Semi-implicit thermal hydraulic transient calculation method for sodium-water vapor generator

Abstract

The invention discloses a semi-implicit thermal hydraulic transient calculation method for a sodium-water vapor generator. The method comprises the following steps: 1, carrying out grid node division on the sodium-water vapor generator; 2, initializing thermal hydraulic parameters of a sodium side, a water side and a pipe wall; 3, semi-implicitly solving the thermal hydraulic parameters of the sodium side (calculating the density of the sodium side, explicitly predicting the speed of the sodium side, explicitly calculating the pressure of the sodium side, explicitly calculating the speed of the sodium side, updating the density of the sodium side, calculating the heat exchange amount between the sodium side and the pipe wall and implicitly calculating the enthalpy value of the sodium side); 4, implicitly solving the pipe wall temperature; 5, semi-implicitly solving water side thermal hydraulic parameters (calculating water side density, explicitly predicting water side speed, explicitly calculating water side pressure, explicitly calculating water side speed, updating water side density, calculating heat exchange amount between the water side and a pipe wall and implicitly calculating a water side enthalpy value); and 6, calculating the relative deviation of the enthalpy values of the sodium side and the water side, if the relative deviation is greater than 10 <-5 >, returning to the step 3, otherwise, advancing the time until the end time. The method is high in stability and high in calculation speed.

Description

Technical Field

[0001] The invention relates to the technical field of nuclear reactor thermal hydraulics, and in particular to a semi-implicit sodium-steam generator thermal hydraulic transient calculation method. Background Art

[0002] As one of the six fourth-generation nuclear energy systems, the sodium-cooled fast reactor (SFR) can multiply fuel and improve fuel utilization by nearly 50 times compared to the traditional pressurized water reactor. It can also transmute long-lived fission products to reduce the generation of nuclear waste. Secondly, sodium has high specific heat capacity, low melting point (98℃), high boiling point (883℃) and lower corrosiveness than lead, making it a good coolant. Sodium-cooled fast reactors generally use sodium-water steam generators to remove heat and generate superheated steam to drive the turbine to do work. Its heat transfer capacity affects the economic efficiency of the reactor. When designing the steam generator, comprehensive considerations should be given to economy, safety, reliability and working performance. At present, the China Demonstration Fast Reactor is in the design and construction stage, so the study of the thermal-hydraulic characteristics of the sodium-water steam generator has important engineering guidance significance.

[0003] The shell side fluid of the sodium-water steam generator is liquid sodium, and the tube side is two-phase flowing water. Due to the instability of the two-phase flow and the complex physical process, the numerical calculation of the steam generator will encounter problems such as slow calculation speed and poor calculation stability. Therefore, a fast, stable and accurate thermal-hydraulic calculation method for sodium-water steam generator is needed. Summary of the invention

[0004] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to develop a semi-implicit sodium-water steam generator thermal-hydraulic transient calculation method, which can realize the calculation of transient thermal-hydraulic processes in the sodium-water steam generator.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A semi-implicit sodium-water steam generator thermal hydraulic transient calculation method comprises the following steps:

[0007] Step 1: Model the sodium side, water side and tube wall of the sodium-water steam generator and divide the nodes;

[0008] Step 2: Initialize the thermal hydraulic parameters, set the initial values ​​for the sodium side temperature, pressure and velocity, the water side temperature, pressure and velocity, and the pipe wall temperature;

[0009] Step 3: Semi-implicitly solve the thermal-hydraulic parameters on the sodium side, that is, solve the velocity and pressure explicitly and solve the enthalpy implicitly;

[0010] Sub-step ①: Calculate the sodium side density

[0011] ρ1=propNaRho(p1,h1) (1)

[0012] Where ρ1 is the sodium side density, p1 is the sodium side pressure, h1 is the sodium side enthalpy, and propNaRho is the sodium side density calculation function;

[0013] Sub-step ②: Calculate the total pressure drop on the sodium side

[0014] Δp1=Δp f1 +Δp l1 +Δp g1 +Δp a1 (2)

[0015] Where Δp1 is the total pressure drop on the sodium side, Δp f1 is the friction pressure drop on the sodium side, Δp l1 is the local pressure drop on the sodium side, Δp g1 is the flow gravity pressure drop on the sodium side, Δp a1 Accelerate the pressure drop for sodium side flow;

