Numerous value diffusion dynamic hybrid process simulation method and apparatus

Abstract

The application provides a dynamic mixing process simulation method and device without numerical diffusion, and the method comprises the following steps: S1, establishing a non-steady flow field model based on a mixer; S2, according to the non-steady flow field model, intercepting a plurality of cross sections perpendicular to the flow direction in the flow field model, setting tracer particles at n τ time intervals in each cross section, inversely tracking the set tracer particles according to the motion trajectories of the tracer particles, obtaining the inlets of the corresponding tracer particles to infer the initial concentration, and simulating video data of the concentration distribution of the convection contribution on the corresponding cross section; and S3, based on the initial concentration of the tracer particles and the diffusion speed of the tracer particles along the corresponding motion trajectories, simulating video data of the concentration distribution of the diffusion contribution through Lagrange equation. The application can accurately simulate the concentration distribution in the mixer under non-steady state without numerical diffusion, and is beneficial to the optimal design of the mixer according to the calculated concentration distribution.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of micro / millireactor technology, and particularly relates to a dynamic mixing process simulation method and device without numerical diffusion. BACKGROUND

[0002] Continuous flow micro / millireactors are widely used in various applications, such as nanomaterial synthesis, sensors, organic synthesis and smart reaction platforms, etc., which have the advantages of fast mass and heat transfer, waste reduction, intrinsic safety, etc. Although the diameter of the reactor is very small, the performance of the reactor is often limited by the mixing efficiency, because the mass transfer is controlled by slow molecular diffusion in laminar flow rather than convection. Fast mixing is crucial for controlling the selectivity of specific reactions and adjusting the size of nanomaterials. Compared to the slow mass transfer speed of the diffusion process driven by the concentration gradient, convection refers to the mass transfer process caused by the macroscopic movement of liquid clusters, which is faster.

[0003] Therefore, it is necessary to develop a high-efficiency mixer that enhances convection without relying on diffusion. The rapid development of the mixer depends on experimental or simulation calculation techniques that quickly and accurately quantify the mixing efficiency to obtain accurate concentration distribution in the mixing process, thereby assisting in the design of corresponding high-efficiency mixers.

[0004] Currently, planar laser-induced fluorescence is an effective method for experimental visualization of mixing efficiency, but it is costly and has a long experimental period. In contrast, the simulation results by commercial software are low-cost, but are affected by numerical diffusion. The simulation concentration distribution relies on the Euler form of the scalar transport equation, and the pseudo-diffusion coefficient introduced by the truncation error of the discretization of the flow field is much larger than the actual diffusion coefficient, also known as numerical diffusion, which causes the simulation results to overestimate the mixing efficiency.

[0005] In addition, a method for accurately simulating mixing efficiency in a steady-state flow field based on the Lagrangian form of the scalar transport equation is also proposed in the prior art (Lab on a Chip, 2013, 13(8): 1515-1521), but this method is not suitable for non-steady state. Non-steady-state flow fields often exhibit higher mixing efficiency than steady-state, and a targeted simulation method needs to be developed to study the mixer optimization problem of non-steady-state flow fields.

[0006] Therefore, in view of the above problems, it is necessary to propose further solutions. SUMMARY

[0007] The present application aims to provide a dynamic mixing process simulation method and device without numerical diffusion to overcome the deficiencies in the prior art.

[0008] To solve the above technical problems, the technical scheme of the present application is as follows:

[0009] A method for simulating a dynamic mixing process without numerical diffusion, comprising the following steps:

[0010] S1, establishing a non-steady flow field model based on a mixer;

[0011] S2, according to the non-steady flow field model, intercepting several cross sections perpendicular to the flow direction in the flow field model, setting tracer particles at n τ intervals Δτ in each cross section, and performing reverse tracking on the set tracer particles according to the motion trajectories of the tracer particles to obtain the entry of the corresponding tracer particles to infer the initial concentration and simulate video data of the concentration distribution of the convection contribution on the corresponding cross section;

[0012] S3, based on the initial concentration of the tracer particles and the diffusion speed along the corresponding motion trajectory, simulating video data of the concentration distribution of the diffusion contribution through the Lagrangian equation.

