Method and device for improving parallel channel flow distribution iteration speed and storage medium

Abstract

The invention relates to the technical field of nuclear reactor thermal hydraulic power, in particular to a method and equipment for improving the parallel channel flow distribution iteration speed and a storage medium, and the method comprises the following steps: S1, constructing a channel flow initialization model, and initializing the flow of each channel inlet; s2, the pressure drop of each channel is calculated, an iterative algorithm model is constructed according to the direct proportion relation between the one-way flow pressure drop and the flow exponential function, and the channel flow after iteration is calculated; and S3, setting an error limit, carrying out iterative convergence judgment, if the iterative convergence is not greater than the error limit, ending iteration, and otherwise, returning to S2 to continue iterative calculation. The method aims at solving the problems that an existing parallel multi-channel flow distribution model is low in efficiency and cannot guarantee convergence of the trial and error process, and efficient and stable numerical solution of an existing nonlinear, large-scale and parallel multi-channel flow distribution theoretical model is achieved.

Description

Technical Field

[0001] The present invention relates to the field of nuclear reactor thermal hydraulic technology, and in particular to a method, a device and a storage medium for improving the iteration speed of parallel channel flow distribution. Background Art

[0002] Parallel channels are widely used in nuclear engineering, electric power, petrochemical engineering and other engineering fields. In the field of nuclear engineering, some advanced reactors use closed fuel grids, and the coolant channels are only connected to the upper and lower chambers at the inlet and outlet. There is no flow mixing of the coolant in the channel, which can be regarded as a set of parallel channels. Therefore, when conducting full core thermal hydraulic analysis of such reactors, the parallel channel flow distribution problem must be solved first, because the coolant flow distribution characteristics are the basis of the fuel heat transfer process.

[0003] In flow distribution calculations, an isobaric surface is usually taken at the connection between the upper and lower chambers of the channel inlet and outlet, and flow distribution is performed according to the law of equal pressure loss in parallel channels. Many researchers have established models based on this law and completed steady-state calculations of flow distribution. However, existing studies have chosen to avoid the key technical issue of how to solve flow distribution.

[0004] For the existing parallel multi-channel flow distribution problem, the mathematical model describing the above flow distribution process is relatively unified, and the mathematical and physical model to be solved is:

[0005] (1) The mass of the fluid before and after the inlet distribution is conserved, that is:

[0006]

[0007] m t Indicates the total inlet flow, m i The inlet flow N obtained by allocating the i-th channel represents the total number of parallel channels, which characterizes the scale of the system, which can range from 2 to tens of thousands. The larger N is, the more difficult it is to find the numerical solution.

[0008] (2) The pressure drop between the inlet and outlet of each channel is approximately equal, which can be written as:

[0009] Δp i =p i,in -p i,out =Δp ave (10)

[0010] Δp i is the pressure drop of channel i, that is, the channel inlet pressure p in and the channel outlet pressure p out The difference between aveis the average pressure drop of all channels. If there are N channels, N-1 independent equations can be obtained through equation (10). Adding equation (9) will give N equations about the inlet flow rate and channel pressure drop of each parallel channel. Since the number of equations is equal to the number of variables, the above equation system has a unique solution in theory.

[0011] In principle, we can continuously try and adjust the inlet flow rate of each channel until the above equations are satisfied, and then the solution can be obtained through trial and error. However, since the pressure drop of the channel may be a non-monotonic function of the inlet flow rate, this is extremely inefficient and cannot guarantee the convergence of the trial and error process. Therefore, it is necessary to provide a method to achieve efficient and stable numerical solution of the existing nonlinear, large-scale, parallel multi-channel flow distribution theoretical model. Summary of the invention

[0012] The purpose of the present invention is to provide a method, device and storage medium for improving the iteration speed of parallel channel flow distribution, so as to solve the problem of efficient and stable numerical solution method of existing nonlinear, large-scale, parallel multi-channel flow distribution theoretical model.

