CN109883649A - A method to study the flow behavior of nanofluids in nanochannels by simulation model - Google Patents

Abstract

The invention discloses a method for studying the flow behavior of nano-fluids in nano-channels through a simulation model, comprising the steps of: 1. building a simulation model; 2. selecting a potential function; 3. setting the parameters of the model; Change the temperature control command; 6. Nanoparticle flow; 7. Statistical fluid flow rate; 8. Calculate effective viscosity; 9. Stabilize flow and calculate effective viscosity. The method uses Lammps software to simulate and build a model of nanofluid flowing between two parallel copper plates. By changing the volume fraction, temperature and size of nanoparticles, the flow rate of nanofluid is calculated and the effective viscosity in the nanochannel is calculated. Due to the influence of the nanoscale of nanofluids, the fluid motion is controlled by surface forces, and the addition of nanoparticles and intermolecular effects make nanofluids unable to satisfy the continuum hypothesis. Therefore, the present invention is convincing using molecular dynamics as a very efficient method to study the flow properties of nanoparticles at the nanoscale.

Description

A method to study the flow behavior of nanofluids in nanochannels by simulation model

technical field

The invention relates to the field of molecular dynamics, in particular to a method for studying the influence of different factors on the flow behavior of nanofluids in nanochannels through a simulation model.

Background technique

At present, most of the methods commonly used to study the flow behavior of nanofluids are experimental and computational.

The experimental method can study the heat transfer performance and flow behavior of different conditions and different types of nanofluids, and can analyze the influence of different factors, but the particle size of nanoparticles is nanometer size. Control of surface forces. Therefore, macroscopic experimental methods have certain limitations in the study of nanoparticles. Besides, it is difficult to accurately control the size of nanoparticles by experimental methods, so the experimental results may have relatively large errors.

Computational method is a molecular dynamics simulation method calculation, and molecular dynamics is a deterministic method. It uses classical mechanics to describe the simulated system, and numerically solves the equation of motion to obtain the trajectory of the particle in the phase space, that is, its microscopic state at any time, and then can study the different properties of the simulated system. The motion of particles in a molecular dynamics simulation system has a correct physical basis. The advantage of this method is that it is highly accurate, and the dynamic and thermodynamic states of the system can be obtained simultaneously. However, the calculation of molecular dynamics simulation method needs to refer to the mathematical integration method, so it can only study the motion of the system in a short time range, but cannot simulate some motion problems with a long time.

SUMMARY OF THE INVENTION

Based on the problems existing in the prior art, the purpose of the present invention is to provide a method for studying the flow behavior of nanofluids in nanochannels through simulation models, which can overcome the limitations of experimental methods on nanometer size and facilitate accurate analysis of different factors in nanometers. Influences on nanofluid flow behavior within channels.

The purpose of this invention is to realize through the following technical solutions:

Embodiments of the present invention provide a method for studying the flow behavior of nanofluids in nanochannels through a simulation model, including:

Step 1. Build a simulation model: use molecular dynamics software to build a simulation model of a nanofluid that includes upper and lower parallel walls, and sets liquid argon and nanoparticles in the liquid argon between the upper and lower parallel walls;

Step 2. Select a potential function: Calculate the interaction between atoms in the simulation model with the Lennard-Jones potential function, which is as follows:

The values of σ and ε between different atoms are calculated according to the Lorentz Berthelot mixing rule with the following formula:

In the above formulas (1), (2) and (3), r _ij is the distance between atom i and atom j, σ and ε are the interaction range and interaction strength between atoms, respectively;

Step 3. Setting the parameters of the simulation model: According to the parameters of the Lennard-Jones potential function, the parameters of the model are set as follows: σ _Cu-Cu is 0.2338 nm; ε _Cu-Cu is 6.563×10 ^-20 J; σ _Ar-Ar is 0.3405 nm; ε _Ar-Ar is 1.67×10 ^-21 J; σ _Cu-Ar is 0.2872 nm; ε _Cu-Ar is 1.041×10 ^-20 J;

Step 4. Equilibrium model: use the NVT ensemble to equilibrate the simulation model in molecular dynamics software, each time step is 2fs, and the equilibration time is 1200ps;

Step 5. Change the temperature control command: Remove the NVT command in the molecular dynamics software, and calculate the temperature through the velocity of the liquid argon atoms in the z direction. The formula for calculating the temperature in molecular dynamics is as follows:

KE=dim/2k _B NT (4)

In the above formula (4), KE is the total kinetic energy of the calculated atomic group; dim is the dimension of the simulation; k _B is the Boltzmann constant, N is the number of atoms in the calculated atomic group; T is the temperature;

Step 6. Nanofluid flow: apply a y-direction force to each liquid argon atom in the simulation model to move the liquid argon in the y-direction;

