Propeller multiphase multi-field error quantitative evaluation method based on verification and confirmation
Through the combination of generalized Richardson extrapolation method and safety coefficient method, the error of propeller multiphase multifields is decomposed and confirmed, and the problem of error evaluation in complex multiphase flow fields is solved, and the simulation results with high accuracy and confidence are achieved.
Patent Information
- Application Number
- CN202510100228.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-22
- Publication Date
- 2025-07-22
AI Technical Summary
Existing verification and confirmation methods cannot effectively evaluate errors in complex multiphase flow fields, especially multiphase turbulent phase change and flow solid acoustic multifield coupling characteristics, making it difficult to quantify the credibility of simulation results.
The generalized Richardson extrapolation method is used to characterize the exact solution and the total error of the numerical solution of the multiphase multi-field target quantity of the propeller, and a five-equivalent error expression based on the total error binary Taylor series expansion. The total error expression is decomposed into numerical error and model error through the five-equivalent error expression, and the uncertainty is calculated in combination with the safety coefficient method, and the error confirmation is used to use the densest grid and experimental results.
The calculation accuracy of propeller multi-phase multi-field error and the credibility of simulation results are improved, the prediction performance is improved, and the reliability and accuracy of simulation results are ensured.
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Abstract
Description
Technical Field
[0001] The present invention relates to a method for quantitatively evaluating the errors of a propeller in multiple phases and multiple fields based on verification and validation, and belongs to the technical fields of shipbuilding industry and fluid machinery. Background Art
[0002] High-fidelity simulation of multiphase and multi-field flows is a frontier academic topic that has received much attention in the field of high-speed hydrodynamics, and is even a core issue related to the leapfrog development of hydraulic machinery such as propellers. At present, commercial software (Ansys CFX), open-source codes (OpenFOAM), and various self-developed programs based on large-eddy simulation methods are widely used in solving the unsteady multiphase and multi-field flow structures of propellers. During the process, numerical models, numerical formats, and grid discretizations will all affect the simulation results. There is a need to develop a method for quantitatively evaluating the errors of a propeller in multiple phases and multiple fields based on verification and validation to quantify the uncertainty of complex multiphase flow fields and evaluate the credibility of numerical simulation results. At present, the verification and validation methods for solving single-phase flow fields based on the RANS method have been relatively perfect. However, for complex multiphase flow fields, due to their characteristics such as multiphase turbulent phase change and multi-field coupling of fluid-structure-acoustics, the existing verification and validation methods are not applicable. Summary of the Invention
[0003] To solve the key problem of multiple sources of errors in multi-field coupling calculations, the main object of the present invention is to provide a method for quantitatively evaluating the errors of a propeller in multiple phases and multiple fields based on verification and validation. Taking the multiphase and multi-field flow of a propeller as the evaluation object, a multi-dimensional verification and validation method around multi-field coupling data is established to comprehensively and quantitatively evaluate the simulation accuracy for the application scenario of the propeller and evaluate the credibility of the simulation results with high precision.
[0004] The object of the present invention is achieved by the following technical solutions.
[0005] A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation. Based on verification and validation, taking the multi-phase and multi-field flow of the propeller as the evaluation object, the generalized Richardson extrapolation method is used to characterize the total error between the exact solution and the numerical solution of the multi-phase and multi-field target quantity of the propeller. A five-equation error expression based on the binary Taylor series expansion of the total error is established. Through the five-equation error expression, the total error of the multi-phase and multi-field of the propeller is decomposed into the numerical error and the model error of the multi-phase and multi-field of the propeller, improving the calculation accuracy of the total error. The model error of the multi-phase and multi-field of the propeller includes the errors generated by two models, namely the implicit large eddy turbulence model and the cavitation model. Five sets of systematically encrypted Cartesian grids and time dimensions are set for the multi-phase and multi-field calculation domain of the propeller, and the boundary conditions of the five sets of multi-phase and multi-field calculation domains of the propeller are kept the same. According to the solved multi-phase and multi-field calculation results of the propeller, the convergence rates of the multi-phase and multi-field calculation results of the propeller for every three adjacent Cartesian grids and time dimensions are calculated respectively, and the convergence type of the target quantity of the multi-phase and multi-field calculation results of the propeller is evaluated according to the convergence rate. According to the convergence of the target quantity of the multi-phase and multi-field calculation results of the propeller with the time step, it is determined whether the error is less than the preset threshold, and the flow field is ensured to reach stability by making the error less than the preset threshold. It is determined whether the order of the numerical error and the order of the model error obtained meet the set range. The order of the numerical error and the order of the model error that do not meet the set range are corrected according to the set range, so that the order of the numerical error and the order of the model error meet the accuracy order requirements of the multi-phase and multi-field numerical calculation method of the propeller, eliminating the influence of numerical instability in the total error calculation on the total error calculation result. Substitute the corrected order of the numerical error and the order of the model error into the established five-equation error expression to obtain a simplified three-equation error expression, and solve the numerical error and the model error of the target quantity of the multi-phase and multi-field calculation results of the propeller again, thereby improving the calculation efficiency and rationality of the numerical error and the model error of the multi-phase and multi-field target quantity of the propeller. For the numerical error and the model error of the target quantity of the multi-phase and multi-field calculation results of the propeller, the simulation uncertainty of the target quantity of the multi-phase and multi-field calculation results of the propeller is calculated based on the safety factor method, and the robustness of the total error of the target quantity of the multi-phase and multi-field calculation results of the propeller is increased according to the set safety factor. A method for calculating the uncertainty of the multi-phase and multi-field of the propeller based on the safety factor method is established to solve the simulation uncertainty of the multi-phase and multi-field. The comparison error between the multi-phase and multi-field calculation results of the propeller with the densest grid and the test results is calculated. Based on the simulation uncertainty and the test uncertainty of the target quantity of the multi-phase and multi-field calculation results of the propeller, the confirmation uncertainty of the target quantity is calculated, and the quantitative evaluation of the multi-phase and multi-field errors of the propeller is realized according to the confirmation uncertainty of the target quantity.
