Efficiency evaluation method and system based on unsteady flow heat exchange numerical simulation

Abstract

The invention discloses an efficiency evaluation method and system based on unsteady flow heat exchange numerical simulation, and the method comprises the steps: a), carrying out the discretization solving of an incompressible Navier-Stokes equation through a single-step time marching algorithm STA, and obtaining an instantaneous flow field; b) on the basis of the instantaneous flow field obtained in the step a), a turbulence model is adopted, turbulence energy k and a turbulence dissipation rate epsilon are updated through single iteration of an STA algorithm, and turbulence viscosity is obtained through calculation; c) utilizing the instantaneous flow field in the step a) and the turbulence viscosity in the step b) to solve an energy equation through single iteration of an STA algorithm, and simulating heat conduction and convective heat transfer phenomena in the fluid to obtain a temperature field; and d) based on the instantaneous flow field, the turbulence viscosity and the temperature field in the steps a) to c), numerical simulation is carried out by controlling the time step delta t and the grid error to meet CFL conditions, and an efficiency evaluation result is obtained. According to the method, the calculation efficiency is greatly improved, and the calculation process of transient flow can be optimized on the premise of ensuring high precision.

Description

Technical Field

[0001] The present invention belongs to the field of computational fluid dynamics (CFD), and in particular relates to an efficiency evaluation method and system based on numerical simulation of unsteady flow and heat transfer. Background Art

[0002] Numerical simulation of unsteady (or transient) flows is a common complex fluid mechanics problem in modern engineering, with widespread applications in fields such as flow within fuel assemblies, heat exchangers, aerospace, and automotive powertrains. With the increasing sophistication of engineering designs and the increasing complexity of flow problems, the demand for numerical simulation of unsteady flows is increasing. For periodic, pulsating flows, simulation accuracy and efficiency are crucial.

[0003] At present, the iterative time marching method (ITA scheme) is widely used in the numerical simulation of unsteady flows. Multiple external iterations are performed in each time step until full convergence is achieved, thereby obtaining second-order time accuracy. However, this method faces enormous computational pressure when dealing with fluid problems with complex structures. For example, in fuel assemblies, due to the complex structure and irregular geometry, the number of discrete grids often reaches tens of millions. In this case, unsteady calculations require a large number of iterations in each time step, especially the calculation of periodic pulsating flows, which requires thousands of time steps and tens of thousands of iterations, and the consumption of computing resources is extremely huge.

[0004] The main drawback of existing technologies is that the traditional iterative time marching method is inefficient and takes too long to compute, making it difficult to quickly obtain accurate transient solutions in engineering applications. Therefore, a more efficient method for numerical simulation of unsteady flows is urgently needed to reduce computational time while ensuring sufficient accuracy.

[0005] Existing numerical simulation techniques for unsteady flows primarily use the iterative time marching method (ITA). This method solves the flow equations through multiple external iterations within each time step to achieve convergence criteria and obtain an accurate transient solution. However, this traditional method has the following major drawbacks:

[0006] Low computational efficiency: In complex flow problems such as pulsating flows, the computational process is extremely time-consuming due to the need for multiple iterations within each time step. For example, a pulsating cycle typically needs to be divided into thousands of time steps, each of which requires dozens of external iterations to reach convergence. This results in tens of thousands of iterations required for the entire computation, significantly increasing computational time.

[0007] Significant computational resource consumption: For complex structures, such as the flow within a fuel assembly, numerical simulations require a fine mesh of complex small structures such as the fuel rods, grids, and mixing vanes. Such meshes, numbering in the tens of millions, are acceptable for steady-state calculations. However, in transient conditions, full convergence is required at every time step, requiring computational resources far exceeding those required for steady-state calculations, making them difficult to complete within a reasonable timeframe.

[0008] Mesh error control is difficult: Traditional methods require continuous external iteration to minimize mesh discretization error to ensure high-precision time stepping. However, reducing mesh error comes at a high computational cost, especially in complex geometries and unsteady operating conditions, where balancing mesh error with time accuracy is difficult to achieve.

