Method for calculating critical flow of high-pressure cooler internal coil breakage

Abstract

The present application relates to a kind of high-pressure cooler internal coil rupture critical flow calculation method, belong to nuclear engineering field.The high-pressure cooler internal coil rupture leakage is modeled as nozzle flow, consider the critical value of high-pressure cooler shell side back pressure, the working medium flow state under high-pressure cooler coil rupture condition is divided into single-phase flow and two-phase flow, the mass flow rate and flow velocity v of single-phase zone when high-pressure cooler internal coil ruptures are calculated using Bernoulli equation;The mass flow rate and flow velocity v of two-phase zone when high-pressure cooler internal coil ruptures are calculated using isentropic stagnation flow formula, when in two-phase zone, the sound speed limit c is considered herein.The present application provides an effective and complete theoretical basis for the calculation of the maximum flow of high-pressure cooler internal coil rupture, suitable for the calculation of the flow of all high-pressure cooler internal coil rupture, the error of calculation conclusion is smaller, the credibility of theoretical basis is higher, suitable for the engineering practice of design requirement and its strict nuclear power and military industry.

Description

TECHNICAL FIELD

[0001] The application relates to a high-pressure cooler internal coil rupture critical flow calculation method and belongs to the nuclear engineering field. BACKGROUND

[0002] The emergency shaft seal injection water system design of a shaft seal type nuclear main pump is usually equipped with an external tube shell type high-pressure cooler which cools and exchanges heat with the emergency injection water so as to ensure that the shaft seal water temperature entering the shaft seal is within the allowable range. However, when the high-pressure cooler internal coil welding position is ruptured or other positions are damaged, the high-pressure cooler is prone to leakage, the leakage is difficult to be detected, the maximum flow of the high-pressure cooler internal coil rupture cannot be exactly known, and the maximum flow of the high-pressure cooler internal coil rupture is mostly calculated by using an empirical formula at present. The calculation conclusion has a large error, lacks a theoretical basis, has low credibility, and is difficult to be applied to engineering practice, especially for the nuclear power and military industries which have strict design requirements. SUMMARY

[0003] In order to solve the problem that the maximum flow of the high-pressure cooler internal coil rupture of the shaft seal type nuclear main pump cannot be estimated, the application discloses a high-pressure cooler internal coil rupture critical flow calculation method, and provides an effective and complete theoretical basis for calculating the maximum flow of the high-pressure cooler internal coil rupture.

[0004] To achieve the above object, the application adopts the following technical scheme:

[0005] A high-pressure cooler internal coil rupture critical flow calculation method, characterized in that the high-pressure cooler internal coil rupture critical flow calculation method under the working condition of the high-pressure cooler internal coil rupture comprises the following specific steps:

[0006] Step 1: input the high-pressure cooler internal coil size, system temperature and system pressure parameters in Matlab;

[0007] Step 2: calculate the density, entropy, enthalpy value and saturation pressure value corresponding to the high-pressure cooler internal coil rupture by using the Refprop property database in Matlab;

[0008] Step 3: calculate the high-pressure cooler shell side back pressure P in the range of 15990kPa to 1000kPa by using the for loop in Matlab, the change interval is 10kPa, and the relative size of the back pressure P and the saturation pressure in the isentropic process is judged;

[0009] Step 4: (1) when the back pressure P in step 3 is greater than or equal to the saturation pressure in the isentropic process, the working medium flow state of the high-pressure cooler rupture working condition is single-phase flow, and the mass flow rate of the high-pressure cooler rupture is calculated by using the Bernoulli equation;

[0010] (2) When the back pressure P in step 3 is less than the saturation pressure in the isentropic process, the working medium flow state in the high-pressure cooler pipe breakage condition is two-phase flow, and the mass flow rate in the two-phase zone of the high-pressure cooler internal coil when the pipe breaks is calculated by using the isentropic stagnation flow formula in the two-phase zone and the flow velocity v;

