Method for calculating Reynolds number of critical separation particles

Abstract

The invention discloses a method for calculating the Reynolds number of critical separation particles, and relates to the technical field of fluid mechanics, drag force, lift force and torque borne by LBM (Lattice Boltzmann Method) are calculated based on the simulation result of the LBM, and in the process, the Reynolds number of the critical separation particles is calculated. The shape (length-width ratio lambda), the flow state (particle Reynolds number Rep) and the attitude (attack angle theta and incidence angle alpha) of particles in a flow field are changed to obtain different stress results, and a set of aerodynamic characteristic prediction equation based on the incidence angle, the attack angle, the length-width ratio and the particle Reynolds number is constructed by deeply researching the influence of each variable. The set of equations can accurately predict forces and moments borne by the ellipsoidal particles under various different conditions, the critical separation particle Reynolds number of the particles can be calculated by combining the equations with a particle separation formula, and a solid theoretical basis is provided for design and maintenance of a hydraulic system.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid mechanics, and particularly relates to a method for calculating the critical separation particle Reynolds number. Background Art

[0002] With the application and development of modern hydraulic technology, the reliability of hydraulic systems and the service life of components have become more prominent and important. Practice has proved that contamination is the main cause of system failures. Contamination control of hydraulic systems is an important way to improve the working reliability of the system and extend the service life of components. Among many pollutants, solid particles have become the most harmful and common pollutants in hydraulic systems. It can cause problems such as a decline in the performance of hydraulic systems, a shortening of service life, and accelerated wear of components. In severe cases, it may even block the oil filter and jam the spool. According to statistics, 70% of aircraft and ship accidents are caused by hydraulic system contamination. Therefore, reducing or even eliminating the impact of pollutants on hydraulic systems is a very important matter.

[0003] However, in hydraulic systems, due to factors such as long-term frictional wear of moving parts, aging and failure of seals, and intrusion of air and dust, it is inevitable that there are solid particle pollutants in hydraulic oil, such as Figure 1 shown, there are still many particle pollutants in brand-new hydraulic oil. When these particles are deposited in the gaps between the sliding friction pairs of hydraulic components, it will cause obvious wear and affect the performance and service life of the components. For example, the gaps between the piston and the cylinder barrel of a piston pump, the spool and the valve body of a slide valve, and the piston and the cylinder barrel of a hydraulic cylinder are all prone to particle deposition.

[0004] Generally, the size of pollutant particles in hydraulic oil is between 20 - 50 microns and shows an obvious non-spherical shape, as Figure 1 shown. The gap of the sliding friction pair can reach 200 microns, and due to the movement of the wall surface, a linear shear flow is formed inside the gap. When the flow cannot drive the separation of the particles in the gap from the wall surface, the deposited particles may cause many problems such as friction and wear; however, when the flow in the gap is sufficient to promote the separation of pollutant particles from the wall surface, the pollutant particles will flow out with the hydraulic oil, thus greatly weakening the impact of pollutants on the hydraulic system. Therefore, it has very important research significance to clarify the wall separation characteristics of ellipsoidal particles in linear shear flow. For this reason, we propose a method for calculating the critical separation particle Reynolds number. Summary of the Invention

[0005] The object of the present invention is to provide a method for accurately calculating the critical separation particle Reynolds number of ellipsoidal particles on the wall surface to solve the problem in the prior art that the critical separation particle Reynolds number of ellipsoidal particles on the wall surface cannot be accurately calculated, thereby helping engineers better understand and predict the behavior of particles in a hydraulic system and providing strong support for the design and maintenance of the hydraulic system. Through the method of the present invention, effective control of solid particle pollutants in the hydraulic system can be achieved, system failures caused by particles can be reduced, and the reliability of the system and the service life of components can be improved.

[0006] In order to achieve the above object, the present invention specifically adopts the following technical solutions:

[0007] Considering the influence of the angle of incidence, angle of attack, and aspect ratio, using LBM simulation software, simulate and analyze the ellipsoid attached to the wall surface in a linear shear flow, and calculate the drag force F D , lift force F L and torque M z . During this process, change the shape (aspect ratio λ) of the particles in the flow field, the flow state (particle Reynolds number Re p ) and the attitude (angle of attack θ: the angle between the long axis of the particle and the wall surface, angle of incidence α: the angle between the projection of the long axis of the particle on the bottom plane and the fluid flow direction) to obtain different force results, and then establish a set of hydrodynamic characteristic prediction equations based on the angle of incidence, angle of attack, aspect ratio, and particle Reynolds number; next, analyze the force on the ellipsoidal particles on the wall surface and the wall separation conditions of the particles to obtain a separation formula; finally, combine the hydrodynamic characteristic prediction equations with the separation formula to calculate the critical separation particle Reynolds number (separation will occur when the particle Reynolds number exceeds this value).