[0009] Limitations on Engineering Applications: The high computational cost and resource consumption of existing methods limit their application in large-scale engineering applications. This is especially true for scenarios such as fuel assemblies and heat exchangers that require extensive transient simulations, where existing technologies struggle to meet the time constraints of actual engineering applications.

[0010] In summary, the existing iterative time marching method faces bottlenecks such as low efficiency, huge resource consumption, and difficulty in controlling grid errors when dealing with unsteady flow problems. An efficient new method is urgently needed to overcome these shortcomings. Summary of the Invention

[0011] The purpose of the present invention is to provide an efficiency evaluation method and system based on numerical simulation of unsteady flow and heat transfer, aiming to solve the problems of low computational efficiency, large computational resource consumption, and difficult grid error control in the existing iterative time marching method in unsteady flow simulation. This technology improves the time step advancing method and adopts the single-step time marching algorithm (STA), so that only one external iteration is performed for each time step to maintain sufficient time accuracy, significantly reducing the computational time and resource consumption required for transient flow simulation, thereby meeting the needs of efficient transient simulation in complex engineering environments. The present invention not only greatly improves the computational efficiency, but also optimizes the calculation process of transient flow while ensuring high accuracy, and is suitable for numerical simulation of complex geometric structures and periodic pulsating flows.

[0012] In order to achieve the above object, the present invention adopts the following technical solutions:

[0013] An efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer includes the following steps:

[0014] a) Discretize and solve the incompressible Navier-Stokes equations using the single-step time marching algorithm (STA) to obtain the instantaneous flow field;

[0015] b) Based on the instantaneous flow field obtained in step a), the turbulent kinetic energy k and the turbulent dissipation rate ε are updated by a single iteration of the STA algorithm using a turbulence model to calculate the turbulent viscosity;

[0016] c) using the instantaneous flow field of step a) and the turbulent viscosity of step b), solving the energy equation by a single iteration of the STA algorithm to simulate the heat conduction and convection heat transfer phenomena in the fluid to obtain the temperature field;

[0017] d) Based on the instantaneous flow field, turbulent viscosity, and temperature field from steps a) to c), numerical simulation is performed to obtain efficiency evaluation results by controlling the time step Δt and mesh error to meet the CFL condition.

[0018] A further improvement of the present invention is that in step a), the incompressible Navier-Stokes equations are discretized using a finite difference method using the STA algorithm, and the predicted velocity field and pressure field are calculated in a single iteration in combination with a prediction-correction method to ensure the incompressibility of the velocity field and obtain the instantaneous flow field.

[0019] A further improvement of the present invention is that in step a), in a complex geometric scenario of a nuclear reactor fuel assembly or an aircraft engine cooling channel, the incompressible Navier-Stokes equations are discretized and solved by the STA algorithm to obtain the instantaneous flow field.

[0020] A further improvement of the present invention is that the step b) adopts the k-ε turbulence model, and the transport equations of turbulent kinetic energy k and turbulent dissipation rate ε are discretized and solved in a single iteration through the STA algorithm, the turbulent viscosity is calculated, and the momentum equation is updated.

[0021] A further improvement of the present invention is that, in step b), based on the instantaneous flow field of step a), the turbulent kinetic energy k and the turbulent dissipation rate ε are updated by a single iteration of the STA algorithm using the k-ε turbulence model in a complex geometric scenario of a nuclear reactor fuel assembly or an aircraft engine cooling channel to calculate the turbulent viscosity.

[0022] A further improvement of the present invention is that the step c) discretizes the energy equation by the finite volume method, calculates the temperature field in a single iteration based on the instantaneous flow field of step a) and the turbulent viscosity of step b), and simulates the heat conduction and convection heat transfer phenomena.

[0023] A further improvement of the present invention is that, in step c), in a complex geometric scenario of a nuclear reactor fuel assembly or an aircraft engine cooling channel, based on the instantaneous flow field of step a) and the turbulent viscosity of step b), the energy equation is solved by a single iteration of the STA algorithm to obtain the temperature field.

[0024] A further improvement of the present invention is that step d) calculates the CFL number, adjusts the time step Δt to match the grid size, and performs numerical simulation based on the instantaneous flow field, turbulent viscosity and temperature field of steps a) to c).