[0016] Sub-step ③: Explicitly predict the sodium side velocity

[0017]

[0018] In the formula is the predicted velocity on the sodium side, The sodium side velocity at the current time step, Δt is the time step;

[0019] Sub-step ④: Explicit calculation of sodium side pressure

[0020]

[0021] In the formula is the required pressure on the sodium side;

[0022] Sub-step ⑤: Explicit calculation of sodium side velocity

[0023]

[0024] In the formula is the velocity to be determined on the sodium side;

[0025] Sub-step ⑥: Update the density using the pressure in sub-step ⑤;

[0026] Sub-step ⑦: Calculate the heat exchange between the sodium side and the tube wall;

[0027] q1=H1A1(T w,out -T1) (6)

[0028] Where q1 is the heat exchange between the sodium side and the tube wall, H1 is the heat transfer coefficient outside the tube, A1 is the heat transfer area outside the tube, Tw,out is the outer surface temperature of the tube wall, T1 is the temperature on the sodium side;

[0029] Sub-step ⑧: implicitly calculate the sodium side enthalpy;

[0030]

[0031] In the formula is the enthalpy value on the sodium side to be solved;

[0032] Step 4: implicitly solve the pipe wall temperature;

[0033] Sub-step ①: Calculate the thermal conductivity, specific heat and density of the tube wall

[0034] k w = propWallK(T w ) (8)

[0035] c pw = propWallCp(T w ) (9)

[0036] ρ w = propWallRho(T w ) (10)

[0037] Where k w is the thermal conductivity of the tube wall, c pw is the specific heat of the tube wall, ρ w is the tube wall density, T w is the wall temperature, propWallK is the wall thermal conductivity function, propWallCp is the wall specific heat function, propWallRho is the wall density function,

[0038] Sub-step ②: Solve the pipe wall temperature equation

[0039]

[0040] Where T w n+1 is the pipe wall temperature to be determined;

[0041] Step 5: Semi-implicitly solve the thermal-hydraulic parameters on the water side, that is, solve the velocity and pressure explicitly and solve the enthalpy implicitly;

[0042] Sub-step ①: Calculate water side density

[0043] ρ2=propH2ORho(p1,h1) (12)

[0044] Where ρ2 is the water side density, p2 is the water side pressure, h2 is the water side enthalpy, and propH2ORho is the water side density calculation function;

[0045] Sub-step ②: Calculate the total pressure drop of the water side flow

[0046] Δp2=Δp f2 +Δp l2 +Δp g2 +Δp a2 (13)

[0047] Where Δp2 is the total pressure drop on the water side, Δp f2 is the friction pressure drop on the water side, Δp l2 is the local pressure drop on the water side, Δp g2 is the flow pressure drop on the water side, Δp a2 Accelerate the pressure drop for water side flow;

[0048] Sub-step ③: Explicitly predict water-side velocity

[0049]

[0050] In the formula is the predicted velocity on the water side, Water side velocity at the current time step;

[0051] Sub-step ④: Explicit calculation of water side pressure

[0052]

[0053] In the formula is the required pressure on the water side;

[0054] Sub-step ⑤: Explicitly calculate the water side velocity

[0055]

[0056] In the formula is the required speed on the water side;

[0057] Sub-step ⑥: Update the density using the pressure in sub-step ⑤;

[0058] Sub-step ⑦: Calculate the heat exchange between the sodium side and the tube wall;

[0059] q2=H2A2(T w,in -T2) (17)

[0060] Where q2 is the heat exchange between the water side and the tube wall, H2 is the heat transfer coefficient outside the tube, A2 is the heat transfer area inside the tube, T w,in is the inner surface temperature of the pipe wall, T2 is the water side temperature;

[0061] Sub-step ⑧: implicitly calculate the water side enthalpy;

[0062]

[0063] In the formula is the enthalpy value on the water side to be solved;

[0064] Step 6: Calculate the relative deviation of the enthalpy values ​​on the sodium side and the water side. If it is greater than 10 -5 Then return to step 3 to continue iterating, otherwise time advances to calculate the next time step.