[0008] The definitions of the particle Reynolds number and the aspect ratio are as follows:

[0009]

[0010] In the formula, b, a, G, D p and ν respectively represent the major axis radius of the particle, the minor axis radius of the particle, the shear rate, the diameter of a sphere with an equivalent volume, and the kinematic viscosity.

[0011] The hydrodynamic characteristic prediction equation is:

[0012] When the angle of attack is 0°, the empirical relationships between the drag force, lift force, and torque coefficients and the angle of incidence, aspect ratio, and particle Reynolds number are as follows:

[0013]

[0014] When the angle of incidence is 0° or 90°, the drag force, lift force, and torque coefficients corresponding to the corresponding angles can be calculated through the following relationships:

[0015]

[0016] When the incident angle is 0°, the empirical relationships of the drag force, lift force, and torque coefficient with respect to the incident angle, aspect ratio, and particle Reynolds number are constructed as follows:

[0017]

[0018] Where:

[0019]

[0020] The particle separation formula is:

[0021]

[0022] Wherein, the adhesion force (F ad ) and the adhesion radius (l ad ) can be determined by the classical adhesion theory JKR model (Johnson-Kendall-Roberts Model); the hydrodynamic forces such as the drag force, lift force, and torque are determined by the above-mentioned hydrodynamic characteristic prediction equations. The torques (M c ) generated by the drag force and lift force are:

[0023]

[0024] Furthermore, when the LBM hydrodynamic simulation software conducts simulation, the methods for grid independence verification and domain independence verification are as follows: Select an ellipsoid with an aspect ratio of 5 (the largest aspect ratio) attached to a smooth wall for the above verification. The largest aspect ratio represents a greater curvature and a longer major axis radius, and at the same time, it also means that the particles are more sensitive to the spatial resolution and domain size. Therefore, the verification results obtained using particles with the largest aspect ratio are applicable to the remaining particles. The verification results show that a resolution of 32 cells / D p and a domain size of x / D p = 32, y / D p = 20, z / D p = 20 are sufficient to obtain stable simulation results.

[0025] Furthermore, the method for verifying the calculation accuracy of the LBM hydrodynamics simulation software is as follows: Case 1, consider the case where an oblate spheroidal particle gradually approaches the wall from a position far away from the wall. Among them, the aspect ratio of the particle is fixed at 2, and the gap h between the particle and the wall is selected as a multiple of the major axis radius (b) of the particle, namely: 1.1b, 1.5b, 2.0b, and 5.0b. In addition, the angle of attack of the particle has two different values (β: 0°, 90°), and the particle Reynolds number is fixed at 0.02. Case 2, consider a particle with an aspect ratio of 1.5 attached to a smooth wall, and the particle has different angles of incidence (α: 0°, 30°, 45°, 60°, and 90°), and the particle Reynolds number (Re p ) is selected as 1.19 and 11.9. In the above two cases, the results of the drag force, lift force, and torque coefficient calculated by the LBM simulation software are compared with the results in the existing literature.

[0026] The beneficial effects of the present invention are as follows:

[0027] 1. By deeply studying the mechanical model and simulation data, the present invention constructs a set of aerodynamic characteristic prediction equations based on the angle of incidence, angle of attack, aspect ratio, and particle Reynolds number. This set of equations can accurately predict the forces borne by oblate spheroidal particles under various different conditions, making an important supplement to the theory of wall particle hydrodynamics and facilitating the analysis of the motion state of oblate spheroidal particles on the wall.