[0025] An efficiency evaluation system based on numerical simulation of unsteady flow and heat transfer, comprising:

[0026] The first solution module discretizes and solves the incompressible Navier-Stokes equations using the single-step time marching algorithm (STA) to obtain the instantaneous flow field.

[0027] The second solution module uses the turbulence model based on the instantaneous flow field obtained by the first solution module, and updates the turbulent kinetic energy k and turbulent dissipation rate ε through a single iteration of the STA algorithm to calculate the turbulent viscosity;

[0028] The third solution module uses the instantaneous flow field of the first solution module and the turbulent viscosity of the second solution module to solve the energy equation through a single iteration of the STA algorithm to simulate the heat conduction and convection heat transfer phenomena in the fluid and obtain the temperature field;

[0029] The numerical simulation module performs numerical simulation based on the instantaneous flow field, turbulent viscosity and temperature field of the first to third solution modules, and obtains efficiency evaluation results by controlling the time step Δt and grid error to meet the CFL condition.

[0030] A further improvement of the present invention is that the first solution module uses a finite difference discretization of the incompressible Navier-Stokes equations through a single-step time marching algorithm STA, and combines the prediction-correction method to calculate the predicted velocity field and pressure field in a single iteration, ensuring the incompressibility of the velocity field and obtaining the instantaneous flow field.

[0031] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0032] (1) Significantly improve computational efficiency and shorten simulation time: This paper adopts the single-step time marching algorithm (STA) to improve the multiple iteration process of the traditional iterative time marching method (ITA) by performing only one external iteration in each time step, thus solving the problem of excessive computational time caused by a large number of iterations in unsteady flow simulation. The STA algorithm greatly reduces the amount of computation by efficiently updating the flow field, turbulence parameters, and temperature field. Implementation cases show that in the simulation of unsteady flow and heat transfer in complex geometric structures, the efficiency of the STA algorithm is improved by more than 60%, significantly improving the response speed of engineering design.

[0033] (2) Reduced computational resource consumption: This method optimizes the time step and meshing, combines it with the Courant-Friedrichs-Lewy (CFL) condition to control errors, and uses locally refined meshes in complex geometric areas while using coarser meshes in non-critical areas. This solves the problem of high resource consumption caused by high-density meshes in traditional methods. Compared to traditional methods that require tens of millions of meshes to maintain accuracy, this method reduces resource requirements through mesh optimization. Implementation cases have shown that high-precision simulations can be achieved with 10.7 million meshes, reducing the burden on computing hardware.

[0034] (3) Ensure high precision and adapt to complex flow fields: This paper combines the STA algorithm with the standard k-ε turbulence model to efficiently update turbulence parameters and optimize the simulation effect of complex flow fields. At the same time, it accurately solves the heat transfer process through a single iteration, supplemented by the CFL condition to balance time and grid errors, solving the problem of traditional methods that are difficult to achieve a balance between accuracy and efficiency in complex flow fields. Implementation case verification shows that the STA algorithm has the same accuracy as traditional methods at appropriate time steps and is suitable for transient simulation of periodic pulsating flows and complex geometric structures.

[0035] (4) Enhanced Engineering Application Capabilities: This paper utilizes the STA algorithm and error control to form an efficient and stable numerical simulation framework. This framework addresses the high computational cost limitations of traditional methods for complex engineering scenarios, such as nuclear reactor fuel assemblies and aircraft engine cooling channels. The STA algorithm efficiently handles transient flow and heat transfer characteristics, with implementation cases demonstrating a 50%-70% reduction in computational time, significantly enhancing the method's practicality and potential for widespread adoption in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 This is the calculation flow chart of the single-step time advancement algorithm.

[0038] Figure 2 Schematic diagram of the fuel assembly grid.

[0039] Figure 3 This is a schematic diagram of the comparison and verification of the calculation accuracy of the embodiment of the present invention.

[0040] Figure 4 Schematic diagram for comparing calculation efficiency of embodiments of the present invention.

