A drag function fitting method for non-spherical particles in arbitrary flow fields based on flow field decomposition

Abstract

The present invention discloses a method for fitting the drag function of non-spherical particles in an arbitrary flow field based on flow field decomposition. The method belongs to the field of multiphase fluid mechanics, and the fitted drag function can be used for motion simulation and prediction of non-spherical particles in an arbitrary flow field. First, by detecting and tracking the motion trajectory and posture of non-spherical particles in the basic flow field, the functional relationship of the particle drag with respect to the particle Reynolds number, posture, and shape, that is, the basic flow field drag function, is fitted; then, through flow field decomposition, the arbitrary flow field to be processed is approximately equivalent to the superposition of several basic flow fields, and then combined with the obtained basic flow field drag function, the non-spherical particle drag function applicable to any flow field is obtained. The advantages of this method are: strong scalability, applicable to arbitrary flow fields and non-spherical particles; the drag data in the basic flow field is directly derived from experiments; and only the linear superposition of a finite number of basic flow field drag functions is utilized.

Description

Technical Field

[0001] The present invention belongs to the field of multiphase fluid mechanics, and specifically relates to a drag function fitting method for non-spherical particles in a general flow field based on flow field decomposition. The fitted drag function can be further used for motion simulation and prediction of non-spherical particles in complex flow fields. Background Art

[0002] Particle two-phase flows are widely present in nature and industrial applications, such as haze, sediment, blood flow, and industrial reactor systems. Therefore, accurately predicting particle two-phase flow systems is of great significance to both industrial production and daily life. In these flows, most particles exhibit non-spherical characteristics and may even deform during motion. Compared with spherical particles, non-spherical particles have more complex fluid dynamics. Their orientation and rotational behavior in the flow field significantly affect the fluid forces acting on them, making it very difficult to accurately predict their motion patterns.

[0003] In granular two-phase flows, drag is an important force that determines the motion characteristics of particles. The drag of particles of general shapes is usually related to factors such as the incoming flow characteristics, particle shape, and particle orientation. Although many experimental and numerical simulation works have explored the drag characteristics of spherical and partially regular non-spherical particles (such as ellipsoids and cylinders), and some empirical drag formulas have been obtained, their scope of application is often very limited, and there is a lack of exploration of the drag characteristics of general non-spherical particles. In addition, the background flow fields of previous works are mostly uniform flows or shear flows, while the real flow fields are often complex nonlinear flow fields. Therefore, there is an urgent need for a fitting method for the drag function of non-spherical particles in general flow fields. Summary of the Invention

[0004] The present invention discloses a method for fitting the drag function of non-spherical particles in a general flow field based on flow field decomposition. The method belongs to the field of multiphase fluid mechanics, and the fitted drag function can be used for motion simulation and prediction of non-spherical particles in a general flow field. The method comprises four steps: basic flow field establishment and data acquisition, data processing in the basic flow field, general flow field decomposition, and particle drag function fitting in the general flow field. First, by detecting and tracking the motion trajectory and posture of non-spherical particles in the basic flow field, the functional relationship of the particle drag with respect to the particle Reynolds number, posture, and shape, i.e., the basic flow field drag function, is fitted; then, through flow field decomposition, the general flow field to be processed is approximately equivalent to the superposition of several basic flow fields, and then, combined with the obtained basic flow field drag function, a non-spherical particle drag function applicable to the general flow field is obtained. The advantages of this method are: strong scalability, applicable to general flow fields and non-spherical particles; the drag data in the basic flow field is directly derived from experiments; and only the linear superposition of a limited number of basic flow field drag functions is utilized.