[0028] 2. By combining the fluid dynamic characteristic prediction equation with the separation formula, the present invention can calculate the critical separation particle Reynolds number of oblate spheroidal particles in a specific linear shear flow. This key numerical value can reveal the separation behavior of particles in the hydraulic system, thus providing an important reference basis for reducing the pollution degree of the hydraulic system, improving the overall reliability of the system, and extending the service life of components. Description of the Drawings

[0029] Figure 1 is a partial enlarged view of the brand-new hydraulic oil in the present invention;

[0030] Figure 2 is a technical roadmap for calculating the critical separation particle Reynolds number in the present invention;

[0031] Figure 3 is a curve diagram showing the influence of the angle of incidence on the drag force, lift force, and torque coefficient acting on the particle in the present invention;

[0032] Figure 4 is a curve diagram showing the influence of the angle of attack on the drag force, lift force, and torque coefficient acting on the particle in the present invention;

[0033] Figure 5It is the influence curve diagram of the aspect ratio on the drag force, lift force and torque coefficient acting on the particles in the present invention;

[0034] Figure 6 It is the force model of a single particle on the wall surface in the present invention

[0035] Figure 7 It is the curve diagram of the grid independence verification result in the present invention;

[0036] Figure 8 It is the curve diagram of the verification result of the watershed independence in the present invention;

[0037] Figure 9 It is the schematic diagram of the numerical verification model at different particle-wall clearances in the present invention;

[0038] Figure 10 It is the comparison result diagram of the drag force coefficient and torque coefficient acting on the particles at different particle-wall clearances with the existing literature data in the present invention;

[0039] Figure 11 It is the schematic diagram of the numerical verification model of the drag force coefficient, lift force coefficient and torque coefficient acting on the particles at different incident angles in the present invention;

[0040] Figure 12 It is the comparison result diagram of the drag force coefficient, lift force coefficient and torque coefficient acting on the particles at different incident angles with the existing literature data in the present invention. Specific embodiments

[0041] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0042] The present invention provides a method for calculating the critical separation particle Reynolds number.

[0043] 1. Considering the influence of the incident angle, angle of attack and aspect ratio, using the verified simulation settings, perform simulation analysis on the ellipsoid attached to the wall surface in the linear shear flow. Based on the simulation results of the LBM fluid mechanics simulation software, calculate the drag force, lift force and torque it receives. During this process, change the shape (aspect ratio λ), flow state (particle Reynolds number Re p ) and attitude (angle of attack θ, incident angle α) of the particles in the flow field to obtain different force results;

[0044] 2. Based on the simulation results, analyze the influence of the change of each parameter on the drag force, lift force and torque coefficient;

[0045] The analysis of the mechanical properties of particles under different conditions is as follows:

[0046] Under the condition that the particle Reynolds number is 1, the effects of the incident angle, the angle of attack, and the aspect ratio on the hydrodynamic characteristics of the particle are as follows Figure 3 , Figure 4 and Figure 5 shown. Generally speaking, when the incident angle and the angle of attack deviate from 0°, the drag force, lift force, and torque coefficient usually increase. For the aspect ratio, at different incident angles, it shows different effects on the drag force and lift coefficient. For example, when the incident angle is 0°, it will cause the lift coefficient to rise, while when it is 90°, it will decrease, as shown in Figure 5 .

[0047] When the angle of attack is 0°, the increase in the incident angle always leads to an increase in the drag force, lift force, and torque coefficient acting on the particle, as shown in Figure 3 . This is because the increase in the incident angle leads to the following changes: First, the increase in the windward area leads to an increase in the drag coefficient. Second, the smaller the contact length of the fluid in the downstream direction, the higher the shear rate on the high-speed side of the particle. Therefore, the increase in the viscous lift force leads to an increase in the total lift coefficient. Finally, the increase in the incident angle causes the torque caused by the pressure difference to increase from a negative value to 0, resulting in an increase in the total moment coefficient.

[0048] When the incident angle is 0°, the effects of the angle of attack change on the drag force, lift force, and torque coefficient are as shown in Figure 4 . As the angle of attack increases from 0° to 90° or decreases from 180° to 90°, the drag coefficient increases, which is due to the increase in the cross-sectional area of the particle perpendicular to the flow direction and the increase in the flow velocity at the center of the particle. It should be noted that when the low particle Reynolds number is less than 10, the drag coefficient image shows obvious symmetry with respect to the β = 90° line. In the range of the angle of attack from 0° to 180°, the lift coefficient changes in a wave-like manner, which reflects the change in the value of the pressure difference force and the change in the angle between it and the lift direction. Finally, due to the change in the flow velocity around the particle, the torque coefficient first increases and then decreases. When the aspect ratio is 1.5, the torque coefficient is the largest at β = 90°; when the aspect ratio is 5, the torque coefficient is the largest at β = 75°.

