JP2010224653A - Fluid analysis method, fluid analysis apparatus, and fluid analysis program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform analysis that obtains an analysis result having a small difference with an actual flow channel even if a lattice interval is increased when performing fluid analysis by the lattice Boltzmann method. <P>SOLUTION: In obtaining particle distribution in a translation process for virtual fluid particles on lattice points adjacent to a porous body 1, a discrete velocity distribution function is used which includes a reflectance rate by which a virtual fluid particle is reflected on the porous body 1 or a transmission factor by which the particle passes through the porous body 1. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a fluid analysis method, apparatus, and program using a lattice Boltzmann method.

  The lattice Boltzmann method is known as one of the fluid analysis methods. In fluid analysis using the lattice Boltzmann method, first, a calculation space partitioned by a lattice is created in an information processing apparatus such as a computer. Next, virtual fluid particles, which are virtual particles moving around on the lattice, are introduced, and fluid analysis is performed by obtaining a change in the distribution (number of particles) of the virtual fluid particles at the lattice points.

In determining the distribution of virtual fluid particles, there are two processes for the behavior of virtual fluid particles: a translation process (a process that moves from one lattice point to another) and a collision process (a process in which virtual fluid particles collide with each other). Suppose that the virtual fluid particle repeats the translation process and the collision process. Further, it is assumed that the time step (time step) δ _t is determined in advance, and in the translation process, the virtual fluid particles always exist on the lattice points for each time step δ _t and cannot stay in the middle of the lattice line. Also assume that the collision occurs instantaneously and occurs only on the grid points.

Furthermore, a discrete velocity distribution function indicating the distribution of virtual fluid particles in the translation process and the collision process is defined. Using this discrete velocity distribution function, for a certain lattice point is calculated for each distribution time increment [delta] _t of the virtual fluid particles in the distribution and collision process virtual fluid particles in translation process. This calculation is performed for a predetermined range of lattice points (for example, all lattice points), and fluid analysis is performed by calculating a change in the distribution of virtual fluid particles.

  In this fluid analysis, fluid analysis may be performed on a flow path including a porous body such as a filter. In this case, the porous body 1 is arranged on the calculation space as shown in FIG. In the prior art, the fluid analysis of the flow path including the porous body 1 is performed by making the discrete velocity distribution function of the collision process different between the lattice points that overlap the porous body 1 and the lattice points that do not overlap the porous body 1. Yes.

  That is, it is known that the behavior of the fluid inside the porous body 1 follows the Brinkman equation. On the other hand, it is known that the behavior of the fluid outside the porous body 1 follows the Navier-Stokes equation. Therefore, in Non-Patent Document 1, the parameters of the discrete velocity distribution function are determined so as to follow the Brinkman equation in the collision process at the lattice point overlapping with the porous body 1, while the lattice points not overlapping with the porous body 1 are determined. Fluid analysis is performed by determining the parameters of the discrete velocity distribution function so as to follow the Navier-Stokes equation.

Hayashi, Kubo “Computer simulation of solitary particles in diesel particulate filter”, computer, calculation and its application (Computers and M p20). Vol. 55, p. 1450-1460

  When the lattice point interval is wide, the number of lattice points overlapping the porous body 1 is reduced, and there is a possibility that the analysis is performed in a state where the influence of the porous body 1 is not accurately reflected. For example, as shown in FIG. 11, the porous body 1 is moved from the inflow side (left side in FIG. 11) to the outflow side (right side) even though the porous body 1 is arranged to block the flow path. There is a possibility that a path 2 that does not pass through a lattice point that overlaps, that is, a path 2 that is not blocked by the porous body 1 in the calculation. When analysis is performed in such a state, an analysis result having a large difference from the actual flow path is output. On the other hand, if the lattice point interval is set narrow and the number of lattice points overlapping the porous body 1 is increased, another problem arises that the calculation load increases.

  Therefore, an object of the present invention is to perform a fluid analysis that can obtain an analysis result with a small error even if the lattice point interval is widened.

