Modeling method of dynamic mathematical model under full working conditions of two-phase heated pipe

Abstract

The invention belongs to the technical field of power station digital simulation, and provides a modeling method for a dynamic mathematical model under all working conditions of a two-phase heated pipe. Comprising the steps of basic working medium equation establishment, control body working medium equation establishment, control body model integration, region type division, hot water region dynamic mathematical model acquisition, steam-water mixing region dynamic mathematical model acquisition, overheat region dynamic mathematical model acquisition, average section steam-containing rate model establishment, transition sub-model establishment and all-working-condition dynamic mathematical model integration. According to the method, the hot water area dynamic mathematical model, the steam-water mixing area dynamic mathematical model and the overheat area dynamic mathematical model are constructed, so that the simulation precision of the models is improved; by constructing a plurality of groups of transition sub-models, the problem of boundary solving during conversion of different pressure ranges and outlet dryness ranges is solved, and the universality of the model is improved.

Description

Technical Field

[0001] The invention relates to the technical field of power station digital simulation, and in particular to a method for modeling a full-operating-condition dynamic mathematical model of a two-phase heated pipe. Background Art

[0002] The main modeling object of the dynamic mathematical model and modeling method of the two-phase heated tube is the steam-water system of the evaporation heating surface of the boiler in a large power plant, which is an important research content in the field of digital simulation technology of power plants. The dynamic mathematical model of the two-phase heated tube is usually a model system composed of multiple mathematical models, and the model composition is relatively complex. The main reason is that there are three regions of hot water, steam-water mixture and superheating in the two-phase heated tube. The physical properties and heat transfer characteristics of the working fluids in different regions are quite different, so they need to be modeled and described separately, and the boundaries must be distinguished when the model is implemented.

[0003] In the mathematical model based on the moving boundary method, the boundary of the above-mentioned area is a model parameter, which avoids the secondary calculation of the boundary. However, the existing model order is relatively low, with a maximum of three segments. In scenarios with high precision requirements, it is necessary to solve the modeling problems of more segment control bodies, especially general models. Under the full range simulation conditions, the range of the above-mentioned area varies greatly, and there are conditions where the area disappears and appears, such as the transcritical pressure change condition, the steam-water mixing area disappears when the load is increased, and appears when the load is reduced. The moving boundary model solution will have rigidity problems, and it is necessary to supplement reasonable transition models and model switching rules. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the purpose of the present invention is to provide a modeling method for a dynamic mathematical model of a two-phase heated tube under all operating conditions, by constructing a dynamic mathematical model of the hot water zone, a dynamic mathematical model of the steam-water mixing zone and a dynamic mathematical model of the superheated zone based on multiple control bodies, so as to improve the simulation accuracy of the model; by constructing multiple groups of transition sub-models, the boundary solution problem when converting between different pressure ranges and outlet dryness ranges is solved, thereby improving the versatility of the model.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for modeling a dynamic mathematical model of a two-phase heated pipe under full working conditions, characterized by comprising:

[0007] Based on the basic principles of heat transfer, the working fluid micro-element mass conservation equation, working fluid micro-element energy conservation equation and tube wall metal micro-element temperature dynamic equation of the target two-phase heated tube are established;

[0008] Calculate the coordinates of the two ends of the target control body relative to the preset origin, and integrate the working fluid micro-element mass conservation equation, the working fluid micro-element energy conservation equation, and the tube wall metal temperature dynamic equation according to the endpoint coordinates of the target control body to obtain the control body mass conservation equation, the control body energy conservation equation, and the control body tube wall metal temperature dynamic equation;

[0009] The control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation form a control body model;

[0010] Dividing the target two-phase heated pipe into a hot water area, a steam-water mixing area, and a superheated area;

[0011] Applying the control body model to the hot water area to obtain a dynamic mathematical model of the hot water area;

[0012] Applying the control body model to the steam-water mixing region where the outlet dryness of the target two-phase heated pipe is in the interval of 0 to 1, respectively, to obtain a first steam-water mixing region dynamic mathematical sub-model and a second steam-water mixing region dynamic mathematical sub-model, and combining the first steam-water mixing region dynamic mathematical sub-model and the second steam-water mixing region dynamic mathematical sub-model into a steam-water mixing region dynamic mathematical model;

[0013] Applying the control body model to the superheated region of the subcritical pressure condition and the supercritical pressure condition respectively, obtaining a first superheated region dynamic mathematical submodel and a second superheated region dynamic mathematical submodel, and combining the first superheated region dynamic mathematical submodel and the second superheated region dynamic mathematical submodel into a superheated region dynamic mathematical model;

[0014] Establishing an average cross-sectional vapor content model based on the vapor-water mixing area;