Step 7. Statistical fluid flow rate: divide the simulation model into 110 layers along the z-axis, count the y-direction sub-velocities of argon atoms in each layer and calculate the average value, output the average velocity of each layer of argon atoms in each time step once;

Step 8. Calculate the effective viscosity: Calculate the flow velocity of each layer of argon atoms in the y direction, and calculate the effective viscosity according to the following formula:

In the above formulas (5) and (6), η is the effective viscosity; dv _y /dz is the shear rate of the nanofluid along the z direction; τ _zy is the shear stress on the zy plane; F _y is the y direction acting on the nanofluid force; A is the contact area between the liquid argon and the upper and lower walls;

Step 9. Stabilize the flow and calculate the effective viscosity: When the nanofluid velocity fluctuation in the entire simulation model converges, it is determined that the nanofluid flow tends to be stable, and the effective viscosity is calculated and obtained according to the above formulas (5) and (6).

It can be seen from the technical solutions provided by the present invention that the method for making a simulation model for studying the flow behavior of nanofluids in nanochannels provided by the embodiments of the present invention has the following beneficial effects:

By using molecular dynamics software to build an initial simulation model, and then through the initial simulation model constructed to simulate the flow state of nanofluids in nanochannels under different factors, the influence of different factors on the flow behavior of nanofluids in nanochannels can be accurately analyzed.

Description of drawings

In order to illustrate the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

1 is a schematic diagram of a simulation model with a nanoparticle volume fraction of 5.72% produced by a method provided in an embodiment of the present invention;

In the figure: 1-upper wall; 2-lower wall; 3-nanoparticles.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the specific content of the present invention. Obviously, the described embodiments are only 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 those of ordinary skill in the art without creative work fall within the protection scope of the present invention. Contents that are not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

Embodiments of the present invention provide a method for studying the flow behavior of nanofluids in nanochannels through a simulation model, including:

Step 1. Build a simulation model: use molecular dynamics software to build a simulation model of a nanofluid that includes upper and lower parallel walls, and sets liquid argon and nanoparticles in the liquid argon between the upper and lower parallel walls;

Step 2. Select the potential function: Calculate the interaction between atoms in the simulation model with the Lennard-Jones potential function. The Lennard-Jones potential function is as follows:

The values of σ and ε between different atoms are calculated according to the Lorentz Berthelot mixing rule with the following formula:

In the above formulas (1), (2) and (3), r _ij is the distance between atom i and atom j, σ and ε are the interaction range and interaction strength between atoms, respectively;

Step 3. Setting the parameters of the simulation model: According to the parameters of the Lennard-Jones potential function, the parameters of the model are set as follows: σ _Cu-Cu is 0.2338 nm; ε _Cu-Cu is 6.563×10 ^-20 J; σ _Ar-Ar is 0.3405 nm; ε _Ar-Ar is 1.67×10 ^-21 J; σ _Cu-Ar is 0.2872 nm; ε _Cu-Ar is 1.041×10 ^-20 J;

Step 4. Equilibrium model: use the NVT ensemble to equilibrate the simulation model in the molecular dynamics software, each time step is 2fs, and the equilibration time is 1200ps; specifically, NVT is applied to the model through the input command of the Lammps software Ensemble; molecular dynamics simulation is to simulate the movement of atoms in a period of time, and the time step is the shortest time interval of the selected simulation;

Step 5. Change the temperature control command: remove the NVT command in the molecular dynamics software (specifically, remove the NVT ensemble applied to the model through the input command of the Lammps software), calculate the temperature by the velocity of the liquid argon atom in the z direction, The formula for calculating temperature in molecular dynamics is as follows:

KE=dim/2k _B NT (4)

In the above formula (4), KE is the total kinetic energy of the calculated atomic group; dim is the dimension of the simulation; k _B is the Boltzmann constant, and N is the calculated atomic group (that is, the calculation temperature required in the simulation process) atomic number in the atomic group); T is the temperature;

Step 6. Nanofluid flow: apply a y-direction force to each liquid argon atom in the simulation model to move the liquid argon in the y-direction;

Step 7. Statistical fluid flow rate: divide the simulation model into 110 layers along the z-axis, count the y-direction sub-velocities of argon atoms in each layer and calculate the average value, output the average velocity of each layer of argon atoms in each time step once;

Step 8. Calculate the effective viscosity: Calculate the flow velocity of each layer of argon atoms in the y direction, and calculate the effective viscosity according to the following formula:

In the above formulas (5) and (6), η is the effective viscosity; dv _y /dz is the shear rate along the z direction; τ _zy is the shear stress in the zy plane; F _y is the force acting on the y direction of the nanofluid ; A is the contact area between the liquid argon and the upper and lower walls;

Step 9. Stabilize the flow and calculate the effective viscosity: when the nanofluid velocity fluctuation in the entire simulation model converges, it is determined that the nanofluid flow tends to be stable, and the effective viscosity is calculated and obtained according to the above formulas (5) and (6).