[0013] The embodiments of the present invention are implemented by the following technical solutions:

[0014] A method for improving the iteration speed of parallel channel flow distribution is proposed, which includes the following steps:

[0015] S1: Construct a channel flow initialization model to initialize the flow at the entrance of each channel;

[0016] S2: Calculate the pressure drop of each channel, and build an iterative algorithm model based on the relationship that the pressure drop of unidirectional flow is proportional to the flow exponential function, and calculate the updated channel flow;

[0017] S3: Set the error limit and make iterative convergence judgment. If the iterative convergence is not greater than the error limit, the iteration is terminated. Otherwise, return to S2 to continue the iterative calculation.

[0018] Furthermore, the channel flow initialization model in S1 is:

[0019]

[0020] Among them, m i represents the initial flow of the ith channel, k A represents the ratio of the cross-sectional area of ​​the ith channel to the area of ​​the reference channel, k D It represents the ratio of the equivalent diameter of the ith channel to the equivalent diameter of the reference channel, N represents the total number of parallel channels, n represents, k represents, m represents t Indicates the total ingress flow.

[0021] Furthermore, the S2 comprises the following sub-steps:

[0022] S21: Calculate the total pressure drop at the inlet and outlet of each channel and the average pressure drop of each channel according to the current inlet flow value of each channel;

[0023] S22: Calculate the gravity pressure drop of each channel;

[0024] S23: A flow iteration algorithm model is constructed according to the relationship that the unidirectional flow pressure drop is proportional to the flow exponential function, and the flow of each channel after iterative update is calculated.

[0025] Furthermore, the average pressure drop of the channel in S21 is calculated by the following formula:

[0026]

[0027] Among them, Δp ave Indicates the average pressure drop in the channel, Δp i represents the voltage drop of channel i, and N represents the total number of parallel channels;

[0028] The gravity pressure drop of each channel in S22 is calculated by the following formula:

[0029]

[0030] Among them, ΔP i,g represents the gravity pressure drop in channel i, is the average density of the fluid in channel i, g is the acceleration due to gravity, and L is the length of channel i;

[0031] The flow iteration algorithm model in S23 is implemented by the following formula:

[0032]

[0033] Among them, m i (k+1) represents the inlet flow of channel i after the k+1th iteration, m i (k) represents the inlet flow of channel i after the kth iteration, and k represents the number of iterations.

[0034] Furthermore, the S2 further includes the following sub-steps:

[0035] S24: summing the updated flow rates and performing normalization correction on the flow rates of each channel;

[0036] The normalization correction formula for each channel is as follows:

[0037]

[0038] Among them, m i (k+1)′ express.

[0039] Furthermore, the Δp i The following formula is used to calculate:

[0040] Δp i =p i,in -p i,out (6)

[0041] Among them, p i,in represents the inlet pressure of channel i, p i,out Indicates the outlet pressure of channel i.

[0042] Furthermore, in S3, the error limit is specified in advance according to the calculation accuracy requirement.

[0043] Furthermore, the iterative convergence judgment in S3 is determined by formula (7) or formula (8):

[0044] max i |Δp i -Δp ave |≤ε p (7)

[0045] (m i (k+1) -m i (k) ) / m i (k+1) ≤ε m (8)

[0046] Among them, m i (k+1) represents the inlet flow of channel i after the k+1th iteration, m i (k) represents the inlet flow of channel i after the kth iteration, ε p It means that ε m express.

[0047] An embodiment of the present invention also proposes an electronic device, comprising: a processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute the steps of the method for improving the iteration speed of parallel channel flow distribution.

[0048] An embodiment of the present invention also proposes a computer-readable storage medium, on which is stored a program for a method for improving the iteration speed of parallel channel flow allocation, and the program for the method for improving the iteration speed of parallel channel flow allocation is executed by a processor to implement the steps of the method for improving the iteration speed of parallel channel flow allocation.

