Pressure loss analysis method, a non-transitory computer readable medium, and a pressure loss analysis apparatus for analyzing pressure loss in a honeycomb structure

A CPU of an analysis apparatus performs a fluid analysis and derives transient distribution information that represents an accumulation distribution of a particulate layer on an inflow-side inner circumferential surface of a honeycomb structure at a time point after a short time interval Δt (step S130). The CPU then repeatedly performs a fluid analysis by taking into account the transient distribution information derived previous time to repeatedly derive transient distribution information (steps S130 to S150) and then derives post-transient-analysis distribution information that represents the accumulation distribution of the particulate layer at a later time point (step S160).

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a pressure loss analysis method, a program for executing the pressure loss analysis method, and a pressure loss analysis apparatus.

2. Description of the Related Art

Honeycomb structures including partition walls that form a plurality of cells serving as flow paths for a fluid are known so far (for example, PTL 1). Honeycomb structures are used to clean exhaust gas from internal combustion engines, for example, automobile engines, and prediction of a pressure loss that occurs when exhaust gas passes through a honeycomb structure is carried out. In PTL 1 for example, a pressure loss is predicted by virtually separating the factors that cause the pressure loss in a honeycomb structure into four kinds of factors on the basis of an internal pressure distribution determined using computational fluid analysis and by adding the values of the pressure loss predicted for the four kinds of factors together. PTL 1 states that a pressure loss can be accurately predicted in this way.

PTL 1 gives an example of a pressure loss prediction method for a catalytic converter that converts harmful substances in gas to harmless substances by just allowing the gas to pass through open flow paths of cells of a honeycomb structure to bring the gas into contact with a catalyst that coats the surfaces of the cell partition walls. Other exemplary usages of a honeycomb structure include the use of a honeycomb structure in which inlets and outlets of cells are alternately plugged such that gas passes through cell partition walls in order to filter particulate matter contained in engine emissions and exhaust gas from other combustion devices and the use of such a structure in order to filter solid particulates contained in a liquid, such as water. In this filtering usage, pressure loss prediction in a state where particulate matter has accumulated is essential because resistance of each partition wall against the passing gas increases due to accumulation of particulate matter on the partition wall. In conventional pressure loss prediction methods for the particulate matter accumulation state, the analysis is performed on the assumption that particulate matter accumulates on the surfaces of the partition walls in a uniform thickness t (t=M/S, where M denotes the total amount of particulate matter and S denotes the total surface area of partition walls of inlet cells) as in NPL 1, for example.

CITATION LIST

Patent Literature

Non Patent Literature

SUMMARY OF THE INVENTION

However, PTL 1 and NPL 1 do not take into account an accumulation distribution of particulate matter, and no method for accurately simulating how particulate matter accumulates at each part of the partition portions when a fluid flows inside a honeycomb structure is known.

The present invention has been made to overcome such an issue, and a main object thereof is to analyze a pressure loss by more accurately simulating the accumulation state of particulate matter.

The present invention employs the following measures to achieve the main object described above.

A pressure loss analysis method of the present invention is a method for analyzing a pressure loss in a honeycomb structure for a case where a fluid flows inside the honeycomb structure, the honeycomb structure including porous partition portions that form a plurality of inflow-side cells and a plurality of outflow-side cells, the pressure loss analysis method comprises:

a transient analysis step of repeatedly performing a particulate-layer-distribution deriving process, in which transient distribution information that represents an accumulation distribution of a particulate layer on an inflow-side inner circumferential surface is derived by performing a fluid analysis for the case where the fluid flows inside the honeycomb structure on the basis of object information that simulates the honeycomb structure with a plurality of mesh portions and by deriving, for each of the mesh portions corresponding to the inflow-side inner circumferential surface that is an inner circumferential surface of each of the inflow-side cells among a surface of the partition portion, a state of the particulate layer, which is a layer in which particulate matter contained in the fluid has accumulated, at a time point after a short time interval, and of deriving post-transient-analysis distribution information that represents the accumulation distribution at a time point after the particulate-layer-distribution deriving process has been performed a plurality of times, by performing the fluid analysis during the particulate-layer-distribution deriving process performed for the second and following times while taking into account the transient distribution information derived in an immediately preceding particulate-layer-distribution deriving process; and

a pressure loss deriving step of deriving a pressure loss for the case where the fluid flows inside the honeycomb structure, by performing a fluid analysis on the basis of the object information and the post-transient-analysis distribution information.

