A micro centrifugal pump blade setting angle correction method based on reynolds number sensitivity analysis

Abstract

The present application relates to the technical field of non-variable displacement pump design, and discloses a micro centrifugal pump blade setting angle correction method based on Reynolds number sensitivity analysis, which comprises the following steps: firstly, constructing a reference parameterized geometric model and a calculation domain; secondly, based on the dynamic similarity principle, constructing an equivalent Reynolds number working condition library by adjusting the fluid dynamic viscosity, performing CFD numerical simulation and extracting a velocity vector; then, calculating an actual fluid outflow angle, constructing a Reynolds number sensitivity function and a slip amplification coefficient; finally, deriving a target theoretical outflow angle based on a target lift, combining a prediction model to perform reverse amplification compensation on the blade setting angle, and automatically reconstructing a corrected impeller entity model. The present application quantifies the nonlinear slip rule under micro scale, ensures that the micro impeller can still output the expected theoretical lift under extremely small space and extremely low Reynolds number, realizes lift standard without repeatedly manufacturing physical prototypes, and greatly reduces trial and error costs.

Description

Technical Field

[0001] This invention belongs to the field of non-variable displacement pump design technology, specifically relating to a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis. Background Technology

[0002] As a core power source for aerospace fuel delivery, micro-propulsion systems, and biomedical auxiliary circulation devices, micro-centrifugal pumps typically require efficient hydraulic transport within extremely small spaces and at extremely high speeds. Currently, the hydraulic design of such micro-pumps largely relies on one-dimensional beam theory based on Euler's equations and the traditional empirical formula for the Stodola slip coefficient. These classic theoretical models are based on the assumptions of "ideal fluid" or "high Reynolds number turbulence," and offer high accuracy in the design of conventional-sized industrial pumps. However, when these theories are applied to micro-impellers with tiny outer diameters, the flow within the pump is often confined to a low Reynolds number range due to their small geometric scale. In this case, viscous forces dominate momentum transfer, replacing inertial forces, leading to a significant increase in the relative thickness of the boundary layer on the blade surface and generating a strong viscous drag effect. This prevents the fluid from flowing closely along the blade ribs as it would on a macroscopic scale, instead resulting in severe outlet slip far exceeding the predictions of traditional empirical formulas. This significant size effect and theoretical deviation often necessitates that R&D personnel rely on costly physical prototypes for repeated trial production and mold modification in actual engineering, or can only make rough estimates of the blade placement angle based on vague engineering experience. Therefore, establishing a systematic design method that can analyze this pattern and perform reverse geometric correction has become an urgent technical challenge.

[0003] Therefore, it is urgent to improve the existing hydraulic design method for micro centrifugal pump impellers and establish a parameterized correction method that considers the microscale viscosity effect. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis, so as to quantify the viscous slip law at the microscale with low computational cost, and to eliminate the slip influence from the design end, thereby realizing the blade placement angle correction design.

[0005] To address the aforementioned technical problems, this invention provides a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis, the specific process of which is as follows:

[0006] S1. Construct a baseline parametric geometric model of the impeller of a micro centrifugal pump;

[0007] S2. Based on the principle of dynamic similarity in fluid dynamics, while keeping the impeller geometry, rotational speed and mesh topology unchanged, an equivalent Reynolds number working condition library is constructed by adjusting the dynamic viscosity of the fluid medium.

[0008] S3. Extract the Reynolds number, radial velocity, and relative tangential velocity at the impeller outlet from each set of working conditions in the equivalent Reynolds number working condition library through computational fluid dynamics numerical simulation, and construct a discrete working condition dataset;

[0009] S4. Based on the discrete operating condition dataset, calculate the actual fluid outlet angle and viscous slip correction under each equivalent Reynolds number condition, fit the Reynolds number sensitivity function, and determine the slip amplification factor based on the rated operating condition. ;

[0010] S5. Based on the Reynolds number sensitivity function and slip amplification factor, perform predictive-correction geometric inverse compensation on the benchmark parameterized geometric model to obtain the blade exit correction placement angle. Then, the corrected baseline parametric geometric model is reconstructed and obtained.

[0011] S6. Perform numerical verification on the corrected baseline parameterized geometric model and conduct a post-evaluation of the prediction accuracy of the slip amplification factor.

[0012] As an improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis is as follows:

[0013] The construction of the baseline parametric geometric model includes:

[0014] (1) Obtain the specific speed of the micro centrifugal pump based on the set rated operating conditions, and set the blade outlet placement angle. and blade inlet placement angle ;

[0015] (2) The meridional flow profile of the wheel hub and wheel cover is constructed using fourth-order Bézier curves;

[0016] (3) Establish a system including the blade outlet placement angle Leaf wrap angle and blade thickness Design variable set And design the engineering constraints of the variable set. .

[0017] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0018] The equivalent Reynolds number operating condition library includes at least: the strong viscosity-dominant region operating condition, the transition sensitive region operating condition, the rated operating condition, and the inertia-dominant region operating condition. The dynamic viscosity of the fluid medium selected for each operating condition is based on the logarithmic gradient distribution principle.

[0019] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0020] The discrete operating condition dataset includes the Reynolds number, radial velocity, and relative tangential velocity at the impeller outlet. The construction process includes:

[0021] (1) Obtain three-dimensional microscopic flow field data through computational fluid dynamics numerical simulation;

[0022] (2) Based on the three-dimensional micro-flow field data, a monitoring surface is established at the impeller outlet diameter. The velocity field on the monitoring surface is integrated using a mass-weighted average algorithm that conforms to the law of mass conservation to obtain the velocity vector under each equivalent Reynolds number condition, including radial velocity and relative tangential velocity.

[0023] (3) Calculate the Reynolds number under each equivalent Reynolds number condition, establish a mapping relationship with the velocity vector, and construct a discrete condition dataset.

[0024] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0025] The formula for calculating the actual fluid outflow angle is:

[0026]

[0027] in, This represents the actual fluid outflow angle under the i-th equivalent Reynolds number condition. Represents the radial velocity under the i-th equivalent Reynolds number condition. Represents the relative tangential velocity under the i-th group of equivalent Reynolds number conditions;

[0028] The formula for calculating the viscous slip correction is as follows:

[0029] =

[0030] in, This represents the viscous slip correction amount under the i-th group of equivalent Reynolds number conditions. The angle at which the blade exits.

[0031] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0032] The Reynolds number sensitivity function is:

[0033]

[0034] in, The parameters to be fitted are... Represents the Reynolds number under the i-th equivalent Reynolds number condition;

[0035] The objective function of the Reynolds number sensitivity function is:

[0036]

[0037] Then, the fitting parameters are obtained by solving the objective function using a numerical iterative optimization algorithm. The value of .

[0038] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0039] The slip amplification factor The calculation method is as follows:

[0040]

[0041]

[0042] in, The actual fluid outflow angle under rated operating conditions. This is an empirical correction factor.