  The present invention provides a fluid analysis method in which a plurality of lattice points are provided in a calculation processing space, and a fluid analysis of a flow path in which a porous body is disposed is performed using a lattice Boltzmann method for obtaining the behavior of virtual fluid particles at the lattice points. And, on the lattice point adjacent to the porous body, as a discrete velocity distribution function during the translation process in the lattice Boltzmann method, the reflectance of the virtual fluid particle reflected by the porous body or the virtual fluid particle is Fluid analysis is performed by using a function including a transmittance that permeates the porous body.

  Further, the present invention is characterized in that the reflectance or the transmittance is calculated using a permeability coefficient of the porous body.

に基づいて前記反射率または前記透過率を算出することを特徴とする。 In the present invention, κ is the permeation coefficient, d is the thickness of the porous body, δ _x is the interval between the plurality of lattice points, R is the reflectance (0 <R <1), and 1-R is the When the transmittance, ν is the kinematic viscosity coefficient, and c _s is the speed of sound of the virtual fluid particle,

The reflectance or the transmittance is calculated based on the above.

  The present invention is the fluid analysis method according to claim 3, wherein the porous body is a filter wall of a gas filter, and fluid analysis of an exhaust gas flow path in the gas filter is performed.

  Furthermore, the present invention provides a calculation unit that provides a plurality of lattice points in a calculation processing space and performs fluid analysis of a flow path in which a porous body is disposed using a lattice Boltzmann method for obtaining the behavior of virtual fluid particles at the lattice points. The calculation unit is configured so that the virtual fluid particles are converted into the porous body as discrete velocity distribution functions during a translation process in the lattice Boltzmann method on the lattice points adjacent to the porous body. The fluid analysis is performed using a function including a reflectance reflected by the light source or a transmittance through which the virtual fluid particles pass through the porous body.

  Furthermore, the present invention provides a fluid analysis in which a plurality of lattice points are provided in a calculation processing space, and a fluid analysis of a flow path in which a porous body is arranged is performed using a lattice Boltzmann method for obtaining the behavior of virtual fluid particles at the lattice points. A program for causing a device to perform fluid analysis, wherein the virtual fluid particle is transmitted to the fluid analysis device as a discrete velocity distribution function during a translation process in the lattice Boltzmann method on the lattice points adjacent to the porous body. The fluid analysis is performed using a function including a reflectance reflected by the porous body and a transmittance through which the virtual fluid particles pass through the porous body.

  According to the present invention, when calculating the behavior of a virtual fluid particle at a lattice point adjacent to the porous body, a discrete velocity distribution including a reflectance at which the virtual fluid particle is repelled by the porous body or a transmittance through the porous body. Use a function. As a result, it is possible to obtain a fluid analysis result with less error even when the lattice point interval is enlarged.

It is a system configuration figure of the fluid analysis device concerning the present invention. It is the figure which has arrange | positioned the porous body in calculation space. It is a figure which shows the translation process of the lattice point adjacent to a porous body. It is a figure which shows the behavior of the virtual fluid particle straddling the porous body and the virtual fluid particle repelled by the porous body. It is a figure which shows the prior art and the fluid analysis method of this invention. It is not shown the prior art and the fluid analysis method of the present invention. It is a figure which shows the graph for calculating | requiring a reflectance. It is a flowchart which shows the calculation process of a calculating part. It is a functional block diagram of the fluid analysis apparatus concerning this invention. It is a figure which shows the fluid analysis result by this invention. It is a figure which shows the fluid analysis result by this invention. It is a figure which shows the fluid analysis method in a prior art. It is a figure which shows the fluid analysis method in a prior art.

  FIG. 1 shows the configuration of a fluid analysis apparatus according to an embodiment of the present invention. As shown in FIG. 1, the fluid analysis device includes a calculation unit 3, an input unit 4, a display unit 5, and a storage unit 6.

The calculation unit 3 is a so-called CPU, and performs a fluid analysis process described later by executing a fluid analysis program stored in the storage unit 6 in advance. The input unit 4 includes input means such as a keyboard, and the size, arrangement and characteristics of the porous body 1 to be subjected to fluid analysis processing, setting of lattice points in the calculation space, and virtual fluid particle distribution of all lattice points Inputs such as (discrete velocity distribution function f _i (x, 0) of each virtual fluid particle), boundary condition, calculation time increment, and end time are received from the user. The input information is stored and held in the storage unit 6. The display unit 5 includes information output means such as a display and a printer, and displays and outputs information such as a calculation space to be subjected to fluid analysis processing, set parameters, processing progress, and processing results. The storage unit 6 includes storage means such as a semiconductor memory and a hard disk, and stores and holds a fluid analysis program, information set for fluid analysis processing, calculation results in the analysis processing, and the like. The storage unit 6 can be appropriately accessed from the calculation unit 3.