[0011] Step 5: When the high-pressure cooler internal coil leaks, the liquid flow velocity will not exceed the sound velocity, so the maximum outlet velocity of the liquid can be obtained on the narrowest cross section at the breakage, and therefore the pressure at the outlet velocity v greater than the sound velocity c is the critical pressure p c ;

[0012] If the fluid is two-phase flow, it is necessary to determine whether the flow velocity calculated in step 4 is greater than or equal to the local sound velocity. If the flow velocity is less than the local sound velocity, the mass flow rate when the high-pressure cooler internal coil breaks is the result of the isentropic stagnation flow formula. If the flow velocity is greater than or equal to the local sound velocity, the mass flow rate when the high-pressure cooler internal coil breaks is the sound velocity multiplied by the density of the working medium at the breakage. If the fluid is single-phase flow, the mass flow rate when the high-pressure cooler internal coil breaks is the fluid velocity at the breakage multiplied by the density.

[0013] The present application is a kind of high-pressure cooler internal coil breakage critical flow calculation method, the mass flow rate of the high-pressure cooler pipe breakage in step 4 is calculated by using Bernoulli equation as follows:

[0014] One-way zone Bernoulli equation:

[0015] Assuming that the high-pressure cooler internal coil is an incompressible ideal fluid, and there is no heat exchange with the outside world, the Bernoulli equation is

[0016]

[0017] Therefore, the Bernoulli equation is satisfied between any two points in the high-pressure cooler internal coil, that is:

[0018]

[0019] Where, v is the velocity, m / s; g is the acceleration of gravity, m / s 2 ; z is the height of the fluid at the position, m; p is the pressure, Pa; ρ is the fluid density, kg / m 3 ; subscripts 1 and 2 are any two points in the high-pressure cooler internal coil;

[0020] The working medium flow state in the high-pressure cooler internal coil is adiabatic single-phase flow, the fluid density change can be ignored, that is, ρ1=ρ2=ρ, and the height change at the fluid position is ignored, that is, z1=z2, the leakage port is stagnation state v1=0 m / s, the above parameters are substituted into formula (2), and the liquid pressure of any first point of the high-pressure cooler internal coil when the high-pressure cooler internal coil is broken is:

[0021]

[0022] Mass flow rate The mass flow rate of the fluid passing through the section per unit time is calculated by the following formula:

[0023]

[0024] Wherein, The mass flow rate is kg / s; the fluid density is kg / m 3 ; the velocity is m / s

[0025] The formula (3) is substituted into the formula (4), and the mass flow rate of any second point of the high-pressure cooler internal coil when the high-pressure cooler internal coil is broken is obtained And the flow velocity v is:

[0026]

[0027] The present application discloses a kind of high-pressure cooler internal coil broken critical flow calculation method, the mass flow rate of two-phase region in step 4 when high-pressure cooler internal coil is broken is calculated using two-phase region isostatic stagnation flow formula And the flow velocity v:

[0028] Two-phase region isostatic stagnation flow formula:

[0029] When the high-pressure cooler internal coil is completely broken, the discharge can be modeled as nozzle flow, and the path of the discharge process is short, the time is short, and it can be considered as a steady-state isentropic expansion process, so the energy equation of the high-pressure cooler internal coil is:

[0030]

[0031] Wherein, q is the heat exchanged with the outside during the flow process, W; h is the enthalpy carried by the fluid, J / kg; w net The work done by the flow process to the outside world is W; the velocity is m / s; g is the acceleration of gravity, m / s 2 ; z is the height of the fluid position, m; the subscripts 1 and 2 are respectively any two points of the high-pressure cooler internal coil when the high-pressure cooler internal coil is completely broken;

[0032] After the complete rupture of the high-pressure cooler internal coil, q = 0, v1 = 0, Δz = 0 and w = 0 in formula (7), and h2 is the enthalpy value of the high-pressure cooler shell side back pressure isentropic process corresponding to h1, so formula (7) can be simplified as: net

[0033]

[0034] That is, the flow rate v at this time is:

[0035]

[0036] The mass flow rate during the isentropic stagnation flow process is:

[0037]

[0038] The step 5 in the high-pressure cooler internal coil rupture critical flow calculation method of the present application is:

[0039] The sound speed empirical formula is:

[0040]

[0041] In Matlab, the change of density with pressure in the isentropic process in the Refprop calculation system is called, and a polynomial fitting formula is used, and the derivative of the obtained formula is taken, to obtain the value used for calculating the sound speed.