[0043] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0044] The specific process of prediction-correction geometric inverse compensation is as follows:

[0045] (1) Calculate the target theoretical outflow angle

[0046] Based on the three-dimensional micro-flow field data under rated operating conditions, the mass-weighted average of the outlet absolute tangential velocity under rated operating conditions is extracted. The reference theoretical head was calculated using the Euler equation. Thus, the target hydraulic efficiency is obtained. :

[0047]

[0048]

[0049] in, This is the efficiency reduction factor under high load. It is the acceleration due to gravity. The circumferential velocity at the impeller outlet. The actual head obtained through computational fluid dynamics numerical simulation under rated operating conditions;

[0050] Target hydraulic efficiency Substituting into the head formula, we can deduce the method to meet the rated head requirement. Required target theoretical head and the corresponding target absolute tangential velocity Then, by combining the velocity triangle formula, the target theoretical outlet angle that meets the rated head requirement can be derived. :

[0051]

[0052] in,

[0053] (2) Calculate the corrected placement angle of the blade exit

[0054]

[0055] in, The predicted slip is obtained by substituting the Reynolds number under rated operating conditions into the Reynolds number sensitivity function;

[0056] (3) Adjust the blade outlet placement angle As a new global design variable input design variable set Keeping the blade inlet angle and meridional flow profile unchanged, the curvature control degree of the blade skeleton is released, and the meridional flow profile of the hub and wheel cover is constructed using fourth-order Bezier curves, thereby obtaining the modified reference parameterized geometric model.

[0057] Check the updated blade wrap angle and blade thickness Is it within the scope of engineering constraints? Internally, a revised baseline parametric geometric model is generated based on the updated blade rib line data.

[0058] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0059] The engineering constraints Including: blade wrap angle Leaf thickness .

[0060] As a further improvement to the present invention, a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis:

[0061] Numerical verification of the modified reference parameterized geometric model includes: calculating the head of the modified reference parameterized geometric model at the rated flow point. With rated head The relative error E should be controlled within the allowable range of the project. ≥ ;

[0062] Post-evaluation of the prediction accuracy of the slip amplification factor includes: calculating the actual corrected slip amount of the modified baseline parameterized geometry. Compared to the viscous slip correction under rated operating conditions The increase is consistent with the slip amplification factor.

[0063] The beneficial effects of this invention are mainly reflected in:

[0064] This invention innovatively proposes a Reynolds number sensitivity analysis strategy based on "virtual variable parameter simulation." Unlike traditional approaches that require manufacturing physical prototypes of different sizes for experiments, this invention simulates flow states at different Reynolds numbers by adjusting the dynamic viscosity of the fluid medium, constructing a dimensionless function relationship between "slip correction and Reynolds number." This fundamentally reveals the physical nature of the size effect in micropumps, making the correction formula universally applicable.

[0065] This invention significantly reduces the trial-and-error costs of micropump development. It utilizes Computational Fluid Dynamics (CFD) to extract the mass-weighted average velocity vector at the impeller outlet section, accurately calculating the actual fluid correction outlet angle, replacing fuzzy empirical coefficients. Simultaneously, it introduces "angle transfer efficiency" and "slip amplification factor" to quantify the nonlinear response of the microscale flow channel to increased geometric angles, completely replacing traditional fuzzy empirical coefficients.

[0066] This invention, based on an established predictive model, directly pre-corrects the blade placement angle during the geometric modeling stage using a reverse compensation algorithm, and reconstructs the blade rib line using parametric software. This closed-loop design method ensures that the micro impeller can still output the expected theoretical head under extremely small space and extremely low Reynolds number conditions, effectively avoiding the need for repeated trial production and mold modification iterations of high-cost physical prototypes. Attached Figure Description

[0067] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0068] Figure 1 This is a flowchart of a method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to the present invention;

[0069] Figure 2This is an example diagram of the impeller solid model design; Figure 2 middle: (a) is a view of the meridional flow channel profile; (b) is a graph showing the distribution of the blade placement angle with the length of the meridional streamline.

[0070] Figure 3 This is a schematic diagram illustrating the construction of the equivalent Reynolds number working condition library based on the principle of dynamic similarity of the present invention;

[0071] Figure 4 This is a fitting curve of the Reynolds number sensitivity function of the present invention;

[0072] Figure 5 This is a schematic diagram of the blade placement angle compensation of the present invention;

[0073] Figure 6 This is a comparison chart of simulation results of head and efficiency of the baseline parameterized geometric model before and after the modification of this invention. Detailed Implementation

[0074] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto:

[0075] Example 1: A method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis, such as... Figure 1 As shown, the specific steps include:

[0076] Step 1: Construct the baseline parametric geometric model and fluid computation domain of the micro centrifugal pump impeller.

[0077] This step aims to establish a baseline parametric geometric model (referred to as the impeller solid model) of a microcentrifugal pump impeller with controllable geometric features and a high-quality mesh topology as a basis for numerical calculations. Because the internal flow of the micropump is extremely sensitive to geometric micro-deformations, traditional fixed-point coordinate modeling cannot be used; instead, a fully parameter-driven geometric model must be constructed. This allows for subsequent reverse compensation by directly mapping back to the 3D impeller solid model through parameter modifications without disrupting the mesh topology. In this embodiment, the rated operating conditions of the microcentrifugal pump are set as follows: rated flow rate... Rated head Rated speed Then, based on the rated operating conditions, the main hydraulic dimensions of the impeller are determined, including the impeller outlet diameter. The outlet width b2 = 2mm, the number of blades (Long blade structure), with a rear cover plate inlet diameter of 6mm. Based on this, the impeller solid model is constructed through the following step-by-step process.

[0078] Step 1.1: Setting Initial Hydraulic Parameters

[0079] Based on one-dimensional beam theory and the empirical formula for the Stodola slip coefficient, the initial morphological parameters of the blade ribs are determined. Then, according to the specific speed formula:

[0080] (1)

[0081] The specific speed of the micro centrifugal pump is obtained based on the rated operating conditions of the micro centrifugal pump. =53, confirming it falls into the category of low specific speed micro pumps. Set the blade outlet angle. The value of is usually selected based on traditional empirical formulas, such as This serves as the initial reference for subsequent corrections. The blade inlet installation angle is set as... To accommodate the inlet pre-spin and the angle of attack of the incoming flow.

[0082] Step 1.2: Parametric Modeling of Impeller Meridional Flow Channel and Blade Bone Line Based on CFturbo

[0083] To achieve precise control of the impeller geometry and rapid reconstruction during subsequent corrections, this embodiment employs a professional turbine mechanical parametric design platform (such as CFturbo software) to construct a three-dimensional solid model of the impeller. This process is implemented through the following parametric logic:

[0084] Because of the extremely small size of micropumps, to prevent abrupt changes in the flow channel area, the meridional flow channel profile view in the software is shown as follows: Figure 2 As shown in (a), this invention abandons the traditional single-circle fitting and uses fourth-order Bézier curves to construct the meridional flow channel profiles of the hub and shroud respectively. For the narrow flow channel characteristic with an outlet width b2 = 2mm in this embodiment, the control point ( The weights of ), where ( ) indicates the first line of the meridian plane. The radial and axial coordinates of each control point are used to ensure that the area change from the inlet to the outlet follows a linear and gradual trend, avoiding local eddies caused by sudden expansion of the flow channel due to microscale effects, and precisely controlling the rate of change of the flow channel cross-sectional area along the axial streamline.

