A method for optimal flow distribution in a core lifetime under a given total flow

Abstract

The application discloses a kind of optimal flow distribution methods under the total flow of given total flow in core life, and the method steps are as follows:1, input parameter: rod or plate fuel element core parameter, core power distribution parameter and assembly non-uniformity coefficient, core calculation control variable parameter.2, calculate channel total power.3, initial flow distribution calculation.4, flow distribution fine adjustment.5, compare the space-time maximum value of core assembly outlet temperature with the calculated value of last step, if greater, carry out next step calculation, if less than or equal to, set flow adjustment proportion coefficient, return to step 4.6, set assembly flow distribution as the calculated value of last step.7, core temperature distribution calculation.8, output optimal flow distribution scheme and core temperature distribution under the scheme.The advantages of the method are as follows:1, flow distribution scheme considers power change in whole life.2, flow distribution fine adjustment sets magnitude, to achieve rapid adjustment while ensuring the accuracy of adjustment amount.

Description

Technical Field

[0001] This invention belongs to the field of reactor thermal-hydraulic technology, specifically relating to an optimal flow distribution method within the core's lifetime under a given total flow rate. Background Technology

[0002] Compact pressurized water reactors (PWRs) employing cascaded fuel assemblies experience significant changes in the three-dimensional power distribution of the core throughout their lifespan, leading to a mismatch between core flow distribution and core power. Applying flow zoning design can significantly flatten the core outlet temperature distribution, increase outlet subcooling, or reduce coolant flow, thereby utilizing the coolant more effectively and substantially improving core design performance. To rationally allocate flow and achieve flattened coolant temperatures at the assembly outlets and increased subcooling, an optimization method considering multiple factors was developed for flow zoning. A closed-channel core flow zoning and water density feedback program, QSubTH, was designed, and the program is capable of performing the following calculations:

[0003] Rapidly calculate the axial water density distribution, fuel temperature distribution in the pellets, cladding temperature distribution, assembly outlet temperature, and subcooling of a closed-channel fuel assembly;

[0004] Given the total core flow rate, three-dimensional coarse mesh power distribution, and inlet temperature, a core flow rate allocation optimization search is performed to maximize the subcooling at the module outlet and flatten the core outlet temperature distribution.

[0005] Given the total core flow rate, the three-dimensional coarse mesh power distribution of several burnup steps, and the inlet temperature, a core flow rate allocation optimization search is performed to maximize the subcooling at the module outlet and flatten the core outlet temperature distribution. Summary of the Invention

[0006] To address the problems existing in the prior art, the present invention aims to provide an optimal flow distribution method for the core lifespan under a given total flow rate. Under given conditions of total core flow rate, three-dimensional coarse mesh power distribution, and inlet temperature, the method performs core flow rate distribution optimization search to maximize the subcooling at the component outlet and flatten the core outlet temperature distribution.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for optimal flow allocation over the core lifetime under a given total flow rate includes the following steps:

[0009] Step 1: Input parameters: including core parameters of rod or plate fuel elements, core power distribution parameters and component non-uniformity coefficient, core calculation control variable parameters, among which the core power distribution parameters and component non-uniformity coefficient are provided by the core physics calculation, including the core location of the component, component power distribution and component non-uniformity coefficient;

[0010] Step 2: Using the core power distribution parameters and component non-uniformity coefficient, sum the axial power of each channel in the core to calculate the total channel power;

[0011] Step 3: Initial Flow Allocation Calculation: Based on the total core flow rate, core inlet temperature, and total core power provided by the user, the energy conservation equation is used to determine the component outlet enthalpy when the core outlet temperature is consistent. The optimal flow rate for each channel is determined by the power of each channel and the calculated component outlet enthalpy. Based on the calculated optimal flow allocation scheme for each set at the corresponding burnout point, the maximum flow rate required for each component throughout its entire lifespan is determined. The initial flow allocation ratio factor is then determined based on the determined maximum flow rates for each component.

[0012] Step 4: Fine-tuning of flow allocation: Calculate the outlet temperature value of each component at each fuel consumption point through the initial flow allocation, search for the maximum outlet temperature of each component and sort them, match different components one by one according to temperature difference, allocate a part of the flow of the component with the smaller outlet temperature to the corresponding component with the larger outlet temperature, and form a new flow allocation scheme.