[0013] As an improvement of the method for simulating a dynamic mixing process without numerical diffusion, based on the mixer, input the corresponding modeling conditions, establish a non-steady flow field model of the mixer through computational fluid dynamics software, and store the calculated time sequence velocity field data, with a time interval of ΔT.

[0014] As an improvement of the method for simulating a dynamic mixing process without numerical diffusion, the mixer based on has at least two inlets and an outlet, the at least two inlets are located at one end of the mixer, and the outlet is located at the other end of the mixer.

[0015] At least one of the inlets is a solvent inlet, at least one of the inlets is a dilute solute inlet, and the outlet is an outlet for a mixed liquid formed by the solvent and the solute.

[0016] As an improvement of the method for simulating a dynamic mixing process without numerical diffusion, the several cross sections are array cross sections of tracer particles set at time intervals Δτ as the dynamic mixing proceeds.

[0017] As an improvement of the method for simulating a dynamic mixing process without numerical diffusion, the tracer particles are Sudan 6G tracers.

[0018] As an improvement of the method for simulating a dynamic mixing process without numerical diffusion, the diameter of the tracer particles is 0.1% to 5% of the size of the pipeline.

[0019] As an improvement of the method for simulating a dynamic mixing process without numerical diffusion, arrayed tracer particles are set on each cross section, and each arrayed tracer particle is tracked in reverse.

[0020] As the improvement of the dynamic mixing process simulation method without numerical diffusion of the present application, the set tracer particles are reversely tracked according to the motion trajectory of the tracer particles, including:

[0021] Taking the tracer particle at the cross-section position of which the concentration distribution is to be calculated as the starting point and the mixer inlet as the end point, the time period for the tracer particle to move from the starting point to the end point is divided into several motion periods ΔT;

[0022] For the nth period, the velocity field is assumed to be steady, and the flow field velocity is taken in the opposite direction, the flow field velocity is unchanged, in order to obtain the velocity and position of the tracer particle, the acceleration and trajectory of the tracer particle are calculated by calculating the drag force on the tracer particle, the position and velocity of the tracer particle at ΔT time, i.e. the position and velocity of the tracer particle at the end of the period iteration, are calculated by linear interpolation of the velocity and position of the two points closest to the ΔT time in the iteration process;

[0023] Based on the velocity and position calculated by linear interpolation, the flow field of the previous period is imported, the velocity is taken in the opposite direction, and the velocity value is unchanged, the drag force on the tracer particle is calculated to continue the reverse tracking of the tracer particle in the previous period.

[0024] As the improvement of the dynamic mixing process simulation method without numerical diffusion of the present application, the relevant conditions are input into the programming software to control the whole calculation process, and the motion trajectory of each particle is calculated and output by the computational fluid dynamics software.

[0025] As the improvement of the dynamic mixing process simulation method without numerical diffusion of the present application, the diffusion velocity is estimated by the diffusion velocity on the cross-section.

[0026] To solve the above technical problems, the technical scheme of the present application is:

[0027] A dynamic mixing process simulation device without numerical diffusion, comprising a processor, a memory and a program, wherein the program is stored in the memory, and the processor calls the program stored in the memory to execute the dynamic mixing process simulation method without numerical diffusion as described above.

[0028] Compared with the prior art, the present application has the following advantages: by establishing a non-steady flow field model based on the mixer, the concentration distribution contributed by convection is calculated by reverse tracking, and the concentration distribution contributed by diffusion is further calculated by Lagrangian equation. Thus, the concentration distribution in the mixer under non-steady state can be accurately simulated without numerical diffusion, which is beneficial to the optimization design of the mixer according to the calculated concentration distribution. BRIEF DESCRIPTION OF DRAWINGS

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is a schematic flowchart of an embodiment of the dynamic mixing process simulation method without numerical diffusion of the present invention, wherein n τ n represents the total number of frames to be simulated. par Δτ is the number of tracer particles, Δτ is the time interval between two adjacent frames, and ΔT is the time interval between two adjacent stored velocity fields.