[0041] Figure 5This is a structural block diagram of an efficiency evaluation system based on numerical simulation of unsteady flow and heat transfer according to the present invention. DETAILED DESCRIPTION

[0042] Hereinafter, only certain exemplary embodiments are briefly described. As will be appreciated by those skilled in the art, the described embodiments may be modified in various ways without departing from the spirit or scope of the present invention. Therefore, the drawings and description are to be considered as illustrative in nature and not restrictive.

[0043] In the description of the present invention, it is to be understood that when used in this specification and the appended claims, the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0044] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0045] It should be further understood that the term "and / or" used in the present description and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0046] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0047] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0048] Example 1

[0049] like Figure 1As shown in the figure, the present invention provides an efficiency evaluation method based on the numerical simulation of unsteady flow heat transfer, which aims to solve the problems of low computational efficiency and high resource consumption of the traditional iterative time marching method in unsteady flow numerical simulation. This technical solution mainly adopts the single-step time advancement algorithm (STA), which only performs one external iteration in each time step to update the velocity field, pressure field and turbulence parameters, thereby significantly reducing the calculation time and improving the computational efficiency. This method is particularly suitable for the numerical simulation of complex geometric structures and periodic pulsating flows.

[0050] 1. Design of non-iterative time-marching algorithm

[0051] This paper employs an improved time marching method, the non-iterative time marching algorithm (STA). By ensuring that the mesh discretization error and the time truncation error are of the same order, this method avoids the multiple iterations required to achieve convergence in traditional methods. Specifically, within each time step, only one external iteration is required to update the flow field information, including the velocity field, pressure field, and other physical quantities.

[0052] Momentum equation solution: Based on the incompressible Navier-Stokes equations, STA solves the velocity change in the flow field by discretizing the momentum equation at each time step. The momentum equation takes the following form:

[0053]

[0054] Where U is the velocity field, P is the pressure, v is the kinematic viscosity of the fluid, and F is the volume force. Within each time step, the velocity field is updated using a single iteration.

[0055] Pressure correction: To ensure the incompressibility of the velocity field, the present invention performs a pressure correction in each time step. The pressure correction equation solves the pressure gradient problem in the velocity field, thereby ensuring that the continuity equation is satisfied:

[0056]

[0057] After correcting the pressure, the velocity field is further adjusted to ensure a reasonable physics update at each time step.

[0058] 2. Solution of temperature field and energy equation

[0059] For flows involving heat exchange, the present invention introduces the solution of the energy equation to simulate the heat conduction and convection phenomena in the flow. The energy equation is in the following form:

[0060]

[0061] Where T is the temperature field, α is the thermal diffusivity, and q is the volumetric heat source. Using the non-iterative time marching method, the energy equation is solved only once per time step, and the temperature field is updated in a single iteration. This method is suitable for simulating transient heat transfer in complex flows and offers high computational efficiency.

[0062] 3. Turbulence model and solution of turbulence parameters

[0063] The present invention adopts a standard k-ε turbulence model to simulate the turbulent kinetic energy k and the turbulent dissipation rate ε in turbulent flow.

[0064] The relevant equation is:

[0065] Turbulent kinetic energy equation:

[0066]

[0067] Turbulence dissipation rate equation:

[0068]

[0069] By updating k and ε in a single iteration, the turbulent viscosity v in the flow is solved t , thereby optimizing the solution of the momentum equation. Compared with traditional methods, this turbulence model is more efficient under the STA framework.

[0070] Example 2

[0071] This paper addresses the unique characteristics of numerical simulations of unsteady flows by proposing an efficient computational method based on the Single-Step Time Advancement (STA) algorithm and designing a corresponding efficiency evaluation mechanism. This method effectively reduces computational resource consumption and shortens computation time while ensuring the accuracy of numerical simulations. Specific implementations are as follows:

[0072] Step 1: Computational domain selection and meshing

[0073] When performing numerical simulations of unsteady flows, the first step is to determine the geometry of the computational domain and the meshing scheme. For typical unsteady flows (such as periodic pulsating flows or flows under complex structures), it is necessary to select an appropriate computational domain based on the flow characteristics and perform meshing.

[0074] 1) Geometry Model Construction: Select a typical physics problem, such as complex flow within a nuclear reactor fuel assembly or periodic pulsating flow within a pipe. The geometry model should include both the fluid domain and solid walls. For a nuclear fuel assembly, the geometry model may include complex structures such as fuel rod bundles, spacer grids, and mixing vanes.