[0049] 3. Based on the above simulation results, establish a set of prediction equations for hydrodynamic characteristics based on the incident angle, angle of attack, aspect ratio, and particle Reynolds number;

[0050] The constructed prediction equation for hydrodynamic characteristics is:

[0051] When the angle of attack is 0°, the empirical relationships between the drag force, lift force, and torque coefficient and the incident angle, aspect ratio, and particle Reynolds number are as follows:

[0052]

[0053] When the incident angle (α) is 0° or 90°, the drag, lift, and torque coefficients for the corresponding angles can be calculated through the following relationships:

[0054]

[0055] When the incident angle is 0°, the empirical relationships for the drag, lift, and torque coefficients with respect to the incident angle, aspect ratio, and particle Reynolds number are constructed as follows:

[0056]

[0057] Where:

[0058]

[0059] 4. Analyze the forces acting on the ellipsoidal particles on the wall surface and construct a separation formula. The particle force model is as shown in Figure 6 . In the separation formula, the adhesion force (F ad ) and the adhesion radius (l ad ) can be determined through the classical adhesion theory JKR model; the hydrodynamic forces such as the drag force (F D ), lift force (F L ), and torque (M z ) are determined through the above hydrodynamic characteristic prediction equations; the horizontal (l x ) and vertical (l y ) distances between the particle-wall contact point and the particle center (O) are approximated using the sine and cosine functions of the major axis radius of the particle;

[0060] The separation formula is established as:

[0061]

[0062] Where the torque (M c ) generated by the drag and lift forces is:

[0063]

[0064] 5. Finally, by combining the hydrodynamic characteristic prediction equations with the separation formula, the critical separation particle Reynolds number can be calculated.

[0065] In this embodiment, when performing simulation using the LBM hydrodynamic simulation software, the grid independence verification and domain independence verification methods are as follows: Select an ellipsoid with an aspect ratio of 5 (the largest aspect ratio) attached to a smooth wall surface for the above verification. The largest aspect ratio represents a greater curvature and a longer major axis radius, and at the same time, it also means that the particles are more sensitive to the spatial resolution and domain size. Therefore, the verification results obtained using the particles with the largest aspect ratio are applicable to the remaining particles. The verification results are as shown in Figure 7 and Figure 8As shown, the verification results show 32 cells / D p resolution and x / D p = 32, y / D p = 20, z / D p The domain size of = 20 is sufficient to obtain stable simulation results.

[0066] The method for verifying the calculation accuracy of the LBM hydrodynamics simulation software is as follows: Numerical verification was carried out with the data of four existing literatures under two cases. The drag and torque results obtained using the aerodynamic characteristic prediction equations based on the angle of incidence, angle of attack, aspect ratio, and particle Reynolds number were compared with the results of the existing literature. Case 1, consider the case where an oblate spheroidal particle gradually approaches the wall from a position far from the wall. Among them, the aspect ratio of the particle is fixed at 2 and the gap h between the particle and the wall is selected as 1.1b, 1.5b, 2.0b, and 5.0b. In addition, the particle has two different values of the angle of attack (β: 0°, 90°), and the particle Reynolds number (Re p ) is fixed at 0.02. The type example is as Figure 9 shown. The comparison of the drag and torque results obtained by the calculation method used in this study with the existing literature is as Figure 10 shown; Case 2, consider a particle with an aspect ratio of 1.5 attached to a smooth wall. The particle has different angles of incidence (α: 0°, 30°, 45°, 60°, and 90°), and the particle Reynolds number (Re p ) is selected as 1.19 and 11.9. The model example is as Figure 11 shown. The comparison of the drag, lift, and torque results obtained by the calculation method used in this study with the existing literature is as Figure 12 shown. The results show that the calculation method used in this study has a very good agreement with the results of the existing literature.

[0067] Working principle and usage process of the invention:

[0068] First, use the LBM hydrodynamics simulation software to simulate the motion state of oblate spheroidal particles in a linear shear flow. During the simulation process, consider the influence of various factors such as the angle of incidence, angle of attack, and aspect ratio to obtain the force conditions of the particles under different conditions. Based on the simulation results, the mechanical parameters such as the drag, lift, and torque exerted on the particles can be calculated.