[0005] The present invention discloses a method for fitting the drag function of non-spherical particles in an arbitrary flow field based on flow field decomposition, which comprises the following steps:

[0006] S1: Build a device for measuring the drag force of non-spherical particles and establish a basic flow field. Through preliminary layout and changing the required parameters of the device, collect the posture and motion trajectory data of non-spherical particles under different conditions;

[0007] S2, processing the motion trajectory and posture data of non-spherical particles in the basic flow field, obtaining the relationship between the drag force of non-spherical particles and the particle Reynolds number, posture and shape, and obtaining the drag function under the basic flow field by fitting;

[0008] S3, using the flow field decomposition method, decompose the arbitrary flow field to be processed into the superposition of multiple basic flow fields, and obtain the decomposition formula of the arbitrary flow field;

[0009] S4, substituting the basic flow field drag function obtained in step S2 into the decomposition formula of the arbitrary flow field to obtain the final drag function of the non-spherical particles in the arbitrary flow field.

[0010] As a preferred embodiment of the present invention, the basic flow field described in S1 refers to the shear flow field and uniform flow field The basic flow field device includes a basic flow field generating device and a three-dimensional particle tracking device; wherein, the basic flow field generating device is used to generate a shear flow field or a uniform flow field; the three-dimensional particle tracking device is used to collect the motion state of non-spherical particles.

[0011] As a preferred embodiment of the present invention, the preliminary arrangement described in S1 includes, in sequence: placing tracer particles into the flow field to observe and verify the flow field state, and after the flow field stabilizes, placing non-spherical particles at uniform intervals in the flow field study area to ensure sufficient data collection; the parameters required for the device include: the assumed drag function form with unknown coefficients, the size and shape parameters of the non-spherical particles, the flow field parameters, the sampling frequency of the three-dimensional particle tracking device, and the flow field decomposition accuracy.

[0012] As a preferred embodiment of the present invention, the fitting to obtain the drag function under the basic flow field described in S2 includes two processes: calculation of the drag of non-spherical particles and fitting of the basic flow field drag function containing parameter variables; specifically, the following steps:

[0013] During the drag calculation process, the velocity vector and acceleration vector of the collected particle position changes are obtained, and then the drag vector of the non-spherical particle in different postures at a certain particle Reynolds number is obtained; it is substituted into the drag function (F) containing parameter variables, and fitting is performed to obtain the drag function relationship within the set parameter range.

[0014] As a preferred embodiment of the present invention, the independent variables of the drag function (F) containing parameters are: particle Reynolds number (Re p ), particle attitude angle, non-spherical particle sphericity (Φ), where the particle attitude angle includes the precession angle α, spin angle β, and nutation angle γ; that is, F = f(Re p ,α,β,γ,Φ); the drag force data of particles in different postures are collected in real time through a three-dimensional particle tracking device; the range of α and β is [0,2π).

[0015] As a preferred embodiment of the present invention, the particle attitude angle is specifically defined as follows: let the fixed reference system be Oxyz, and the particle coordinate system be Ox'y'z', and call the intersection of the xy plane and the x'y' plane M, then α is the angle between the x-axis and the intersection M, β is the angle between the z-axis and the z'axis, and γ is the angle between the x'axis and the intersection M; when β = 0, let α be the angle between the x'axis and the x-axis and γ = 0; in the shear flow field, the change of γ only causes the maximum flow velocity at both ends to change, which is equivalent to the drag state of the same α, β and γ = 0 under different particle Reynolds numbers; and in the uniform flow field, γ does not affect the drag, so the basic flow field drag function is simplified to: F = f(Re p ,α,β,Φ); In the basic flow field, the x-axis is defined as the flow direction. Therefore, when the flow direction changes to the y-axis or z-axis in the decomposed flow field, the particle attitude angle in the corresponding drag function changes as follows: if the y-axis is the flow direction, α'=α+π / 2, β'=β; if the z-axis is the flow direction, α'=α, β'=β+π / 2; the corresponding drag function is F=f(Re p ,α',β',Φ).