[0075] 2) Grid division:

[0076] Locally Refined Meshes: In geometrically complex regions (such as slits, curved surfaces, and mixing vanes), locally refined meshes are used to accurately capture flow details and boundary layer characteristics. Refined meshes can effectively improve computational accuracy in these regions.

[0077] Coarser mesh areas: Use a coarser mesh in areas where the flow is relatively simple (such as the central flow region away from the solid boundary). By reducing the number of meshes in non-critical areas, the overall computational effort can be significantly reduced.

[0078] Mesh optimization: Through mesh independence analysis, ensure that the mesh density is sufficient to capture the characteristics of unsteady flow while avoiding excessive refinement that leads to waste of computing resources.

[0079] 3) Time step selection:

[0080] Determination of time step: The selection of time step Δt should be based on the characteristics of the flow. For periodic pulsating flow, the time step is usually selected as 1 / 1000 of the flow period T (i.e., At = T / 1000), ensuring that there are enough time steps in each cycle to capture the flow details.

[0081] CFL number checking: By monitoring the Courant-Friedrichs-Lewy (CFL) number, ensure that the time step size matches the mesh density to avoid numerical instability issues.

[0082] Step 2: Setting initial and boundary conditions

[0083] In order to perform numerical simulation, initial conditions and boundary conditions need to be set for the fluid domain to ensure that the physical quantities can reasonably evolve from the initial state to the steady state or unsteady state.

[0084] 1) Initial condition setting:

[0085] Velocity Field Initial Conditions: The velocity initial conditions for the fluid domain can be obtained from a steady-state solution or set to zero velocity field depending on the physical context. For periodic flows, using a steady-state solution as the initial condition can help reduce convergence time during the initial calculation phase.

[0086] Initial conditions of the pressure field: The initial pressure field is usually set to a uniform ambient pressure, or an appropriate pressure distribution is set according to the specific characteristics of the flow field.

[0087] Initial conditions of temperature field (for heat transfer problems): Set the initial distribution of the temperature field, usually the temperature distribution under steady-state flow conditions, or set according to experimental data.

[0088] 2) Boundary condition setting

[0089] Inlet Boundary Conditions: Set the inlet velocity or pressure boundary conditions based on the flow field characteristics. For example, in periodic pulsating flow, the inlet velocity can be set as a periodic function of time, U(t) = U0sin(wt).

[0090] Outlet boundary conditions: The outlet usually uses the pressure outlet boundary condition to set the time-varying characteristics of the ambient pressure or outlet velocity.

[0091] Solid wall boundary conditions: Use no-slip boundary conditions, that is, the fluid velocity at the wall is zero. For heat transfer problems, the wall can be set to a fixed temperature or adiabatic boundary conditions.

[0092] Step 3: Solve the momentum equation using the single-step time marching algorithm (STA)

[0093] The STA algorithm performs only one iteration per time step, solving the momentum equations to update the velocity and pressure fields. Unlike traditional iterative methods, STA performs only one external iteration per time step and uses pressure corrections to ensure accuracy.

[0094] 3) Discretization and solution of momentum equation:

[0095] Momentum equation: Based on the incompressible Navier-Stokes equations, the discretized form of the momentum equation is:

[0096]

[0097] Among them, U n is the velocity field of the previous time step, P n is the pressure field at the previous time step, v is the kinematic viscosity of the fluid, and F is the volume force.

[0098] 4) Predicted velocity field: In each time step, the predicted velocity field U* is first calculated by ignoring the pressure term

[0099]

[0100] The predicted velocity field U* is an approximation of the velocity field before pressure correction in the momentum equation.

[0101] 5) Pressure correction equation: To ensure the incompressibility condition, solve the pressure correction equation:

[0102]

[0103] 6) Update velocity field: The final velocity field Un+1 is updated through the corrected pressure field as:

[0104]

[0105] This process only needs to be performed once at each time step, significantly reducing the computational cost of multiple external iterations in traditional methods.

