A method for constructing nanofluid aggregation model based on molecular dynamics

Abstract

The present invention relates to a method for constructing a nanofluid agglomeration model based on molecular dynamics, and belongs to the technical field of nanofluid enhanced heat transfer simulation. The specific steps are: (1) establishment of a nanofluid agglomeration model; (2) determination of boundary conditions; (3) selection of potential functions; (4) determination of initial parameters; (5) system relaxation; (6) core algorithm simulation calculation; (7) data processing and visualization. Based on the Green-Kubo principle, water-based nanofluids are used as research objects, and a numerical model of agglomeration is established through LAMMPS software. The various parameters of the established model are analyzed, and it is found that the model can accurately obtain a stable nanofluid agglomeration model, saving precious calculation time. It is a reliable nanofluid agglomeration modeling method with good simulation effect and high accuracy.

Description

Technical Field

[0001] The invention relates to a method for constructing a nanofluid agglomeration model based on molecular dynamics, and belongs to the technical field of nanofluid enhanced heat transfer simulation. Technical Background

[0002] Compared with experimental research, molecular dynamics simulation technology has the following advantages: (1) strong economy; (2) high safety; (3) easy control; (4) can study the microscopic mechanism of phenomena that cannot be directly observed, so it is increasingly favored by researchers. Molecular dynamics simulation is the most widely used computational method in large and complex systems. Molecular dynamics methods can complement theory and experiment. In recent years, the application of molecular dynamics simulation to the research on the mechanism of enhanced heat transfer of nanofluids has become increasingly mature. Particle agglomeration is of great significance to the enhancement of heat transfer of nanofluids, but the influence of nanofluid agglomeration has not been systematically studied, and the mechanism of its influence on the transport properties of nanofluids is still unclear. Therefore, solving the problem of molecular dynamics modeling of particle agglomerates in nanofluids is of great significance for improving the speed and accuracy of nanofluid simulation modeling, accelerating calculation efficiency and reducing calculation costs. Summary of the invention

[0003] In response to the above-mentioned existing problems, the present invention provides a method for constructing a nanofluid agglomeration model based on molecular dynamics. The present invention can assist in supporting the exploration and analysis of the mechanism of the effect of nanoparticle agglomeration morphology on the thermal properties of nanofluids at the molecular level, aiming to overcome the shortcomings existing in the background technology.

[0004] To achieve the above object, the technical solution adopted by the present invention is as follows: A method for constructing a nanofluid agglomeration model based on molecular dynamics, comprising the following steps:

[0005] The first step is to build a nanofluid agglomeration model. Specifically, the model of nanoparticles is extracted using MS software, and a single water molecule model is established using LAMMPS software. The water molecule adopts the SPC / E model. Then, the nanoparticles are placed in a simulation box using LAMMPS, and the rest of the box is filled with water molecules. The water molecules are arranged in FCC, so as to establish nanofluid agglomeration models with different volume fractions.

[0006] The second step is to determine the boundary conditions: impose periodic boundary conditions and introduce the nearest neighbor image convention to calculate the atomic motion and interaction within the central cell;

[0007] The third step is to select the potential function: select the EAM potential to describe the interaction between nanoparticles in the nanofluid, and select the LJ potential function to describe the interaction between the base fluids;

[0008] Step 4, determination of initial parameters: setting initial values ​​of relevant parameters in the nanofluid agglomeration model;

[0009] Step 5, system relaxation: the system is relaxed through an isothermal isobaric (NVT) ensemble to allow the initial model of the nanofluid agglomeration model to reach an equilibrium state;

[0010] Step 6: Core algorithm simulation calculation: determine the initial position of the atom and give it a random initial velocity, calculate the potential energy of the system and the force on the atom, determine the position of the atom at the next moment according to the Verlet integration algorithm, and count the calculation results at each moment;

[0011] Step 7: Data processing and visualization: When the nanofluid agglomeration model reaches equilibrium, the calculation results of the particle agglomeration heat transfer research in the nanofluid are obtained by statistically analyzing the calculation results at each moment. The calculation results include the change information of variable parameters and atomic coordinates, which will be intuitively displayed through Ovito. Among them, data processing is performed through Origin software.