[0016] As a preferred embodiment of the present invention, the flow field decomposition method described in S3 is: first, the spatial flow field is decomposed into a spatial unidirectional flow field distributed along the x, y and z axes according to the flow field coordinate system, and the flow field characteristics along the particles in the unidirectional flow field are further extracted to obtain an arbitrary nonlinear planar flow field, and then a linearized approximation of the arbitrary nonlinear flow field is obtained through linearization processing, that is, it is converted into a superposition of a finite number of basic flow fields.

[0017] As a preferred embodiment of the present invention, the method of extracting the flow field characteristics along the particles in the unidirectional flow field to obtain an arbitrary nonlinear planar flow field is as follows: because the main research objects of the particle posture in the basic flow field are the precession angle α and the spin angle β, that is, the angle between the x' axis and the x axis in the xy plane and the spin angle of the particle around the x' axis, so x' is set as the main axis of the particle; it is stipulated that any flow field on the main axis in the unidirectional flow field is a general nonlinear planar flow field. When the main axis direction is parallel to the flow field direction, it is equivalent to α=0 or π in the basic flow field. At this time, the flow field on the y' axis is taken as the plane flow field.

[0018] As a preferred embodiment of the present invention, the linearization process refers to performing a linear approximation on the nonlinear flow field according to the set accuracy requirements. Specifically, if there is a plane nonlinear flow field V on the principal axis of the particle, assuming that the number of decompositions along the principal axis is w, it is decomposed into w equivalent linear flow fields: Linear flow field V linear,i And by superposition of the basic flow field we get: Finally, the general nonlinear planar flow field along the particle's principal axis is transformed into a linear flow field:

[0019] As a preferred embodiment of the present invention, the drag function of non-spherical particles in the general flow field described in S4 is obtained by superimposing the drag functions of the basic flow fields. Specifically, because the drag functions F under the two basic flow fields of shear flow field and uniform flow field are s With F u The drag force along a certain coordinate axis is obtained by fitting the decomposition results described in S3 and superimposing them. The total drag force vector F acting on the non-spherical particle is finally obtained by superimposing the drag force vectors along the coordinate axis. total .

[0020] Furthermore, the output results may include drag force fitting function and particle motion law.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1) The present invention directly uses the collected experimental data to fit and derive the drag function of non-spherical particles under the basic flow field. Compared with existing simulation calculations, the results are more reliable;

[0023] 2) This invention introduces the particle attitude angle to fully describe the different attitudes of non-spherical particles in a flow field. Compared to the conventional non-spherical particle drag function that uses only sphericity as an independent variable, this method can more completely describe the drag force on non-spherical particles in any flow field under different attitudes.

[0024] 3) The flow field decomposition method proposed in this invention mainly decomposes any flow field into the superposition of a finite number of basic flow fields. Combined with the obtained basic flow field drag function, the drag force on non-spherical particles in any flow field can be quickly obtained, moderately alleviating the contradiction between the existing technology of accurately solving the drag force of non-spherical particles and achieving fast calculation;

[0025] 4) The present invention is highly scalable. This method is not limited to any specific fluid dynamics algorithm or flow field. It can be applied to scientific research and engineering problems requiring high precision in simulating non-spherical particles. Compared with existing technologies, it has a wider range of applications and provides a new approach for deriving the drag function for non-spherical particles in arbitrary flow fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Flowchart of the method of the present invention.

[0027] Figure 2 It is a basic flow field experimental device for uniform flow.

[0028] Figure 3 It is the basic flow field experimental device of shear flow.

[0029] Figure 4 Schematic diagram of particle attitude angle.

[0030] Figure 5 It is a spatial nonlinear flow field decomposition method.

[0031] Among them: 1. Propeller, 2. Processor, 3-5. Tracking camera, 6. Image acquisition area, 7. Particle inlet, 8. Circulating water tank, 9. Flow direction of flow field, 10. Guide plate, 11. Laser plane, 12. Laser, 13. Wall drive. DETAILED DESCRIPTION

[0032] The present invention will be further described and illustrated below in conjunction with specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without conflict.