[0085] Conformal mapping is used to map the three-dimensional flow surface onto a two-dimensional (u, m) plane to generate the blade rib lines. The blade placement angle is defined in the parameterization settings. Blade rib distribution function along normalized meridional streamline length m ,like Figure 2 As shown in (b) of the diagram. Based on the boundary conditions determined in step 1.1, the blade inlet placement angle is locked. Angle of blade exit As a fixed endpoint, the inlet and outlet are connected using polynomial curves or spline curves to control the twisting pattern of the middle part of the blade.

[0086] To facilitate subsequent Reynolds number sensitivity correction, a design variable vector set is established. ,in, It is the blade wrap angle, which is the central angle covered by the blade extending from the inlet edge to the outlet edge; This refers to blade thickness, typically indicating the solid thickness distribution along the blade's rib line normal. Blade exit angle. It is set as a globally variable parameter. Once the slip correction is calculated in subsequent steps, this variable value only needs to be updated in the software. The system can then automatically regenerate a smooth solid model based on parametric logic, without needing to redraw the sketch, thus ensuring the consistency of the mesh topology. (Blade wrap angle) The blade thickness t is not an actively solved variable, but a passively generated auxiliary constraint variable. Its main function is to provide a clear engineering constraint range for reconstructing the curve in the subsequent step 5.2, so as to perform physical legality and interference verification of the solid model.

[0087] To ensure that the impeller solid model generated subsequently based on Reynolds number correction is physically manufacturable and hydraulically optimal, this invention, when constructing the impeller solid model, specifically sets clear engineering constraints for the auxiliary geometric variables in the design variable vector set X, particularly for high-speed micro-impeller design scenarios. Strict upper and lower limits were set for blade thickness and blade wrap angle to ensure that it meets structural strength requirements while preventing flow channel blockage and guaranteeing stable operation. Engineering constraints. The specific upper and lower limits and their physical basis are as follows:

[0088] Regarding the impeller outlet diameter in this embodiment In miniature centrifugal pumps, the blade wrap angle determines the effective length of the flow channel. According to the slip coefficient theory, an excessively small wrap angle leads to insufficient blade grid angle, exacerbating fluid detachment from the suction surface of the blades and resulting in severe secondary flow losses. Therefore, a minimum working length must be ensured, with a lower limit set at [insert lower limit here]. .

[0089] In this embodiment, the impeller outlet width b2 is only 2mm, resulting in an extremely narrow flow channel. If the blade thickness exceeds 1.5mm, it will lead to an excessively high outlet rejection coefficient, causing a strong jet-wake structure and disrupting flow field stability. Considering the centrifugal tensile load at a high speed of 8000 r / min and the mold filling limit of the micro-injection molding process, a minimum solid wall thickness of 0.5mm must be maintained to prevent structural breakage or molding defects.

[0090] Step 1.3: Construction of the fluid computational domain and refinement of the boundary layer mesh

[0091] Based on the aforementioned impeller solid model, the fluid computational domain is extracted and subjected to high-precision spatial discretization. To simulate a realistic pumping environment, the flow field computational domain consists of three parts: a length of 5 times the inlet diameter... It includes an inlet extension section (used to ensure sufficient development of the inlet flow), a rotating domain containing the impeller flow channel, and a stationary domain containing the volute and outlet pipe.

[0092] Considering that the core of this invention lies in capturing the "viscous slip" characteristic at low Reynolds numbers, and the outlet flow channel width is only 2mm, the mesh generation strategy must focus on analyzing the near-wall boundary layer. A structured hexahedral mesh is used to discretize the entire domain, and boundary layer refinement is applied to the suction and pressure surfaces of the blades. The height y of the first mesh layer is strictly controlled to ensure dimensionless wall distance. To meet SST k- The turbulence model requires analytical precision for the viscous sublayer to accurately capture the shear stress and separation flow between the fluid and the wall at a microscale. The mesh is generated using the minimum dynamic viscosity (i.e., the highest Reynolds number; in this embodiment, the minimum dynamic viscosity is set to...). The first layer of mesh height is controlled based on the working condition to ensure dimensionless wall distances under all virtual working conditions. All meet the requirements of the turbulence model.

[0093] This completes the spatial discretization of the entire computational domain, outputting a mesh model of the fluid domain for the microcentrifugal pump. The model specifically comprises three mesh sections: one with a length of 5 times the inlet diameter. The grid consists of the inlet extension section, the rotating domain grid containing the impeller flow channel, and the stationary domain grid containing the volute and the outlet pipe.

[0094] Step 2: Based on the principle of dynamic similarity in fluid mechanics, construct an equivalent Reynolds number case library.

[0095] This step aims to establish a numerical experimental scheme capable of quantitatively analyzing the viscous slip behavior at the microscale. Since the flow state within a micropump is primarily controlled by the dimensionless Reynolds number (Re), traditional physical parameter variation methods (i.e., changing the impeller diameter) are insufficient. Changing the Reynolds number (Re) not only requires rebuilding the geometric model and meshing, but also introduces discretization errors due to inconsistencies in the mesh topology, causing weak viscous effects to be masked by numerical errors. To address this, this invention introduces the classic principle of hydrodynamic dynamic similarity and constructs a "virtual parameter variation" strategy for extracting the slip characteristics of micropumps. This strategy maintains the impeller geometry, rotational speed, and mesh topology unchanged, and constructs an equivalent Reynolds number operating condition library by adjusting only the dynamic viscosity properties of the fluid medium. This library includes a series of virtual operating conditions that are dynamically equivalent to micropumps of different sizes, thereby achieving a full-spectrum scan of slip characteristics across a wide Reynolds number range with minimal computational cost. The process is as follows: Figure 3 As shown. The specific implementation process is as follows:

[0096] Step 2.1: Basis for constructing the equivalent Reynolds number simulation model and definition of the governing equations

[0097] The core basis of this strategy is derived from the Reynolds-averaged Navier-Stokes (RANS) equations in fluid mechanics and their dimensionless derivation. To accurately capture viscous slip at the microscale in numerical calculations, the fluid control equations defined in this invention include a continuity equation and a momentum conservation equation. The continuity equation in tensor form in Cartesian coordinates is as follows:

[0098] (2)

[0099] The momentum conservation equation is:

[0100] (3)

[0101] in, For fluid density, and All are velocity components. For pressure, For dynamic viscosity, This is the Reynolds stress term. and τ represents the spatial coordinate components in the Cartesian coordinate system; i and j in this formula are tensor indices of spatial directions, usually taking values ​​of 1, 2, and 3, corresponding to the x, y, and z coordinate axes in three-dimensional space, respectively; τ represents time.

[0102] According to the dynamic similarity theory of fluid mechanics, after the above equations are dimensionless, the solution depends only on the dimensionless characteristic number—the Reynolds number (Re):

[0103] (4)

[0104] in, This indicates the angular velocity of the impeller.

[0105] From this, we can derive the core equivalent substitution logic of this invention: In an incompressible rotating flow field, if the impeller outlet diameter is kept constant... and rotational angular velocity The viscosity remains unchanged, only the dynamic viscosity of the fluid medium is changed. Its influence on the dynamic characteristics of the flow field and changes in geometric scale They are completely equivalent (i.e.) and This means that the fluid viscosity is artificially amplified in the CFD solver. In physics and mathematics, this is strictly equivalent to reducing the characteristic size of the pump by a factor of 100. The viscous effect generated by the viscous force. Based on this theoretical support, this invention constructs a virtual fluid with geometrically identical properties but different dynamic characteristics to the actual hydraulic model by customizing material properties during CFD preprocessing. This allows for the precise isolation of the independent influence of viscous force on the outlet slip angle within a single mesh system, eliminating numerical noise interference caused by mesh distortion and reconstruction, and ensuring the purity and physical reality of the slip correction law.