[0031] Figure 2 This is a schematic diagram of a T-type mixer in one embodiment of the dynamic mixing process simulation method without numerical diffusion of the present invention.

[0032] Figure 3 This is an example of tracer particles being uniformly arranged on a cross section in one embodiment of the dynamic mixing process simulation method without numerical diffusion of the present invention.

[0033] Figure 4 This is a concentration distribution diagram of the convection contribution on a cross section in one embodiment of the dynamic mixing process simulation method without numerical diffusion of the present invention.

[0034] Figure 5 This invention provides a comparison of the simulated concentration distribution on a cross section with experimental and commercial software simulation values ​​in one embodiment of the dynamic mixing process simulation method without numerical diffusion. Figure a shows the experimental results obtained using a prior art diffusion method, with the diffusion situation at a certain moment of the experimental results used as the simulation object. Figure b shows the experimental results simulated using the method of this invention based on the simulation object in Figure a. Figure c shows the experimental results simulated using a conventional method based on the simulation object in Figure a. Condition: Both inlet Reynolds numbers are 237. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] One embodiment of the present invention provides a method for simulating dynamic mixing processes without numerical diffusion, which can accurately simulate the concentration distribution in a T-type mixer under unsteady conditions without numerical diffusion. The obtained concentration distribution data can be used as a reference for the optimized design of the T-type mixer.

[0037] like Figure 1 As shown, the simulation method for dynamic mixing processes without numerical diffusion in this embodiment includes the following steps:

[0038] S1. Establish an unsteady flow field model based on a mixer.

[0039] The mixer, used for mixing solvent and solute, has at least two inlets and one outlet. The at least two inlets are located at one end of the mixer, and the outlet is located at the other end. At least one inlet is a solvent inlet, at least one inlet is a diluted solute inlet, and the outlet is the outlet for the mixture formed by the solvent and solute.

[0040] In one embodiment, the mixer may be a T-type mixer 10. For example... Figure 2 As shown, the T-type mixer 10 includes two vertically connected channels 11 and 12. One end 111 of channel 11 is a tracer inlet, and the other end 112 is a water inlet. One end of the other channel 12 is a mixture outlet 121. In this way, the incoming tracer and water gradually mix in channel 12.

[0041] The T-type mixer 10 has a channel 11 with a length of 80 mm, a tracer inlet and a water inlet with a width of 10 mm, a channel 12 with a length of approximately 200 mm, and a mixed liquid outlet with a height of 10 mm and a width of 20 mm.

[0042] To establish an unsteady flow field model based on a T-type mixer, the model can be constructed using mesh generation software and computational fluid dynamics software, based on the T-type mixer described in the above embodiments and the input of corresponding modeling conditions. The modeling conditions include: water density, inlet width, average inlet velocity, viscosity, and pressure. A series of calculated flow field files are stored, with a time interval of ΔT between adjacent files. Since the establishment of the unsteady flow field model is existing technology, it will not be described in detail here.

[0043] S2. Based on the unsteady flow field model, several cross-sections perpendicular to the flow direction are selected from the flow field model. In each cross-section, n τ Tracer particles are set at intervals Δτ. Based on the trajectory of the tracer particles, the set tracer particles are tracked in reverse to obtain the entry point of the corresponding tracer particles to infer the initial concentration. Video data of the concentration distribution of convection contribution on the corresponding cross section is simulated and generated (e.g., ...). Figure 4 (As shown).

[0044] Step S2 employs a reverse tracking method to study the diffusion of tracer particles. The principle is as follows: assuming the velocity field is steady-state within a certain period ΔT, the velocity direction is reversed while its magnitude remains unchanged. Based on the position of the target tracer particle in the previous time period, the drag vector acting on the tracer particle is calculated. The direction of the associated component in the drag vector is used to track the target tracer particle's position in the previous time period. This process is repeated until the initial position of the tracer particle is reached, and its corresponding initial concentration is obtained, leading to the concentration distribution of the convection contribution on the corresponding cross-section.