[0049] The technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects:

[0050] (1) Based on the physical law of the influence of flow on the friction pressure drop of the channel, the present invention proposes an iterative solution model for the parallel multi-channel flow distribution model on the basis of theoretical analysis and approximation, and provides a detailed initialization and iterative solution scheme, which can achieve a robust and rapid solution to the flow distribution problem of multiple channels and single-phase flow, that is, according to the given number of channels, geometric dimensions, and inlet parameters, the inlet flow distribution result of each channel can be accurately obtained by calculation;

[0051] (2) The iterative algorithm model proposed in the present invention strictly satisfies the mass conservation equation, and the model does not involve complex matrix operations. Therefore, as the number of channels increases, the amount of calculation increases slightly. It is particularly suitable for numerical solutions to large-scale, parallel multi-channel flow distribution problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments of the present invention are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0053] Figure 1 A schematic diagram of a parallel channel flow process provided by an embodiment of the present invention;

[0054] Figure 2 A flow chart of a method for improving the iteration speed of parallel channel flow distribution according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0056] It should be understood that the "system", "device", "unit" and / or "module" used herein are a method for distinguishing different components, elements, parts, portions or assemblies at different levels. However, if other words can achieve the same purpose, the words can be replaced by other expressions.

[0057] As shown in this specification and claims, unless the context clearly indicates an exception, the words "a", "an", "an" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "comprise" and "include" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0058] Flowcharts are used in this specification to illustrate the operations performed by the system according to the embodiments of this specification. It should be understood that the preceding or following operations are not necessarily performed precisely in order. Instead, the steps may be processed in reverse order or simultaneously. At the same time, other operations may also be added to these processes, or one or more operations may be removed from these processes.

[0059] The physical problems to be solved in this paper are as follows Figure 1 As shown, the total flow rate m at the inlet is given t , distributed to each parallel / parallel channel; after flowing through each channel, it converges in the outlet chamber and flows out. Due to the differences in the geometric dimensions and thermal conditions of the parallel / parallel channels, the flow rates allocated to each channel are not equal. To determine the flow distribution results of each parallel / parallel channel, a method is developed Figure 1 The premise and key to heat transfer calculation and safety analysis of the system shown.

[0060] for Figure 1 The mathematical model describing the above flow distribution process is relatively unified, and the mathematical and physical model to be solved is:

[0061] (1) The mass of the fluid before and after the inlet distribution is conserved, that is:

[0062]

[0063] m t Indicates the total inlet flow, m i represents the inlet flow rate allocated to the i-th channel; N represents the total number of parallel channels, which characterizes the scale of the system, which can range from 2 to tens of thousands; the larger N is, the more difficult it is to find the numerical solution.

[0064] (2) The pressure drop between the inlet and outlet of each channel is approximately equal, which can be written as:

[0065] Δp i =p i,in -p i,out =Δp ave (10)

[0066] Δp i is the pressure drop of channel i, that is, the channel inlet pressure p in and the channel outlet pressure pout The difference between ave is the average pressure drop of all channels. If there are N channels, N-1 independent equations can be obtained through equation (10). Adding equation (9) will give N equations about the inlet flow rate and channel pressure drop of each parallel channel. Since the number of equations is equal to the number of variables, the above equation system has a unique solution in theory.

[0067] In principle, we can keep trying and adjusting the inlet flow rate of each channel until the above equations are satisfied, and then the solution is obtained through trial and error. However, since the pressure drop of the channel may be a non-monotonic function of the inlet flow rate, this is extremely inefficient and cannot guarantee the convergence of the trial and error process. In particular, the more channels there are, the more it is necessary to construct a robust and efficient iterative format for program calculations.

[0068] For the above-mentioned problems of multiple channels, the calculation methods of the above-mentioned models are not given in the public literature due to technical confidentiality. This scheme invents a fast iterative solution algorithm for the parallel multi-channel flow distribution problem, which can quickly and stably obtain the numerical solution of the flow distribution problem. The algorithm has extremely high solution efficiency, and the efficiency improvement is more obvious when the number of channels is larger. The algorithm automatically has the property of mass conservation and can be applied to the program calculation of related flow and heat transfer problems.