[0015] The dynamic mathematical model of the steam-water mixing zone and the dynamic mathematical model of the superheating zone are respectively applied to the steam-water mixing zone and the superheating zone where the dimensionless velocity ratio of the working fluid is in the interval from the first critical value to the second critical value, is at the subcritical pressure, and the outlet dryness is equal to 1, to obtain a first steam-water mixing zone transition submodel and a superheating zone transition submodel;

[0016] Applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is between the first critical value and the second critical value, the pressure is subcritical, and the outlet dryness is less than 1, to obtain a second steam-water mixing zone transition submodel;

[0017] Applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is greater than the second critical value, the pressure is subcritical, and the outlet dryness is less than 1, to obtain a third steam-water mixing zone transition submodel;

[0018] Applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is greater than the second critical value, the pressure is subcritical, and the outlet dryness is equal to 1, to obtain a fourth steam-water mixing zone transition submodel;

[0019] The superheating zone transition submodel, the first steam-water mixing zone transition submodel, the second steam-water mixing zone transition submodel, the third steam-water mixing zone transition submodel and the fourth steam-water mixing zone transition submodel form a variable operating condition transition mathematical model;

[0020] The dynamic mathematical model of the hot water zone, the dynamic mathematical model of the steam-water mixing zone, the dynamic mathematical model of the superheated zone, the average cross-sectional steam content model and the variable operating condition transition mathematical model are combined to obtain a dynamic mathematical model of the full operating condition.

[0021] Preferably, the calculation formulas of the working fluid micro-element mass conservation equation, the working fluid micro-element energy conservation equation and the tube wall metal micro-element temperature dynamic equation are respectively:

[0022]

[0023] as well as

[0024]

[0025] Where, F is the cross-sectional area of ​​the flow in the tube; ρ is the density of the working fluid in the tube; D is the flow rate of the working fluid in the tube; h is the specific enthalpy of the working fluid in the tube; p is the pressure of the working fluid in the tube; U2 is the circumference of the flow cross-sectional area in the tube; α2 is the heat release coefficient of the tube wall metal to the fluid; T j is the metal temperature of the tube wall; T is the working fluid temperature in the tube; m j is the metal mass of the tube wall per unit length; c j is the heat capacity of the tube wall metal; q1 is the heat flow per unit length transferred from the outside of the tube to the tube wall metal; τ is the time variable; z is the length variable.

[0026] Preferably, the calculation formulas of the control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation are respectively:

[0027]

[0028] as well as

[0029]

[0030] Among them, Q 1,AB =q1(L B -L A ); A and B are the boundary marks at both ends of the control body; L A , L B are the lengths of the two ends of the control body A and B relative to the coordinate origin; Q 1,AB The heat flux transferred from the outside of the control body tube to the tube wall metal; is the average density of the control volume working fluid; ρ A , B are the working fluid densities at the inlet and outlet of the control body respectively; h A 、h B are the specific enthalpy of the working fluid at the inlet and outlet of the control body respectively; D A , D B are the inlet and outlet flow rates of the control body respectively; is the heat per unit volume of the control body; is the average metal temperature of the control body wall; is the average temperature of the control body working fluid; T j,A 、T j,B are the metal temperatures of the inlet and outlet pipe walls of the control body respectively.

[0031] Preferably, the calculation formula of the average cross-sectional vapor fraction model includes:

[0032] and

[0033]

[0034] Among them, γ i-1 , γ i are the steam content of the inlet and outlet sections of the i-th control body respectively; is the average cross-sectional vapor content of the i-th control volume; h i is the specific enthalpy of the working fluid at the outlet of the i-th control body; h′ and h″ are the saturated water enthalpy and saturated steam enthalpy at the current operating pressure respectively; μ is the two-phase saturated density ratio at the current operating pressure; S is the two-phase slip ratio.

[0035] Preferably, L of the hot water area B and L B -L A The calculation formulas are: and Wherein, L1 is the length of the hot water area; N1 is the number of the control bodies in the hot water area.

[0036] Preferably, L of the soda-water mixing areaB and L B -L A The calculation formulas are: and Among them, j=i-N1; j is the number of the control body in the soda-water mixing area; L2 is the length of the soda-water mixing area; N2 is the number of the control bodies in the soda-water mixing area.

[0037] Preferably, L of the overheating area B and L B -L A The calculation formulas are:

[0038] and

[0039] Among them, k=i-N1-N2; L3=L-L1-L2; k is the number of the control body in the overheating area; L3 is the length of the overheating area; N3 is the number of the control bodies in the overheating area.