[0033] like Figure 1 The flowchart of the method of the present invention is shown, and the method of the present invention mainly comprises the following steps:

[0034] S1, basic flow field establishment and data acquisition. First, a basic flow field device for non-spherical particle drag force measurement is established, which mainly includes a basic flow field generating device and a three-dimensional particle tracking device. Among them, the basic flow field generating device is used to generate a shear flow field or a uniform flow field; the three-dimensional particle tracking device is used to collect the motion state of non-spherical particles. The basic flow field mentioned in the present invention refers to the shear flow field. and uniform flow field Figure 2 This diagram illustrates the basic uniform flow experimental setup, which primarily includes a propeller, a circulating water tank, a guide plate, and a particle inlet. The propeller drives the flow, the circulating water tank ensures continuous flow within the test area, the guide plate ensures a stable, uniform flow within the test area, and the particle inlet is used to release the non-spherical particles required for the test. Figure 3 The basic flow field experimental device of shear flow is shown in the figure. Figure 2 The difference is that the drive device is changed from propeller drive to wall drive and the guide plate structure is cancelled. Figure 4 The particle attitude angle is shown. Figure 4 First, define the flow field coordinate system xyz and the non-spherical particle coordinate system x'y'z'.

[0035] Tracer particles are introduced into the flow field to observe and verify the flow field state. Once the flow field stabilizes, non-spherical particles are evenly spaced within the flow field study area to ensure sufficient data collection. The required equipment parameters for this method include: an assumed drag function with undetermined coefficients, non-spherical particle size and shape parameters, flow field parameters, the sampling frequency of the three-dimensional particle tracking device, and flow field decomposition accuracy. The posture and trajectory of the non-spherical particles are collected, and the collection ends when sufficient data is collected.

[0036] S2. Fitting the drag function for non-spherical particles in the basic flow field. By processing the trajectory and posture data of the non-spherical particles in the basic flow field, the relationship between the drag force of the non-spherical particles and the particle Reynolds number, posture, and shape can be obtained. Once sufficient data has been collected, it is substituted into the drag function containing parameters. Common fitting methods (such as the least squares method) can be used to fit the drag function to determine the drag function relationship within the set parameter range.

[0037] According to a preferred embodiment of the present invention, the fitting step S2 to obtain the drag function under the basic flow field includes two steps: calculating the drag of non-spherical particles and fitting the basic flow field drag function containing parameters; specifically, the following steps:

[0038] During the drag calculation process, the velocity vector and acceleration vector of the collected particle position changes are obtained, and then the drag vector of the non-spherical particle in different postures at a certain particle Reynolds number is obtained; it is substituted into the drag function (F) containing parameter variables, and fitting is performed to obtain the drag function relationship within the set parameter range.

[0039] The independent variables of the drag force function (F) with parameters are: particle Reynolds number (Re p ), particle attitude angle (α, β, γ), non-spherical particle sphericity (Φ), that is, F = f(Re p ,α,β,γ,Φ); the drag force data of the particles under different postures are collected in real time through the posture tracking device; in order to consider the irregularity of the cross section of non-spherical particles and the variability along the axial direction, the range of α and β is [0,2π).

[0040] The specific definition of the particle attitude angle is as follows: the particle attitude is described by the Euler angle (α, β, γ), the fixed reference system is Oxyz and the particle coordinate system is Ox'y'z', the intersection of the xy plane and the x'y' plane is called M, then α (precession angle) is the angle between the x axis and the intersection M, β (spin angle) is the angle between the z axis and the z' axis, γ (nutation angle) is the angle between the x' axis and the intersection M; specially when β = 0, let α be the angle between the x' axis and the x axis and γ = 0. In the shear flow field, the change of γ only leads to the change of the maximum flow velocity at both ends, which is equivalent to the drag state of the same α, β and γ = 0 under different particle Reynolds numbers; while in the uniform flow field, γ does not affect the drag, so the basic flow field drag function can be simplified to: F = f(Re p ,α,β,Φ). Because the x-axis is defined as the flow direction in the basic flow field, when the flow direction changes to the y-axis or z-axis in the decomposed flow field, the particle attitude angle in the corresponding drag function changes as follows: if the y-axis is the flow direction, α'=α+π / 2, β'=β; if the z-axis is the flow direction, α'=α, β'=β+π / 2; the corresponding drag function is F=f(Re p ,α',β',Φ).