[0012] Optionally, in the first step, constructing a nanofluid agglomeration model further includes:

[0013] In order to exclude the influence of particle volume concentration in nanofluids in simulations, the volume fraction needs to be unified.

[0014] Optionally, in the first step, when establishing the nanofluid agglomeration model, the initial positions of the nanoparticles are placed together and fixed so that they maintain an agglomerated shape in the base liquid. The initial positions of the particles in the nanofluid agglomeration model are calculated by the distance between the particle mass centers. In the simulation calculation of the nanofluid agglomeration model, the nanofluid volume fraction and the simulation box size are fixed, and nanoparticle agglomerates of different forms are established by changing the nanoparticle size.

[0015] Optionally, in the second step, the simulation dimension is three-dimensional, and the boundary conditions are divided into fixed boundary conditions, free boundary conditions and periodic boundary conditions. In order to reduce the influence of the "size effect" of the model and control the calculation workload, the present invention adopts periodic boundary conditions.

[0016] Optionally, in the third step, the EAM potential energy E between the nanoparticles i The expression is as follows:

[0017]

[0018] In the formula, F α is the embedding energy of element α, ρ β is the sum of the electron cloud densities generated by the extranuclear electrons of all other atoms except the βth atom at the βth atom, ρ β (rij ) is the charge density contributed by the extranuclear electrons of the jth atom at the ith atom, r ij is the distance between the ith atom and the jth atom, φ αβ It is the potential energy interaction between element α and element β. The first term on the right side of the equal sign in the formula represents the short-range repulsive force between molecules, and the second term is the potential term, which can take different forms according to needs.

[0019] The calculation formula of the LJ potential function between the base liquids is as follows:

[0020]

[0021] E(r ij )=0,r ij ≥r c

[0022] In the formula, r ij is the distance between atoms i and j, ε ij and σ ij are the energy and length parameters between atoms i and j, r c is the cutoff radius.

[0023] The potential function parameters between the nanoparticles and the base liquid atoms are calculated by the Lorentz-Berthelot mixing law. The Lorentz-Berthelot mixing law is expressed as:

[0024]

[0025]

[0026] Wherein, the subscripts l and s represent the liquid phase and the solid phase, respectively.

[0027] Optionally, in step 4, use a precision of 10 -4 The PPPM solver imposes periodic boundary conditions, calculates the atomic motion and its interaction in the central cell, and solves the equations of motion using the standard Velocity-Verlet algorithm.

[0028] Optionally, in the fifth step, before calculating the various parameters of the nanofluid agglomeration model, the model is first relaxed to reach thermodynamic equilibrium to ensure that the simulation conditions of the calculation process are stable, and the accuracy of the simulation model is verified using literature data. The realization of system equilibrium can be monitored by kinetic energy, potential energy, total energy and temperature.

[0029] Optionally, in the sixth step, various parameters of the nanofluid agglomeration model are calculated as needed. For the application of molecular dynamics to simulate the enhanced heat transfer mechanism of nanofluids, the equilibrium molecular dynamics (EMD) method based on the Green-Kubo relationship is used to simulate the thermal conductivity and viscosity of the material. The formula for calculating the thermal conductivity λ and the viscosity μ using the Green-Kubo method is as follows:

[0030]

[0031]

[0032] Where M is the integration time step, k B is the Boltzmann constant (1.38×10 -23 J / K), is the volume fraction, T is the temperature, N is the number of time steps required for the simulation, J(m+n) is the heat flow autocorrelation function for the time step (m+n), and P is the independent component of the stress tensor.

[0033] Optionally, the method further comprises visualizing the obtained calculation results of the heat transfer study of particle agglomerates in the nanofluid by using Ovito software.