[0106] Step 2.2: Establishment of an equivalent Reynolds number working condition library covering the viscosity-sensitive region.

[0107] To construct a high-precision correction function, the selected operating points must cover the nonlinear variation range of the micropump flow from the laminar / turbulent transition zone to the fully turbulent zone. Based on boundary layer theory, the friction coefficient of the micropump blade surface... It exhibits a nonlinear exponential decay with respect to Reynolds number, especially in Within this range, the flow is extremely sensitive to changes in viscosity. Therefore, based on the principle of logarithmic gradient distribution, this embodiment selects four sets of virtual medium viscosities with clear physical characteristics to construct a gradient-based equivalent Reynolds number case library:

[0108] Operating Condition Set-1 (Strong Viscosity Dominant Region): Set the dynamic viscosity This viscosity is five times that of standard water, corresponding to an equivalent Reynolds number of approximately one-fifth of the rated operating condition. This value was chosen to simulate flow conditions in extremely small sizes (or low-temperature, high-viscosity media), where the viscous sublayer is extremely thick, aiming to capture the data boundaries where slippage is most severe.

[0109] Operating Condition Set-2 (Transition Sensitive Zone): Set the dynamic viscosity This point is located in the middle region between the rated operating condition and the extreme operating condition. It is used to capture the nonlinear inflection point of the slip change with the Reynolds number and prevent underfitting of the fitted curve.

[0110] Operating Condition Set-3 (Rated Operating Condition, Reference Calibration Area): Sets the dynamic viscosity. (i.e., 20℃ standard water). This is the actual rated operating point of the micropump, used to calibrate the zero-point deviation of the correction function and ensure prediction accuracy under normal operating conditions.

[0111] Operating Condition Set-4 (Inertia-Dominated Region): Set dynamic viscosity This operating condition simulates high Reynolds number flow, aiming to verify whether the calculation results of this invention can asymptotically converge to the theoretical solution of the traditional Euler equation when the viscous effect weakens, thereby verifying the physical correctness of the modified model. Through these four sets of gradient settings, this invention successfully constructed a database covering the flow states that a micropump may encounter throughout its entire life cycle, providing solid data support for subsequent fitting of high-confidence modified functions.

[0112] Step 3: Perform multi-condition CFD numerical simulation and extract velocity vectors to construct a discrete condition dataset.

[0113] This step aims to utilize computational fluid dynamics (CFD) methods to perform high-fidelity numerical solutions on the gradient-based equivalent Reynolds number case library constructed in Step 2, and to extract key physical quantities characterizing slip properties from the complex flow field. Unlike Step 1, which focuses on geometric discretization, this step emphasizes the solution strategy for the physical field and data post-processing. To ensure the rigorous comparability of calculation results under different viscosity conditions, a unified solver setting and convergence criterion must be adopted, and a data sampling mechanism conforming to the principles of fluid dynamics must be established to reduce the dimensionality of the three-dimensional flow field information into scalar data that can be used for mathematical fitting. The specific execution process is as follows:

[0114] Step 3.1: Numerical Solution Strategy and Boundary Condition Setting

[0115] The fluid domain mesh model of the microcentrifugal pump generated in step 1 was imported into a CFD solver (such as ANSYS Fluent) for CFD numerical simulation. For each set of working conditions in the equivalent Reynolds number case library defined in step 2, a completely consistent physical model setting was used to eliminate algorithm errors. Considering the low Reynolds number and significant rotating shear flow inside the micro-pump, the SST k-ω model, which has extremely high accuracy in capturing low Reynolds number flow near the wall and adverse pressure gradient, was selected as the turbulence model, and the low Reynolds number correction option was enabled. The kinematic parameters of the boundary conditions were strictly kept consistent with the rated working conditions of the microcentrifugal pump set in step 1: the inlet boundary was set as a velocity inlet with a given rated velocity V and a specified turbulence intensity of 5%; the outlet boundary was set as a natural outflow. The fluid domain motion reference system was set as a rotating coordinate system, and the rated rotational speed was kept constant at n = 8000 r / min. The solution algorithm adopted the pressure-velocity coupled SIMPLEC algorithm. The momentum equation, turbulent kinetic energy equation, and dissipation rate equation were all discretized using a second-order upwind scheme to ensure numerical accuracy. The convergence criterion is set as follows: all residual curves decrease to 10. -4The following conditions are met, and the error in the conservation of inlet and outlet flow rates is less than 0.1%, ensuring that the numerical solution converges to the physical true solution.

[0116] Through the above CFD numerical simulation process, each set of working conditions (set as working condition number i) in the equivalent Reynolds number working condition library is simulated and converged three-dimensional micro-flow field data is obtained by CFD numerical solution, which provides the basic physical field for the next step of statistical extraction.

[0117] Step 3.2: Statistical extraction and physical basis analysis of microscopic flow field characteristic data

[0118] Based on the converged three-dimensional microscopic flow field data obtained from the simulation in step 3.1, key flow field data capable of inverting the velocity triangle needs to be extracted in post-processing. At the impeller outlet diameter ( A cylindrical surface was established as the monitoring surface. To eliminate the interference of uneven grid node distribution and local backflow vortices on data representativeness at the microscale, the traditional arithmetic mean method was abandoned, and a mass-weighted average algorithm conforming to the law of mass conservation was adopted as the statistical extraction method. The velocity field on the monitoring surface was integrated to obtain the velocity vector, including the radial velocity under the i-th equivalent Reynolds number condition. and relative tangential velocity ,in, This indicates the operating condition number in the equivalent Reynolds number operating condition library (corresponding to operating condition Set-1 to operating condition Set-4 respectively).

[0119] radial velocity The relative tangential velocity directly determines the impeller's flow capacity (i.e., the displacement effect), reflecting the impact of boundary layer blockage on the effective flow area. It is the actual hysteresis velocity of the fluid following the blade's motion in a rotating reference frame, directly reflecting the strength of the slip effect.

[0120] By combining the two, the true outflow angle of the fluid at the outlet can be accurately reconstructed using inverse trigonometric functions. This method decouples the most essential kinematic characteristics from the complex three-dimensional flow field by inversely deriving the outflow coefficient from the critical flow function, providing underlying data support with clear physical meaning for the subsequent construction of correction functions.

[0121] Step 3.3 Extract discrete working condition dataset

[0122] For each set of virtual dynamic viscosity set in step 2 Calculate the Reynolds number corresponding to four equivalent Reynolds number conditions based on the Reynolds number formula. The Reynolds number under each operating condition. A corresponding mapping relationship is established with the extracted velocity vectors to construct a discrete working condition dataset covering the entire range from low Reynolds number (viscosity-dominated) to high Reynolds number (inertia-dominated) (including the Reynolds number at the impeller outlet under the i-th equivalent Reynolds number working condition). radial velocity and relative tangential velocity This dataset will serve as the numerical basis for analyzing the slip law and calibrating the amplification factor model in step 4.