[0045] Specifically, the aforementioned cross-sections are tracer particle array cross-sections spaced at time intervals Δτ as dynamic mixing progresses, for reverse particle tracking. Furthermore, the concentration of each tracer particle can represent the concentration distribution of the cross-section, simulating n... τ The concentration distribution of each frame is used to form a video simulation result showing the concentration distribution of convection contribution. Preferably, the time interval Δτ between two frame sections can be 0.1s.

[0046] At least 8*4 tracer particles can be placed in the cross-section to calculate the concentration distribution of the convection contribution of that cross-section. In one embodiment, such as... Figure 3 As shown, tracer particles can be arranged in an array on each cross-section. Preferably, the diameter of the tracer particles is 0.1%-5% of the pipe size. In this case, reverse tracking is performed on each tracer particle in the array. Specifically, this includes:

[0047] Taking the cross-sectional position where the concentration distribution of the tracer particle is to be calculated as the starting point and the inlet position as the ending point, the time period from the starting point to the ending point of the tracer particle is divided into several motion periods ΔT.

[0048] For the nth cycle, the flow field corresponding to that cycle is imported. Assuming the velocity field is in a steady state within a certain ΔT cycle, the velocity direction is reversed while the magnitude remains unchanged. To obtain the velocity and position of the tracer particle, the drag force vector acting on the tracer particle is calculated. Based on the direction of the associated component in the drag force vector, its acceleration is calculated, and its trajectory is calculated. Its position and velocity at time ΔT (at the end of the iteration of this cycle) are determined by the two points closest to time ΔT during the iteration process. Figure 2 China T n k and T n k+1 The velocity and position are obtained by linear interpolation.

[0049] Based on the velocity and position obtained from interpolation, the previous flow field is imported, and the velocity is reversed while the magnitude remains unchanged. The trajectory of the tracer particle in the previous cycle is then tracked.

[0050] The trajectory of the tracer particles can be calculated by software. In one embodiment, relevant conditions are input into programming software, and the trajectory of each particle is output by computational fluid dynamics software. The total time for each particle to run is...

[0051] S3. Based on the initial concentration of tracer particles and their diffusion velocity along the corresponding motion trajectory, video data of the concentration distribution of diffusion contribution is generated by simulating the Lagrange equation.

[0052] Since the concentration field is unknown, the diffusion velocity along the trajectory cannot be calculated and cannot be directly integrated using the Eulerian scalar transport equation (Equation 1). Therefore, the diffusion velocity is estimated using the Lagrangian scalar transport equation (Equation 2) based on the diffusion velocity at the cross-section. Then, the diffusion velocity at the cross-section is discretized according to Equation 3, thus the concentration of each tracer particle is correlated with the concentrations of the four surrounding tracer particles (see [reference]). Figure 3 ). C on the edge of the tracer particle array m,n There are no four particles surrounding it, and its concentration is set as C of adjacent particles. m,n+1 The concentration (Equation 4). The tracer particle C at the corner. p,q The concentration is set as the average of the concentrations of two adjacent particles (Equation 5). Thus, the concentration of each particle in the tracer particle array is related to the concentration of its surrounding particles. A system of equations can be established and solved to obtain the concentration of each tracer particle. Figure 5 Accurate concentration distribution.

[0053]

[0054]

[0055]

[0056] C m,n =C m,n+1 (4)

[0057] C p,q =(C p-1,q +C p,q-1 ) / 2 (5)

[0058] Where dl is Figure 3 The distance between the two tracer particles, D, is the diffusion coefficient, which controls the diffusion rate, and C... p,q C p-1,q C p,q-1 C m,n and C m,n+1 The relative position of Figure 3 The bid was successful.

[0059] Depend onFigure 5 As can be seen, compared to simulations using commercial software, the simulated concentration distribution relies on the Eulerian scalar transport equation. The truncation error introduced by the discretization of the flow field results in a pseudo-diffusion coefficient that is much larger than the actual diffusion coefficient, also known as numerical diffusion, causing the simulation results to severely overestimate the mixing efficiency. In contrast, the simulation method in this embodiment is based on the Lagrange scalar mass transfer equation and does not suffer from the numerical diffusion problem.