[0034] Compared with the background technology, the present invention has the following advantages:

[0035] The present invention can accurately obtain a stable nanofluid agglomeration model, save precious computing time, have good simulation effect and high accuracy, and is a reliable nanofluid agglomeration modeling method. It is of great significance for revealing the nanofluid enhanced heat transfer mechanism and promoting the application of nanofluids. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in describing the embodiments are briefly introduced below.

[0037] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0038] Figure 2 A diagram showing a copper nanoparticle and a water molecule model according to an embodiment of the present invention;

[0039] Figure 3 This is a model diagram of nanofluid agglomeration of different forms of copper nanoparticles with a diameter of 2.67 nm in an embodiment of the present invention;

[0040] Figure 4 This is a model diagram of nanofluid agglomeration with different forms of copper nanoparticles with a diameter of 2 nm in an embodiment of the present invention;

[0041] Figure 5 This is a model diagram of nanofluid agglomeration of different forms of copper nanoparticles with a diameter of 1.47 nm in an embodiment of the present invention;

[0042] Figure 6 A table showing the aggregation morphology of nanoparticles in the nanofluid aggregation model of Examples 1 to 3 of the present invention;

[0043] Figure 7 A diagram showing the balance process of kinetic energy, potential energy and total energy according to an embodiment of the present invention;

[0044] Figure 8 is the thermal conductivity of the aggregate models with different shapes according to the embodiments of the present invention;

[0045] Fig. 9 Graph 1 shows the viscosity of the aggregate models with different shapes according to the embodiments of the present invention. DETAILED DESCRIPTION

[0046] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods. The described embodiments are applicable to a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] Example 1: Reference Figure 1 , is a flow chart of a method for constructing a nanofluid agglomeration model based on molecular dynamics provided in an embodiment of the present application, comprising the following steps:

[0048] The first step is to construct a nanofluid agglomeration model. Specifically, the following steps are used: First, the model of copper nanoparticles is extracted using MS software, such as Figure 2 (a), Cu atoms are arranged in FCC with a lattice constant of 0.3615 nm. The LAMMPS software is used to build a single water molecule model, as shown in Figure 2 (b), the water molecules adopt the SPC / E model. Then, LAMMPS is used to place the nanoparticles in the simulation box, and the rest of the box is filled with water molecules. The water molecules are arranged in FCC with a lattice constant of 0.54 nm. Different nanofluid aggregation models are established, such as Figure 3 to Figure 5 shown.

[0049] The second step is to determine the boundary conditions. Periodic boundary conditions are imposed and the nearest neighbor image convention is introduced to calculate the atomic motion and interaction within the central cell. The simulation dimension is three-dimensional, and the boundary conditions are divided into fixed boundary conditions, free boundary conditions and periodic boundary conditions. In order to reduce the influence of the model "size effect" and control the calculation workload, it is appropriate to use periodic boundary conditions.

[0050] The third step is to select the potential function. Select the EAM potential to describe the interaction between Cu-Cu in the nanofluid, and select the LJ potential function to describe the interaction between Cu-H2O and H2O-H2O; the potential function parameters between nanoparticles and base liquid atoms are calculated by the Lorentz-Berthelot mixing rule;

[0051] The fourth step is to determine the initial parameters. During the simulation, for long-range Coulomb interactions, an accuracy of 10 -4 The PPPM solver is used. In order to reduce the size effect, periodic boundary conditions are set in the x, y and z directions of the simulation system. The equations of motion are solved using the standard Velocity-Verlet algorithm, and the time step is set to 1 fs.

[0052] Step 5: System relaxation. Before calculating the parameters of the nanofluid model, the model is first relaxed through the isothermal and isobaric (NVT) ensemble to allow the initial model of the nanofluid agglomeration model to reach thermodynamic equilibrium, to ensure that the simulation conditions of the calculation process are stable, and to verify the accuracy of the simulation model using literature data. The realization of system equilibrium can be monitored by kinetic energy, potential energy, total energy and temperature, see Figure 7 .

