motion equation in the y direction is: wherein is an inductance, dimension [H], whose value is equal to is a physical quantity related to the fluid inertia; is a resistance, dimension [Ω], whose value is equal to is a physical quantity related to the fluid flow resistance, is a voltage, dimension [V], whose value is equal to is a variable of dimension [Pa]; is an electric potential, dimension [V], whose value is equal to p (i,j) ; is an electric current, dimension [A], whose value is equal to is the liquid mass flow rate along the x-axis direction through the control volume (i,j), is the liquid mass flow rate along the y-axis direction through the control volume (i,j); The energy equation is: wherein, is a capacitance, dimension of [F], whose value is equal to represents the heat capacity of the liquid within the control volume (i,j); is a resistance, dimension of [Ω], whose value is equal to represents the thermal resistance of the liquid within the control volume (i,j) in the x direction; represents the thermal resistance of the liquid within the control volume (i,j) in the y direction; is a current, dimension of [A], whose value is equal to the enthalpy mobility of the liquid leaving the control volume (i,j) from the x and y axes, respectively; is a potential, dimension of [V], whose value is equal to T (i,j) ; In step S3, two-dimensional equivalent circuit of the fluid mechanical movement in the pipe is established according to the calculation formula (22) and (23); the node (i, j) in the circuit is analogous to the control volume (i, j) in the liquid, the node potential is analogous to the liquid pressure in the control volume, and the current between the nodes is analogous to the liquid volume flow rate between the control volumes; the node (i, j) in the circuit represents the control volume (i, j), and two adjacent nodes in the x direction are connected through a branch composed of a variable resistor with a size equal to , an inductor with a size equal to , and a controlled voltage source with an output voltage equal to ; two adjacent nodes in the y direction are connected through a branch composed of a variable resistor with a size equal to , an inductor with a size equal to , and a controlled voltage source with an output voltage equal to . In step S4, a two-dimensional equivalent circuit of the thermal dynamics of the fluid in the pipe is established according to the calculation formula (24); the node (i, j) in the circuit is analogous to the control volume (i, j) in the liquid, the node potential is analogous to the average temperature of the liquid in the control volume, and the current between the nodes is analogous to the enthalpy mobility or the heat conductivity between the control volumes; the node (i, j) in the circuit represents the control volume (i, j), two adjacent nodes in the x direction are connected by a branch containing a resistor , and two adjacent nodes in the y direction are connected by a branch containing a resistor ; the node and the ground point are connected by two branches in parallel: one branch contains a capacitor , and the other branch is connected by a resistor and a controlled voltage source with an output voltage of in series.

2. The fluid multi-physics simulation method for an electromagnetic transient simulation environment according to claim 1, characterized in that, The fluid motion is two-dimensional or three-dimensional motion.

3. The fluid multi-physics simulation method for an electromagnetic transient simulation environment according to claim 2, characterized in that, In step S1, when the fluid motion is two-dimensional, the continuity equation reflecting the law of conservation of mass is: The continuous two-dimensional motion equation is: x-axis direction: y-axis direction: Wherein, ρ is the liquid density, p is the liquid pressure, μ is the dynamic viscosity of the liquid, and g is the acceleration of gravity; The continuous energy equation is: where: c p is the specific heat capacity of the liquid, T is the temperature of the liquid, k is the thermal conductivity of the liquid, and μΦ represents the viscous dissipation of the liquid, represents the heat generation rate of the heat source per unit volume of the liquid; The discrete two-dimensional motion equation is: x-axis direction: In the formula: Wherein: the liquid is virtually divided into several segments along the x direction and several layers along the y direction, i represents the i-th segment along the x axis direction, and j represents the j-th layer along the y axis direction; after the division, a plurality of control volumes are formed, each control volume has a length of Δx in the x direction and a height of Δy in the y direction; is the mass flow rate of the liquid flowing through the control volume (i, j) along the x axis direction; is a physical quantity related to fluid inertia; is a physical quantity related to fluid flow resistance; is a variable with a dimension of [Pa]; is the cross-sectional area of the control volume (i, j) perpendicular to the x axis, is the cross-sectional area of the control volume (i, j) perpendicular to the y axis; y-axis direction: In the formula: wherein: is the liquid mass flow rate along the y-axis direction through the control volume (i, j); describes a physical quantity related to fluid inertia; describes a physical quantity related to fluid flow resistance; is a variable with dimension [Pa]; The discrete energy equation is: where: Describes the rate of change of enthalpy within the control volume; Describes the enthalpy flux into and out of the control volume from the x and y axes, respectively; Describes the heat dissipation of the liquid within the control volume (i,j) to the surrounding environment; represents the thermal conduction between the control volume (i, j) and its adjacent control volumes (i, j + 1), (i, j - 1), (i + 1, j) and (i - 1, j), respectively; Wherein: where: represents the heat capacity of the liquid in control volume (i,j); represents the thermal resistance of the liquid in control volume (i,j) in the x-direction; represents the thermal resistance of the liquid in control volume (i,j) in the y-direction; represents the equivalent thermal resistance between the liquid in control volume (i,j) and the environment outside the tube.

4. The fluid multi-physics simulation method oriented to an electromagnetic transient simulation environment according to claim 3, characterized in that, The calculation formula of the liquid density ρ is: ρ (T) = ρ0 (1-β (T-T0) ) (21) Wherein, ρ0 is the density of the liquid at the standard temperature T0=298.15K; and β is the thermal expansion coefficient of the liquid.

5. The electromagnetic transient simulation environment oriented fluid multi-physics simulation method of claim 1, wherein: In step S2, the liquid pressure, flow rate, friction impedance, capacity, and inductive reactance in the difference equations of fluid mechanical motion in S1 are respectively replaced with electric potential, electric current, resistance, capacitance, and inductance; and the liquid temperature, enthalpy mobility or thermal conductivity, thermal resistance, and thermal capacity in the difference equations of fluid thermal motion in S1 are respectively replaced with electric potential, electric current, resistance, and capacitance.

6. The fluid multi-physics simulation method oriented to an electromagnetic transient simulation environment according to any one of claims 1-5, characterized in that, The fluid comprises gas and liquid.

7. Application of the fluid multi-physical field simulation method for electromagnetic transient simulation environment in claim 1-5 in simulating liquid or gas motion.

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