  Next, the fluid analysis process performed by the calculation unit 3 will be described. In the present invention, fluid analysis is performed by replacing a part of the calculation process for obtaining the behavior of the fluid particles in the porous body 1 in the conventional lattice Boltzmann method with a new calculation process.

  In describing the lattice Boltzmann method, the collision process will be described first. Here, in the conventional collision process, the Brinkman equation is applied to the analysis of the fluid at the lattice point that overlaps the porous body 1, and the Navier-Stokes equation is applied to the analysis of the fluid at the lattice point that does not overlap with the porous body 1. However, as will be described later, in the present invention, fluid analysis can be performed without overlapping lattice points on the porous body 1, and analysis can be performed only by applying the Navier-Stokes equation. Therefore, in this embodiment, as shown in FIG. 2, the porous body 1 is arranged such that the lattice point interval is larger than the width of the porous body 1 and there is no lattice point overlapping the porous body 1. The collision process in which the Navier-Stokes equation is applied to lattice points that do not overlap with the porous body 1 will be described below.

At time t, of the virtual fluid particles present on the lattice points represented by the position vector x, the discrete velocity distribution represents the distribution of virtual fluid particle discrete velocity vector is a vector representing the movement between the lattice points is e _i The function g _i (x, t) is expressed by Equation 1 below.

Here, f _i (x, t) on the right side indicates the distribution of virtual fluid particles in the translation process before the collision process. A suffix _i of the discrete velocity vector e _i indicates a direction in which particles can move in the three-dimensional fluid analysis. For example, when each grid point is stationary and movable in 14 directions, values from 0 to 14 are taken as shown in the following formula 2.

Further, τ is a dimensionless coefficient called a single time relaxation coefficient, and τδ _t [sec] represents a time until the virtual fluid particle reaches an equilibrium state. The single time relaxation coefficient τ can be set to an arbitrary value in the range of 0.5 <τ <∞. F _i ^(eq) (x, t) is a distribution function of virtual fluid particles when an equilibrium state is reached in a certain spatial region. That is, Formula 1 represents that the distribution of the virtual fluid particles moves toward an equilibrium state every time the virtual fluid particles collide.

Here, f _i ^(eq) (x, t) will be described. As described above, the behavior of the virtual fluid particle follows the Navier-Stokes equation at the lattice point that does not overlap the porous body 1. When various parameters are determined so as to follow the Navier-Stokes equation, f _i ^(eq) (x, t) is expressed by Equation 3 below.

ここで、ｗ_ｉは重み係数を表し、接尾辞ｉによって下記数式４のような値をとる。

Here, w _i represents a weighting coefficient, and takes a value as shown in the following Equation 4 depending on the suffix i.

Moreover, p is a pressure and u represents a flow velocity vector. Here, since the weighting coefficient wi, the minimum speed c, and the discrete speed vector ei are given in advance in Equation 3, fi ^(eq) (x, t) is derived by obtaining the pressure p and the flow velocity vector u. Is done. The pressure p and the flow velocity vector u can be obtained as Equations 5 and 6, respectively.

  That is, the pressure p and the flow velocity vector u can be derived from the distribution of the virtual fluid particles in the translation process before the collision process. Therefore, the discrete velocity distribution function in the translation process will be described below.

  In the present invention, in the translation process, the application conditions of the discrete velocity distribution function are changed between the lattice points adjacent to the porous body 1 and the lattice points not adjacent to the porous body 1. Thereby, the process in which the virtual fluid particles are repelled by the porous body 1 or permeated through the porous body 1 is reflected in the calculation. Here, the lattice points adjacent to the porous body 1 indicate lattice points at both ends of a lattice line overlapping the porous body 1.

First, the following formula 7 is applied to the discrete velocity distribution function f _i (x, t) in the translation process for lattice points that are not adjacent to the porous body 1.

  Here, the right side shows the distribution of the virtual fluid particles in the collision process before the translation process.