[0013] Step 5: Calculate the core assembly outlet temperature based on the new flow distribution scheme obtained in Step 4. Compare the calculated spatiotemporal maximum value of the core assembly outlet temperature with the calculated value in the previous step. If it is greater than the calculated value in the previous step, stop the calculation and proceed to the next step. If it is less than or equal to the calculated value in the previous step, set the flow adjustment ratio coefficient and return to Step 4 to readjust the flow distribution.

[0014] Step 6: Set the component traffic allocation to the value calculated in the previous step;

[0015] Step 7: Core temperature distribution calculation: The coolant temperature in each component is determined by the energy conservation equation. Then, using the heat transfer coefficient relationship and the thermal conductivity of the material, Fourier's law and Newton's cooling formula are applied to calculate the axial temperature distribution of the outer cladding layer, inner cladding layer, fuel surface, and fuel center from the outside to the inside.

[0016] Step 8: Output the optimal flow distribution scheme and the core temperature distribution under this scheme.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] 1. The input parameters in step 1 include the core location of the component, the power distribution of the component, and the component non-uniformity coefficient, taking into account the power variation during the core's lifespan; the core flow control variable in the input parameters improves the flow optimization efficiency.

[0019] 2. In step 3, the initial flow allocation calculation is performed. The total core flow is provided by the user. A custom flow allocation interface is also provided to allow users to control the flow freely. Users can customize the initial flow allocation, the upper limit and lower limit of the flow allocation, thereby improving the calculation efficiency and the overall level of the minimum subcooling at the core outlet.

[0020] 3. In step 3, the optimal allocation scheme for each set of corresponding fuel consumption points is relatively independent and the time effect of power distribution is not taken into account; the initial flow allocation ratio factor is determined based on the maximum flow of each component, and then the initial flow of each channel is allocated according to the ratio factor, so that the time effect of power distribution is initially taken into account in the flow allocation.

[0021] 4. In step 4, fine-tuning the flow distribution using a constant value is not suitable for every situation. During the iteration process, in order to ensure the conservation of total flow, positional compensation is performed. Each adjustment is a certain proportion of the original component flow. The adjustment ratio is set to three levels to achieve rapid adjustment while ensuring the accuracy of the adjustment amount. Attached Figure Description

[0022] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0024] like Figure 1 As shown, the present invention provides a method for estimating the minimum core flow rate, comprising the following steps:

[0025] Step 1: Input parameters: including core parameters for rod or plate fuel elements (including core bypass coefficient, thermal conductivity of the gap between cladding and fuel pellets, center-to-center distance between adjacent fuel rods, core active zone height, core minimum flow estimation flow iteration coefficient, number of guide tubes in the assembly, number of core assemblies, number of axial control volumes, number of assemblies in the calculation region, number of calculation regions, number of fuel rods in the assembly, number of burnup points, core pressure, total core power, inner radius of fuel rod cladding, inner and outer diameters of fuel rod cladding, fuel pellet radius, guide tube radius, minimum subcooling design value at the assembly outlet, core inlet coolant temperature, and coolant flow rate in the channels). The parameters include: volume, square component width, and net core coolant flow rate. If the fuel is plate-shaped, the plate element length, number of fuel plates, cladding thickness, plate element thickness, and plate element width also need to be entered. Core power distribution parameters and component non-uniformity coefficient (the corresponding data are provided after core physics calculation, including the core location of the component, component power distribution, and component non-uniformity coefficient) and core calculation control variable parameters (including core flow control variable, component power distribution, core outlet temperature comparison calculation control variable under different flow distributions, fuel type control variable, calculation type control variable, and reference flow input control variable (used for comparison calculations of different flow rates)).

[0026] Step 2: Using the core power distribution parameters and component non-uniformity coefficient, sum the axial power of each channel to calculate the total power of the channel.