[0106] Step 4: Solving the energy equation

[0107] For unsteady flows involving heat transfer problems, the present invention solves the energy equation using a single-step time-marching algorithm to simulate the temperature field changes in the fluid:

[0108] 1) Discretization and solution of energy equation: The discrete form of energy equation is:

[0109]

[0110] Where T is the temperature field, α is the thermal diffusivity, and q is the volumetric heat source term. The temperature distribution of the flow field is updated by discretizing the energy equation.

[0111] 2) Temperature field update: Based on the updated velocity field Un+1, the temperature field Tn+1 is updated using a single iteration, and the heat conduction and convection characteristics in the flow are calculated.

[0112] Step 5: Application of turbulence model

[0113] In simulating turbulent flows, this paper uses the standard k-ε turbulence model to solve for the fluid's turbulent kinetic energy k and turbulent dissipation rate ε. Using the Single-Step Time Marching Algorithm (STA), the turbulence parameters are efficiently updated within each time step, ensuring accurate simulation of complex turbulent flows.

[0114] Turbulent kinetic energy equation

[0115]

[0116] in:

[0117] k is the turbulent kinetic energy, which represents the turbulent energy per unit volume. P is the generation term of turbulent kinetic energy, which represents the turbulent kinetic energy generated by the velocity gradient. ε is the turbulent dissipation rate, which represents the rate at which turbulent kinetic energy is dissipated into internal energy through viscous diffusion. v t is the turbulent viscosity

[0118] Turbulence dissipation rate equation:

[0119]

[0120] Among them, C1 and C2 are empirical constants of the turbulence model.

[0121] STA requires only a single external iteration at each time step to obtain updated values ​​for the turbulent kinetic energy and turbulent dissipation rate. This significantly improves computational efficiency while maintaining similar accuracy to traditional multi-iteration methods. The results of the turbulence model directly impact the solution of the momentum and energy equations, significantly improving simulation accuracy, especially when the flow field contains complex turbulent eddy structures.

[0122] Example 3:

[0123] The calculation model of the 5×5 rod bundle channel has a geometric structure of a square channel with a side length of 65mm, a rod outer diameter of 9.5mm, and a rod spacing of 12.6mm. A positioning grid is installed 500mm from the inlet, and the total length of the entire rod bundle calculation domain is 1100mm. The rod bundle channel area is meshed using a polyhedron network. The grid causes the flow parameters of the rod bundle channel to change dramatically due to sudden contraction and expansion, so the grid needs to be locally encrypted. The grid details downstream of the grid are as follows: Figure 2 According to the grid independence analysis, the final number of grids is 10.7 million.

[0124] At present, the iterative time marching method (ITA) is widely used for numerical simulation of unsteady flow and heat transfer to solve the calculation in each time step. Its characteristic is that it is necessary to perform multiple external iterations in each time step to achieve complete convergence in order to achieve the theoretical second-order time accuracy. If the time step of the unsteady calculation is selected as 1 / 1000T, 1000 time steps need to be calculated for each cycle. In addition, for the pulsating flow condition calculated from the steady-state condition as the initial value, it is necessary to calculate 5 cycles to reach the cycle after the fully developed pulsating flow before it can be used as the research object. According to this calculation, 5000 time steps need to be completed for pulsating flows under different working conditions. For the ITA scheme to solve transient problems, each time step can usually reach convergence within 15 iterations. Therefore, a set of pulsating flow conditions requires 75,000 iterations before the calculation results can be used. The STA method proposed in the present invention is used together with the traditional ITA-SIMPLEC and ITA-PISO algorithms to calculate the time-varying curves of the pressure difference in the inlet and outlet of the rod bundle channel under different working conditions. (Working condition 1: pulsating flow amplitude is 0.3 cycle: 10s, working condition 2: pulsating flow amplitude is 0.5 cycle: 10s). Figure 3 The figure shows a comparison of the calculation accuracy. The figures show that the instantaneous pressure drop calculated by the two ITA algorithms is almost identical at the same time step, while the STA and ITA results show some deviation. When the STA algorithm's time step is reduced by an order of magnitude, the calculated results are consistent with those of the ITA algorithm. This indicates that the STA method is sensitive to the time step, but when a reasonable time step is selected, the algorithm has good calculation accuracy.