[0069] like Figure 2 As shown, an embodiment of the present invention provides a method for improving the iteration speed of parallel channel flow distribution, specifically, comprising the following steps:

[0070] (1) Initialization

[0071] The following formula is used to initialize the flow rate of each channel. This is the theoretical solution of flow distribution that ignores the influence of shape resistance and power, and can better reflect the influence of channel size on flow distribution:

[0072]

[0073] k A and k D They represent the channel area ratio and hydraulic diameter ratio respectively, and the first channel is selected as the reference value and divided by them, that is, k A represents the ratio of the cross-sectional area of ​​the i-th channel to the area of ​​the reference channel (the first channel); k D It represents the ratio of the equivalent diameter of the ith channel to the equivalent diameter of the reference channel (the first channel). In particular, if the geometric dimensions of each channel are the same, the above formula is simplified to:

[0074]

[0075] (2) According to the current inlet flow value of each channel, the total inlet and outlet pressure drop Δp of each channel is calculatedi ; The average pressure drop of the channel is calculated according to the following formula:

[0076]

[0077] Store the channel inlet flow and total pressure drop; calculate the gravity pressure drop of each channel according to formula (3):

[0078]

[0079] (3) According to formula (4), the updated flow of each channel is obtained:

[0080]

[0081] (4) Sum the updated flow and normalize the flow of each channel:

[0082]

[0083] Specifically, this scheme proposes a set of numerical solution algorithms by mathematically transforming the model equations, including the construction of iterative functions, initialization methods and iterative solution formats.

[0084] The channel pressure drop calculation formula is:

[0085]

[0086] Where f represents the friction coefficient of the flow, referred to as the friction coefficient; L, D represent the length and equivalent diameter of the channel respectively; ρ represents the density of the fluid; u represents the flow velocity, where the flow velocity is defined as:

[0087]

[0088] Where A represents the cross-sectional area of ​​the channel.

[0089] For a single-phase adiabatic flow channel, the friction coefficient of the flow is an exponential function of the Reynolds number:

[0090] f=c Re -n (12b)

[0091] Where c is the coefficient and n is the exponent. For single-phase flow, n is usually 0.20 or 0.25.

[0092] The Reynolds number is defined as:

[0093]

[0094] Where μ represents the viscosity coefficient (physical parameter) of the fluid.

[0095] Combining the above formulas, we can get:

[0096]

[0097] In the above formula, represents the flow rate in the channel, and the exponent n is 0.25 or 0.20. This formula shows that the pressure drop of single-phase flow is proportional to the exponential function of the flow rate. Based on this, a flow distribution iterative solution format can be constructed.

[0098] The above explains the theoretical basis for constructing the numerical solution format.

[0099] Under heating and two-phase flow conditions, due to the changes in density and viscosity coefficient, although this relationship does not hold strictly, it can be used as a valid approximation.

[0100] The total pressure drop in the channel includes friction pressure drop, acceleration pressure drop and gravity pressure drop. If the acceleration pressure drop is further ignored, then the reference (12d) formula is approximately:

[0101] Δp i -Δp i,g ≈Cm 2-n (3a)

[0102] Where Δp i represents the total pressure drop in channel i; Δp i,g represents the gravity pressure drop of channel i. The calculation of gravity pressure drop is very simple:

[0103]

[0104] That is, the gravity pressure drop is the product of the average density of the fluid in the channel, the gravitational acceleration and the channel length. After the calculation converges, the total pressure drop of each channel is equal and equal to the average pressure drop, see formula (10), so the following formula still holds:

[0105] Δp ave ∞ -Δp i,g ∞ ≈C(m i ∞ ) 2-n (3b)

[0106] The superscript ∞ represents the value after the calculation converges. Note that the above derivation is not to obtain the theoretical solution of the flow distribution model, but to artificially construct an iterative calculation format through the analysis of the channel pressure drop law and boundary conditions. The overall requirement of the numerical solution format is to satisfy the constraints of the boundary conditions after convergence, that is, to transform the boundary conditions into the above formula.