[0041] S3, general flow field decomposition. This implementation adopts Figure 5 The method described above performs flow field decomposition, and the process of the method is as follows:

[0042] Step 1: Convert the three-dimensional flow into a unidirectional flow in space; Step 2: Take the x′ axis as the principal axis of the particle to obtain a nonlinear plane flow field. Since the flow field is continuous (indicated by the curve envelope), only a finite number of arrows are used here to represent its characteristics; Step 3: Taking w=4 as an example, decompose it into four parts along the principal axis of the particle (dividing it into four equal parts along the particle), and then simplify the general nonlinear flow field into a linear flow field; Step 4, process each section separately to obtain four linear flow fields; Step 5: Convert each of the four linear flow fields in the previous step into the form of superposition of two basic flow fields ( Figure 5 Only the basic flow fields a1 and a2 are graphically represented).

[0043] Specifically, the present invention first decomposes the spatial flow field into a spatial unidirectional flow field distributed along the x, y, and z axes according to the flow field coordinate system. The flow field characteristics of the particles in the unidirectional flow field are further extracted to obtain a general nonlinear plane flow field. Then, a linearized approximation of any nonlinear flow field is obtained through linearization processing, that is, it is converted into a superposition of a finite number of basic flow fields.

[0044] S4, general flow field drag function fitting. Because the drag function F under the two basic flow fields of shear flow and uniform flow s With F u The particle drag force along a certain coordinate axis can be obtained by superimposing the decomposition results described above. The total drag force vector F acting on the non-spherical particle is finally obtained by superimposing the drag force vectors along the coordinate axis. total .

[0045] The method of the present invention can be applied to the fitting of the drag function of non-spherical particles in any flow field. The obtained drag function can be further applied to the simulation and prediction of relevant particle multiphase flow systems in the fields of fluid mechanics, chemical engineering, energy, and medicine, thereby improving the simulation accuracy and moderately reducing the amount of calculation.

[0046] The above-described embodiments merely represent several implementation methods of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for fitting the drag function of non-spherical particles in an arbitrary flow field based on flow field decomposition, characterized in that: The following steps are involved: S1: Build a device for measuring the drag force of non-spherical particles and establish a basic flow field. Through preliminary layout and changing the required parameters of the device, collect the posture and motion trajectory data of non-spherical particles under different conditions; S2, processing the motion trajectory and posture data of non-spherical particles in the basic flow field, obtaining the relationship between the drag force of non-spherical particles and the particle Reynolds number, posture and shape, and obtaining the drag function under the basic flow field by fitting; S3, using the flow field decomposition method, decompose the arbitrary flow field to be processed into the superposition of multiple basic flow fields, and obtain the decomposition formula of the arbitrary flow field; The flow field decomposition method described in S3 is as follows: first, the spatial flow field is decomposed into spatial unidirectional flow fields distributed along the x, y, and z axes according to the flow field coordinate system, and the flow field characteristics along the particles in the unidirectional flow field are further extracted to obtain an arbitrary nonlinear plane flow field. Then, a linearized approximation of the arbitrary nonlinear flow field is obtained through linearization processing, that is, it is converted into a superposition of a finite number of basic flow fields. S4, substituting the basic flow field drag function obtained in step S2 into the decomposition formula of the arbitrary flow field to obtain the final drag function of the non-spherical particles in the arbitrary flow field.

2. The method according to claim 1, characterized in that The basic flow field described in S1 refers to the shear flow field and uniform flow field ; The basic flow field device includes a basic flow field generating device and a three-dimensional particle tracking device; wherein, the basic flow field generating device is used to generate a shear flow field or a uniform flow field; the three-dimensional particle tracking device is used to collect the motion state of non-spherical particles.