[0123] Step 4: Physical quantification and construction of Reynolds number sensitivity function and slip amplification factor for actual fluid slip characteristics.

[0124] This step aims to extract continuous physical laws from discrete operating condition datasets. This invention innovatively introduces a full-spectrum fitting strategy to construct a universal mathematical model (Reynolds number sensitivity function) capable of describing the slip characteristics of the micropump at any Reynolds number, and determines the slip amplification factor by combining the angle transfer efficiency. The specific implementation process is as follows:

[0125] Step 4.1: Calculation of the actual fluid outflow angle and viscous slip correction based on velocity triangle inversion.

[0126] Based on Euler's turbine principle, the velocity triangle at the impeller outlet is composed of the circumferential velocity... Absolute speed The relative velocity W is composed of the fluid velocity and the relative velocity W. However, in micropumps, due to the strong viscous shear at low Reynolds numbers, the actual fluid's relative streamline angle is not equal to the blade outlet angle. To accurately quantify this physical difference, this step is based on the radial velocity extracted in step 3. and relative tangential velocity Inversion calculations are performed. This differs from traditional designs that directly use the blade exit angle. To perform one-dimensional estimation, this invention defines the actual fluid outflow angle. Let be the angle between the actual fluid particle and the impeller rotation direction, and be the actual fluid outlet angle under the i-th equivalent Reynolds number condition. The calculation formula is:

[0127] (5)

[0128] This allows us to calculate the actual fluid outlet angle under various equivalent Reynolds number conditions. Based on this, the blade exit angle is adjusted. Angle of actual fluid outflow The difference between them is used as the viscous slip correction amount under the i-th equivalent Reynolds number condition. ,Right now:

[0129] = (6)

[0130] This physical quantity profoundly reflects the combined effect of boundary layer blockage (increasing radial velocity) and viscous hysteresis (reducing relative tangential velocity) caused by the narrow flow channel in the micropump, and serves as the quantitative basis for subsequent geometric reverse compensation.

[0131] Step 4.2: Construct the Reynolds number sensitivity function

[0132] To eliminate single-point calculation errors and reveal physical laws, a nonlinear regression analysis method is used to construct a viscous slip correction quantity. The equivalent Reynolds number Re in the discrete working condition dataset i The functional relationship is shown. The Reynolds number sensitivity function takes the form of a power-law fitting function:

[0133] (7)

[0134] in, The parameters to be fitted are determined by nonlinear regression from discrete operating condition data. The constructed Reynolds number sensitivity function is used to characterize the response of the viscous slip correction to the Reynolds number within the target operating Reynolds number range, and serves as the basis for subsequent calculations of slip prediction and blade placement angle correction under the target operating condition.

[0135] Parameters to be fitted All were obtained through least squares nonlinear regression fitting, specifically: the actual fluid outflow angle under each equivalent Reynolds number condition in step 4.1 was obtained using the least squares method. and viscous slip correction amount The objective function for fitting and constructing the Reynolds number sensitivity function is to find a set of parameters. This minimizes the sum of squared residuals S between the theoretical prediction and the CFD simulation values.

[0136] The objective function is constructed as follows:

[0137] (8)

[0138] The above least squares objective function is optimized using numerical iterative optimization algorithms (such as the Gauss-Newton method). The equation is solved iteratively to make the objective function... The fitting parameters can be obtained by converging to the minimum value. .

[0139] Reynolds number sensitivity function The ability to accurately predict the basic slip level of the micropump at any target Reynolds number forms the predictive foundation of the correction strategy.

[0140] Step 4.3: Determine the slip amplification factor

[0141] The concept of angle transfer efficiency is introduced to quantify the response capability of microscale flow channels to changes in geometric angle. The angle transfer efficiency is calculated under rated operating conditions (or reference Reynolds number points, i.e., operating condition Set-3 (baseline calibration area) in the equivalent Reynolds number operating condition library). Slip amplification factor Defined as the reciprocal of angle transmission efficiency and incorporating an empirical correction factor. (Usually taken as 0.8-1.0):

[0142] (9)

[0143] (10)

[0144] in, The actual fluid outflow angle under rated operating conditions. This is an engineering correction factor used to correct the difference between the theoretical magnification and the actual magnification used in engineering. It mainly considers factors such as nonlinear slip magnification under large-angle correction conditions, additional diffusion loss, and the engineering rounding of the blade outlet placement angle.

[0145] Angular transmission efficiency This primarily reflects the ability of the geometric flow channel structure based on the reference parameterized geometric model of this invention to control the fluid flow direction (i.e., geometric angle conversion rate) under rated operating conditions. Because the flow channel space of the micropump is extremely small (e.g., the outlet width in this embodiment is only 2mm), the deflection of the fluid flow direction is mainly constrained by the rigid geometric boundaries. Therefore, the direct impact of Reynolds number variation on this conversion rate is greatly weakened. Meanwhile, considering that the ultimate engineering goal of this method is to ensure that the micropump meets performance standards under the actual rated design medium, although the angle transfer efficiency at different Reynolds numbers... There will be slight fluctuations, but in the reverse correction strategy, in order to accurately anchor the target operating point and avoid introducing excessive nonlinear iterative complexity during geometric reconstruction, it is treated as a characteristic constant to determine the slip amplification factor during correction. Slip amplification factor It represents the geometric angle multiplier required to obtain a unit effective flow angle increment in an inefficient flow channel.

[0146] Step 5: Prediction-correction geometric inverse compensation based on Reynolds number sensitivity function and slip amplification factor

[0147] This step is crucial in translating the mathematical principles established in Step 4 into concrete physical entity design. The design process shifts from microscopic flow field analysis to macroscopic geometric reconstruction. The core logic lies in sensitivity-based inverse compensation: not only must the basic slip of the fluid at the microscale be predicted, but also the nonlinear amplification effect of slip caused by the increase in geometric angles must be anticipated. By applying a lead angle corrected by an amplification factor in advance at the geometric design stage, the actual trajectory of the fluid after experiencing severe viscous hysteresis is forced to fall back precisely within the expected vector range that meets the rated head. The specific implementation process is as follows:

[0148] Step 5.1: Derivation and Correction Strategy of Target Parameters Based on Measured Data of the Benchmark Flow Field

[0149] First, determine the target design operating point of the micropump, namely, the rated flow rate, rated speed, and working medium viscosity under rated operating conditions. This is to eliminate the need for estimating hydraulic efficiency in traditional one-dimensional design. To address the head deviation caused by inaccurate calculations, this invention establishes a reverse logic based on Euler's equations and measured flow field data. The derivation and calculation process are as follows:

[0150] Based on Euler's turbine machinery equations, assuming no inlet pre-swirl of the fluid, the theoretical head is... Circumferential speed at the impeller outlet and the absolute tangential velocity at the exit The relationship is:

[0151] (11)

[0152] (12)

[0153] in, Let n be the acceleration due to gravity, and n be the rated speed of the impeller.

[0154] Considering the pump's hydraulic efficiency The rated head must meet the requirements. Combining the exit velocity triangle relationship, the absolute tangential velocity at the exit... It can be represented as:

[0155] (13)

[0156] in, For the target theoretical outflow angle, This indicates the radial velocity under rated operating conditions.