[0040] The present invention discloses the following technical effects:

[0041] The present invention provides a modeling method for a dynamic mathematical model of a two-phase heated tube under all working conditions. By constructing a dynamic mathematical model of a hot water zone, a dynamic mathematical model of a steam-water mixing zone and a dynamic mathematical model of a superheated zone based on multiple control bodies, the defect of low precision of a conventional moving boundary mathematical model during large-scale simulation is solved, and independent simulation of multiple region types, multiple pressure ranges and multiple outlet dryness ranges is realized. By constructing multiple groups of transition sub-models, the boundary solution problem during conversion of different pressure ranges and outlet dryness ranges is solved, and smooth operation of the model during simulation is realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0043] Figure 1 A schematic diagram of a modeling process of a full-operating-condition dynamic mathematical model of a two-phase heated pipe provided in an embodiment of the present invention;

[0044] Figure 2 A schematic diagram of control body coordinates provided by an embodiment of the present invention;

[0045] Figure 3 A schematic diagram of the relationship between the control body number and the regional coordinates provided in an embodiment of the present invention;

[0046] Figure 4 A graph showing the relationship between specific heat of steam and water and temperature under subcritical and supercritical pressures provided by an embodiment of the present invention;

[0047] Figure 5 A relationship diagram between a steam-water saturation line and a quasi-critical parameter line provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in 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 creative work are within the scope of protection of the present invention.

[0049] The purpose of the present invention is to provide a modeling method for a dynamic mathematical model of a two-phase heated tube under all working conditions, and to improve the simulation accuracy of the model by constructing a dynamic mathematical model of a hot water zone, a dynamic mathematical model of a steam-water mixing zone, and a dynamic mathematical model of a superheated zone of multiple control bodies; and to solve the boundary solution problem when converting between different pressure ranges and outlet dryness ranges by constructing multiple groups of transition sub-models, thereby improving the versatility of the model.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Figure 1 A schematic diagram of a modeling process of a two-phase heated pipe full-operating condition dynamic mathematical model provided by an embodiment of the present invention is shown in FIG. Figure 1 As shown, the present invention provides a method for modeling a dynamic mathematical model of a two-phase heated pipe under full working conditions, which is characterized by comprising:

[0052] Step 100: Based on the basic principles of heat transfer, establish the working fluid micro-element mass conservation equation, working fluid micro-element energy conservation equation and tube wall metal micro-element temperature dynamic equation of the target two-phase heated tube;

[0053] Step 200: Calculate the coordinates of the two ends of the target control body relative to the preset origin, and integrate the working fluid micro-element mass conservation equation, the working fluid micro-element energy conservation equation, and the tube wall metal temperature dynamic equation according to the endpoint coordinates of the target control body to obtain the control body mass conservation equation, the control body energy conservation equation, and the control body tube wall metal temperature dynamic equation;

[0054] Step 300: Combining the control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation into a control body model;

[0055] Step 400: Divide the target two-phase heated pipe into a hot water area, a steam-water mixed area, and a superheated area;

[0056] Step 500: applying the control body model to the hot water area to obtain a dynamic mathematical model of the hot water area;

[0057] Step 600: applying the control body model to the steam-water mixing region where the outlet dryness of the target two-phase heated pipe is in the range of 0 to 1, respectively, to obtain a first steam-water mixing region dynamic mathematical sub-model and a second steam-water mixing region dynamic mathematical sub-model, and combining the first steam-water mixing region dynamic mathematical sub-model and the second steam-water mixing region dynamic mathematical sub-model into a steam-water mixing region dynamic mathematical model;

[0058] Step 700: applying the control body model to the superheated region of the subcritical pressure condition and the supercritical pressure condition respectively, obtaining a first superheated region dynamic mathematical submodel and a second superheated region dynamic mathematical submodel, and combining the first superheated region dynamic mathematical submodel and the second superheated region dynamic mathematical submodel into a superheated region dynamic mathematical model;

[0059] Step 800: establishing an average cross-sectional steam content model based on the steam-water mixing area;

[0060] Step 900: applying the dynamic mathematical model of the steam-water mixing zone and the dynamic mathematical model of the superheating zone to the steam-water mixing zone and the superheating zone respectively where the dimensionless velocity ratio of the working fluid is in the interval from the first critical value to the second critical value, at the subcritical pressure and the outlet dryness is equal to 1, to obtain a first steam-water mixing zone transition submodel and a superheating zone transition submodel;

[0061] Step 1000: applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is between the first critical value and the second critical value, the pressure is subcritical, and the outlet dryness is less than 1, to obtain a second steam-water mixing zone transition submodel;

[0062] Step 1100: applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is greater than the second critical value, the pressure is subcritical, and the outlet dryness is less than 1, to obtain a third steam-water mixing zone transition submodel;

[0063] Step 1200: applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is greater than the second critical value, the pressure is subcritical, and the outlet dryness is equal to 1, to obtain a fourth steam-water mixing zone transition submodel;

[0064] Step 1300: The superheating zone transition submodel, the first steam-water mixing zone transition submodel, the second steam-water mixing zone transition submodel, the third steam-water mixing zone transition submodel and the fourth steam-water mixing zone transition submodel form a variable operating condition transition mathematical model;

[0065] Step 1400: Combine the hot water zone dynamic mathematical model, the steam-water mixing zone dynamic mathematical model, the superheat zone dynamic mathematical model, the average cross-sectional steam content model and the variable operating condition transition mathematical model to obtain a full operating condition dynamic mathematical model.