[0027] Step 3: Initial Flow Allocation Calculation: Based on the total core flow rate, core inlet temperature, and total core power provided by the user, the energy conservation equation is used to determine the component outlet enthalpy when the core outlet temperature is consistent. The optimal flow rate for each channel is determined by the power of each channel and the calculated component outlet enthalpy. The optimal flow allocation scheme for each set at the corresponding burnout point is searched to determine the maximum flow rate required for each component throughout its entire lifespan. To ensure the conservation of the total core flow rate, the initial flow allocation ratio factor is determined based on the determined maximum flow rate of each component.

[0028] For a single power distribution shape, the maximum outlet subcooling of the module can be obtained when the temperatures at the outlets of all channels are equal. Given the total core flow rate, inlet temperature, and total core power, the module outlet enthalpy when the outlet temperatures are uniform can be determined using the energy conservation equation.

[0029]

[0030] In the above formula:

[0031] h out —The enthalpy of the component outlet when the flow allocation is optimal;

[0032] h in —The enthalpy of the coolant at the inlet;

[0033] P tot —Total core power;

[0034] W tot —Total coolant flow rate in the reactor core.

[0035] The optimal flow rate allocation for each channel is then determined by the power of each channel and the calculated outlet enthalpy.

[0036]

[0037] In the above formula:

[0038] W(i) — the optimal allocated flow for channel i;

[0039] P(i) — Total power corresponding to channel i.

[0040] Throughout its lifespan, the core power distribution changes as burnup intensifies. To obtain the optimal flow distribution over the entire lifespan, the time effect of the power distribution needs to be taken into account. In the program, the maximum outlet temperature of the module is used as the standard for evaluating the quality of the flow distribution scheme.

[0041] For each burnout point, there is an optimal flow allocation scheme. Each scheme is relatively independent and does not take into account the time effect of power distribution. When determining the initial allocation scheme, the calculated optimal allocation schemes for each corresponding burnout point are first searched to determine the maximum flow required by each component throughout its entire lifespan. In order to ensure the conservation of the total core flow, the initial flow allocation ratio factor is determined based on the determined maximum flow of each component.

[0042]

[0043] W k (i), the maximum flow rate required by component i during its lifespan to ensure the minimum outlet temperature.

[0044] Then, the initial flow rate of each channel is allocated using a proportional factor based on the total amount. This allows the time effect of power distribution to be initially considered in the flow rate allocation.

[0045] Step 4: Fine-tuning of flow allocation. Calculate the outlet temperature values ​​of each component at each burnout point using the initial flow allocation. Search for and sort the maximum outlet temperatures of each component, mapping different components one-to-one according to temperature differences. For example, the component with the highest outlet temperature corresponds to the component with the lowest outlet temperature, and the component with the second highest outlet temperature corresponds to the component with the second lowest outlet temperature. Then, allocate a portion of the flow from the component with the lower outlet temperature to its corresponding component with the higher outlet temperature, forming a new flow allocation scheme for the next step of calculating the core component outlet temperature. This iterative calculation continues until the spatiotemporal maximum value of the core component outlet temperature is greater than the value calculated in the previous step. The calculation stops then, and the flow allocation calculated in the previous step is the optimal scheme determined by the program. During the iteration process, to ensure the conservation of total flow and positional compensation, the adjustment amount each time is a certain proportion of the original component flow. The adjustment proportion is set at three orders of magnitude to achieve rapid adjustment while ensuring the accuracy of the adjustment amount.

[0046] Step 5: Calculate the core assembly outlet temperature based on the new flow distribution scheme obtained in Step 4. Compare the calculated spatiotemporal maximum value of the core assembly outlet temperature with the value calculated in the previous step. If it is greater than the value calculated in the previous step, stop the calculation and proceed to the next step. If it is less than or equal to the value calculated in the previous step, set the flow adjustment ratio coefficient and return to Step 4 to readjust the flow distribution.

[0047] Step 6: Set the component traffic allocation to the value calculated in the previous step.

[0048] Step 7: Core temperature distribution calculation. The coolant temperature in each component is determined by the energy conservation equation. Then, using the heat transfer coefficient relationship and the thermal conductivity of the material, Fourier's law and Newton's cooling formula are applied to calculate the axial distribution of the temperature from the outside to the inside: outer cladding layer, inner cladding layer, fuel surface, and fuel center.