[0006] A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation includes the following steps:
[0007] Step 1: Taking the multiphase and multi-field flow of the propeller as the evaluation object, based on verification and validation, the generalized Richardson extrapolation method is used to characterize the total error between the exact solution and the numerical solution of the target quantities of the propeller's multiphase and multi-field. A five-equation error expression for the binary Taylor series expansion of the total error is established. Through the five-equation error expression, the total error of the propeller's multiphase and multi-field is decomposed into the numerical error and the model error of the propeller's multiphase and multi-field, improving the calculation accuracy of the total error. The model error of the propeller's multiphase and multi-field includes the errors generated by two models, namely the implicit large eddy turbulence model and the cavitation model.
[0008] The target quantities include the multiphase and multi-field velocity, pressure, thrust, torque, and turbulent kinetic energy of the propeller.
[0009] Step 2: According to the five-equation error expression constructed in Step 1, five sets of systematically encrypted Cartesian grids and time dimensions are set for the calculation domain of the propeller's multiphase and multi-field. And the boundary conditions of the five sets of calculation domains of the propeller's multiphase and multi-field are kept the same. Based on the implicit large eddy model and the cavitation model, the numerical solution of the flow characteristics of the propeller's multiphase and multi-field is obtained, and the calculation results of the propeller's multiphase and multi-field are obtained.
[0010] The boundary conditions include the incoming flow velocity, the outlet pressure, and the wall conditions.
[0011] Step 3: According to the calculation results of the propeller's multiphase and multi-field obtained in Step 2, the convergence rates of the calculation results of the propeller's multiphase and multi-field for every three adjacent Cartesian grids and time dimensions are calculated respectively. According to the convergence rates, the convergence types of the target quantities of the calculation results in Step 2 are evaluated. According to the convergence of the target quantities of the calculation results of the propeller's multiphase and multi-field obtained in Step 2 with the time step, it is determined whether the error is less than the preset threshold. By making the error less than the preset threshold, it is ensured that the flow field reaches stability. The numerical error, model error, numerical error order, and model error order of the target quantities of the propeller's multiphase and multi-field are calculated according to the five-equation error expression established in Step 1.
[0012] The unknowns of the numerical error term include the numerical error coefficient and the numerical error order, and the model error term includes the model error coefficient and the model error order.
[0013] Step 4: Determine whether the numerical error order and the model error order obtained in Step 3 meet the set range. The numerical error order and the model error order that do not meet the set range are corrected according to the set range so that the numerical error order and the model error order meet the accuracy order requirements of the numerical calculation method for propeller multiphase and multi-field, and the influence of numerical instability in the total error calculation on the total error calculation result is eliminated. Substitute the corrected numerical error order and model error order into the established error expression of the five-equation method to obtain a simplified error expression of the three-equation method, and solve the numerical error and model error of the target quantity of the propeller multiphase and multi-field calculation result again, thereby improving the calculation efficiency and accuracy of the numerical error and model error of the propeller multiphase and multi-field target quantity.
[0014] Step 5: Based on the numerical error and model error of the target quantity of the propeller multiphase and multi-field calculation result in Step 4, calculate the simulation uncertainty of the target quantity of the propeller multiphase and multi-field calculation result based on the safety factor method, and increase the robustness of the total error of the target quantity of the propeller multiphase and multi-field calculation result according to the set safety factor.