[0066] Furthermore, the calculation formulas of the working fluid micro-element mass conservation equation, the working fluid micro-element energy conservation equation, and the tube wall metal micro-element temperature dynamic equation are respectively:

[0067]

[0068] as well as

[0069]

[0070] Where, F is the cross-sectional area of ​​the flow in the tube; ρ is the density of the working fluid in the tube; D is the flow rate of the working fluid in the tube; h is the specific enthalpy of the working fluid in the tube; p is the pressure of the working fluid in the tube; U2 is the circumference of the flow cross-sectional area in the tube; α2 is the heat release coefficient of the tube wall metal to the fluid; T j is the metal temperature of the tube wall; T is the working fluid temperature in the tube; m j is the metal mass of the tube wall per unit length; c j is the heat capacity of the tube wall metal; q1 is the heat flow per unit length transferred from the outside of the tube to the tube wall metal; τ is the time variable; z is the length variable.

[0071] Specifically, the calculation formulas of the control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation are respectively:

[0072]

[0073] as well as

[0074]

[0075] Among them, Q 1,AB =q1(L B -L A ); A and B are the boundary marks at both ends of the control body; L A , L B are the lengths of the two ends of the control body A and B relative to the coordinate origin; Q 1,ABThe heat flux transferred from the outside of the control body tube to the tube wall metal; is the average density of the control volume working fluid; ρ A , B are the working fluid densities at the inlet and outlet of the control body respectively; h A 、h B are the specific enthalpy of the working fluid at the inlet and outlet of the control body respectively; D A , D B are the inlet and outlet flow rates of the control body respectively; is the heat per unit volume of the control body; is the average metal temperature of the control body wall; is the average temperature of the control body working fluid; T j,A , T j,B are the metal temperatures of the inlet and outlet pipe walls of the control body respectively.

[0076] Furthermore, the calculation formula of the average cross-sectional steam content model includes:

[0077] and

[0078]

[0079] Among them, γ i-1 , γ i are the steam content of the inlet and outlet sections of the i-th control body respectively; is the average cross-sectional vapor content of the i-th control volume; h i is the specific enthalpy of the working medium at the outlet of the i-th control body; h′ and h″ are the saturated water enthalpy and saturated steam enthalpy at the current operating pressure respectively; μ is the two-phase saturated density ratio at the current operating pressure; S is the two-phase slip ratio.

[0080] Specifically, the L of the hot water area B and L B -L A The calculation formulas are: and Wherein, L1 is the length of the hot water area; N1 is the number of the control bodies in the hot water area.

[0081] Furthermore, L of the soda-water mixing area B and L B -L A The calculation formulas are: and Among them, j=i-N1; j is the number of the control body in the soda-water mixing area; L2 is the length of the soda-water mixing area; N2 is the number of the control bodies in the soda-water mixing area.

[0082] Specifically, the L in the overheating area B and L B -L A The calculation formulas are:

[0083] and

[0084] Among them, k=i-N1-N2; L3=L-L1-L2; k is the number of the control body in the overheating area; L3 is the length of the overheating area; N3 is the number of the control bodies in the overheating area.

[0085] Preferably, the physical structure of the two-phase heated tube is appropriately simplified to establish the microelement and control body model, specifically including: (1) the inner diameter and wall thickness of the heated tube remain unchanged along the tube length, and the entire evaporation zone is equivalent to a single tube; (2) the fluid properties in the same cross section at any position are uniform, so that the working fluid in the tube can be simplified to one dimension in terms of spatial dimension; (3) in the steam-water mixing area, the dryness of the working fluid in the tube is linearly distributed along the tube length, and the working fluid temperature is the saturation temperature under the corresponding pressure; (4) there is no pressure difference along the tube length, and it is considered that the pressure in the heated tube is consistent, so the present invention omits the momentum conservation equation; (5) the heat conduction of the tube wall along the tube length is ignored, and the metal temperature on a single control body is uniform.

[0086] Preferably, the average cross-sectional steam content model is used for calculating the physical properties of the steam-water mixture; the transition model equation group is combined with the dynamic equation group to solve the model rigidity problem caused by regional changes under variable working conditions.