[0053] Step 6: Core algorithm simulation calculation: determine the initial position of the atom and give it a random initial velocity, calculate the potential energy of the system and the force on the atom, determine the position of the atom at the next moment according to the Verlet integration algorithm, and count the calculation results at each moment;

[0054] The simulation temperature range is 20-60℃, and the Nose-Hoover method is used to set the temperature of the entire system. In this step, various parameters of the nanofluid agglomeration model can be calculated as needed. For the molecular dynamics simulation of the enhanced heat transfer mechanism of nanofluids, the thermal conductivity and viscosity of the nanofluid are calculated using the EMD method based on the Green-Kubo relationship, and compared with experimental data and theoretical models. The calculation process is run under the microcanonical (NVE) ensemble.

[0055] Step 7: Data processing and visualization. When the nanofluid agglomeration model reaches equilibrium, the calculation results of the heat transfer study of particle agglomeration in nanofluids are obtained by statistically analyzing the calculation results at each moment, and the data is processed by Origin software. The phenomena in the heat transfer study of particle agglomerates in nanofluids are visualized by Ovito software.

[0056] The size of the simulation box was set to 10 nm × 10 nm × 10 nm. Copper nanoparticles with a diameter of 2.67 nm were used. According to different agglomeration morphologies, two nanoparticles were placed in the simulation box, and the rest was filled with water molecules with a volume fraction of 2.0 vol%. By fixing the position of the nanoparticles, the agglomerate morphology was maintained, as shown in Figure 6 shown.

[0057] Before the calculation, the system was relaxed for 10000 steps in the NVT ensemble to achieve equilibrium.

[0058] After relaxing the system, the thermal conductivity and viscosity of the nanofluid were calculated using the Green-Kubo method in the NVE ensemble over a temperature range of 20 to 60 °C.

[0059] Embodiment 2: This embodiment has the same method steps as Embodiment 1, except that:

[0060] The size of the simulation box was set to 10 nm × 10 nm × 10 nm. Copper nanoparticles with a diameter of 2 nm were used. Four nanoparticles were placed in the simulation box according to different agglomeration morphologies, and the rest was filled with water molecules with a volume fraction of 2.0 vol%. The position of the nanoparticles was fixed to maintain the agglomerate morphology, e.g. Figure 6 shown.

[0061] Before the calculation, the system was relaxed for 10000 steps in the NVT ensemble to achieve equilibrium.

[0062] After relaxing the system, the thermal conductivity and viscosity of the nanofluid were calculated using the Green-Kubo method in the NVE ensemble over a temperature range of 20 to 60 °C.

[0063] Embodiment 3: This embodiment has the same method steps as Embodiment 1, except that:

[0064] The size of the simulation box was set to 10 nm × 10 nm × 10 nm. Copper nanoparticles with a diameter of 1.47 nm were used. According to different agglomeration morphologies, 12 nanoparticles were placed in the simulated box, and the rest was filled with water molecules with a volume fraction of 2.0 vol%. By fixing the position of the nanoparticles, the agglomerate morphology was maintained, as shown in Figure 6 shown.

[0065] Before the calculation, the system was relaxed for 10000 steps in the NVT ensemble to achieve equilibrium.

[0066] After relaxing the system, the thermal conductivity and viscosity of the nanofluid were calculated using the Green-Kubo method in the NVE ensemble over a temperature range of 20 to 60 °C.

[0067] The volume fractions are all set to 2.0 vol% to exclude the influence of the volume concentration of particles in the nanofluid. The initial positions of the particles in the nanoparticle agglomeration model are calculated from the distance between the particle mass centers. As the number of particles increases, the possible configurations of the agglomerated particles also increase, which makes it almost impossible to capture all possible situations. Therefore, in order to illustrate the effect of the agglomeration morphology of nanoparticles on the energy transport in nanofluids, for the case of multiple nanoparticles, this embodiment uses four different particle agglomeration morphologies, such as uniform dispersion, compact spherical and chain-like agglomeration morphologies, to calculate the thermal conductivity and viscosity of the nanofluid agglomeration model, as shown in FIG. Figure 8 and Fig. 9 .