On the other hand, the discrete velocity distribution function f _i (x, t) in the translation process of the lattice points adjacent to the porous body 1 is classified according to the discrete velocity vector e _i . This case division will be described with reference to FIG. The lattice point x is adjacent to the porous body 1. In this case, there is a porosity between the lattice points x-e _i and x, such as between x and x-e ₁ , between x and x-e _2, and between x and x-e _3. When the field 1 does not exist, the above formula 7 is applied. On the other hand, as between the lattice points x and x-e _4, when the porous body 1 is present between the grid point x-e _i and x, Equation 8 below is applied.

Here, both g _i (x, t) and g _i (x−e _i , t) on the right side indicate the distribution of virtual fluid particles in the collision process before the translation process. Of the suffixes f and g, -i represents a virtual fluid particle traveling in the opposite direction to i. R is a reflectance (0 <R <1), and indicates a ratio at which the virtual fluid particles are repelled by the porous body 1. On the other hand, (1-R) is the transmittance and indicates the ratio of the temporary fluid particles passing through the porous body 1.

  Here, Formula 8 will be described with reference to FIG. In the first expression of Expression 8, the first term on the right side is repelled by the porous body 1 and returned to the original lattice point x when moving to the adjacent lattice point among the virtual fluid particles at the lattice point x. The virtual fluid particle is represented, and the second term on the right side represents the virtual fluid particle that has moved through the porous body 1 and moved to the lattice point x among the virtual fluid particles located at the lattice point adjacent to the lattice point x across the porous body 1. ing.

  Thus, in the present invention, the fluid flow analysis including the porous body 1 is accurately performed by using the discrete velocity distribution function including the reflectance or transmittance for the translation process on the lattice point adjacent to the porous body 1. Can be done. Taking the above-described FIG. 11 as an example, a path that can move from the inflow side to the outflow side without passing through the lattice points to which the discrete velocity distribution function including the reflectance or transmittance is applied cannot be taken. Thus, even when the lattice point interval is wide, the analysis can be performed in a state that accurately reflects the structure of the flow path in which the porous body 1 is arranged so as to block the flow.

  Furthermore, in the present invention, the discrete velocity distribution function including the reflectance or transmittance is applied to the lattice points adjacent to the porous body 1, so that the virtual fluid particles are reflected by the porous body 1 or the porous body 1. In order to include the permeation process in the calculation, the fluid analysis can be performed without overlapping the lattice points on the porous body 1. Therefore, as shown in FIG. 2 described above, the porous body 1 can be arranged so that there is no lattice point overlapping the porous body 1, and fluid analysis can be performed using only the Navier-Stokes equation. In the prior art, in addition to the Navier-Stokes equation, the Brinkman equation is used for lattice points overlapping the porous body 1. However, in the present invention, fluid analysis can be performed without applying the Brinkman equation, compared with the prior art. The analysis method is simplified. For the convenience of the shape of the porous body 1 and the arrangement of the porous body 1, when there are lattice points that overlap the porous body 1, the Brinkman equation is applied to the lattice points.

  Next, derivation of the reflectance R in Expression 8 will be described. The present inventors have found that the reflectance R can be derived based on the following formula 9. This will be described below.

である。 Here, κ represents the permeation coefficient of the porous body 1, d represents the thickness of the porous body 1, and ν represents the kinematic viscosity coefficient (the viscosity coefficient μ divided by the density ρ). C _s indicates the speed of sound of the virtual fluid particle, and is treated as a constant in the incompressible fluid. For example, when analysis is performed with a two-dimensional square lattice

It is.

  In deriving the reflectance R, as shown in FIG. 5a, consider a flow path in which an infinitely long porous body 1 is linearly arranged on lattice points so as to block the flow of fluid. Next, let us consider a channel in which the position of the porous body 1 is slightly shifted as shown in FIG.

The discrete distribution velocity functions f _i (x, t) and g _i (x, t) of the virtual fluid particles at the lattice points in FIG. 5a can be derived from the Brinkman equation which is a conventional technique. Here, since FIG. 5a and FIG. 5b represent the same flow path, it is understood that the distribution of the virtual fluid particles at the same point in both figures is the same. Accordingly, the distribution of virtual fluid particles at the lattice points 7 in the porous body 1 of FIG. 5a is calculated using the Brinkman equation, and the calculated distribution of virtual fluid particles corresponds to the lattice points 7 of FIG. 5a in FIG. 5b. The reflectance R at the lattice point 8 is calculated by substituting the calculated virtual fluid particle distribution into Formula 8 assuming that the distribution of the virtual fluid particle at the lattice point 8 is substantially equal.