[0087] Specifically, based on the basic principles of heat transfer, the mass conservation equation of the working fluid microelement, the energy conservation equation of the working fluid microelement and the temperature dynamic equation of the tube wall metal microelement are established, and the expressions are:

[0088]

[0089] Where, F is the cross-sectional area of ​​the flow in the tube; ρ is the density of the working fluid in the tube; D is the flow rate of the working fluid in the tube; h is the specific enthalpy of the working fluid in the tube; p is the pressure of the working fluid in the tube; U2 is the circumference of the flow cross-sectional area in the tube; α2 is the heat release coefficient of the tube wall metal to the fluid; T j is the metal temperature of the tube wall; T is the working fluid temperature in the tube; m j is the metal mass of the tube wall per unit length; c j is the heat capacity of the tube wall metal; q1 is the heat flow per unit length transferred from the outside of the tube to the tube wall metal; τ is the time variable; z is the length variable.

[0090] Furthermore, the coordinate origin is set, and the coordinates of the two ends of the control body in the same area are L A and L B(like Figure 2 As shown), the control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation can be obtained by integration. The calculation formulas of the control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation are respectively:

[0091]

[0092]

[0093] Among them, Q 1,AB =q1(L B -L A ); A and B are the boundary marks of the inlet and outlet of the control body respectively; L A , L B are the lengths of the inlet and outlet of the control body relative to the coordinate origin; Q 1,AB The heat flux transferred from the outside of the control body tube to the tube wall metal; is the average density of the working fluid in the control body; A , B are the working fluid densities at the inlet and outlet of the control body respectively; h A 、h B are the specific enthalpy of the working fluid at the inlet and outlet of the control body respectively; D A , D B are the inlet and outlet flow rates of the control body respectively; To control the heat per unit volume of the body; To control the average temperature of the tube wall metal; is the average temperature of the working fluid in the control body; T j,A , T j,B are the metal temperatures of the inlet and outlet walls of the control body respectively.

[0094] Preferably, the control body model is established on the basis of an appropriate simplification of the physical structure of the two-phase heated tube, specifically including: (1) in terms of structure, the inner diameter and wall thickness of the heated tube remain unchanged along the tube length, and the entire evaporation zone is equivalent to a single tube; (2) the fluid properties in the same cross section at any position are uniform, so that the working fluid in the tube can be simplified to one dimension in terms of spatial dimension; (3) in the steam-water mixing area, the dryness of the working fluid in the tube is linearly distributed along the tube length, and the working fluid temperature is the saturation temperature under the corresponding pressure; (4) there is no pressure difference along the tube length, and it is considered that the pressure in the heated tube is consistent, so the present invention omits the momentum conservation equation; (5) the heat conduction of the tube wall along the tube length is ignored, and the metal temperature on a single control body is uniform.

[0095] Alternatively, taking the mass conservation equation as an example, the integral processing method is as follows:

[0096] First, integrate the differential equation. Since the upper and lower limits of the integral are variables, the integral result is

[0097]

[0098] Secondly, the remaining integral term ρ in the above equation is replaced by the lumped parameter, and the result is

[0099]

[0100] Again, substitute the equation of state for water and steam

[0101]

[0102] Finally, the mass conservation equation of the control body is obtained. The energy conservation equation of the control body and the metal temperature equation of the tube wall are obtained in the same way.

[0103] Furthermore, in order to utilize the control volume model, each region is divided into a number of control volumes, and the control volumes are uniformly numbered. The corresponding relationship between the numbers and the coordinates is as follows: Figure 3 As shown in the figure, considering that the number of control bodies in each region is not equal, the number of control bodies in each region is expressed in the form of parameters, and the length of control bodies in the same region is considered to be equal, in order to achieve the purpose of simplification and generalization. Specifically include:

[0104] S1, applying the control body model to the hot water area, the integral upper limit and control body length of the i-th control body in the hot water area are respectively;

[0105]

[0106] Among them, i is the unified number of the control body. Since the inlet of the two-phase heated pipe always starts from the hot water area, i is also the control body number of the hot water area; L1 is the length of the hot water area; N1 is the number of control bodies in the hot water area.

[0107] The mass conservation equation, energy conservation equation and wall metal temperature dynamic equation of the control body in the hot water area are:

[0108]

[0109]

[0110] Among them, α 2,i is the heat release coefficient between the tube wall of the control body i and the working fluid; is the total metal temperature of the tube wall of the control body i; T j,i-1 、T j,i are the metal temperatures of the tube wall at the inlet and outlet of the control body respectively; is the total temperature of the working fluid in control volume i; is the heat flux transferred outside the tube on control body i; is the lumped parameter of working fluid density of control volume i; ρ i-1 , i are the working fluid densities at the inlet and outlet of control i respectively; h i-1 、h i are the specific enthalpy of the working fluid at the inlet and outlet of the control body i respectively; i-1 , D i are the working fluid flow rates at the inlet and outlet of control body i respectively; D in is the inlet flow rate of the heated tube; ρ′ is the saturated water density under the working fluid pressure; h′ is the saturated water specific enthalpy under the working fluid pressure.