[0060] In summary, this invention establishes an unsteady flow field model based on a T-type mixer and calculates the concentration distribution of convection contribution through a back-tracking method. Furthermore, it calculates the concentration distribution of diffusion contribution using the Lagrange equation. Thus, as... Figure 5 As shown, the concentration distribution in a T-type mixer under unsteady conditions can be accurately simulated without numerical diffusion, which is beneficial for optimizing the design of the mixer based on the calculated concentration distribution.

[0061] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0062] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for simulating dynamic mixing processes without numerical diffusion, characterized in that, The dynamic mixing process simulation method includes the following steps: S1. Establish an unsteady flow field model based on a mixer; S2. Based on the unsteady flow field model, several cross-sections perpendicular to the flow direction are selected from the flow field model. In each cross-section, n t Tracer particles are set at intervals Δt. Based on the trajectory of the tracer particles, the set tracer particles are tracked in reverse to obtain the entry of the corresponding tracer particles to infer the initial concentration, and video data of the concentration distribution of the convection contribution on the corresponding cross section is simulated and generated. S3. Based on the initial concentration of tracer particles and their diffusion velocity along the corresponding motion trajectory, video data of the concentration distribution of diffusion contribution is generated by simulating the Lagrange equation. Reverse tracking of the set tracer particles based on their motion trajectories includes: Taking the tracer particle at the cross-sectional position where the concentration distribution to be calculated is the starting point and the mixer inlet is the ending point, the time period from the starting point to the ending point of the tracer particle is divided into several motion cycles DT. For the nth cycle, assuming the velocity field is in a steady state, and the flow field velocity is reversed while the flow field velocity remains constant, in order to obtain the velocity and position of the tracer particle, the acceleration and trajectory are calculated by calculating the drag force on the tracer particle. Its position and velocity at the DT time, that is, at the end of the iteration of this cycle, are obtained by linear interpolation of the velocity and position of the two points closest to the DT time during the iteration process. Based on the velocity and position calculated by linear interpolation, the flow field of the previous cycle is imported, and the velocity is reversed while the velocity value remains unchanged. The drag force on the tracer particle is calculated to continue the reverse tracking of the tracer particle of the previous cycle.

2. The method for simulating dynamic mixing processes without numerical diffusion according to claim 1, characterized in that, Based on the mixer, the corresponding modeling conditions are input, and an unsteady flow field model of the mixer is established using computational fluid dynamics software. The calculated time series velocity field data is stored, with a velocity field time interval of DT.

3. The method for simulating dynamic mixing processes without numerical diffusion according to claim 2, characterized in that, The mixer on which it is based has at least two inlets and one outlet, the at least two inlets being located at one end of the mixer and the outlet being located at the other end of the mixer; At least one inlet is a solvent inlet, at least one inlet is a diluted solute inlet, and the outlet is an outlet for the mixture formed by the solvent and solute.

4. The method for simulating dynamic mixing processes without numerical diffusion according to claim 1, characterized in that, The aforementioned cross sections are tracer particle array cross sections set at time intervals of Δt as dynamic mixing proceeds, in order to perform reverse particle tracking.

5. The method for simulating dynamic mixing processes without numerical diffusion according to claim 1, characterized in that, The tracer particles are Sudan Red 6G tracers.

6. The method for simulating dynamic mixing processes without numerical diffusion according to claim 1, characterized in that, Tracer particles are arranged in an array on each cross section, and reverse tracking is performed on each tracer particle in the array.

7. The method for simulating dynamic mixing processes without numerical diffusion according to claim 1, characterized in that, The relevant conditions are input into the programming software to control the entire calculation process, and the motion trajectory of each particle is calculated and output by the computational fluid dynamics software.

8. The method for simulating dynamic mixing processes without numerical diffusion according to claim 1, characterized in that, The diffusion rate is estimated by the diffusion rate on the cross section.

9. A dynamic mixing process simulation device without numerical diffusion, characterized in that, The device includes: a processor, memory, and a program; The program is stored in the memory, and the processor calls the program stored in the memory to execute the dynamic mixing process simulation method without numerical diffusion as described in claim 1.

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