In this pressure loss analysis method, transient distribution information that represents an accumulation distribution of a particulate layer on an inflow-side inner circumferential surface of a honeycomb structure at a time point after a short time interval is derived by performing a fluid analysis. Then, transient distribution information is repeatedly derived by performing a fluid analysis while taking into account the transient distribution information derived previous time, and consequently post-transient-analysis distribution information that represents the accumulation distribution of the particulate layer at a later time point is derived. By repeatedly analyzing the accumulation distribution of the particulate layer at each time point after the short time interval in this way, a transient change in the accumulation distribution of the particulate layer over time can be accurately analyzed. Thus, the accumulation state (accumulation distribution) of the particulate layer at a time point after the short time interval has passed a plurality of times is accurately simulated by the post-transient-analysis distribution information. For example, the state closer to the actual accumulation state of the particulate layer can be simulated compared with the case of simulating a state where the particulate layer has evenly accumulated at every position on the inflow-side inner circumferential surface (state where the particulate layer is distributed evenly). Since a pressure loss for the case where the fluid flows inside the honeycomb structure is derived on the basis of this post-transient-analysis distribution information, the pressure loss can be analyzed by more accurately simulating the accumulation state of the particulate matter.

In the pressure loss analysis method according to the present invention, during the particulate-layer-distribution deriving process, the transient distribution information may be derived on the basis of information regarding a concentration of the particulate matter in the fluid and information regarding a flow rate of the fluid that flows into each of the mesh portions corresponding to the inflow-side inner circumferential surface, the information regarding the flow rate being a value derived through the fluid analysis performed during the particulate-layer-distribution deriving process. Here, the higher the concentration of the particulate matter in the fluid and the larger the flow rate of the fluid that flows through the inflow-side inner circumferential surface, the more the particulate matter accumulates. Accordingly, the transient distribution information can be appropriately derived by using the information regarding the concentration of the particulate matter in the fluid and the information regarding the flow rate of the fluid. That is, the accumulation state of the particulate layer can be appropriately simulated.

In the pressure loss analysis method according to the present invention, each of the transient distribution information and the post-transient-analysis distribution information may be information including at least one of a distribution of thickness of the particulate layer, a distribution of permeability of the particulate layer, and a distribution of flow resistance of the particulate layer. Since thickness, permeability, and flow resistance are information that influences a pressure loss that occurs when the fluid passes through the particulate layer, they are suitable as information representing the accumulation distribution of the particulate layer (the transient distribution information and the post-transient-analysis distribution information).

In the pressure loss analysis method according to the present invention, in the transient analysis step, the particulate-layer-distribution deriving process may be performed repeatedly until at least one of a total amount of the particulate matter that has accumulated on the inflow-side inner circumferential surface reaches a predetermined target amount or the sum of the short time intervals reaches a predetermined target period. With such a configuration, the accumulation state of the particulate layer in a state for which analysis of the pressure loss is desired (state where the target amount or the target period has been reached) can be simulated relatively easily, and the pressure loss in that state can be derived easily.

In the pressure loss analysis method according to the present invention, the object information may be information that simulates the honeycomb structure having an area ratio A of 15% or greater. The area ratio A is a ratio of an inflow-inflow facing area to an area of the inflow-side inner circumferential surface. The inflow-inflow facing area is an area of a portion of the inflow-side inner circumferential surface facing the inflow-side inner circumferential surface of another inflow-side cell. When a fluid containing particulate matter passes through the honeycomb structure, the particulate matter is unlikely to accumulate evenly on the inflow-side inner circumferential surface in the honeycomb structure having the area ratio A of 15% or greater. Accordingly, the value of the pressure loss derived by simulating the state where the particulate layer is evenly distributed tends to deviate from the actually measured value of the pressure loss measured using the honeycomb structure in which the same amount of particulate matter has accumulated. That is, the accuracy of the pressure loss analysis tends to decrease. In contrast, a deviation of the value derived using the pressure loss analysis method according to the present invention from the actually measured value is small also for the honeycomb structure having the area ratio A of 15% or greater, and thus the pressure loss analysis can be performed more accurately. Therefore, it is beneficial to employ the present invention when the pressure loss analysis is performed for the honeycomb structure having the area ratio A of 15% or greater.

A program according to the present invention is a program causing one or a plurality of computers to perform the individual steps of the above-described pressure loss analysis method. This program may be stored on a computer-readable recording medium (e.g., a hard disk, a ROM, an FD, a CD, a DVD, or the like), distributed from a certain computer to another computer via a transmission medium (network such as the Internet or a LAN), or transmitted and received in any other way. Since the individual steps of the above-described pressure loss analysis method are performed when this program is executed by one computer or a plurality of computers by distributing processes to the respective computers, advantageous effects similar to those of the method are obtained.