[0111] The reason why the mass conservation equation and energy conservation equation of the control body contain multiple equations is that i=1 and i=N1 are respectively at the inlet and outlet of the hot water area. Unlike the control body in the middle position, the inlet and outlet parameters at this position are input parameters or pressure-related parameters and need to be processed separately. The steam-water mixing area and the superheated area are also processed in a similar way.

[0112] S2, applying the control body model to the soda-water mixing area, the integral upper limit and control body length of the j-th control body in the soda-water mixing area are:

[0113]

[0114] Wherein, j is the control body number of the soda-water mixing area, j=i-N1; L2 is the length of the soda-water mixing area, unit: m; N2 is the number of control bodies in the soda-water mixing area.

[0115] The dynamic mathematical model of the steam-water mixing area is divided into two categories due to the different dryness of the outlet of the two-phase heating tube:

[0116] 1) When the outlet dryness of the subcritical two-phase heated tube is equal to 1 (overheated), the mass conservation equation, energy conservation equation and tube wall metal temperature dynamic equation of the steam-water mixing area are:

[0117]

[0118] Wherein, ρ″ is the density of saturated steam at the working fluid pressure; h″ is the specific enthalpy of saturated steam at the working fluid pressure.

[0119] 2) When the outlet dryness of the subcritical two-phase heating tube is less than 1 (steam-water two-phase), L2 is not an independent parameter, L2 = L-L1, L is the total length of the two-phase heating tube, unit is m. The dynamic term of L2 is replaced by the following formula

[0120]

[0121] Under this condition, the mass conservation equation of the control body in the steam-water mixing area, the energy conservation equation of the control body, and the dynamic equation of the metal temperature of the control body tube wall are:

[0122]

[0123] S3, applying the control body model to the overheating area, the integral upper limit and control body length of the kth control body in the overheating area are respectively

[0124]

[0125] Among them, k is the number of the overheating area control body, k = i-N1-N2; L3 is the length of the overheating area, L3 = L-L1-L2, unit: m; N3 is the number of overheating area control bodies. L3 is not an independent parameter, and its dynamic term is replaced by the following formula

[0126]

[0127] The mass conservation equation, energy conservation equation and tube wall metal temperature dynamic equation of the control body in the overheating area are:

[0128]

[0129] S4, under supercritical pressure conditions, L2 = 0, and the dynamic term of L2 does not appear in the model. Under supercritical pressure conditions, the length of the superheated area L3 is not an independent parameter, and its dynamic term is replaced by the following formula:

[0130]

[0131] Under supercritical pressure conditions, the mass conservation equation, energy conservation equation and wall metal temperature dynamic equation of the control volume in the superheated area are respectively

[0132]

[0133] The reason why the two-phase heated tube is still divided into the hot water area and the superheated area under supercritical conditions is that: under supercritical pressure (greater than 22.064MPa), the constant pressure specific heat of the working fluid has a maximum value point in the process of temperature change. The maximum specific heat point is usually called the pseudo-critical point (pseudo-critical pressure and pseudo-critical temperature) or quasi-critical point (some literature also uses the maximum specific volume point as the pseudo-critical point, which is actually the same point). Under the same pressure, as the temperature rises, the working fluid specific heat gradually increases, and the working fluid specific heat reaches the maximum value at the pseudo-critical temperature point, and then the working fluid specific heat gradually decreases, such as Figure 4 Other physical properties, such as specific volume, also have similar change patterns. This has the same trend as the change of physical properties of water and steam under subcritical pressure, except that the pseudo-critical point is replaced by the saturation point (saturation pressure and saturation temperature). Figure 5It shows that the saturation temperature line under subcritical pressure and the pseudo-critical temperature line under supercritical pressure are smoothly transitioned, which is equivalent to the steam-water two-phase boundary under subcritical pressure extending to supercritical pressure. This provides a unified sub-regional mode for realizing the full-condition dynamic mathematical model and its transition model, thereby simplifying the model implementation.

[0134] Furthermore, the calculation formula of the average cross-sectional steam content model of the steam-water mixing zone includes:

[0135]

[0136] Among them, γ i-1 , γ i are the steam content of the inlet and outlet sections of the i-th control body respectively; is the average cross-sectional vapor content of the i-th control volume; h i is the specific enthalpy of the working fluid at the outlet of the i-th control body; h′ and h″ are the saturated water enthalpy and saturated steam enthalpy at the current operating pressure respectively; S is the two-phase slip ratio; μ is the two-phase saturated density ratio at the current operating pressure.