[0065] Compared with the prior art, the present invention has the following advantages:

[0066] 1. The thermal hydraulic transient calculation method for the sodium-water steam generator proposed in the present invention has high numerical stability. In the present invention, the velocity and pressure on the sodium side and the water side are calculated separately, and the velocity is predicted first and then solved, which reduces the instability caused by the coupled solution of velocity and pressure; the present invention adopts a semi-implicit algorithm, the velocity and pressure are solved explicitly, and the enthalpy is solved implicitly, wherein the explicit calculation has good stability within a reasonable time step; the present invention solves the sodium side, the water side and the pipe wall separately, and then performs multiple iterations, which reduces the influence of instability on the sodium side when solving the two-phase flow on the water side, and further enhances the numerical stability.

[0067] 2. The thermal hydraulic transient calculation method for the sodium-water steam generator proposed in the present invention has a fast calculation speed. The present invention adopts a semi-implicit algorithm, solves the velocity and pressure explicitly, and solves the enthalpy implicitly. When solving explicitly, it is not necessary to construct and solve a linear equation group, which reduces the amount of calculation when solving the sodium side and the water side, and speeds up the calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A block diagram of a method for calculating thermal hydraulic transients of a semi-implicit sodium-water steam generator of the present invention;

[0069] Figure 2 Modeling and node partitioning diagram for sodium-water steam generator; DETAILED DESCRIPTION

[0070] Combine the following Figure 1 and Figure 2 , a semi-implicit sodium-steam generator thermal-hydraulic transient calculation method proposed in the present invention is described in detail.

[0071] The present invention proposes a semi-implicit sodium-water steam generator thermal hydraulic transient calculation method, comprising the following steps (see Appendix Figure 1 shown):

[0072] Step 1: Model the sodium side, water side and tube wall of the sodium-water steam generator and divide the nodes, as shown in the attached figure. Figure 2 As shown, the water side and the sodium side use a one-dimensional grid in the Cartesian coordinate system, and the tube wall uses a one-dimensional grid in the cylindrical coordinate system;

[0073] Step 2: Set initial values ​​for the temperature, pressure and velocity on the sodium side, the temperature, pressure and velocity on the water side, and the pipe wall temperature. The temperature and pressure are initialized using linear distribution, and the velocity is initialized using the inlet velocity.

[0074] Step 3: Semi-implicitly solve the thermal-hydraulic parameters on the sodium side, that is, solve the velocity and pressure explicitly, and solve the enthalpy implicitly. The inlet boundary conditions are fixed velocity boundary and zero gradient pressure boundary, and the outlet boundary conditions are fixed pressure boundary and zero gradient velocity boundary.

[0075] Sub-step ①: Calculate the sodium side density

[0076] ρ1=propNaRho(p1,h1) (1)

[0077] Where ρ1 is the sodium side density, p1 is the sodium side pressure, h1 is the sodium side enthalpy, and propNaRho is the sodium side density calculation function;

[0078] Sub-step ②: Calculate the total pressure drop on the sodium side

[0079] Δp1=Δp f1 +Δp l1 +Δp g1 +Δp a1 (2)

[0080] Where Δp1 is the total pressure drop on the sodium side, Δp f1 is the friction pressure drop on the sodium side, Δp l1 is the local pressure drop on the sodium side, Δp g1 is the flow gravity pressure drop on the sodium side, Δp a1 Accelerate the pressure drop for sodium side flow;

[0081] Sub-step ③: Explicitly predict the sodium side velocity

[0082]

[0083] In the formula is the predicted velocity on the sodium side, The sodium side velocity at the current time step, Δt is the time step;

[0084] Sub-step ④: Explicitly calculate the pressure on the sodium side. The predicted velocity on the sodium side uses the value calculated in step ③.