[0042] The present application has the following beneficial effects:

[0043] The high-pressure cooler internal coil rupture critical flow calculation method of the present application provides an effective and complete theoretical basis for calculating the maximum flow of the high-pressure cooler internal coil rupture, which is suitable for calculating the flow of all high-pressure cooler internal coil ruptures, has a smaller calculation conclusion error, a higher theoretical basis credibility, and is suitable for engineering practice in the nuclear power and military industries with strict design requirements. BRIEF DESCRIPTION OF DRAWINGS

[0044] The present application will be further described below in combination with the drawings and examples.

[0045] Figure 1 is the flow chart of the high-pressure cooler coil rupture condition maximum flow calculation method of the present application;

[0046] Figure 2 is the high-pressure cooler internal coil schematic diagram in the present application;

[0047] Figure 3 is the high-pressure cooler internal coil maximum rupture nozzle schematic diagram in the present application; ​

[0048] Figure 4 This is the temperature-entropy-dryness-enthalpy diagram of water and water vapor in this invention;

[0049] Figure 5 This is a water and water vapor partitioning diagram in this invention;

[0050] Figure 6 This is the density variation curve with pressure during the isentropic process of the system parameters in this invention;

[0051] Figure 7 This is the "back pressure-flow rate" relationship curve when the internal coil of the high-pressure cooler in this invention ruptures;

[0052] Figure 8 This is the "back pressure-flow velocity" relationship curve when the internal coil of the high-pressure cooler in this invention ruptures. Detailed Implementation

[0053] The present invention will now be described in further detail with reference to the embodiments.

[0054] Example 1: As Figures 1-8 The flowchart illustrates a method for calculating the maximum flow rate under the condition of a high-pressure cooler internal coil rupture. This method involves detailed modeling of the flow after a high-pressure cooler coil rupture, employing a nozzle flow model, and using corresponding fluid dynamics equations based on different fluid flow properties (single-phase flow and two-phase flow). The influence of sound velocity limitations and the critical value of the shell side back pressure is specifically considered, thereby accurately predicting the critical flow rate at the time of coil rupture. The specific steps of the method for calculating the critical flow rate under the condition of a high-pressure cooler internal coil rupture are as follows:

[0055] Step 1: Input the internal coil dimensions of the high-pressure cooler, system temperature, and system pressure parameters into Matlab;

[0056] Step 2: Use Matlab to call the Refprop property database to calculate the density, entropy, enthalpy and saturation pressure values ​​corresponding to the internal coil of the high-pressure cooler when it breaks;

[0057] Step 3: Using Matlab, call the Refprop property database calculation system to obtain the high-pressure cooler shell back pressure P, which varies from 15990 kPa to 1000 kPa with a variation interval of 10 kPa, and determine the relative magnitude of the back pressure P and the saturation pressure in the isentropic process.

[0058] Step 4: (1) When the back pressure P in step 3 is greater than or equal to the saturation pressure in the isentropic process, the working fluid flow state under the high-pressure cooler tube rupture condition is a single-phase flow. The mass flow rate of the high-pressure cooler tube rupture under this condition is calculated using Bernoulli's equation:

[0059] Bernoulli's equation for one-way regions:

[0060] Assuming that the high-pressure cooler internal coil is an incompressible ideal fluid, and there is no heat exchange with the outside world, Bernoulli's equation is

[0061]

[0062] Therefore, Bernoulli's equation is satisfied between any two points in the high-pressure cooler internal coil, that is:

[0063]

[0064] Where v is the velocity, m / s; g is the acceleration of gravity, m / s 2 ; z is the height of the fluid at the location, m; p is the pressure, Pa; ρ is the fluid density, kg / m 3 ; subscripts 1 and 2 are any two points in the high-pressure cooler internal coil;