[0137] The simplified processing method of the cross-sectional vapor content model is as follows: Assume that the change of the dryness in the steam-water mixing area is linearly distributed along the tube length in the steady state and dynamic process. In the steady state, the working fluid specific enthalpy and the dryness in the steam-water mixing area are linearly related, and the working fluid specific enthalpy in the tube also changes linearly along the tube length. From the simulation results of this embodiment, the dynamic mathematical model based on this assumption can still accurately reflect the dynamic process of the two-phase heated tube.

[0138] Furthermore, when the dimensionless velocity ratio of the working fluid in the region and When , the number of regional control bodies N is reduced to 1. Among them, CF1 and CF2 are the first critical value and the second critical value respectively; is the average velocity of the working fluid in the region, Δτ is the calculation time step; ΔL is the region length; N is the number of regional control bodies.

[0139] In actual simulation, the transition model switching is concentrated in the steam-water mixing area and the superheated area under subcritical pressure.

[0140] 1) When the two-phase heated tube is under subcritical pressure and the outlet dryness is less than 1, the steam-water mixing area transition model includes:

[0141] The mass conservation equation:

[0142]

[0143] Energy conservation equation:

[0144]

[0145] Metal temperature dynamic equation:

[0146]

[0147] 2) When the heated tube is at subcritical pressure and the outlet dryness is equal to 1, the steam-water mixing area transition model includes:

[0148] The mass conservation equation:

[0149]

[0150] Energy conservation equation:

[0151]

[0152] Metal temperature dynamic equation:

[0153]

[0154] 3) When the heated tube is at subcritical pressure and the outlet dryness is equal to 1, the superheated area transition model includes:

[0155] The mass conservation equation:

[0156]

[0157] Energy conservation equation:

[0158]

[0159] Metal temperature dynamic equation:

[0160]

[0161] Furthermore, when the dimensionless velocity ratio of the working fluid in the region When the control volume in the region is static, the transition model is switched to focus on the steam-water mixing region and the superheated region under subcritical pressure.

[0162] 1) When the two-phase heated tube is at subcritical pressure and the outlet dryness is less than 1, the mass conservation equation of the transition model in the steam-water mixing area is:

[0163] D i =D i-1

[0164] Energy conservation equation:

[0165]

[0166] Metal temperature equation:

[0167]

[0168] 2) The mass conservation equation of the transition model of the steam-water mixing region is:

[0169]

[0170] Metal temperature equation:

[0171]

[0172] Under this condition, the regional inlet and outlet parameters are all saturated parameters and are only related to pressure, so there is no need to model the energy conservation equation separately.

[0173] The beneficial effects of the present invention are as follows:

[0174] The present invention improves the simulation accuracy of the model by constructing a dynamic mathematical model of the hot water zone, a dynamic mathematical model of the steam-water mixing zone, and a dynamic mathematical model of the superheated zone; by constructing multiple groups of transition sub-models, the boundary solution problem when converting different pressure ranges and outlet dryness ranges is solved, thereby improving the versatility of the model.

[0175] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0176] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for modeling a dynamic mathematical model of a two-phase heated pipe under full working conditions, characterized in that: include: Based on the basic principles of heat transfer, the working fluid micro-element mass conservation equation, working fluid micro-element energy conservation equation and tube wall metal micro-element temperature dynamic equation of the target two-phase heated tube are established; Calculate the coordinates of the two ends of the target control body relative to the preset origin, and integrate the working fluid micro-element mass conservation equation, the working fluid micro-element energy conservation equation, and the tube wall metal temperature dynamic equation according to the endpoint coordinates of the target control body to obtain the control body mass conservation equation, the control body energy conservation equation, and the control body tube wall metal temperature dynamic equation; The control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation form a control body model; Dividing the target two-phase heated pipe into a hot water area, a steam-water mixing area, and a superheated area; Applying the control body model to the hot water area to obtain a dynamic mathematical model of the hot water area; Applying the control body model to the steam-water mixing region where the outlet dryness of the target two-phase heated pipe is in the interval of 0 to 1, respectively, to obtain a first steam-water mixing region dynamic mathematical sub-model and a second steam-water mixing region dynamic mathematical sub-model, and combining the first steam-water mixing region dynamic mathematical sub-model and the second steam-water mixing region dynamic mathematical sub-model into a steam-water mixing region dynamic mathematical model; Applying the control body model to the superheated region of the subcritical pressure condition and the supercritical pressure condition respectively, obtaining a first superheated region dynamic mathematical submodel and a second superheated region dynamic mathematical submodel, and combining the first superheated region dynamic mathematical submodel and the second superheated region dynamic mathematical submodel into a superheated region dynamic mathematical model; Establishing an average cross-sectional vapor content model based on the vapor-water mixing area; The dynamic mathematical model of the steam-water mixing zone and the dynamic mathematical model of the superheating zone are respectively applied to the steam-water mixing zone and the superheating zone where the dimensionless velocity ratio of the working fluid is in the interval from the first critical value to the second critical value, is at the subcritical pressure, and the outlet dryness is equal to 1, to obtain a first steam-water mixing zone transition submodel and a superheating zone transition submodel; Applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is between the first critical value and the second critical value, the pressure is subcritical, and the outlet dryness is less than 1, to obtain a second steam-water mixing zone transition submodel; Applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is greater than the second critical value, the pressure is subcritical, and the outlet dryness is less than 1, to obtain a third steam-water mixing zone transition submodel; Applying the dynamic mathematical model of the steam-water mixing zone to the steam-water mixing zone where the dimensionless velocity ratio of the working fluid is greater than the second critical value, the pressure is subcritical, and the outlet dryness is equal to 1, to obtain a fourth steam-water mixing zone transition submodel; The superheating zone transition submodel, the first steam-water mixing zone transition submodel, the second steam-water mixing zone transition submodel, the third steam-water mixing zone transition submodel and the fourth steam-water mixing zone transition submodel form a variable operating condition transition mathematical model; The dynamic mathematical model of the hot water zone, the dynamic mathematical model of the steam-water mixing zone, the dynamic mathematical model of the superheated zone, the average cross-sectional steam content model and the variable operating condition transition mathematical model are combined to obtain a dynamic mathematical model of the entire operating condition.