[0049] The heat transfer issues involved in the reactor core mainly include: heat conduction of fuel pellets, heat conduction between fuel rods, heat conduction of the cladding, and heat exchange between the outer cladding layer and the coolant. Since the temperature difference between adjacent components inside the reactor core is not very large, radiative heat transfer is ignored here.

[0050] The fuel rods in the same component are homogenized, and it is assumed that the temperature distribution of the fuel rods in the same component is consistent. The temperature of the coolant in each component is determined by the energy conservation equation. Then, based on the heat transfer coefficient relationship and the thermal conductivity of the material, the axial distribution of the temperature of the outer shell, inner shell, fuel surface and fuel center is calculated from the outside to the inside by Fourier's law and Newton's cooling formula.

[0051] Coolant heat transfer is calculated using appropriate empirical formulas. Since a certain degree of subcooling is required at the core outlet, the coolant is in a single-phase liquid state. Therefore, the heat transfer model uses single-phase liquid heat transfer formulas, divided into high, medium, and low flow rate sections based on the flow rate:

[0052] (1) High flow rate (Re > 2500)

[0053] Dittus-Boelter relation

[0054]

[0055] Sieder-Tate Relation

[0056]

[0057] Mihaiyeph relation

[0058]

[0059] (2) Collier's relation for low flow rates (Re < 1800)

[0060]

[0061]

[0062] In the above formula: h — heat transfer coefficient, W / (m²) 2 ·K); λ c — Thermal conductivity, W / (m·K); D e — Equivalent diameter of the flow channel, m; Re — Reynolds number;

[0063] Pr – Prandtl number;

[0064] Pr st-water —Prantz number for saturated water; Gr —Grashof number;

[0065] g — acceleration due to gravity, m·s -2 ;

[0066] μ—dynamic viscosity coefficient, N·s / m 2 ;

[0067] μ f — Fluid dynamic viscosity coefficient, N·s / m 2 ;

[0068] μ wall — Wall dynamic viscosity coefficient, N·s / m 2 ;

[0069] ρ — density, kg / m³3 ;

[0070] T wall —Wall temperature, K;

[0071] T f — Fluid temperature, K;

[0072] β—volume change coefficient.

[0073] (3) Medium flow rate (1800≤Re≤2500)

[0074] Linear interpolation is performed at the endpoint values ​​in the two cases described above to obtain the heat transfer coefficient at the corresponding Reynolds number. For cladding heat conduction related calculations, different steady-state heat conduction calculation models are selected based on the fuel geometry:

[0075]

[0076]

[0077] In the above relation:

[0078] q l —Heat flow per unit length;

[0079] λ — thermal conductivity of the material;

[0080] t1-t2 — Temperature difference between the inside and outside of the cylinder wall;

[0081] d2—Outer diameter of the cylinder;

[0082] d1—Inner diameter of the cylinder;

[0083] L wi —Board width;

[0084] L th — Plate thickness.

[0085] The thermal conductivity of the fuel rod cladding is determined according to the property relationship of Zr-4 alloy:

[0086]

[0087] In the above relation:

[0088] λ clad — Thermal conductivity of fuel rod cladding, W / (m·K);

[0089] T—Clad temperature, °C.

[0090] The gap thermal conductivity is obtained from an empirical value input from an external file, and the gap heat flux density is calculated based on the one-dimensional thermal conductivity formula in cylindrical coordinates; the fuel center temperature is calculated using the integral thermal conductivity.

[0091]

[0092] In the above formula:

[0093] t uo —Radius is r uo Core temperature, K;

[0094] t ui —Radius is r ui Core temperature, K;

[0095] k u — Thermal conductivity of fuel pellets, W / (m·K).

[0096] Step 8: Output the optimal flow distribution scheme and the core temperature distribution under this scheme.