[0015] Step 6: Calculate the comparison error between the propeller multiphase and multi-field calculation result of the densest grid in Step 2 and the test result, calculate the confirmation uncertainty of the target quantity based on the simulation uncertainty and test uncertainty of the target quantity of the propeller multiphase and multi-field calculation result, and realize the quantitative evaluation of the propeller multiphase and multi-field error according to the confirmation uncertainty of the target quantity.
[0016] It further includes Step 7: According to the confirmation uncertainty of the target quantity obtained in Step 6, judge whether the comparison error is less than the confirmation uncertainty range. If it is less than the confirmation uncertainty range, it is determined that the propeller multiphase and multi-field calculation result is realized, and then it is determined that the predicted result of the propeller multiphase and multi-field that is realized meets the credibility requirements, which can optimize the error evaluation method and improve the prediction performance of the propeller in the multiphase and multi-field.
[0017] Preferably, in Step 1, taking the propeller multiphase and multi-field flow as the evaluation object, based on verification and validation, the generalized Richardson extrapolation method is used to characterize the total error between the exact solution and the numerical solution of the propeller multiphase and multi-field target quantity, and the total error is expressed as:
[0018] y num -y exact =δ tot (1)
[0019] Wherein, y num is the numerical solution of the numerical calculation target quantity, y exact is the exact solution of the target quantity, δ tot is the total error between the numerical solution and the exact solution of the target quantity. Establish an error expression of the five-equation method based on the total error expanded by the binary Taylor series. Through the error expression of the five-equation method, the total error of the propeller multiphase and multi-field is decomposed into the numerical error δ of the propeller multiphase and multi-fieldnum Error δ of the propeller multiphase and multi-field model mo , improving the calculation accuracy of the total error:
[0020]
[0021] Among them, Δt is the time step, Δh is the grid spacing of the Cartesian grid. Based on implicit large-eddy simulation, the numerical dissipation term generated by the numerical format is used to replace the eddy viscosity sub-grid scale model. Δ is the filtering size, that is, Δ = Δh. The model error caused by the cavitation model is related to the radius R of the cavitation cluster. The size of the cavitation can be characterized by the grid spacing, that is, R = nΔh. To improve the calculation efficiency, the turbulence model error and the cavitation model error are considered together, and the resulting error is covered by the final uncertainty. c N With c M are the numerical and model error coefficients, p N With p M are the numerical and model error orders. The error of the propeller multiphase and multi-field model includes the errors caused by two models: the implicit large-eddy turbulence model and the cavitation model.
[0022] The error expression of the five-equation method obtained is as follows:
[0023]
[0024] Among them, y num1～5 are the numerical solutions of the target quantities of the five groups of systematically refined Cartesian grids respectively, and Δt 1～5 are the five groups of systematically refined time steps respectively, and Δh 1～5 are the grid spacings of the five groups of systematically refined Cartesian grids respectively, and Δ 1～5 are the filtering sizes of the five groups of systematically refined Cartesian grids respectively.
[0025] Preferably, in step 2, according to the error expression of the five-equation method constructed in step 1, five groups of systematically refined Cartesian grids and time sizes are set for the propeller multiphase and multi-field calculation domain. To simplify the equation solving, the specific settings are as follows:
[0026]
[0027] Among them, r h and r t are the refinement ratios of the grid and time sizes respectively. And the boundary conditions of the five groups of propeller multiphase and multi-field calculation domains are all set the same. Based on the implicit large-eddy model and the cavitation model, the numerical solution of the propeller multiphase and multi-field flow characteristics is obtained, and the calculation results of the propeller multiphase and multi-field are obtained.
[0028] Preferably, in step 3, according to the calculation results of the multiphase and multi-field of the propeller obtained in step 2, the convergence rates of the calculation results of the multiphase and multi-field of the propeller with every three adjacent Cartesian grids and time dimensions are calculated respectively. According to formula (6), the convergence type of the numerical simulation target quantity in step 2 is evaluated, which is defined as follows:
[0029]
[0030] where R is the convergence rate, which can be divided into: monotonic convergence (0 < R < 1) and oscillatory convergence (-1 < R < 0), monotonic divergence (1 < R), oscillatory divergence (R < -1). The numerical simulation of the target quantity needs to meet the convergence condition.
[0031] According to the convergence of the target quantity of the calculation results of the multiphase and multi-field of the propeller obtained in step 2 with the time step, it is determined whether the error is less than the preset threshold. By making the error less than the preset threshold, the flow field is ensured to reach stability, the stability of the unsteady multiphase and multi-field flow development of the propeller is evaluated, and whether the flow has the characteristics of periodic evolution law is observed. According to the error expression of the five-equation method established in step 1, a set of nonlinear function relational expressions (7) is further constructed, and the numerical error, model error, numerical error order and model error order of the target quantity of the multiphase and multi-field of the propeller are calculated:
[0032]
[0033] where the following principles are followed for solving the set of nonlinear function relational expressions (7): ① The nonlinear function relational expressions are sensitive to the initial values, and the initial guess is selected as [y exact c N c M p N p M = [y num1 1 1 1 1]; ② There may be multiple solutions to the nonlinear equations, and unreasonable solutions are deleted according to the physical background; ③ The target quantity of the calculation results, the exact solution, the grid scale and the time dimension are normalized to make the orders of magnitude of the parameters consistent.