[0065] The working fluid in the high-pressure cooler internal coil is an adiabatic single-phase flow, and the change in fluid density can be ignored, that is, ρ1=ρ2=ρ, and the change in height of the fluid at the location can be ignored, that is, z1=z2, the leakage port is at rest v1=0 m / s, and the above parameters are substituted into formula (2). The liquid pressure of any point 1 in the high-pressure cooler internal coil when it breaks is:

[0066]

[0067] Mass flow rate The mass flow rate through the cross section per unit time is calculated as:

[0068]

[0069] Where is the mass flow rate, kg / s; ρ is the fluid density, kg / m 3 ; v is the velocity, m / s

[0070] Substituting formula (3) into formula (4) gives the mass flow rate of any point 2 in the high-pressure cooler internal coil when it breaks And the flow rate v is:

[0071]

[0072] (2) When the back pressure P in step 3 is less than or equal to the saturation pressure in the isentropic process, the working fluid in the high-pressure cooler at the pipe break condition is two-phase flow. The two-phase zone isentropic stagnation flow formula is used to calculate the mass flow rate of the two-phase zone in the high-pressure cooler internal coil when it breaks And the flow rate v:

[0073] Two-phase zone isentropic stagnation flow formula:

[0074] When the high-pressure cooler internal coil is completely broken, the discharge flow can be modeled as a nozzle flow, and the path of the discharge process is short and the time is short, so it can be considered as a steady-state isentropic expansion process. The steady flow energy equation of any two points of the high-pressure cooler internal coil is:

[0075]

[0076] wherein q is the heat exchanged with the outside during the flow process, W; h is the enthalpy carried by the fluid, J / kg; w net is the work done by the flow process to the outside, W; v is the velocity, m / s; g is the acceleration of gravity, m / s 2 ; z is the height of the fluid at the location, m; the subscripts 1 and 2 are any two points of the high-pressure cooler internal coil when the high-pressure cooler internal coil is completely broken;

[0077] After the high-pressure cooler internal coil is completely broken, q = 0, v1 = 0, Δz = 0, and w net = 0 in formula (7), and h2 is the enthalpy value of the isentropic process of the high-pressure cooler shell side back pressure corresponding to h1, so formula (7) can be simplified as:

[0078]

[0079] That is, the flow velocity v at this time is:

[0080]

[0081] The mass flow rate during the isentropic stagnation flow process is:

[0082]

[0083] Step 5: When the high-pressure cooler internal coil discharges, the liquid flow velocity will not exceed the sound velocity, so the maximum outlet velocity of the liquid can be obtained on the narrowest cross section at the breakage, and the pressure at the outlet velocity v greater than the sound velocity c is the critical pressure p c ;

[0084] The empirical formula of the sound velocity is:

[0085]

[0086] In Matlab, the change of the density with the pressure in the isentropic process in the Refprop calculation system is called, a polynomial fitting formula is used, and the derivative of the obtained formula is taken to obtain the value used to calculate the sound velocity (see Figure 6 : System parameter isentropic process density changes with pressure curve);

[0087] If the fluid is in two-phase flow, it is necessary to determine whether the flow velocity calculated in step 4 is greater than or equal to the local speed of sound. If the flow velocity is less than the local speed of sound, the mass flow rate when the coil inside the high-pressure cooler ruptures is the result of the isentropic stagnant flow formula. If the flow velocity is greater than or equal to the local speed of sound, the mass flow rate when the coil inside the high-pressure cooler ruptures is the speed of sound multiplied by the density of the working fluid at the rupture point. If the fluid is in one-phase flow, the mass flow rate when the coil inside the high-pressure cooler ruptures is the fluid velocity at the rupture point multiplied by the density.

[0088] Step 6: Based on steps 1-5, obtain the mass flow rate under different operating conditions when the internal coil of the high-pressure cooler ruptures. The critical mass for rupture is determined by comparing the flow state and the flow velocity with the sound velocity.