[0097] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. However, it should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A method for optimal flow distribution over core lifetime at given total flow, characterized in that: The method comprises the following steps: Step 1: input parameters: including rod or plate fuel element core parameters, core power distribution parameters and assembly non-uniformity coefficients, and core calculation control variable parameters, wherein the core power distribution parameters and the assembly non-uniformity coefficients are provided by corresponding data of core physical calculation, including the core position of the assembly, the assembly power distribution and the assembly non-uniformity coefficient; Step 2: using the core power distribution parameters and the assembly non-uniformity coefficients, the axial power of each channel in the core is summed up, and the total power of the channel is calculated; Step 3: initial flow distribution calculation: the total flow of the core, the core inlet temperature and the total power of the core are provided by the user, the enthalpy value of the assembly outlet when the core outlet temperature is uniform is determined by the energy conservation equation, the optimal flow of the channel is determined according to the power of each channel and the calculated enthalpy value of the assembly outlet, the maximum flow required by each assembly in the entire service life is determined according to the optimal flow distribution scheme at each corresponding burnup point, and the initial flow distribution proportion factor is determined according to the maximum flow of each assembly; Step 4: flow distribution fine adjustment: the outlet temperature value of each assembly at each burnup point is calculated through the initial distribution flow, the maximum outlet temperature of each assembly is searched and sorted, different assemblies are one-to-one corresponding according to the temperature difference, a part of the flow of the assembly with smaller outlet temperature is distributed to the assembly with larger outlet temperature corresponding thereto, and a new flow distribution scheme is formed; Step 5: according to the new flow distribution scheme obtained in step 4, the outlet temperature of the core assembly is calculated, the time-space maximum value of the calculated outlet temperature of the core assembly is compared with the calculated value in the previous step, if the time-space maximum value is greater than the calculated value in the previous step, the calculation is stopped, and the next step is calculated; if the time-space maximum value is less than or equal to the calculated value in the previous step, a flow adjustment proportion factor is set, and the flow distribution fine adjustment is performed again in step 4; Step 6: setting the assembly flow distribution to the calculated value in the previous step; Step 7: core temperature distribution calculation: the coolant temperature in each assembly is determined through the energy conservation equation, and then the axial distribution of the outer layer of the cladding, the inner layer of the cladding, the fuel surface and the fuel center temperature is calculated from outside to inside in turn through the heat transfer coefficient relationship and the thermal conductivity of the material according to the Fourier law and the Newton cooling formula; Step 8: output the optimal flow distribution scheme and the core temperature distribution under the scheme.

2. The method for optimal flow distribution over core lifetime at a given total flow rate according to claim 1, characterized in that: The rod or plate fuel element core parameters in step 1 include core bypass flow coefficient, gap thermal conductivity coefficient between cladding and fuel pellet, adjacent fuel rod center distance, core active zone height, core minimum flow estimation flow iteration coefficient, number of guide tubes in assembly, number of core assemblies, number of axially divided control volumes, number of assemblies in calculation region, number of divided calculation regions, number of fuel rods in assembly, number of burnup points, core pressure, core total power, fuel rod cladding inner radius, fuel rod cladding inner and outer diameters, fuel pellet radius, guide tube radius, assembly outlet minimum subcooling degree design value, core inlet coolant temperature, channel coolant flow, square assembly width and core coolant net flow, and if it is a plate fuel, plate element length, number of fuel plates, cladding thickness, plate element thickness and plate element width are also needed to be input; the core calculation control variable parameters include core flow control variable, assembly power distribution, core outlet temperature comparison calculation control variable under different flow distribution, fuel type control variable, calculation type control variable and reference flow input control variable for different flow comparison calculation.

3. The method of claim 1, wherein: The initial flow distribution calculation in step 3 is performed according to the total core flow provided by the user, and a flow distribution customization interface is provided to facilitate user control, and the user can customize the initial flow distribution, upper and lower limits of the flow distribution, thereby improving the calculation efficiency and the overall level of the calculated core outlet minimum subcooling degree.

4. The method of claim 1, wherein: The initial flow distribution proportion factor in step 3 is determined according to the determined maximum flow of each assembly, and is proportional to the mass flow of each assembly, and the initial flow of each channel is distributed according to the proportion factor, so that the time effect of power distribution is preliminarily considered in the flow distribution, and the flow distribution can be more quickly and accurately performed.

5. The method of claim 1, wherein: The flow distribution fine tuning in step 4 is performed in the iteration process, and in order to ensure the conservation of total flow, the adjustment is performed according to the original assembly flow, and the adjustment amount is a certain proportion of the original assembly flow; the adjustment proportion is set to three orders of magnitude, so that the adjustment can be quickly performed while the adjustment amount is ensured to be accurate.

Images