[0068] The present invention can be applied to the process of molecular dynamics simulation example calculation, and can truly simulate and calculate the relationship between physical parameters such as nanofluid thermal conductivity and viscosity and changes in nanoparticle agglomeration morphology at different temperatures and nanoparticle sizes.

[0069] The present invention can accurately obtain a stable nanofluid agglomeration model, save precious computing time, have good simulation effect and high accuracy, and is a reliable nanofluid agglomeration modeling method. It is of great significance for revealing the nanofluid enhanced heat transfer mechanism and promoting the application of nanofluids.

[0070] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A method for constructing a nanofluid aggregation model based on molecular dynamics, characterized in that: The method comprises: (1) Constructing a nanofluid agglomeration model: First, the model of the nanoparticles was extracted using MS software, and a single water molecule model was established using LAMMPS software. The water molecule used the SPC / E model. Then, LAMMPS was used to place the nanoparticles in a simulation box, and the rest of the box was filled with water molecules. This established a nanofluid agglomeration model with different volume fractions. (2) Determine boundary conditions: Apply periodic boundary conditions and introduce the nearest neighbor convention to calculate the atomic motion and interaction within the central cell; (3) Select potential function: select EAM potential to describe the interaction between nanoparticles in nanofluids, and select LJ potential function to describe the interaction between base fluids; (4) Determination of initial parameters: setting initial values ​​of relevant parameters in the nanofluid agglomeration model; (5) System relaxation: The system is relaxed through an isothermal and isobaric NVT ensemble to allow the initial model of the nanofluid agglomeration model to reach an equilibrium state; (6) Core algorithm simulation calculation: determine the initial position of the atom and give it a random initial velocity, calculate the potential energy of the system and the force on the atom, determine the position of the atom at the next moment according to the Verlet integration algorithm, and count the calculation results at each moment; (7) Data processing and visualization: When the nanofluid agglomeration model reaches equilibrium, the calculation results of the particle agglomeration heat transfer research in the nanofluid are obtained by statistically analyzing the calculation results at each moment. The calculation results include the change information of variable parameters and atomic coordinates, which will be intuitively displayed through Ovito.

2. The method for constructing a nanofluid aggregation model based on molecular dynamics according to claim 1, characterized in that: In step (1), when establishing the nanofluid agglomeration model, the initial positions of the nanoparticles are placed together and fixed so that they maintain an agglomerated shape in the base liquid. The initial positions of the particles in the nanofluid agglomeration model are calculated by the distance between the particle mass centers. In the simulation calculation of the nanofluid agglomeration model, the nanofluid volume fraction and the simulation box size are fixed, and nanoparticle agglomerates of different shapes are established by changing the nanoparticle size.

3. The method for constructing a nanofluid aggregation model based on molecular dynamics according to claim 1, characterized in that: In step (2), the simulation dimension is three-dimensional and the boundary conditions adopt periodic boundary conditions.

4. The method for constructing a nanofluid aggregation model based on molecular dynamics according to claim 1, characterized in that: In step (3), the potential function parameters between the nanoparticles and the base liquid atoms are calculated using the Lorentz-Berthelot mixing rule.

5. The method for constructing a nanofluid aggregation model based on molecular dynamics according to claim 1, characterized in that: In step (4), the equations of motion are solved using the standard Velocity-Verlet algorithm.

6. The method for constructing a nanofluid aggregation model based on molecular dynamics according to claim 1, characterized in that: In step (5), before calculating the various parameters of the nanofluid agglomeration model, the model is first relaxed to achieve thermodynamic equilibrium to ensure that the simulation conditions of the calculation process are stable, and the accuracy of the simulation model is verified using literature data. The realization of system equilibrium is monitored by kinetic energy, potential energy, total energy and temperature.

7. The method for constructing a nanofluid aggregation model based on molecular dynamics according to claim 1, characterized in that: In step (6), various parameters of the nanofluid agglomeration model are calculated as needed. For the molecular dynamics simulation of nanofluid enhanced heat transfer mechanism, the EMD method based on the Green-Kubo relationship is used in the MD simulation to calculate the thermal conductivity and viscosity of the nanofluid.

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