[0089] Example 2: Figures 1-8 As shown, a method for calculating the maximum flow rate under the condition of internal coil rupture in a high-pressure cooler is described. When the liquid inside the high-pressure cooler is in critical flow, and the pressure (back pressure) on the shell side of the high-pressure cooler reaches a critical value, the leakage flow rate of the internal coil reaches its maximum value, Q. max This flow rate is the critical flow rate. Due to the short path and time of the leakage process, it can be considered an isentropic expansion process. The actual back pressure on the shell side of the high-pressure cooler cannot be accurately obtained, and the inflowing fluid may increase the shell-side pressure. Therefore, in this calculation method, the back pressure of the high-pressure cooler is set as the dependent variable, varying it from the system pressure (p0 = 16 MPa) to 1 MPa, with a pressure update step of 10 kPa, to analyze the leakage flow rate of the high-pressure cooler under different back pressure conditions.

[0090] A schematic diagram of the internal coils of the high-pressure cooler is shown below. Figure 2 As shown in the diagram, the maximum rupture nozzle of the internal coil is as follows: Figure 3 As shown.

[0091] At the outlet, the fluid inside the high-pressure cooler coil is subcooled, with the system temperature (293℃) and the system pressure (16MPa). The isentropic saturation pressure corresponding to this isentropic process is 7.41MPa. Therefore, under these system parameters, the fluid on the pipe side is subcooled. During leakage, if the shell-side back pressure is greater than the corresponding saturation pressure, the leakage is single-phase flow; if the shell-side back pressure is less than the corresponding saturation pressure, it is two-phase flow. In this method for calculating the maximum flow rate under the high-pressure cooler coil rupture condition, if the high-pressure cooler coil is in single-phase flow, the Bernoulli equation is used to derive the leakage flow rate; if the high-pressure cooler coil is in two-phase flow, the isentropic stagnant flow formula is used with local sound velocity as a constraint to derive the leakage flow rate.

[0092] 1. Bernoulli's equation for one-way regions:

[0093] Assuming that the high-pressure cooler internal coil is an incompressible ideal fluid, and there is no heat exchange with the outside world, Bernoulli equation is

[0094]

[0095] Therefore, Bernoulli equation is satisfied between any two points in the high-pressure cooler internal coil, that is:

[0096]

[0097] Where, v is the velocity, m / s; g is the acceleration of gravity, m / s 2 ; z is the height of the fluid at the location, m; p is the pressure, Pa; ρ is the fluid density, kg / m 3 ; subscripts 1 and 2 are any two points in the high-pressure cooler internal coil.

[0098] The liquid in the high-pressure cooler internal coil is an adiabatic single-phase flow, and the change of fluid density can be ignored, that is, ρ1=ρ2=ρ, and the height change of the fluid at the location is ignored, that is, z1=z2, the leakage port is stagnant state v1=0 m / s, the above parameters are substituted into formula (13), then the liquid pressure of any 1st point in the high-pressure cooler internal coil when it is broken is:

[0099]

[0100] Mass flow rate The mass flow rate through the cross section per unit time is calculated as:

[0101]

[0102] Where, is the mass flow rate, kg / s; ρ is the fluid density, kg / m 3 ; v is the velocity, m / s

[0103] Substituting formula (14) into formula (15) can obtain the mass flow rate of any 2nd point in the high-pressure cooler internal coil when it is broken And the flow rate v is:

[0104]

[0105] 2. Two-phase region isentropic stagnant flow equation

[0106] When the high-pressure cooler internal coil is completely broken, the leakage can be modeled as nozzle flow, and the path of the leakage process is short and the time is short, which can be considered as a steady-state isentropic expansion process, then the energy equation of the stable flow of any two points in the high-pressure cooler internal coil is:

[0107]

[0108] where q is the heat exchanged with the outside during the flow process, W; h is the enthalpy carried by the fluid, J / kg; w net is the work done by the flow process to the outside, W; v is the velocity, m / s; g is the gravitational acceleration, m / s 2 ; z is the height at which the fluid is located, m; the subscripts 1 and 2 are respectively any two points of the fluid when the internal coil of the high-pressure cooler is completely broken.