In step 1 of the above method, the molecular dynamics software used is: Lammps software.

In the above method, the base fluid of the nanofluid is liquid argon, and the nanoparticles can be copper balls in the nanofluid.

In step 1 of the above method, the simulation models are divided into two categories, including:

In the first type of simulation model, the volume fraction of nanoparticles in the nanofluid is changed, and the volume fraction is controlled by changing the number of nanoparticles with the same diameter;

In the second type of simulation model, the diameter of the nanoparticles of the nanofluid is changed, and the particle size is controlled by changing the number of nanoparticles with a fixed volume fraction.

The method of the present invention can simulate the flow behavior of nanofluids in nanochannels by making a model based on molecular dynamics to study the influence of nanoparticles on the flow behavior of fluid between infinite flat plates, and can overcome the limitation of experiments on nanometer size. , through this method, the influence of different factors of nanoparticles on the flow behavior of nanofluid in the nanochannel can be accurately analyzed.

The embodiments of the present invention will be described in further detail below.

In the method of the present invention, a simulation model including upper and lower walls, liquid argon and nanoparticles is first constructed (see Fig. 1), and the Lennard-Jones potential function is selected to calculate the interaction between atoms, and the NVT ensemble is used to conduct the whole system. Equilibrium, the equilibration time is 1200ps; after the system is balanced, remove the NVT command and modify it to calculate the temperature only by the velocity of the liquid argon atoms in the z direction; apply a y-direction force to each liquid argon atom to move the liquid in the y-direction ; Divide the simulation box into 110 layers along the z-axis, count the sub-velocities of each layer of argon atoms in the y-direction and calculate the average value, and output the average velocity of each layer of argon atoms in each time step once; when the nanofluid flow tends to When stable, the effective viscosity is calculated and output.

Specifically, the method of the present invention comprises the following steps:

Step 1. Build a simulation model: the simulation includes the upper and lower walls, liquid argon and nanoparticles; the simulation model is divided into two categories: the first type is to only change the volume fraction of nanoparticles, by changing the size of nanoparticles with the same diameter. The second type is to change the diameter of nanoparticles, by changing the number of nanoparticles with a fixed volume fraction to control their particle size;

Step 2. Select the potential function: Use the Lennard-Jones potential function to calculate the interaction between the atoms in the model. The potential function is as follows:

The values of σ and ε between different atoms are calculated according to the Lorentz Berthelot mixing rule with the following formula:

In the above formulas (1), (2) and (3), r _ij represents the distance between atom i and atom j; σ and ε represent the interaction range and interaction strength between atoms, respectively;

Step 3. Parameter setting of the model: See Table 1 for the parameters.

Table 1 is the parameter table of the Lennard-Jones potential function

parameter Numerical value σ_Cu-Cu 0.2338nm ε_Cu-Cu 6.563×10^-20J σ_Ar-Ar 0.3405nm ε_Ar-Ar 1.67×10^-21J σ_Cu-Ar 0.2872nm ε_Cu-Ar 1.041×10^-20J

Step 4. Balance of the model: Because it is a man-made configuration, the internal energy distribution is uneven, so the simulation needs to go through a balance process; all models use the NVT ensemble to balance the overall system, each time step is 2fs, and the balance time is 1200ps ;

Step 5. Change the temperature control command: The formula for calculating temperature in molecular dynamics is as follows:

KE=dim/2k _B NT (4)

In the above formula (4), KE represents the total kinetic energy of the calculated atomic group; dim represents the dimension of the simulation; k _B represents the Boltzmann constant; N represents the number of atoms in the computed atomic group; T represents the temperature; The liquid flow causes the temperature of the system to increase, the NVT command is removed, and the temperature is calculated only by the velocity of the liquid argon atoms in the z direction;

Step 6. Nanofluid flow: apply a y-direction force to each liquid argon atom to move the liquid in the y-direction;

Step 7. Statistical fluid flow rate: divide the upper and lower walls of the simulation model into 110 layers along the z-axis, count the y-direction sub-velocities of argon atoms in each layer and calculate the average value, and output the time step once per time step. the average velocity of the layer argon atoms;

Step 8. Calculate the effective viscosity: Calculate the flow velocity of each layer of argon atoms in the y direction, and calculate the effective viscosity according to the formula:

where η is the effective viscosity, dv _y /dz is the shear rate along the z direction, τ _zy is the shear stress in the zy plane, F _y is the force acting in the y direction of the nanofluid, A is the liquid argon and the upper and lower the contact area of the wall;

Step 9. Stabilize the flow and calculate the effective viscosity: When the velocity fluctuation of the whole system converges, confirm that the nanofluid flow tends to be stable, and calculate and output the effective viscosity according to equations (5) and (6).