On the other hand, based on the virtual fluid particle distribution obtained by the Brinkman equation, the pressure p is obtained by Expression 5 and the velocity u is calculated by Expression 6. Based on the p and the following Equation 10 △ ^{p ~} is calculated and also obtains the value of the calculated and △ ^p ~ / ^{u ~} a ^{u ~} based on u and the following Equation 11.

As a result, it is set between the reflectance R and △ ^{p ~} / ^u ~ when taking a certain value virtual fluid particle distribution ^{(R, △ p ~ / u} ~). Various combinations of (R, Δp ^~ / u ^~ ) are obtained by variously changing the virtual fluid particle distribution. Next, as shown in FIG. 6, a graph in which the relationship between Δp ^~ / u ^~ and R is plotted is created. When a function along this plot is obtained by fitting or the like, the following Expression 12 is obtained.

  Here, in the fluid analysis based on the Brinkman equation, it is known that the behavior of the fluid follows the Darcy law expressed by the following formula 13.

From Expressions 12 and 13, Expression 9 is obtained. In Expression 9, δ _x , c _s , and d are determined in advance, and κ can also be obtained by experiment. Furthermore, ν varies depending on the density ρ. However, in an incompressible fluid, ρ can be derived by a function having only the pressure p as a variable, and ν can be derived by calculating p in Expression 5. By substituting these values into Equation 9, the reflectance R can be derived. By obtaining R, the distribution of the virtual fluid particles in the translation process can be calculated in Equation 8.

  As described above, by repeatedly calculating the distribution of the virtual fluid particles in the collision process and the distribution of the virtual fluid particles in the translation process, and obtaining the change in the distribution of the virtual fluid particles at each lattice point, the fluid analysis of the flow path Is done.

  The fluid analysis method according to the present invention has been described above. Next, a specific procedure of the fluid analysis process will be described with reference to the flowchart of FIG. The calculation unit 3 executes the following processing by executing the fluid analysis processing program stored in the storage unit 6. Thereby, as will be described later, the fluid analyzing apparatus 9 functions as each unit shown in FIG. The following processing is performed on all virtual fluid particles positioned at all grid points set in the calculation space for each calculation time step. When the processing for all the particles existing in the calculation space is completed, the operation shifts to the next calculation time step.

First, the calculation unit 3 acquires the shape, initial conditions, boundary conditions, and the like of the porous body 1 stored in the storage unit 6 (S1). Here, the initial conditions include virtual fluid particle distributions at all lattice points at t = 0 (discrete velocity distribution function f _i (x, 0) of each virtual fluid particle). The boundary condition includes a condition such that the virtual fluid particles do not move in the direction of penetrating the wall of the flow path.

Next, the computing unit 3 obtains the pressure p by substituting the virtual fluid particle distribution f _i (x, t) at the previous time t into Equation 5. Also, f _i (x, t) is substituted into Equation 6 to obtain the speed u (S2). By substituting the pressure p and the velocity u obtained here into Equation 3, a virtual fluid particle distribution f _i ^(eq) (x, t) in an equilibrium state is obtained (S3). Further, by substituting f _i (x, t) and f _i ^(eq) (x, t) into Equation 1, a virtual fluid particle distribution g _i (x, t) of the collision process at the current time t is obtained ( S4).

The calculation unit 3 calculates a translation process following the collision process. First arithmetic unit 3 confirms the lattice point x to be operational, whether the porous body 1 is present between the neighboring lattice points x-e _i (S5). If the porous body 1 does not exist, the virtual fluid particle distribution f _i (x, t + δ _t ) in the translation process is obtained by substituting g _i (x−e _i , t) into Equation 7 (S6).

On the other hand, if the porous body 1 is present between the grid point x-e _i and the adjacent grid point x to be calculated for target calculation unit 3 calculates the reflectance on the basis of Equation 9 (S7). By substituting this reflectance and g _−i (x, t) and g _i (x−e _i , t) calculated in S4 into Equation 8, the virtual fluid particle distribution f _i (x, t + δ _t ) in the translation process is obtained. Obtain (S8).