[0109] After the internal coil of the high-pressure cooler is completely broken, q = 0, v1 = 0, Δz = 0 and w net = 0 in formula (18), and h2 is the enthalpy value corresponding to the isentropic process of the back pressure of the shell side of the high-pressure cooler. Therefore, formula (18) can be simplified as:

[0110]

[0111] That is, the flow velocity v at this time is:

[0112]

[0113] The mass flow rate during the isentropic stagnation flow process is:

[0114]

[0115] 3. Speed of sound limitation

[0116] When the internal coil of the high-pressure cooler is broken, the flow velocity of the liquid will not exceed the speed of sound, so the maximum outlet velocity of the liquid can be obtained at the narrowest cross section at the broken part, and the pressure at which the outlet velocity v is greater than the speed of sound c is the critical pressure p c .

[0117] The empirical formula of the speed of sound is:

[0118]

[0119] In Matlab, the change of the density with the pressure during the isentropic process in the Refprop calculation system is called, a polynomial fitting formula is used, and the derivative of the obtained formula is calculated to obtain the s value used for calculating the speed of sound (see Figure 6 : System parameter isentropic process density change curve with pressure).

[0120] The mass flow rate and the flow velocity v are calculated by using the Bernoulli equation when the internal coil of the high-pressure cooler is broken and unidirectional flow occurs, and the mass flow rate is calculated by using the isentropic stagnation flow formula when two-phase flow occurs. And flow rate v, using the sound speed to two-phase flow mass flow rate to make constraint to improve the accuracy and applicability of the calculation method in this paper, considering the nozzle effect, the maximum flow rate of fluid will not exceed the sound speed, finally get the high pressure cooler internal coil rupture fluid "back pressure-flow" characteristic curve and "back pressure-flow rate" characteristic curve as shown in Figure 7 And Figure 8 As shown.

[0121] The above, only for the preferred embodiments of the present application, these embodiments are based on the overall concept of the present application under different ways, and the scope of protection of the present application is not limited to this, any skilled in the art of the technical personnel in the technical range of the present application disclosed, can easily think of changes or replacement, should be covered in the scope of protection of the present application. Therefore, the scope of protection of the present application should be subject to the scope of protection of the claims.

Claims

1. A method for calculating the critical flow rate at which the internal coil of a high-pressure cooler ruptures, characterized in that, The specific steps for calculating the critical flow rate under the condition of internal coil rupture in the high-pressure cooler are as follows: Step 1: Input the internal coil dimensions of the high-pressure cooler, system temperature, and system pressure parameters in Matlab; Step 2: Use Matlab to call the Refprop property database to calculate the density, entropy, enthalpy and saturation pressure values ​​corresponding to the inside coil of the high-pressure cooler when the tube breaks; Step 3: Using Matlab, call the Refprop property database calculation system to obtain the high-pressure cooler shell back pressure P, which varies from 15990 kPa to 1000 kPa with a variation interval of 10 kPa, and determine the relative magnitude of the back pressure P and the saturation pressure in the isentropic process. Step 4: (1) When the back pressure P in step 3 is greater than or equal to the saturation pressure in the isentropic process, the working fluid flow state under the high pressure cooler tube breakage condition is a single phase flow. The mass flow rate of the high pressure cooler tube breakage condition is calculated using the Bernoulli equation. (2) When the back pressure P in step 3 is less than the saturation pressure in the isentropic process, the working fluid flow state under the tube rupture condition of the high-pressure cooler is two-phase flow. The mass flow rate of the two-phase region when the internal coil of the high-pressure cooler ruptures is calculated using the isentropic stagnant flow formula in the two-phase region. and flow velocity v; Step 5: When leakage occurs in the internal coil of the high-pressure cooler, the liquid flow velocity will not exceed the speed of sound. Therefore, the maximum liquid outlet velocity can be obtained at the narrowest cross-section at the fracture point. Thus, the pressure at the point where the outlet velocity v is greater than the speed of sound c is the critical pressure p. c ; If the fluid is in two-phase flow, it is necessary to determine whether the flow velocity calculated in step 4 is greater than or equal to the local speed of sound. If the flow velocity is less than the local speed of sound, the mass flow rate when the coil inside the high-pressure cooler ruptures is the result of the isentropic stagnant flow formula. If the flow velocity is greater than or equal to the local speed of sound, the mass flow rate when the coil inside the high-pressure cooler ruptures is the speed of sound multiplied by the density of the working fluid at the rupture point. If the fluid is in one-phase flow, the mass flow rate when the coil inside the high-pressure cooler ruptures is the fluid velocity at the rupture point multiplied by the density.