[0034] Preferably, in step 4, it is determined whether the numerical error order and the model error order obtained in step 3 meet the set range. The numerical error order and the model error order that do not meet the set range are corrected according to the set range, so that the numerical error order and the model error order meet the accuracy order requirements of the numerical calculation method for the multiphase and multi-field of the propeller, and p N 、p M ∈ [0.5, 2]. The influence of numerical instability in the total error calculation on the total error calculation result is eliminated.
[0035] Substitute the corrected numerical error order and model error order into the established error expression of the five-equation method to obtain a simplified error expression of the three-equation method:
[0036]
[0037] where the initial guess suggests choosing [y exact c N c M = [y num1 1 1], re - solve the numerical error and model error of the target quantity of the propeller multiphase and multi - field calculation results, and further improve the calculation efficiency and rationality of the numerical error and model error of the propeller multiphase and multi - field target quantity. To ensure a total error with good credibility, it is necessary to normalize the variables.
[0038] Preferably, in step 5, based on the numerical error and model error of the target quantity of the propeller multiphase and multi - field calculation results in step 4, calculate the simulation uncertainty of the target quantity of the propeller multiphase and multi - field calculation results based on the safety factor method:
[0039] U num = FS num |δ tot | (9)
[0040] where U num is the multiphase and multi - field flow simulation uncertainty, FS num is the safety factor, and the robustness of the total error of the target quantity of the propeller multiphase and multi - field calculation results is increased according to the set safety factor.
[0041] Preferably, in step 6, calculate the comparison error between the propeller multiphase and multi - field calculation results of the densest grid in step 2 and the test results, calculate the confirmation uncertainty of the target quantity based on the simulation uncertainty and test uncertainty of the target quantity of the propeller multiphase and multi - field calculation results, and realize the quantitative evaluation of the propeller multiphase and multi - field error according to the confirmation uncertainty of the target quantity:
[0042]
[0043] E = δ exp - δ tot = (y exp - y exact ) - (y num - y exact ) = y exp - y num (11)
[0044] where U V is the confirmation uncertainty, U exp is the test result uncertainty, E is the comparison error, δ exp is the error between the test value and the exact solution of the target quantity, y expis the experimental value of the target quantity. Due to the numerical calculation characteristics of multiphase and multi-field flows, the established uncertainty evaluation strategy is indirectly developed by comprehensively considering the experimental results.
[0045] Beneficial effects:
[0046] 1. A method for quantitatively evaluating the multiphase and multi-field errors of a propeller based on verification and validation disclosed by the present invention. The multiphase and multi-field model errors of the propeller include the errors generated by two models, namely, the implicit large eddy turbulence model and the cavitation model. The high-precision implicit large eddy model adopted is more suitable for gas-liquid-solid multiphase simulations and can improve the prediction accuracy of the multiphase and multi-field errors of the propeller.
[0047] 2. A method for quantitatively evaluating the multiphase and multi-field errors of a propeller based on verification and validation disclosed by the present invention. Based on verification and validation, taking the multiphase and multi-field flow of the propeller as the evaluation object, the generalized Richardson extrapolation method is used to characterize the total error between the exact solution and the numerical solution of the target quantity of the multiphase and multi-field of the propeller. A five-equation error expression based on the binary Taylor series expansion of the total error is established. The total error of the multiphase and multi-field of the propeller is decomposed into the numerical error of the multiphase and multi-field of the propeller and the model error of the multiphase and multi-field of the propeller, improving the calculation accuracy of the total error.
[0048] 3. A method for quantitatively evaluating the multiphase and multi-field errors of a propeller based on verification and validation disclosed by the present invention. Based on the safety factor method, the simulation uncertainty of the target quantity of the multiphase and multi-field calculation result of the propeller is calculated, and the robustness of the total error of the target quantity of the multiphase and multi-field calculation result of the propeller is increased according to the set safety factor; a method for calculating the uncertainty of the multiphase and multi-field of the propeller based on the safety factor method is established to solve the simulation uncertainty of the multiphase and multi-field; the most dense grid of the multiphase and multi-field calculation result of the propeller and the experimental result are used to calculate the comparison error. Based on the simulation uncertainty of the target quantity of the multiphase and multi-field calculation result of the propeller and the experimental uncertainty, the confirmation uncertainty of the target quantity is calculated. It is judged whether the comparison error is less than the range of the confirmation uncertainty. If it is less than the range of the confirmation uncertainty, it is determined that the multiphase and multi-field calculation result of the propeller is confirmed. Furthermore, it is determined that the predicted result of the multiphase and multi-field of the propeller that is confirmed meets the credibility requirements, improving the prediction performance of the propeller in the multiphase and multi-field. Description of the drawings
[0049] Figure 1 is a flowchart of a method for quantitatively evaluating the multiphase and multi-field errors of a propeller based on verification and validation disclosed by the present invention.