[0125] Considering that unsteady-state numerical simulations require large computational resources, it is necessary to quantitatively evaluate the computational efficiency of different iterative schemes.

[0126] For unsteady-state calculations, the total calculation time for a set of operating conditions can be determined by the single iteration time, the number of iterations per time step, and the calculation time step. Assume that the ITA scheme requires 15 iterations to reach convergence within a time step, and M represents the time required for each iteration, in seconds. The time interval between each time step is Δt1, in seconds. The calculation time t required for one cycle can be calculated as

[0127] t1=15M×T / Δt1

[0128] If the STA scheme requires N,s for each time step. The time interval between each time step is Δt2,s. Then the computation time required for one cycle can be calculated as

[0129] t2=N×T / Δt2

[0130] To quantitatively evaluate the computational efficiency improvement ratio of the STA scheme compared to the ITA scheme under unsteady conditions, the computational time of the two schemes is compared to obtain the computational efficiency improvement rate γ, which is defined as γ as follows. According to the accuracy results of different time marching algorithms, if the STA scheme wants to achieve the computational accuracy of the ITA scheme, the time step Δt2 = 2Δt1.

[0131]

[0132] Figure 4 A graph shows the computational efficiency improvement γ of the parallel STA algorithm as a function of the number of grid cells, using a 22-core, 44-thread Intel Xeon E5-2699 v4 (Broadwell-EP) processor at 2.2 GHz. The graph shows that the STA algorithm saves at least 50% and up to 70% of CPU time. For example, using the ITA-SIMPLEC algorithm to calculate a 5×5 non-heated rod bundle channel with an 18.8 million grid cell, the average iteration time is 23.28 seconds. With a time step of 1 / 1000T, the computation of five pulsating flow cycles requires approximately 485 hours, assuming 15 iterations per time step to converge. Using the STA-FSM algorithm with the same configuration, the iteration time per time step is 62.81 seconds. With a time step of 1 / 2000T and only one iteration per time step, the computation of five pulsating flow cycles requires only approximately 174.47 hours, a 64% reduction in computational time. Therefore, the STA scheme used in this study has higher computational efficiency (after considering the energy equation, the improvement rate γ is larger).

[0133] Example 4

[0134] like Figure 5 As shown, the present invention provides an efficiency evaluation system based on numerical simulation of unsteady flow and heat transfer, comprising:

[0135] The first solution module discretizes and solves the incompressible Navier-Stokes equations using the single-step time marching algorithm (STA) to obtain the instantaneous flow field.

[0136] The second solution module uses the turbulence model based on the instantaneous flow field obtained by the first solution module, and updates the turbulent kinetic energy k and turbulent dissipation rate ε through a single iteration of the STA algorithm to calculate the turbulent viscosity;

[0137] The third solution module uses the instantaneous flow field of the first solution module and the turbulent viscosity of the second solution module to solve the energy equation through a single iteration of the STA algorithm to simulate the heat conduction and convection heat transfer phenomena in the fluid and obtain the temperature field;

[0138] The numerical simulation module performs numerical simulation based on the instantaneous flow field, turbulent viscosity and temperature field of the first to third solution modules, and obtains efficiency evaluation results by controlling the time step Δt and grid error to meet the CFL condition.

[0139] In this embodiment, the first solution module uses the single-step time marching algorithm STA to discretize the incompressible Navier-Stokes equations using finite differences, and combines the prediction-correction method to calculate the predicted velocity field and pressure field in a single iteration to ensure the incompressibility of the velocity field and obtain the instantaneous flow field.

[0140] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, from all points of view, the embodiments should be regarded as illustrative and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and range of equivalents of the claims are included in the present invention. Any reference signs in the claims should not be construed as limiting the claim to which they relate.

[0141] In addition, it should be understood that although this specification describes the embodiments, not every embodiment contains only one independent technical solution. This description is for clarity only. Those skilled in the art should consider the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for the purpose of illustrating the technical concept of the present invention and cannot be used to limit the scope of protection of the present invention. Any changes made based on the technical solution in accordance with the technical concept proposed by the present invention fall within the scope of protection of the claims of the present invention.