[0157] Unlike traditional methods that rely directly on experience and pre-set parameters, This step involves using computational fluid dynamics (CFD) numerical simulation to extract the three-dimensional microscopic flow field data of the benchmark parametric geometric model obtained in step 3.1 under rated operating conditions (condition Set-3) for precise calibration. The mass-weighted average of the absolute tangential velocity at the impeller outlet section of the benchmark model under rated operating conditions is then extracted. Substitute the values ​​into the Euler equation (Equation 12) above to calculate the reference theoretical head under rated operating conditions. The actual head obtained under rated operating conditions using computational fluid dynamics (CFD) numerical simulation. The actual hydraulic efficiency of the current flow channel is calculated. :

[0158] (14)

[0159] Considering that increasing the blade placement angle during subsequent modifications will cause flow channel diffusion losses, a high-load efficiency reduction factor is introduced. (Typically taken as 0.95-0.98), determine the corrected target hydraulic efficiency. .

[0160] (15)

[0161] Will Substituting into the head formula, we can deduce the method to meet the rated head requirement. Required target theoretical head and the corresponding target absolute tangential velocity Finally, by combining the velocity triangle formulas, the target theoretical outlet angle that satisfies the rated head requirement is derived. :

[0162] (16)

[0163] (17)

[0164] Through the above steps, a target theoretical outflow angle that conforms to physical reality was established. This provides an accurate benchmark for subsequent geometric corrections using the slip function.

[0165] Secondly, determine the Reynolds number at the target operating point (i.e., the rated operating condition). Unlike traditional methods that directly use simulation values, this invention uses the Reynolds number under rated operating conditions. Substitute the Reynolds number sensitivity function obtained in step 4 In the process, the predicted slip after fitting and smoothing is calculated. With slip amplification factor In conjunction with this, a reverse correction strategy is formulated. Unlike traditional designs that only compensate for viscous slip, this invention defines a corrected blade exit angle. The calculation formula is as follows:

[0166] (18)

[0167] in, As a slip amplification factor, it is used to quantify the sensitivity of slip to angular changes. This formula indicates that, in order to compensate for the effects caused by microscale boundary layer separation... To mitigate angular losses and overcome the increased slippage introduced by large-angle designs, the geometric angles must be set to values ​​significantly larger than those in traditional designs. This enables precise control of physical slippage by compensating for geometric overload.

[0168] Step 5.2: Automatic updating of the parametric model and bone line smoothing reconstruction

[0169] The calculated blade exit correction angle As a new global variable, it is input into the design variable vector X of the parametric design platform constructed in step 1.2 as the new blade outlet placement angle. At this time, the system maintains the blade inlet placement angle. The meridional flow profile remains unchanged, only the curvature control degree of freedom of the blade rib lines is released. To ensure the second-order geometric continuity of the blade profile and avoid profile distortion or inflection points caused by a significant increase in angle, a fourth-order Bézier curve is used to regenerate the meridional flow profile from the hub and wheel cover, and then the blade rib line distribution function from the inlet to the new outlet is regenerated. Simultaneously, the system automatically executes a geometric constraint verification procedure: checking the updated blade wrap angle. Whether it is within the set effective working range (90°~120°) is checked to prevent the control capability of the fluid from weakening due to an excessively small wrap angle caused by an increased angle, and whether the blade thickness distribution causes the throat area of ​​the flow channel to be less than the critical blockage threshold. If the verification passes, the system will automatically generate a corrected reference parametric geometric model of the micro centrifugal pump impeller based on the new bone line data, and automatically map the mesh topology defined in step 1.3 to generate a computational mesh for final verification, thereby completing the automated closed-loop update from mathematical correction to geometric entity.

[0170] Step 6: Numerical verification of the modified model and post-evaluation of the slip amplification mechanism

[0171] This step aims to verify whether the baseline parametric geometric model, after reverse correction in step 5, can achieve the expected design specifications, and to retrospectively evaluate the accuracy of the predicted slip amplification factor from a physical mechanism perspective. The following verification is performed by simulating the corrected model in a CFD solution environment identical to that of step 3:

[0172] Step 6.1: Numerical verification of the corrected baseline parametric geometric model.

[0173] Steady-state numerical simulations of the baseline parameterized geometric model before and after modification were performed under full flow conditions. The head H of the baseline parameterized geometric model before modification was obtained through computational fluid dynamics simulation. b With efficiency The head H of the corrected reference parameterized geometric model c With efficiency This allows for the construction of a regular curve that varies with flow rate, such as... Figure 6 As shown. The focus is on examining the head of the modified reference parameterized geometric model at the rated flow point. With efficiency Indicator. The head at the rated flow point. With rated head Compare and calculate the relative error. If the relative error E is controlled within the allowable range for engineering (usually <3%), and ≥ This preliminarily proves that the blade exit correction placement angle It provides sufficient functionality.

[0174] Step 6.2 Verification of Microscopic Flow Field and Slip Amplification Law

[0175] To prove the scientific validity of the method proposed in this invention, it is necessary to delve into the internal flow field for mechanism verification. The actual velocity vector at the outlet of the corrected reference parametric geometric model (i.e., the radial velocity and relative tangential velocity at the impeller outlet of the corrected reference parametric geometric model) is extracted, and the corrected outlet angle of the actual fluid is calculated in reverse. And calculate the actual corrected slip amount. :

[0176] (19)

[0177] examine Does it fall back to the target theoretical outflow angle calculated in step 5.1? Nearby. If the two match, it indicates that the final motion vector of the fluid conforms to the requirements of the Euler equation. According to the theory of this invention, in this embodiment, the actual corrected slip amount... Compared to the viscous slip correction under rated operating conditions It should increase significantly, and its increase is consistent with the slip amplification factor predicted in step 4.3.

[0178] If both macroscopic and microscopic conditions are met, then the slip amplification factor constructed in step 4 is fully proven. The invention accurately predicted the nonlinear growth of slip caused by the increase in angle at low Reynolds numbers. This indicates that the invention is not a simple error correction, but rather a successful achievement of the design objective of accurately compensating for physical slip with geometric overload through the prediction of physical laws, verifying the accuracy and universality of the method in micropump design.

[0179] Example 2: Design and Verification of a Micropump Based on Virtual Variable Parameter Sensitivity Analysis

[0180] This embodiment, using specific data, elaborates in detail the complete process of hydraulic correction of a micro centrifugal pump using the method described in this invention. The micro centrifugal pump design parameters selected in this embodiment are: rated flow rate... Rated head Rated speed The working medium is 20℃ clean water, with a dynamic viscosity of... .

[0181] Step 1: Construct the baseline parametric geometric model and fluid domain of the micro centrifugal pump impeller.

[0182] Based on one-dimensional beam theory and the empirical formula for the Stodola slip coefficient, the initial design blade exit angle is determined as follows: Based on these parameters, a baseline parametric geometric model (impeller solid model) of the micro centrifugal pump impeller is constructed, and a structured mesh is generated. This model serves as the benchmark for subsequent performance comparisons and the physical basis for Reynolds number sensitivity analysis.

[0183] Step 2: Based on the principle of dynamic similarity in fluid mechanics, construct an equivalent Reynolds number case library.