2. The method for calculating the critical flow rate of internal coil rupture in a high-pressure cooler according to claim 1, characterized in that, In step 4, the Bernoulli equation is used to calculate the mass flow rate at the point of tube rupture in the high-pressure cooler: Bernoulli's equation for one-way regions: Assuming the internal coils of the high-pressure cooler are incompressible ideal fluids, and there is no heat exchange with the outside environment, Bernoulli's equation is: Therefore, Bernoulli's equation is satisfied between any two points on the coil inside the high-pressure cooler, that is: Where v is the velocity, m / s; g is the gravitational acceleration, m / s². 2 z is the height of the fluid's location, in meters; p is the pressure, in Pa; ρ is the fluid density, in kilograms per cubic meter of water. 3 Subscripts 1 and 2 represent any two points on the internal coil of the high-pressure cooler. The working fluid in the coil inside the high-pressure cooler is in an adiabatic single-phase flow state, and the change in fluid density can be ignored, i.e., ρ1=ρ2=ρ. Furthermore, the change in height at the fluid's location is ignored, i.e., z1=z2. The leak point is in a stagnant state, v1=0m / s. Substituting these parameters into formula (2), the liquid pressure at any point 1 when the coil inside the high-pressure cooler ruptures is: mass flow rate The formula for calculating the mass of fluid passing through the cross-section per unit time is: in, ρ is the mass flow rate, kg / s; ρ is the fluid density, kg / m³. 3 v is velocity, m / s Substituting formula (3) into formula (4) yields the mass flow rate at any second point when the coil inside the high-pressure cooler ruptures. The flow velocity v and the velocity v are respectively:

3. The method for calculating the critical flow rate of internal coil rupture in a high-pressure cooler according to claim 1, characterized in that, In step 4, the isentropic stagnant flow formula for the two-phase region is used to calculate the mass flow rate of the two-phase region when the internal coil of the high-pressure cooler ruptures. and flow velocity v: Formula for isentropic stagnant flow in a two-phase region: When the discharge after the internal coil of the high-pressure cooler completely ruptures can be modeled as nozzle flow, and the discharge process has a short path and short time, it can be considered as a steady-state isentropic expansion process. Then, the steady-state flow energy equation at any two points of the internal coil of the high-pressure cooler is: Where q is the heat exchanged with the surroundings during the flow process, in W; h is the enthalpy carried by the fluid, in J / kg; w net W is the work done by the flow on its surroundings; v is the velocity, m / s; g is the acceleration due to gravity, m / s². 2 z represents the height of the fluid's location, in meters; subscripts 1 and 2 represent any two points of fluid within the high-pressure cooler's internal coil when the coil is completely ruptured. After the internal coil of the high-pressure cooler completely ruptures, in formula (7), q=0, v1=0, Δz=0, and w net =0, and h2 is the enthalpy of the isentropic process of the back pressure on the high-pressure cooler shell side corresponding to h1, so formula (7) can be simplified to: That is, the flow velocity v at this time is: The mass flow rate during isentropic stagnant flow is for:

4. The method for calculating the critical flow rate of internal coil rupture in a high-pressure cooler according to claim 1, characterized in that, In step 5, the speed of sound c is: The empirical formula for the speed of sound is: In Matlab, the Refprop algorithm is used to calculate the density change with pressure during an isentropic process. A polynomial fitting formula is then used, and the derivative of the resulting formula is taken to obtain the density coefficients used to calculate the speed of sound. value.

Images