2. A method for modeling a two-phase heated pipe full-operating condition dynamic mathematical model according to claim 1, characterized in that: The calculation formulas of the working fluid micro-element mass conservation equation, the working fluid micro-element energy conservation equation and the tube wall metal micro-element temperature dynamic equation are respectively: Where, F is the cross-sectional area of ​​the flow in the tube; ρ is the density of the working fluid in the tube; D is the flow rate of the working fluid in the tube; h is the specific enthalpy of the working fluid in the tube; p is the pressure of the working fluid in the tube; U2 is the circumference of the flow cross-sectional area in the tube; α2 is the heat release coefficient of the tube wall metal to the fluid; T j is the metal temperature of the tube wall; T is the working fluid temperature in the tube; m j is the metal mass of the tube wall per unit length; c j is the heat capacity of the tube wall metal; q1 is the heat flow per unit length transferred from the outside of the tube to the tube wall metal; τ is the time variable; z is the length variable.

3. A method for modeling a two-phase heated pipe full-operating condition dynamic mathematical model according to claim 2, characterized in that: The calculation formulas of the control body mass conservation equation, the control body energy conservation equation and the control body tube wall metal temperature dynamic equation are respectively: Among them, Q 1,AB =q1(L B -L A ); A and B are the boundary marks at both ends of the control body; L A , L B are the lengths of the two ends of the control body A and B relative to the coordinate origin; Q 1,AB The heat flux transferred from the outside of the control body tube to the tube wall metal; is the average density of the working fluid in the control body; ρ A , B are the working fluid densities at the inlet and outlet of the control body respectively; h A 、h B are the specific enthalpy of the working fluid at the inlet and outlet of the control body respectively; D A , D B are the inlet and outlet flow rates of the control body respectively; is the heat per unit volume of the control body; is the average metal temperature of the control body wall; is the average temperature of the control body working fluid; T j,A , T j,B are the metal temperatures of the inlet and outlet pipe walls of the control body respectively.

4. A method for modeling a two-phase heated pipe full-operating condition dynamic mathematical model according to claim 3, characterized in that: The calculation formula of the average cross-sectional vapor fraction model is include: Among them, γ i-1 , γ i are the steam content of the inlet and outlet sections of the i-th control body respectively; is the average cross-sectional vapor content of the i-th control volume; h i is the specific enthalpy of the working medium at the outlet of the i-th control body; h′ and h″ are the saturated water enthalpy and saturated steam enthalpy at the current operating pressure respectively; μ is the two-phase saturated density ratio at the current operating pressure; S is the two-phase slip ratio.

5. A method for modeling a dynamic mathematical model of a two-phase heated pipe under full working conditions according to claim 4, characterized in that: The L of the hot water area B and L B -L A The calculation formulas are: and Wherein, L1 is the length of the hot water area; N1 is the number of the control bodies in the hot water area.

6. A method for modeling a two-phase heated pipe full-operating-condition dynamic mathematical model according to claim 4, characterized in that: The L of the soda-water mixing area B and L B -L A The calculation formulas are: and Among them, j=i-N1; j is the number of the control body in the soda-water mixing area; L2 is the length of the soda-water mixing area; N2 is the number of the control bodies in the soda-water mixing area.

7. A method for modeling a two-phase heated pipe full-operating-condition dynamic mathematical model according to claim 4, characterized in that: The L of the overheating area B and L B -L A The calculation formulas are: Among them, k=i-N1-N2; L3=L-L1-L2; k is the number of the control body in the overheating area; L3 is the length of the overheating area; N3 is the number of the control bodies in the overheating area.

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