[0184] To analyze the viscous slip behavior at the microscale, the virtual parametric strategy of this invention is applied. Keeping the geometric model unchanged, four sets of gradient-based virtual fluid media are defined, with varying dynamic viscosities. The values ​​are 0.005, 0.002, 0.001, and 0.0005 Pa·s, respectively, to construct a virtual operating condition library covering the strong viscosity region to the inertia-dominated region.

[0185] Step 3: Perform multi-condition CFD numerical simulation and extract velocity vectors to construct a discrete condition dataset.

[0186] For the impeller solid model ( Steady-state numerical simulations were performed under four equivalent Reynolds number conditions constructed in Example 1. A mass-weighted averaging algorithm conforming to the law of mass conservation was used to statistically extract the microscopic flow field characteristic data, and the mass-weighted average radial velocity V was extracted at the impeller outlet section. i,m2 and relative tangential velocity W i,u2 The statistical data is shown in Table 1:

[0187] Table 1. Sensitivity analysis data of slip characteristics of microscale flow field as a function of Reynolds number.

[0188]

[0189] Step 4: Physical quantification and construction of Reynolds number sensitivity function and slip amplification factor for actual fluid slip characteristics.

[0190] Step 4.1: Calculation of actual outflow angle based on velocity triangle inversion and quantization of viscous slip.

[0191] Based on the simulation data from step 3, under rated operating conditions (Set-3), the blade outlet angle is... for Actual fluid outflow angle for:

[0192] (20)

[0193] (twenty one)

[0194] in, Indicates the radial velocity under rated operating conditions. This indicates the relative tangential velocity under rated operating conditions.

[0195] The baseline viscous slip correction amount is thus calculated. for:

[0196] (twenty two)

[0197] This data quantifies the severe angular loss caused by microscale effects under existing designs.

[0198] Step 4.2: Construct the Reynolds number sensitivity function

[0199] To obtain a universally applicable prediction model, nonlinear regression analysis was used to analyze the data in Table 1. , The data points were fitted and analyzed. The Reynolds number sensitivity function was selected. To perform fitting, the objective function S of the residual sum of squares is constructed using the least squares method, and then iteratively solved using a numerical iterative optimization algorithm (such as the Gauss-Newton method) to obtain the feature parameters. The process is as follows:

[0200] Four sets of sample points are extracted from the CFD simulation results in step 3 as the input data for fitting:

[0201] (twenty three)

[0202] (twenty four)

[0203] (25)

[0204] (26)

[0205] Substitute the above four sets of sample data into the objective function S.

[0206] (27)

[0207] The above objective function is optimized using numerical iterative optimization algorithms (such as the Gauss-Newton method). The equation is solved iteratively to make the objective function... The parameters can be obtained by converging to the minimum value. :

[0208] , , (28)

[0209] Substituting the solved parameters back into the equation, the Reynolds number sensitivity correction function for the micropump in this embodiment is established as follows:

[0210] (29)

[0211] The constructed Reynolds number sensitivity correction function curve is as follows: Figure 4 As shown. To verify the fitting accuracy, the Reynolds number under rated operating conditions was used. Substitute into the function to perform the prediction calculation:

[0212] (30)

[0213] This predicted value reflects the overall physical trend after removing individual point numerical fluctuations, and serves as the baseline input for geometric correction in subsequent step 5.

[0214] Step 4.3: Determine the slip amplification factor

[0215] The concept of angle transfer efficiency is introduced to quantify the response capability of microscale flow channels to changes in geometric angle. Based on baseline model data, the angle transfer efficiency under rated operating conditions is calculated. :

[0216] (31)

[0217] This value means that, under the current flow channel constraints, for every increase in the geometric angle... The actual fluid angle can only increase by approximately To obtain the desired flow angle increment, reverse amplification is necessary. An empirical correction factor k=0.9 is introduced to calculate the slip amplification coefficient. :

[0218] (32)

[0219] At this time, the coefficient This indicates that subsequent corrections must compensate for the expected slip loss by an order of magnitude of 2.

[0220] Step 5: Prediction-correction geometric inverse compensation based on Reynolds number sensitivity function and slip amplification factor

[0221] Step 5.1: Derivation and Correction Strategy of Target Parameters Based on Measured Data of the Benchmark Flow Field

[0222] To accurately obtain the energy conversion efficiency of the micropump's flow channel and avoid estimation errors caused by empirical formulas, this step directly extracts simulation data from the benchmark model under rated operating conditions (set-3) for reverse calibration. In CFD post-processing, the mass-weighted average of the absolute tangential velocity at the impeller outlet section is extracted and denoted as... Based on Euler's equations, calculate the theoretical head corresponding to the rated operating condition. :

[0223] (33)

[0224] (34)

[0225] Refer to the simulation data from step 3 to determine the actual head of the benchmark model under rated operating conditions. By comparing the actual head with the benchmark theoretical head, the true hydraulic efficiency of the benchmark flow channel can be calculated. :

[0226] (35)

[0227] This value reflects the upper limit of the actual efficiency of fluid in converting mechanical energy into pressure energy under the current microchannel structure.

[0228] To meet the design rated head Considering that the correction process will significantly increase the blade placement angle, the increased blade displacement and flow channel diffusion will inevitably introduce additional hydraulic losses. To ensure design margin, a high-load efficiency reduction factor is set. The corrected target hydraulic efficiency is... The estimate is:

[0229] (36)

[0230] Back-inference target theory outflow angle Based on the reduced target efficiency, calculate the head that meets the rated head requirement. Required target theoretical head :

[0231] (37)

[0232] Then calculate the target absolute tangential velocity required to achieve the theoretical head of the target. :

[0233] (38)

[0234] Substituting into the velocity triangle formula (radial velocity) (Maintaining the rated operating speed of 1.12 m / s)

[0235] (39)

[0236] Solving the inverse tangent function yields the target theoretical outflow angle.

[0237] The prediction model constructed in step 4 (predicting slip) ) and slip amplification factor ( ), calculate the final blade exit correction angle:

[0238] (40)

[0239] Taking into account manufacturing processes and engineering rounding, the final blade exit correction angle was set as follows: .

[0240] Step 5.2: Automatic updating of the parametric model and bone line smoothing reconstruction

[0241] Will As a new global design variable input parameterization platform, while keeping the blade inlet angle and meridional flow channel unchanged, the blade skeleton line is reconstructed by high-order Bézier curves to generate a modified benchmark parameterized geometric model of the micro centrifugal pump impeller and automatically map the mesh topology.

[0242] Step 6: Numerical verification of the modified model and post-evaluation of the slip amplification mechanism

[0243] This step aims to verify whether the model after the reverse correction in step 5 can achieve the expected design specifications, and to retrospectively evaluate the prediction accuracy of the slip amplification factor from a physical mechanism perspective. The following verification is performed by simulating the corrected model in a CFD solution environment identical to that in step 3:

[0244] Step 6.1 Verification of Macroscopic Hydraulic Performance Indicators

[0245] Steady-state numerical simulations were performed on the corrected model under full flow conditions. Simulation data were extracted at the rated flow rate (500 L / h).

[0246] Head compliance verification: Actual head H obtained from simulation S The result is 12.24m. This result not only meets the design target (12m) but also has a slight margin (error <2%), proving that the geometric compensation strategy proposed in this invention successfully overcomes the head loss problem at the microscale.