[0050] Figure 2 is a verification and validation framework.
[0051] Figure 3 is a characteristic diagram of the periodic evolution law of the propeller flow.
[0052] Figure 4Results of the calculation of the hydrodynamic performance error and uncertainty of the propeller in multiphase and multi-field Specific implementation mode
[0053] To better illustrate the purpose and advantages of the present invention, the following combines the drawings with specific examples to detail the implementation mode of the present invention.
[0054] As Figure 1 shown, a method for quantitatively evaluating the error of the propeller in multiphase and multi-field based on verification and validation disclosed in this embodiment is specifically implemented as follows:
[0055] Step 1: Taking the multiphase and multi-field flow of the propeller as the evaluation object, based on verification and validation, the generalized Richardson extrapolation method is used to characterize the total error between the exact solution and the numerical solution of the target quantity of the propeller in multiphase and multi-field. The total error is expressed as:
[0056] y num -y exact =δ tot (1)
[0057] Among them, y num is the numerical solution of the target quantity of numerical calculation, y exact is the exact solution of the target quantity, δ tot is the total error between the numerical solution and the exact solution of the target quantity. A five-equation error expression based on the total error expanded by the binary Taylor series is established. Through the five-equation error expression, the total error of the propeller in multiphase and multi-field is decomposed into the numerical error δ num of the propeller in multiphase and multi-field and the model error δ mo of the propeller in multiphase and multi-field to improve the calculation accuracy of the total error:
[0058]
[0059] Among them, Δt is the time step, Δh is the grid spacing of the Cartesian grid. Based on implicit large-eddy simulation in this patent, the numerical dissipation term generated by the numerical format is used to replace the eddy viscosity sub-grid scale model. Δ is the filtering size, that is, Δ = Δh. The model error caused by the cavitation model is related to the radius R of the cavitation cluster. The size of the cavitation can be characterized by the grid spacing, that is, R = nΔh. To improve the calculation efficiency, the turbulence model error and the cavitation model error are combined and considered. The resulting error is covered by the final uncertainty. c N and c M are the numerical and model error coefficients, p N and p M are the numerical and model error orders. The model error of the propeller in multiphase and multi-field includes the errors caused by two models, namely the implicit large-eddy turbulence model and the cavitation model.
[0060] The obtained five-equation error expression is as follows:
[0061]
[0062] where y num1～5 are the numerical solutions of the five groups of system-encrypted Cartesian grid target quantities respectively, and Δt 1～5 are 0.00011, 0.00015, 000019, 0.00025, 0.00032 (*l / U0s) respectively, and Δh 1～5 are 0.0017, 0.0022, 0.0028, 0.0037, 0.0048 (*lm) respectively, and Δ 1～5 are 0.0017, 0.0022, 0.0028, 0.0037, 0.0048 (*lm) respectively.
[0063] Step 2: According to the five-equation method error expression constructed in Step 1, set five groups of system-encrypted Cartesian grids and time dimensions for the propeller multiphase and multi-field calculation domain. For simplifying the equation solution, the specific settings are as follows:
[0064]
[0065] where r h and r t are the refinement ratios of the grid and time dimension respectively, and the optimal value range is 1.3 - 2.0. And the boundary conditions of the five groups of propeller multiphase and multi-field calculation domains are all set the same. Based on the implicit large eddy model and cavitation model, numerically solve the flow characteristics of the propeller multiphase and multi-field to obtain the calculation results of the propeller multiphase and multi-field. Select r h = r t = 1.3 as the refinement ratio of the grid scale and time step.
[0066] Step 3: According to the calculation results of the propeller multiphase and multi-field obtained in Step 2, calculate the convergence rates of the calculation results of the propeller multiphase and multi-field for every three adjacent Cartesian grid and time dimension settings respectively. According to Equation (6), evaluate the convergence type of the target quantity of the numerical simulation in Step 2, which is defined as follows:
[0067]
[0068] where R is the convergence rate, which can be divided into: monotonic convergence (0 < R < 1) and oscillatory convergence (-1 < R < 0), monotonic divergence (1 < R) and oscillatory divergence (R < -1). The numerical simulation of the target quantity needs to meet the convergence condition. Where R is the convergence rate and satisfies -1 < R < 1.