[0107] Where:

[0108] m i : The last calculated value of the inlet flow rate of subchannel i, kg·s-1 ;

[0109] m i ∞ : Convergence value of the inlet flow rate of subchannel i, kg·s -1 ;

[0110] Δp i,g : gravity pressure drop in subchannel i, Pa;

[0111] C: The pressure drop characteristic coefficient of subchannel i is mainly related to the geometry of the channel and is therefore a constant.

[0112] Then based on equation (3a) and equation (3b), we can get:

[0113]

[0114] Based on this, the iterative relationship of traffic can be constructed:

[0115]

[0116] The above table (k) represents the number of iterations.

[0117] Obviously, when the iteration converges, since the pressure drop of each channel is equal to the average pressure drop, the flow rate will no longer change, so the format satisfies the restriction of formula (10). However, the above format does not necessarily satisfy formula (11), so it needs to be further normalized. That is, considering the given total inlet flow rate, see formula (11), the flow rate in channel i should be further corrected as follows to satisfy the mass conservation law:

[0118]

[0119] The construction of this iterative function has certain physical significance, has an extremely fast convergence speed, and does not involve a large number of matrix calculations in the iteration (the amount of matrix operations increases exponentially with the increase of the matrix size). Therefore, its advantages are more obvious for large-scale parallel channels.

[0120] (5) Judgment of iterative convergence

[0121] The pressure between channels will be nearly equal:

[0122] max i |Δp i -Δp ave |≤ε p (7)

[0123] It can also be judged by the flow change

[0124] (m i (k+1) -m i(k) ) / m i (k+1) ≤ε m (8)

[0125] The error limit is specified in advance according to the calculation accuracy requirements.

[0126] If the convergence criterion is met, the iteration ends; otherwise, return to step (2) to continue the iterative calculation. It can be seen that the computational complexity of the iterative format proposed in this scheme is only a linear function of the number of channels N; while the matrix operation is an exponential function of N, so the computational speed and iterative efficiency of this scheme are very high.

[0127] The basic concepts have been described above. Obviously, for those skilled in the art, the above detailed disclosure is only for example and does not constitute a limitation of this specification. Although not explicitly stated here, those skilled in the art may make various modifications, improvements and corrections to this specification. Such modifications, improvements and corrections are suggested in this specification, so such modifications, improvements and corrections still belong to the spirit and scope of the exemplary embodiments of this specification.

[0128] At the same time, this specification uses specific words to describe the embodiments of this specification. For example, "one embodiment", "an embodiment", and / or "some embodiments" refer to a certain feature, structure or characteristic related to at least one embodiment of this specification. Therefore, it should be emphasized and noted that "one embodiment" or "an embodiment" or "an alternative embodiment" mentioned twice or more in different positions in this specification does not necessarily refer to the same embodiment. In addition, certain features, structures or characteristics in one or more embodiments of this specification can be appropriately combined.

[0129] In addition, unless explicitly stated in the claims, the order of the processing elements and sequences described in this specification, the use of alphanumeric characters, or the use of other names are not intended to limit the order of the processes and methods of this specification. Although the above disclosure discusses some invention embodiments that are currently considered useful through various examples, it should be understood that such details are only for illustrative purposes, and the attached claims are not limited to the disclosed embodiments. On the contrary, the claims are intended to cover all modifications and equivalent combinations that are consistent with the essence and scope of the embodiments of this specification. For example, although the system components described above can be implemented by hardware devices, they can also be implemented only by software solutions, such as installing the described system on an existing server or mobile device.

[0130] Similarly, it should be noted that in order to simplify the description disclosed in this specification and thus help understand one or more embodiments of the invention, in the above description of the embodiments of this specification, multiple features are sometimes combined into one embodiment, figure or description thereof. However, this disclosure method does not mean that the features required by the subject matter of this specification are more than the features mentioned in the claims. In fact, the features of the embodiments are less than all the features of the single embodiment disclosed above.

[0131] Finally, it should be understood that the embodiments described in this specification are only used to illustrate the principles of the embodiments of this specification. Other variations may also fall within the scope of this specification. Therefore, as an example and not a limitation, alternative configurations of the embodiments of this specification may be considered consistent with the teachings of this specification. Accordingly, the embodiments of this specification are not limited to the embodiments explicitly introduced and described in this specification.