[0247] Efficiency prediction verification: such as Figure 6 As shown, under rated flow conditions, the efficiency obtained from the simulation of the corrected model is... The efficiency was 66.76%. Compared to the model before modification, the modified model still maintains a high efficiency level near the rated operating conditions, indicating that the present invention does not cause a significant deterioration in efficiency while increasing the head. Combined with the head achievement results, it can be shown that the high-load efficiency reduction treatment introduced in the design stage of the present invention can reasonably reflect the performance changes brought about by large-angle correction, thereby ensuring that the design results have good engineering reliability.

[0248] Step 6.2 Verification of Microscopic Flow Field and Slip Amplification Law

[0249] To verify the slip amplification factor To ensure accuracy, the microscopic flow field data at the outlet of the model in the embodiment was extracted: corrected radial velocity. Corrected relative tangential velocity To correct the outflow angle by reverse calculation of the actual fluid. :

[0250] (41)

[0251] Calculate the actual slip of the model in the embodiment. :

[0252] (42)

[0253] Verification conclusion: such as Figure 5 As shown, the actual corrected slip amount ( It is approximately the viscous slip correction amount under rated operating conditions. This is 2.11 times that of the predicted slip amplification factor in step 4.3. The results are largely consistent. This fully confirms the physical law that the viscous slip in the micropump amplifies nonlinearly with increasing geometric angle, and the modified model constructed in this invention accurately captures this law, achieving the design objective of accurately compensating for physical slip with geometric overload.

[0254] Finally, it should be noted that the above examples are merely some specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis, characterized in that... The specific process includes the following: S1. Construct a baseline parametric geometric model of the impeller of a micro centrifugal pump; S2. Based on the principle of dynamic similarity in fluid dynamics, while keeping the impeller geometry, rotational speed and mesh topology unchanged, an equivalent Reynolds number working condition library is constructed by adjusting the dynamic viscosity of the fluid medium. S3. Extract the Reynolds number, radial velocity, and relative tangential velocity at the impeller outlet from each set of working conditions in the equivalent Reynolds number working condition library through computational fluid dynamics numerical simulation, and construct a discrete working condition dataset; S4. Based on the discrete operating condition dataset, calculate the actual fluid outlet angle and viscous slip correction under each equivalent Reynolds number condition, fit the Reynolds number sensitivity function, and determine the slip amplification factor based on the rated operating condition. ; S5. Based on the Reynolds number sensitivity function and slip amplification factor, perform predictive-correction geometric inverse compensation on the benchmark parameterized geometric model to obtain the blade exit correction placement angle. Then, the corrected baseline parametric geometric model is reconstructed and obtained. S6. Perform numerical verification on the corrected baseline parameterized geometric model and conduct a post-evaluation of the prediction accuracy of the slip amplification factor.

2. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 1, characterized in that: The construction of the baseline parametric geometric model includes: (1) Obtain the specific speed of the micro centrifugal pump based on the set rated operating conditions, and set the blade outlet placement angle. and blade inlet placement angle ; (2) The meridional flow profile of the wheel hub and wheel cover is constructed using fourth-order Bézier curves; (3) Establish a system including the blade outlet placement angle Leaf wrap angle and blade thickness Design variable set And design the engineering constraints of the variable set. .

3. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 2, characterized in that: The equivalent Reynolds number operating condition library includes at least: the strong viscosity-dominant region operating condition, the transition sensitive region operating condition, the rated operating condition, and the inertia-dominant region operating condition. The dynamic viscosity of the fluid medium selected for each operating condition is based on the logarithmic gradient distribution principle.

4. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 3, characterized in that: The discrete operating condition dataset includes the Reynolds number, radial velocity, and relative tangential velocity at the impeller outlet. The construction process includes: (1) Obtain three-dimensional microscopic flow field data through computational fluid dynamics numerical simulation; (2) Based on the three-dimensional micro-flow field data, a monitoring surface is established at the impeller outlet diameter. The velocity field on the monitoring surface is integrated using a mass-weighted average algorithm that conforms to the law of mass conservation to obtain the velocity vector under each equivalent Reynolds number condition, including radial velocity and relative tangential velocity. (3) Calculate the Reynolds number under each equivalent Reynolds number condition, establish a mapping relationship with the velocity vector, and construct a discrete condition dataset.

5. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 4, characterized in that: The formula for calculating the actual fluid outflow angle is: in, This represents the actual fluid outflow angle under the i-th equivalent Reynolds number condition. Represents the radial velocity under the i-th equivalent Reynolds number condition. Represents the relative tangential velocity under the i-th group of equivalent Reynolds number conditions; The formula for calculating the viscous slip correction is as follows: = in, This represents the viscous slip correction amount under the i-th group of equivalent Reynolds number conditions. The angle at which the blade exits.

6. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 5, characterized in that: The Reynolds number sensitivity function is: in, The parameters to be fitted are... Represents the Reynolds number under the i-th equivalent Reynolds number condition; The objective function of the Reynolds number sensitivity function is: Then, the fitting parameters are obtained by solving the objective function using a numerical iterative optimization algorithm. The value of .

7. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 6, characterized in that: The slip amplification factor The calculation method is as follows: in, The actual fluid outflow angle under rated operating conditions. This is an empirical correction factor.

8. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 7, characterized in that: The specific process of prediction-correction geometric inverse compensation is as follows: (1) Calculate the target theoretical outflow angle Based on the three-dimensional micro-flow field data under rated operating conditions, the mass-weighted average of the outlet absolute tangential velocity under rated operating conditions is extracted. The reference theoretical head was calculated using the Euler equation. Thus, the target hydraulic efficiency is obtained. : in, This is the efficiency reduction factor under high load. It is the acceleration due to gravity. The circumferential velocity at the impeller outlet. The actual head obtained through computational fluid dynamics numerical simulation under rated operating conditions; Target hydraulic efficiency Substituting into the head formula, we can deduce the method to meet the rated head requirement. Required target theoretical head and the corresponding target absolute tangential velocity Then, by combining the velocity triangle formula, the target theoretical outlet angle that meets the rated head requirement can be derived. : in, ; (2) Calculate the corrected placement angle of the blade exit in, The predicted slip is obtained by substituting the Reynolds number under rated operating conditions into the Reynolds number sensitivity function; (3) Adjust the blade outlet placement angle As a new global design variable input design variable set Keeping the blade inlet angle and meridional flow profile unchanged, the curvature control degree of the blade skeleton is released, and the meridional flow profile of the hub and wheel cover is constructed using fourth-order Bezier curves, thereby obtaining the modified reference parameterized geometric model. Check the updated blade wrap angle and blade thickness Is it within the scope of engineering constraints? Internally, a revised baseline parametric geometric model is generated based on the updated blade rib line data.

9. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 8, characterized in that: The engineering constraints Including: blade wrap angle Leaf thickness .

10. The method for correcting the blade placement angle of a micro centrifugal pump based on Reynolds number sensitivity analysis according to claim 9, characterized in that: Numerical verification of the modified reference parameterized geometric model includes: calculating the head of the modified reference parameterized geometric model at the rated flow point. With rated head The relative error E should be controlled within the allowable range of the project. ≥ ; Post-evaluation of the prediction accuracy of the slip amplification factor includes: calculating the actual corrected slip amount of the modified baseline parameterized geometry. Compared to the viscous slip correction under rated operating conditions The increase is consistent with the slip amplification factor.

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