[0069] Based on the convergence of the target quantity of the propeller multiphase and multi-field calculation results solved in step 2 with the time step, determine whether the error is less than the preset threshold. Ensure the flow field reaches stability by making the error less than the preset threshold, evaluate the stability of the unsteady multiphase and multi-field flow development of the propeller, and observe whether the flow has the characteristics of periodic evolution rules, such as Figure 3 As shown. Further construct the nonlinear function relation group formula (7) according to the error expression of the five-equation method established in step 1, and calculate the numerical error, model error, numerical error order, and model error order of the propeller multiphase and multi-field target quantity:
[0070]
[0071] Among them, solving the nonlinear function relation group formula (7) follows the following principles: ① The nonlinear function relation is sensitive to the initial value, and the initial guess is selected as [K Texact c N c M p N p M = [K T1 1 1 1 1], [u exact / U0 c N c M p N p M = [u1 / U0 1 1 1 1]; ② The nonlinear equation system may have multiple solutions, and unreasonable solutions are deleted according to the physical background; ③ Normalize the calculation result target quantity, exact solution, grid scale, and time dimension to make the orders of magnitude of the parameters consistent.
[0072] Step 4, determine whether the numerical error order and model error order obtained in step 3 meet the set range. The numerical error order and model error order that do not meet the set range are corrected according to the set range to make the numerical error order and model error order meet the accuracy order requirements of the propeller multiphase and multi-field numerical calculation method, and limit p N 、p M ∈[0.5, 2]. Eliminate the influence of numerical instability in the total error calculation on the total error calculation result.
[0073] Substitute the corrected numerical error order and model error order into the established five-equation method error expression to obtain the simplified three-equation method error expression:
[0074]
[0075] Among them, the initial guess is recommended to be selected as [K Texact c N c M = [K T1 1 1], [u exact / U0 c N c M =[u1 / U0 11]. Solve the numerical error and model error of the target quantity of the propeller multiphase multi-field calculation results again, so as to improve the calculation efficiency and rationality of the numerical error and model error of the propeller multiphase multi-field target quantity. To ensure a total error with good credibility, it is necessary to normalize the variables.
[0076] In step 5, based on the numerical error and model error of the target quantity of the propeller multiphase multi-field calculation results in step 4, calculate the simulation uncertainty of the target quantity of the propeller multiphase multi-field calculation results based on the safety factor method:
[0077] U num =FS num |δ tot | (9)
[0078] where U num is the simulation uncertainty of the multiphase multi-field flow, FS num is the safety factor, and taking values of 1.5 or 3 can meet a relatively high confidence level. Due to its complexity, the propeller multiphase multi-field takes a value of 3. According to the set safety factor, increase the robustness of the total error of the target quantity of the propeller multiphase multi-field calculation results.
[0079] In step 6, calculate the comparison error between the propeller multiphase multi-field calculation results of the densest grid in step 2 and the test results, calculate the confirmation uncertainty of the target quantity based on the simulation uncertainty and test uncertainty of the target quantity of the propeller multiphase multi-field calculation results, and realize the quantitative evaluation of the propeller multiphase multi-field error according to the confirmation uncertainty of the target quantity:
[0080]
[0081] E = δ exp -δ tot =(y exp -y exact )-(y num -y exact ) = y exp -y num (11)
[0082] where U V is the confirmation uncertainty, U exp is the test result uncertainty, E is the comparison error, δ exp is the error between the test value of the target quantity and the exact solution, and y exp is the test value of the target quantity. The calculation results are as Figure 4 , and it can be seen that |E KT | < U VKT , |E KQ | < U VKQ, implementation confirmation is achieved, and it is determined that the predicted results of the propeller's multiphase and multi-field meet the credibility requirements, improving the prediction performance of the propeller in multiphase and multi-field. Due to the numerical calculation characteristics of multiphase and multi-field flows, the established uncertainty assessment strategy is indirectly carried out by comprehensively considering the test results.
[0083] The specific descriptions mentioned above further elaborate on the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.