[0085]

[0086] In the formula is the required pressure on the sodium side;

[0087] Sub-step ⑤: Explicit calculation of sodium side velocity

[0088]

[0089] In the formula is the velocity to be determined on the sodium side;

[0090] Sub-step ⑥: Update the density using the pressure in sub-step ⑤;

[0091] Sub-step ⑦: Calculate the heat exchange between the sodium side and the tube wall;

[0092] q1=H1A1(T w,out -T1) (6)

[0093] Where q1 is the heat exchange between the sodium side and the tube wall, H1 is the heat transfer coefficient outside the tube, A1 is the heat transfer area outside the tube, T w,out is the outer surface temperature of the tube wall, T1 is the temperature on the sodium side;

[0094] Sub-step ⑧: implicitly calculate the sodium side enthalpy;

[0095]

[0096] In the formula is the enthalpy value on the sodium side to be solved;

[0097] Step 4: implicitly solve the pipe wall temperature, using a fixed value boundary for the inlet temperature and a zero gradient boundary for the outlet temperature;

[0098] Sub-step ①: Calculate the thermal conductivity, specific heat and density of the tube wall

[0099] k w = propWallK(T w ) (8)

[0100] c pw = propWallCp(T w ) (9)

[0101] ρ w = propWallRho(T w ) (10)

[0102] Where k w is the thermal conductivity of the tube wall, c pw is the specific heat of the tube wall, ρ w is the tube wall density, T w is the wall temperature, propWallK is the wall thermal conductivity function, propWallCp is the wall specific heat function, propWallRho is the wall density function,

[0103] Sub-step ②: Solve the pipe wall temperature equation, and use the second type boundary conditions for the inner and outer walls

[0104]

[0105] Where T w n+1 is the pipe wall temperature to be determined;

[0106] Step 5: Semi-implicitly solve the thermal-hydraulic parameters on the water side, that is, solve the velocity and pressure explicitly, and solve the enthalpy implicitly. The inlet boundary conditions are fixed velocity boundary and zero gradient pressure boundary, and the outlet boundary conditions are fixed pressure boundary and zero gradient velocity boundary.

[0107] Sub-step ①: Calculate water side density

[0108] ρ2=propH2ORho(p1,h1) (12)

[0109] Where ρ2 is the water side density, p2 is the water side pressure, h2 is the water side enthalpy, and propH2ORho is the water side density calculation function;

[0110] Sub-step ②: Calculate the total pressure drop of the water side flow

[0111] Δp2=Δp f2 +Δp l2 +Δp g2 +Δp a2 (13)

[0112] Where Δp2 is the total pressure drop on the water side, Δp f2 is the friction pressure drop on the water side, Δp l2 is the local pressure drop on the water side, Δp g2 is the flow pressure drop on the water side, Δp a2 Accelerate the pressure drop for water side flow;

[0113] Sub-step ③: Explicitly predict water-side velocity

[0114]

[0115] In the formula is the predicted velocity on the water side, Water side velocity at the current time step;

[0116] Sub-step ④: Explicit calculation of water side pressure

[0117]

[0118] In the formula is the required pressure on the water side;

[0119] Sub-step ⑤: Explicitly calculate the water side velocity

[0120]

[0121] In the formula is the required speed on the water side;

[0122] Sub-step ⑥: Update the density using the pressure in sub-step ⑤;

[0123] Sub-step ⑦: Calculate the heat exchange between the sodium side and the tube wall;

[0124] q2=H2A2(T w,in -T2) (17)

[0125] Where q2 is the heat exchange between the water side and the tube wall, H2 is the heat transfer coefficient outside the tube, A2 is the heat transfer area inside the tube, T w,in is the inner surface temperature of the pipe wall, T2 is the water side temperature;

[0126] Sub-step ⑧: implicitly calculate the water side enthalpy;

[0127]

[0128] In the formula is the enthalpy value on the water side to be solved;

[0129] Step 6: Calculate the relative deviation of the enthalpy values ​​on the sodium side and the water side. If it is greater than 10 -5 Then return to step 3 to continue iterating, otherwise time advances to calculate the next time step.