Claims

1. An efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer, characterized in that: The following steps are involved: a) Discretize and solve the incompressible Navier-Stokes equations using the single-step time marching algorithm (STA) to obtain the instantaneous flow field; b) Based on the instantaneous flow field obtained in step a), the turbulent kinetic energy k and the turbulent dissipation rate ε are updated by a single iteration of the STA algorithm using a turbulence model to calculate the turbulent viscosity; c) using the instantaneous flow field of step a) and the turbulent viscosity of step b), solving the energy equation by a single iteration of the STA algorithm to simulate the heat conduction and convection heat transfer phenomena in the fluid to obtain the temperature field; d) Based on the instantaneous flow field, turbulent viscosity, and temperature field from steps a) to c), numerical simulation is performed to obtain efficiency evaluation results by controlling the time step Δt and mesh error to meet the CFL condition.

2. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 1, characterized in that: In step a), the incompressible Navier-Stokes equations are discretized using the STA algorithm with finite differences, and the predicted velocity field and pressure field are calculated in a single iteration in combination with the prediction-correction method to ensure the incompressibility of the velocity field and obtain the instantaneous flow field.

3. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 2, characterized in that: In the step a), in a complex geometric scene of a nuclear reactor fuel assembly or an aircraft engine cooling channel, the incompressible Navier-Stokes equations are discretized and solved by the STA algorithm to obtain an instantaneous flow field.

4. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 1, characterized in that: In step b), the k-ε turbulence model is used to discretize and solve the transport equations of turbulent kinetic energy k and turbulent dissipation rate ε in a single iteration through the STA algorithm, calculate the turbulent viscosity, and update the momentum equation.

5. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 4 is characterized in that: In the step b), in a complex geometric scenario of a nuclear reactor fuel assembly or an aircraft engine cooling channel, based on the instantaneous flow field of step a), the k-ε turbulence model is used to update the turbulent kinetic energy k and the turbulent dissipation rate ε through a single iteration of the STA algorithm to calculate the turbulent viscosity.

6. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 1, characterized in that: The step c) discretizes the energy equation by the finite volume method, calculates the temperature field in a single iteration based on the instantaneous flow field of step a) and the turbulent viscosity of step b), and simulates the heat conduction and convection heat transfer phenomena.

7. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 6, characterized in that: In the step c), based on the instantaneous flow field of step a) and the turbulent viscosity of step b), the energy equation is solved by a single iteration of the STA algorithm in a complex geometric scenario of a nuclear reactor fuel assembly or an aircraft engine cooling channel to obtain a temperature field.

8. The efficiency evaluation method based on numerical simulation of unsteady flow and heat transfer according to claim 1, characterized in that: The step d) calculates the CFL number, adjusts the time step Δt to match the grid size, and performs numerical simulation based on the instantaneous flow field, turbulent viscosity, and temperature field of steps a) to c).

9. An efficiency evaluation system based on numerical simulation of unsteady flow and heat transfer, characterized in that: include: The first solution module discretizes and solves the incompressible Navier-Stokes equations using the single-step time marching algorithm (STA) to obtain the instantaneous flow field. The second solution module uses the turbulence model based on the instantaneous flow field obtained by the first solution module, and updates the turbulent kinetic energy k and turbulent dissipation rate ε through a single iteration of the STA algorithm to calculate the turbulent viscosity; The third solution module uses the instantaneous flow field of the first solution module and the turbulent viscosity of the second solution module to solve the energy equation through a single iteration of the STA algorithm to simulate the heat conduction and convection heat transfer phenomena in the fluid and obtain the temperature field; The numerical simulation module performs numerical simulation based on the instantaneous flow field, turbulent viscosity and temperature field of the first to third solution modules, and obtains efficiency evaluation results by controlling the time step Δt and grid error to meet the CFL condition.

10. The efficiency evaluation system based on unsteady flow heat transfer numerical simulation according to claim 1, characterized in that: The first solution module uses the single-step time marching algorithm (STA) to discretize the incompressible Navier-Stokes equations using finite differences, and combines the prediction-correction method to calculate the predicted velocity field and pressure field in a single iteration to ensure the incompressibility of the velocity field and obtain the instantaneous flow field.

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