Claims

1. A method for improving the iteration speed of parallel channel flow distribution, characterized in that: The steps include: S1: Construct a channel flow initialization model to initialize the flow at the entrance of each channel; S2: Calculate the pressure drop of each channel, and build an iterative algorithm model based on the relationship that the pressure drop of unidirectional flow is proportional to the flow exponential function, and calculate the channel flow after iterative update; S3: Set the error limit and make iterative convergence judgment. If the iterative convergence is not greater than the error limit, the iteration is terminated. Otherwise, return to S2 to continue the iterative calculation.

2. The method for improving the iteration speed of parallel channel flow distribution according to claim 1, characterized in that: The channel flow initialization model in S1 is: Among them, m i represents the initial flow of the ith channel, k A represents the ratio of the cross-sectional area of ​​the ith channel to the area of ​​the reference channel, k D It represents the ratio of the equivalent diameter of the ith channel to the equivalent diameter of the reference channel. N represents the total number of parallel channels. n is a constant, which can be 0.25 or 0.

20. m t Indicates the total ingress flow.

3. The method for improving the iteration speed of parallel channel flow distribution according to claim 1, characterized in that: The S2 comprises the following sub-steps: S21: Calculate the total pressure drop at the inlet and outlet of each channel and the average pressure drop of each channel according to the current inlet flow value of each channel; S22: Calculate the gravity pressure drop of each channel; S23: A flow iteration algorithm model is constructed based on the relationship that the one-way flow pressure drop is proportional to the flow exponential function, and the updated flow of each channel is calculated.

4. The method for improving the iteration speed of parallel channel flow distribution according to claim 3, characterized in that: The average pressure drop in the channel of S21 is calculated by the following formula: Among them, Δp ave Indicates the average pressure drop in the channel, Δp i represents the voltage drop of channel i, and N represents the total number of parallel channels; The gravity pressure drop of each channel in S22 is calculated by the following formula: Among them, Δp i,g represents the gravity pressure drop in channel i, is the average density of the fluid in channel i, g is the acceleration due to gravity, and L is the length of channel i; The flow iteration algorithm model in S23 is implemented by the following formula: Among them, m i (k+1) represents the inlet flow of channel i after the k+1th iteration, m i (k) represents the inlet flow of channel i after the kth iteration, and k represents the number of iterations.

5. The method for improving the iteration speed of parallel channel flow distribution according to claim 1, characterized in that: The S2 further comprises the following sub-steps: S24: summing the updated flow rates and performing normalization correction on the flow rates of each channel; The normalization correction formula for each channel is as follows: Among them, m i (k+1)′ represents the inlet flow of the i-th channel after normalization.

6. The method for improving the iteration speed of parallel channel flow distribution according to claim 4, characterized in that: The Δp i The following formula is used to calculate: Δp i =p i,in -p i,out (6) Among them, p i,in represents the inlet pressure of channel i, p i,out Indicates the outlet pressure of channel i.

7. The method for improving the iteration speed of parallel channel flow distribution according to claim 1, characterized in that: In S3, the error limit is specified in advance according to the calculation accuracy requirement.

8. The method for improving the iteration speed of parallel channel flow distribution according to claim 1, characterized in that: The iterative convergence judgment in S3 is determined by formula (7) or formula (8): max i |Δp i -Δp ave |≤ε p (7) (8) Where m i (k+1) represents the inlet flow of channel i after the k+1th iteration, m i (k) represents the inlet flow of channel i after the kth iteration, ε p Indicates the error limit for the pressure drop deviation.

9. An electronic device, characterized in that: The electronic device includes: a processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor so that the processor can execute the steps of the method for improving the iteration speed of parallel channel flow distribution as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a program for a method for improving the iteration speed of parallel channel flow allocation, and the program for the method for improving the iteration speed of parallel channel flow allocation is executed by a processor to implement the steps of the method for improving the iteration speed of parallel channel flow allocation as described in any one of claims 1 to 8.

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