3. The method according to claim 1, characterized in that The preliminary arrangements described in S1 include, in sequence: placing tracer particles into the flow field to observe and verify the flow field state; after the flow field stabilizes, placing non-spherical particles at uniform intervals within the flow field study area to ensure sufficient data collection; the parameters required for the device include: the assumed drag function form with unknown coefficients, the size and shape parameters of the non-spherical particles, the flow field parameters, the sampling frequency of the three-dimensional particle tracking device, and the flow field decomposition accuracy.

4. The method according to claim 1, wherein The fitting process described in S2 to obtain the drag function under the basic flow field includes two steps: calculation of the drag force of non-spherical particles and fitting of the basic flow field drag function containing parameters. Specifically, In the drag calculation process, the velocity vector and acceleration vector of the particle are obtained by collecting the particle position changes, and then the drag vector of the non-spherical particle in different postures at a certain particle Reynolds number is obtained; Substitute it into the drag function (F) containing parameter variables and perform fitting to obtain the drag function relationship within the set parameter range.

5. The method according to claim 4, characterized in that The independent variables of the drag force function (F) with parameters are: particle Reynolds number (Re p ), particle attitude angle, sphericity of non-spherical particles , where the particle attitude angle includes the precession angle , spin angle , nutation angle ;Right now ;Use a three-dimensional particle tracking device to collect real-time data on the drag force on particles in different postures; and The range is [0,2π).

6. The method according to claim 5, characterized in that The particle attitude angle is specifically defined as follows: let the fixed reference system be Oxyz, and the particle coordinate system be , called the xy plane and The intersection line of the planes is M, then we have is the angle between the x-axis and the intersection line M, The z-axis and Axis angle, for The angle between the axis and the intersection line M; when season for Axis and The angle between the axes and In shear flow The change only causes the maximum flow rate at both ends to change, which is equivalent to the same Reynolds number under different particles. and Drag state; while in uniform flow field It does not affect the drag force, so the basic flow field drag function is simplified to: In the basic flow field, the x-axis is defined as the flow direction. Therefore, when the flow direction in the decomposed flow field changes to the y-axis or z-axis, the particle attitude angle in the corresponding drag function changes as follows: If the y-axis is the flow direction, ; If the z axis is the flow direction, The corresponding drag function is .

7. The method according to claim 1, characterized in that The method of extracting the flow field characteristics along the particle in the unidirectional flow field to obtain an arbitrary nonlinear plane flow field is as follows: since the main research object of the particle posture in the basic flow field is the precession angle and spin angle ,Right now The angle between the axis in the xy plane and the x-axis and the particle's rotation The spin angle of the axis, so let is the particle main axis; It is stipulated that any flow field on the principal axis in a unidirectional flow field is a general nonlinear plane flow field. When the principal axis direction is parallel to the flow field direction, it is equivalent to the basic flow field. or , at this time The flow field on the axis is a plane flow field.

8. The method according to claim 7, characterized in that The linearization process mentioned above refers to the linear approximation of the nonlinear flow field according to the set accuracy requirements. Specifically, if there is a plane nonlinear flow field on the particle principal axis , assuming that the number of decompositions along the principal axis is , which is decomposed into An equivalent linear flow field: ; Linear flow field And by superposition of the basic flow field we get: ; Finally, the general nonlinear planar flow field along the particle's principal axis is transformed into a linear flow field: .

9. The method according to claim 6, characterized in that The drag function of non-spherical particles in any flow field described in S4 is obtained by superimposing the drag functions of the basic flow fields. Specifically, because the drag function F under the two basic flow fields of shear flow field and uniform flow field is s With F u The drag force along a certain coordinate axis is obtained by fitting and superimposing the decomposition result of S3. ; The drag force vectors along each coordinate axis are superimposed to obtain the total drag force vector acting on the non-spherical particle. .

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