Claims

1. A semi-implicit thermal hydraulic transient calculation method for a sodium-water steam generator, characterized in that: The steps include: Step 1: Model the sodium side, water side and tube wall of the sodium-water steam generator and divide the nodes; Step 2: Initialize the thermal hydraulic parameters, set the initial values ​​for the sodium side temperature, pressure and velocity, the water side temperature, pressure and velocity, and the pipe wall temperature; Step 3: Semi-implicitly solve the thermal-hydraulic parameters on the sodium side, that is, solve the velocity and pressure explicitly and solve the enthalpy implicitly; Sub-step ①: Calculate the sodium side density ρ1=propNaRho(p1,h1) (1) Where ρ1 is the sodium side density, p1 is the sodium side pressure, h1 is the sodium side enthalpy, and propNaRho is the sodium side density calculation function; Sub-step ②: Calculate the total pressure drop on the sodium side Δp1=Δp f1 +Δp l1 +Δp g1 +Δp a1 (2) Where Δp1 is the total pressure drop on the sodium side, Δp f1 is the friction pressure drop on the sodium side, Δp l1 is the local pressure drop on the sodium side, Δp g1 is the flow gravity pressure drop on the sodium side, Δp a1 Accelerate the pressure drop for sodium side flow; Sub-step ③: Explicitly predict the sodium side velocity In the formula is the predicted velocity on the sodium side, The sodium side velocity at the current time step, Δt is the time step; Sub-step ④: Explicit calculation of sodium side pressure In the formula is the required pressure on the sodium side; Sub-step ⑤: Explicit calculation of sodium side velocity In the formula is the velocity to be determined on the sodium side; Sub-step ⑥: Update the density using the pressure in sub-step ⑤; Sub-step ⑦: Calculate the heat exchange between the sodium side and the tube wall; q1=H1A1(T w,out -T1) (6) Where q1 is the heat exchange between the sodium side and the tube wall, H1 is the heat transfer coefficient outside the tube, A1 is the heat transfer area outside the tube, T w,out is the outer surface temperature of the tube wall, T1 is the temperature on the sodium side; Sub-step ⑧: implicitly calculate the sodium side enthalpy; In the formula is the enthalpy value on the sodium side to be solved; Step 4: implicitly solve the pipe wall temperature; Sub-step ①: Calculate the thermal conductivity, specific heat and density of the tube wall k w =propWallK(T w ) (8) c pw =propWallCp(T w ) (9) ρ w =propWallRho(T w ) (10) Where k w is the thermal conductivity of the tube wall, c pw is the specific heat of the tube wall, ρ w is the tube wall density, T w is the wall temperature, propWallK is the wall thermal conductivity function, propWallCp is the wall specific heat function, propWallRho is the wall density function, Sub-step ②: Solve the pipe wall temperature equation In the formula is the pipe wall temperature to be determined; Step 5: Semi-implicitly solve the thermal-hydraulic parameters on the water side, that is, solve the velocity and pressure explicitly and solve the enthalpy implicitly; Sub-step ①: Calculate water side density ρ2=propH2ORho(p1,h1) (12) Where ρ2 is the water side density, p2 is the water side pressure, h2 is the water side enthalpy, and propH2ORho is the water side density calculation function; Sub-step ②: Calculate the total pressure drop of the water side flow Δp2=Δp f2 +Δp l2 +Δp g2 +Δp a2 (13) Where Δp2 is the total pressure drop on the water side, Δp f2 is the friction pressure drop on the water side, Δp l2 is the local pressure drop on the water side, Δp g2 is the flow pressure drop on the water side, Δp a2 Accelerate the pressure drop for water side flow; Sub-step ③: Explicitly predict water-side velocity In the formula is the predicted velocity on the water side, Water side velocity at the current time step; Sub-step ④: Explicit calculation of water side pressure In the formula is the required pressure on the water side; Sub-step ⑤: Explicitly calculate the water side velocity In the formula is the required speed on the water side; Sub-step ⑥: Update the density using the pressure in sub-step ⑤; Sub-step ⑦: Calculate the heat exchange between the sodium side and the tube wall; <h2 style=";text-align:left;direction:ltr">q2=H2A2(T<h2 style=";text-align:left;direction:ltr"> w,in <h2 style=";text-align:left;direction:ltr"> -T2) (17) Where q2 is the heat exchange between the water side and the tube wall, H2 is the heat transfer coefficient outside the tube, A2 is the heat transfer area inside the tube, T w,in is the inner surface temperature of the pipe wall, T2 is the water side temperature; Sub-step ⑧: implicitly calculate the water side enthalpy; In the formula is the enthalpy value on the water side to be solved; Step 6: Calculate the relative deviation of the enthalpy values ​​on the sodium side and the water side. If it is greater than 10 -5 Then return to step 3 to continue iterating, otherwise time advances to calculate the next time step.

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