The method of the present invention uses Lammps software to simulate and construct a model of nanofluid (flowing nanoparticles) flowing between two parallel copper plates, and by changing the volume fraction, temperature and size of nanoparticles, the flow rate of nanofluid is calculated and calculated in this Effective viscosity within nanochannels. Due to the influence of nanoparticle size, the fluid motion is controlled by surface forces, and the addition of nanoparticles and intermolecular effects make nanofluids unable to satisfy the continuum hypothesis. It is solved that it is difficult to predict the influence of nanoparticles on the fluid flow resistance in the pipeline because the size of the nanoparticles does not exceed 100 nm, and the current method is difficult to study the influence of nanoparticles on the flow behavior of nanofluids from the microscopic level. The present invention uses molecular dynamics as a very effective method to study the flow properties of nanofluids at the nanometer level.

The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited to this. Substitutions should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (3)

1. a kind of method for studying nano-fluid flow behavior in nanochannel by simulation model characterized by comprising

Step 1. constructs simulation model: including upper and lower parallel wall surface using molecular dynamics software building, and upper and lower parallel Liquid Argon is set between wall surface and the simulation model of the nano-fluid of nano particle is set in the Liquid Argon；

Step 2. selects potential function: being calculated with Lennard-Jones potential function mutual between each atom in the simulation model Effect, the Lennard-Jones potential function are as follows:

The value of the σ between homoatomic and ε is not calculated according to Lorentz Berthelot mixing rule, and formula is as follows:

In above formula (1), (2) and (3), r_ijFor the distance of atom i and atom j, σ and ε be respectively sphere of action between atom with Action intensity；

The parameter of step 3. setting simulation model: each parameter of model described in the parameter setting by Lennard-Jones potential function Are as follows: σ_Cu-CuFor 0.2338nm；ε_Cu-CuIt is 6.563 × 10^-20J；σ_Ar-ArFor 0.3405nm；ε_Ar-ArIt is 1.67 × 10^-21J；σ_Cu-Ar For 0.2872nm；ε_Cu-ArIt is 1.041 × 10^-20J；

Step 4. balance model: the simulation model is balanced using NVT assemblage in molecular dynamics software, Mei Geshi The a length of 2fs of spacer step, when balance a length of 1200ps；

Step 5. changes temperature control order: removing NVT order in molecular dynamics software, passes through the speed in the direction liquid ar atmo z Degree calculates temperature, and the formula that temperature is calculated in molecular dynamics is as follows:

KE=dim/2k_BNT (4)

In above formula (4), KE by calculating atom group total kinetic energy；Dim is the dimension of simulation；k_BFor Boltzmann constant, N is institute Calculate the atomicity in atom group；T is temperature；

Step 6. nano-fluid flowing: to liquid ar atmo each in simulation model apply a direction y power, make Liquid Argon to The direction y is mobile；

Step 7. counts fluid flow rate: simulation model being divided into 110 layers along z-axis, counts the component velocity in each layer of direction ar atmo y And average value is calculated, each time step exports the average speed of every layer of ar atmo of the primary time step；

Step 8. calculates effective viscosity: counting the flowing velocity in each layer of direction ar atmo y, calculates according to the following formula effective Viscosity are as follows:

In above formula (5), (6), η is effective viscosity；dv_y/ dz is the shear rate of nano-fluid in the z-direction；τ_zyFor zy plane Shear stress；F_yFor the power for acting on the direction nano-fluid y；A is the contact area of Liquid Argon and wall surface；

Step 9. steady flow simultaneously calculates effective viscosity: when the nano-fluid velocity perturbation convergence in entire simulation model, really Determine nano-fluid flowing to tend towards stability, is calculated according to above formula (5) and (6) and obtain effective viscosity.

2. the method according to claim 1 that nano-fluid flow behavior in nanochannel is studied by simulation model, It is characterized in that, in the step 1 of the method, the molecular dynamics software of use are as follows: Lammps software.

3. the side according to claim 1 or 2 for studying nano-fluid flow behavior in nanochannel by simulation model Method, which is characterized in that in the method, simulation model is two classes, comprising:

In first kind simulation model, change the volume fraction of the nano particle of nano-fluid, by the nanometer for changing same diameter The number of particle controls its volume fraction；

In second analoglike model, change the nano-particle diameter of nano-fluid, by the nanometer for changing fixed volume score Grain number controls its particle size.