Claims
1. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: It includes the following steps: Step 1: Taking the propeller multiphase and multi-field flow as the evaluation object, based on verification and validation, using the generalized Richardson extrapolation method to characterize the total error between the exact solution and the numerical solution of the propeller multiphase and multi-field target quantity, establishing a five-equation error expression for the binary Taylor series expansion of the total error, and decomposing the total error of the propeller multiphase and multi-field into the numerical error and the model error of the propeller multiphase and multi-field through the five-equation error expression, so as to improve the calculation accuracy of the total error; The model error of the propeller multiphase and multi-field includes the errors generated by two models, namely the implicit large eddy turbulence model and the cavitation model; The target quantity includes the propeller multiphase and multi-field velocity, pressure, thrust, torque, and turbulent kinetic energy; Step 2: According to the five-equation error expression constructed in Step 1, set five groups of systematically encrypted Cartesian grids and time dimensions for the propeller multiphase and multi-field calculation domain, and keep the boundary conditions of the five groups of propeller multiphase and multi-field calculation domains the same. Based on the implicit large eddy model and the cavitation model, numerically solve the flow characteristics of the propeller multiphase and multi-field to obtain the calculation results of the propeller multiphase and multi-field; The boundary conditions include the incoming flow velocity, the outlet pressure, and the wall conditions; Step 3: According to the calculation results of the propeller multiphase and multi-field obtained in Step 2, calculate the convergence rates of the calculation results of the propeller multiphase and multi-field for every three adjacent Cartesian grids and time dimensions respectively, and evaluate the convergence type of the target quantity of the calculation results in Step 2 according to the convergence rates; According to the convergence of the target quantity of the propeller multiphase and multi-field calculation results obtained in Step 2 with respect to the time step, determine whether the error is less than the preset threshold, and ensure that the flow field reaches stability by making the error less than the preset threshold; Calculate the numerical error, model error, numerical error order, and model error order of the propeller multiphase and multi-field target quantity according to the five-equation error expression established in Step 1; The unknowns of the numerical error term include the numerical error coefficient and the numerical error order, and the model error term includes the model error coefficient and the model error order; Step 4: Determine whether the numerical error order and the model error order obtained in Step 3 meet the set range. The numerical error order and the model error order that do not meet the set range are corrected according to the set range to make the numerical error order and the model error order meet the accuracy order requirements of the propeller multiphase and multi-field numerical calculation method, and eliminate the influence of numerical instability in the total error calculation on the total error calculation result; Substitute the corrected numerical error order and model error order into the established five-equation error expression to obtain a simplified three-equation error expression, and solve the numerical error and model error of the propeller multiphase and multi-field calculation result target quantity again, thereby improving the calculation efficiency and accuracy of the numerical error and model error of the propeller multiphase and multi-field target quantity; Step 5: Based on the numerical error and model error of the propeller multiphase and multi-field calculation result target quantity in Step 4, calculate the simulation uncertainty of the propeller multiphase and multi-field calculation result target quantity based on the safety factor method, and increase the robustness of the total error of the propeller multiphase and multi-field calculation result target quantity according to the set safety factor; Step 6: Calculate the comparison error between the propeller multiphase multi-field calculation results of the densest grid in Step 2 and the test results. Based on the simulation uncertainty and test uncertainty of the target quantity in the propeller multiphase multi-field calculation results, calculate the confirmation uncertainty of the target quantity. Realize the quantitative evaluation of the propeller multiphase multi-field error according to the confirmation uncertainty of the target quantity.
2. The method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation according to claim 1, wherein: It further includes Step 7: According to the confirmation uncertainty of the target quantity obtained in Step 6, judge whether the comparison error is less than the confirmation uncertainty range. If it is less than the confirmation uncertainty range, it is determined that the propeller multiphase multi-field calculation results are confirmed. Furthermore, it is determined that the predicted results of the propeller multiphase multi-field that are confirmed meet the credibility requirements, can optimize the error evaluation method, and improve the working performance of the propeller in the multiphase multi-field.
3. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: In the above Step 1, taking the propeller multiphase multi-field flow as the evaluation object, based on verification and confirmation, the generalized Richardson extrapolation method is used to characterize the total error between the exact solution and the numerical solution of the propeller multiphase multi-field target quantity. The total error is expressed as: y num -y exact = δ tot (1) Among them, y num is the numerical solution of the numerical calculation target quantity, and y exact is the exact solution of the target quantity. δ tot is the total error between the numerical solution and the exact solution of the target quantity. An error expression of the five-equation method based on the total error expanded by the binary Taylor series is established. Through the error expression of the five-equation method, the total error of the multiphase and multi-field of the propeller is decomposed into the numerical error δ num of the multiphase and multi-field of the propeller and the model error δ mo of the multiphase and multi-field of the propeller, improving the calculation accuracy of the total error: where Δt is the time step, Δh is the grid spacing of the Cartesian grid. Based on implicit large-eddy simulation, the numerical dissipation term generated by the numerical format is used to replace the eddy-viscosity sub-grid scale model. Δ is the filtering size, i.e., Δ = Δh. The model error caused by the cavitation model is related to the radius R of the cavitation cluster. The size of the cavitation can be characterized by the grid spacing, i.e., R = nΔh. To improve the computational efficiency, the turbulence model error and the cavitation model error are considered together. The resulting error is covered by the final uncertainty; c N and c M is the numerical and model error coefficient, p N and p M is the numerical and model error order; the propeller multiphase multi-field model error includes the errors caused by two models, namely the implicit large-eddy turbulence model and the cavitation model; The error expression of the five-equation method obtained is as follows: Among them, y num1～5 are respectively the numerical solutions of the target quantities of five groups of systematically encrypted Cartesian grids, and Δt 1～5 are respectively the time step sizes of five groups of systematic encryption, and Δh 1～5 are respectively the grid spacings of five groups of systematically encrypted Cartesian grids, and Δ 1～5 are respectively the filtering sizes of five groups of systematically encrypted Cartesian grids.
4. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: In the above Step 2, according to the five-equation method error expression constructed in Step 1, five groups of systematically encrypted Cartesian grids and time dimensions are set for the propeller multiphase multi-field calculation domain. For simplifying the equation solving, the specific settings are as follows: where r h and r t are the refinement ratios of the grid and the time dimension respectively; and the boundary conditions of the five groups of propeller multiphase multi-field calculation domains are all set the same. Based on the implicit large eddy model and the cavitation model, the numerical solution is used to obtain the multiphase multi-field flow characteristics of the propeller, and the multiphase multi-field calculation results of the propeller are obtained.
5. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: In the above Step 3, according to the propeller multiphase multi-field calculation results solved in Step 2, calculate the convergence rate of the propeller multiphase multi-field calculation results set for every three adjacent Cartesian grids and time dimensions respectively. Evaluate the convergence type of the numerical simulation target quantity in Step 2 according to Equation (6), and the definition is as follows: Where R is the convergence rate, which can be divided into: monotonic convergence (0 < R < 1), oscillatory convergence (-1 < R < 0), monotonic divergence (1 < R), oscillatory divergence (R < -1). The numerical simulation of the target quantity needs to meet the convergence condition. According to the convergence situation of the propeller multiphase multi-field calculation result target quantity with time steps solved in Step 2, judge whether the error is less than the preset threshold. Ensure that the flow field reaches stability by making the error less than the preset threshold, evaluate the development stability of the propeller unsteady multiphase multi-field flow, and observe whether the flow has the characteristics of periodic evolution law. Further construct a set of non-linear function relationships Equation (7) according to the five-equation method error expression established in Step 1, and calculate the numerical error, model error, numerical error order, and model error order of the propeller multiphase multi-field target quantity: Among them, solving the system of nonlinear function relations in Equation (7) follows the following principles: ① The nonlinear function relations are sensitive to the initial values, and the initial guess is selected as [y exact c N c M p N p M = [y num1 1 1 1 1]; ② The system of nonlinear equations may have multiple solutions, and unreasonable solutions are deleted according to the physical background; ③ The target quantity, exact solution, grid scale, and time dimension of the calculation results are normalized to make the orders of magnitude of the parameters consistent.
6. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: In the said step 4, it is determined whether the numerical error order and the model error order obtained in step 3 satisfy the set range. The numerical error order and the model error order that do not satisfy the set range are corrected according to the set range, so that the numerical error order and the model error order meet the accuracy order requirements of the numerical calculation method for multiphase and multi-field of the propeller, and p N and p M ∈[0.5, 2]; Eliminate the influence of numerical instability in the total error calculation on the total error calculation result; Substitute the corrected numerical error order and model error order into the established five-equation method error expression to obtain a simplified three-equation method error expression: Among them, the initial guess suggests choosing [y exact c N c M = [y num1 1 1], and solve the numerical error and model error of the target quantity of the propeller multiphase multi-field calculation results again, so as to improve the calculation efficiency and rationality of the numerical error and model error of the propeller multiphase multi-field target quantity. To ensure a total error with good credibility, it is necessary to normalize the variables.
7. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: In the above Step 5, based on the numerical error and model error of the propeller multiphase multi-field calculation result target quantity in Step 4, calculate the simulation uncertainty of the propeller multiphase multi-field calculation result target quantity based on the safety factor method: U num = FS num |δ tot | (9) Among which U num is the uncertainty of multiphase and multi-field flow simulation, and FS num is the safety factor, and the robustness of the total error of the target quantity of the propeller multiphase and multi-field calculation results is increased according to the set safety factor.
8. A method for quantitatively evaluating the multi-phase and multi-field errors of a propeller based on verification and validation, characterized in that: In the above Step 6, calculate the comparison error between the propeller multiphase multi-field calculation results of the densest grid in Step 2 and the test results. Based on the simulation uncertainty and test uncertainty of the propeller multiphase multi-field calculation result target quantity, calculate the confirmation uncertainty of the target quantity. Realize the quantitative evaluation of the propeller multiphase multi-field error according to the confirmation uncertainty of the target quantity: E = δ exp -δ tot = (y exp - y exact ) - (y num - y exact ) = y exp - y num (11) Among them, U V is the uncertainty confirmation, U exp is the uncertainty of the test result, E is the comparison error, and δ exp is the error between the test value of the target quantity and the exact solution, and y exp is the test value of the target quantity.