[0069] Next, through in-depth research on the mechanical model and simulation data, a set of aerodynamic characteristic prediction equations based on the angle of incidence, angle of attack, aspect ratio, and particle Reynolds number was successfully constructed. This set of equations can accurately predict the forces borne by oblate spheroidal particles under various different conditions, making an important supplement to the theory of wall particle hydrodynamics and facilitating the analysis of the motion state of oblate spheroidal particles on the wall.

[0070] Then, analyze the force state of the ellipsoidal particles on the wall surface and construct a separation formula. In the separation formula, the adhesion force (F ad ) and the adhesion radius (l ad ) can be determined by the classical adhesion theory JKR model; the hydrodynamic forces such as drag force, lift force, and torque are determined by the above-mentioned hydrodynamic characteristic prediction equations. The horizontal (l x ) and vertical (l y ) distances between the particle-wall contact point and the particle center (O) are approximated using the sine and cosine functions of the major axis radius of the particle.

[0071] Finally, by combining the hydrodynamic characteristic prediction equations with the separation formula, the critical separation particle Reynolds number of the ellipsoidal particles in a specific linear shear flow can be calculated. This key numerical value can reveal the separation behavior of the particles in the hydraulic system, thus providing an important reference basis for reducing the pollution degree of the hydraulic system, improving the overall reliability of the system, and extending the service life of the components.

[0072] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather should be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the Reynolds number of critical separation particles, characterized in that: Considering the effects of the incident angle, angle of attack, and aspect ratio, the ellipsoid attached to the wall in the linear shear flow is simulated and analyzed using the verified simulation settings. Based on the simulation results of the Lattice Boltzmann Method (LBM) fluid mechanics simulation software, the drag, lift, and torque are calculated. In this process, the shape of the particles in the flow field (aspect ratio λ), the flow state (particle Reynolds number Re p ) and posture (angle of attack θ, angle of incidence α) to obtain different force results, and then a set of fluid dynamic characteristics prediction equations based on the incident angle, angle of attack, aspect ratio and particle Reynolds number are established; next, the forces on the ellipsoidal particles on the wall and the wall separation conditions of the particles are analyzed to obtain the particle separation formula; finally, the fluid dynamic characteristics prediction equations are combined with the separation formula to calculate the critical separation particle Reynolds number. The prediction equation for fluid dynamic characteristics is: When the angle of attack is 0°, the empirical relationships between drag, lift and torque coefficients and the incident angle, aspect ratio and particle Reynolds number are as follows: When the incident angle (α) is 0° or 90°, the drag, lift and torque coefficients at the corresponding angles can be calculated using the following relationships: When the incident angle is 0°, the empirical relationships between drag, lift and torque coefficients and the incident angle, aspect ratio and particle Reynolds number are as follows: in: The particle separation formula is: The torque (M) generated by the drag and lift at the center of rotation (C) is c )for:

2. The method for calculating the critical separation particle Reynolds number according to claim 1, characterized in that: When the LBM fluid mechanics simulation software is used for simulation, the grid independence verification and the basin independence verification method are as follows: an ellipsoid with an aspect ratio of 5 (the largest aspect ratio) attached to a smooth wall is selected for the above verification. The largest aspect ratio represents a larger curvature and a longer major axis radius, which also means that the particles are more sensitive to spatial resolution and basin size. Therefore, the verification results obtained using the particles with the largest aspect ratio are applicable to the remaining particles. The verification results show that 32 cells / D p Resolution and x / D p =32,y / D p =20,z / D p = 20 is sufficient to obtain stable simulation results.

3. The method for calculating the critical separation particle Reynolds number according to claim 1, characterized in that: The calculation accuracy verification method of the LBM fluid mechanics simulation software is as follows: Case 1, consider a situation where a long ellipsoidal particle gradually approaches the wall from a position far away from the wall, where the aspect ratio of the particle is fixed to 2 and the gap h between the particle and the wall is selected as a multiple of the particle major axis radius (b), namely: 1.1b, 1.5b, 2.0b and 5.0b. In addition, the particle's angle of attack has two different values ​​(β: 0°, 90°), and the particle Reynolds number (Re p ) is fixed to 0.

02. Case 2: Consider a particle with an aspect ratio of 1.5 attached to a smooth wall. The particle has different incident angles (α: 0°, 30°, 45°, 60°, and 90°). The particle Reynolds number (Re p ) was selected as 1.19 and 11.

9. In the above two cases, the drag, lift and torque coefficients calculated by LBM simulation software were compared with the existing literature results.

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