  The above calculation of the distribution of the virtual fluid particles in the collision process and the translation process is performed until the end time stored in the storage unit 6. If the end time has not yet been reached, the process returns to S2 and repeats the calculation (S9). When the end time is reached, the calculation is terminated and the analysis result is output to the display unit 5 (S10).

  FIG. 8 shows a functional block diagram of the fluid analysis device 9 that executes the fluid analysis processing described above. The fluid analysis device 9 includes an input data acquisition unit 10 that executes S1, a collision process calculation unit 11 that executes S2 to S4, a translation process calculation unit 12 that executes S5 to S8, and an end time confirmation unit that executes S9. 13 and the analysis result output means 14 which performs S10 are comprised.

  The result of the fluid analysis according to the present invention is shown in FIG. 9b. FIG. 9 a is a flow path including the porous body 1 input from the input unit 4, and FIG. 9 b is a result of performing a simulation according to the present invention for the flow path. Thus, it is understood that in the fluid analysis according to the present invention, the analysis is performed in a state in which the flow path structure is accurately reflected.

  The fluid analysis according to the present invention has been described above. This fluid analysis can be performed on various porous bodies and fluids. For example, it is possible to analyze the behavior of exhaust gas in a flow path including a porous exhaust gas filter, or to analyze the behavior of exhaust gas in the gas filter.

DESCRIPTION OF SYMBOLS 1 Porous body, 2 path | route, 3 calculating part, 4 input part, 5 display part, 6 memory | storage part, 9 fluid analyzer, 10 input data acquisition means, 11 collision process calculating means, 12 translation process calculating means, 13 end time confirmation Means, 14 Analysis result output means.

Claims (6)

A fluid analysis method in which a plurality of lattice points are provided in a calculation processing space, and a fluid analysis of a flow path in which a porous body is disposed is performed using a lattice Boltzmann method for obtaining the behavior of virtual fluid particles at the lattice points,
On the lattice points adjacent to the porous body, as a discrete velocity distribution function during the translation process in the lattice Boltzmann method, the reflectance at which the virtual fluid particles are reflected by the porous body or the virtual fluid particles are the porous body Fluid analysis is performed by using a function including the transmittance that passes through
A fluid analysis method characterized by the above.   The fluid analysis method according to claim 1, wherein the reflectance or the transmittance is calculated using a permeability coefficient of the porous body. 3. The fluid analysis method according to claim 2, wherein κ is the permeation coefficient, d is the thickness of the porous body, δ _x is an interval between the plurality of lattice points, and R is the reflectance (0 <R <1). , 1-R is the transmittance, ν is the kinematic viscosity coefficient, and c _s is the sound velocity of the virtual fluid particle,

The fluid analysis method, wherein the reflectance or the transmittance is calculated based on   The fluid analysis method according to claim 3, wherein the porous body is a filter wall of a gas filter, and a fluid analysis of an exhaust gas flow path in the gas filter is performed. A fluid analysis apparatus provided with a calculation unit that provides a plurality of lattice points in a calculation processing space and performs fluid analysis of a flow path in which a porous body is arranged, using a lattice Boltzmann method for obtaining the behavior of virtual fluid particles at the lattice points Because
The calculation unit is configured such that, on the lattice points adjacent to the porous body, the reflectance at which the virtual fluid particles are reflected by the porous body or the virtual fluid as a discrete velocity distribution function during the translation process in the lattice Boltzmann method Fluid analysis is performed using a function including the transmittance of particles through the porous body.
A fluid analysis apparatus characterized by that. Using a lattice Boltzmann method to calculate the behavior of virtual fluid particles at the lattice points provided in the calculation processing space, perform fluid analysis on a fluid analysis device that performs fluid analysis of the flow path in which the porous body is placed A program to
On the lattice point adjacent to the porous body, the fluid analysis device has a reflectance at which the virtual fluid particles are reflected by the porous body as a discrete velocity distribution function during the translation process in the lattice Boltzmann method, and Fluid analysis is performed using a function including a permeability of the virtual fluid particles through the porous body,
A program characterized by that.

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