A pressure loss analysis apparatus of the present invention is an apparatus for analyzing a pressure loss in a honeycomb structure for a case where a fluid flows inside the honeycomb structure, the honeycomb structure including porous partition portions that form a plurality of inflow-side cells and a plurality of outflow-side cells, the pressure loss analysis apparatus comprises:transient analysis device for repeatedly performing a particulate-layer-distribution deriving process, in which transient distribution information that represents an accumulation distribution of a particulate layer on an inflow-side inner circumferential surface is derived by performing a fluid analysis for the case where the fluid flows inside the honeycomb structure on the basis of object information that simulates the honeycomb structure with a plurality of mesh portions and by deriving, for each of the mesh portions corresponding to the inflow-side inner circumferential surface that is an inner circumferential surface of each of the inflow-side cells among a surface of the partition portion, a state of the particulate layer, which is a layer in which particulate matter contained in the fluid has accumulated, at a time point after a short time interval, and for deriving post-transient-analysis distribution information that represents the accumulation distribution at a time point after the particulate-layer-distribution deriving process has been performed a plurality of times, by performing the fluid analysis during the particulate-layer-distribution deriving process performed for the second and following times while taking into account the transient distribution information derived in an immediately preceding particulate-layer-distribution deriving process; andpressure loss deriving device for deriving a pressure loss for the case where the fluid flows inside the honeycomb structure, by performing a fluid analysis on the basis of the object information and the post-transient-analysis distribution information.

This pressure loss analysis apparatus is capable of analyzing a pressure loss by more accurately simulating the accumulation state of particulate matter, like the pressure loss analysis method described above. Note that each device of this pressure loss analysis apparatus may perform an additional operation or an additional device may be added to this pressure loss analysis apparatus so that the above-described various embodiments of the pressure loss analysis method are implemented.

DETAILED DESCRIPTION OF THE INVENTION

An embodiment of the present invention will be described next by using the drawings.FIG. 1is a diagram illustrating a schematic configuration of an analysis apparatus10, which is an embodiment of the present invention. This analysis apparatus10is implemented as a computer, such as a personal computer, and includes a controller11and an HDD15. The controller11includes a CPU12that performs various processes, a ROM13that stores programs for the various processes and the like, and a RAM14that temporarily stores data, for example. The HDD15is a large-capacity memory that stores various processing programs, such as an analysis process program, and various kinds of data used in the analysis process. The analysis apparatus10also includes a display16that displays various kinds of information on its screen, and an input device17such as a mouse and keyboard used by a user to input various kinds of instructions. Although details will be described later, the HDD15stores object information19and the like. The object information19is information that simulates an object subjected to an analysis. This analysis apparatus10analyzes a pressure loss that occurs when a fluid flows inside an object simulated by the object information19, on the basis of the object information19and the like stored on the HDD15.

Now, an object subjected to an analysis by the analysis apparatus10will be described.FIG. 2is an explanatory diagram illustrating an example of a schematic configuration of a honeycomb structure20, which is an example of an object subjected to an analysis.FIG. 3is an explanatory diagram of partition portions22and cells32of the honeycomb structure20. Note that the up-down direction and the front-rear direction are assumed as illustrated inFIG. 2in this embodiment. In addition, a direction perpendicular to the up-down direction and the front-rear direction is assumed as the right-left direction (seeFIG. 3). Further, it is assumed that the right direction is the X-direction (positive direction on the X axis), the up direction is the Y direction (positive direction on the Y axis), and the rear direction is the Z direction (positive direction on the Z axis). The honeycomb structure20is used as a diesel particulate filter (DPF) having a function of filtering particulate matter (PM) contained in exhaust gas from a diesel engine, for example.

As illustrated inFIG. 2, the honeycomb structure20includes porous partition portions22that form a plurality of cells32serving as flow paths for a fluid (exhaust gas), front-side plugging portions37that plug one end of some of the cells32, and rear-side plugging portions38that plug one end of some of the cells32. The external shape of the honeycomb structure20may be, but not limited to, circular cylindrical, quadrangular cylindrical, elliptical cylindrical, or hexagonal cylindrical, for example. The external shape is assumed to be circular cylindrical in this embodiment. As illustrated inFIG. 3, the partition portions22form a plurality of inflow-side cells33and a plurality of outflow-side cells34, both of which constitute the plurality of cells32. The inflow-side cells33have a hexagonal cross-section. One end (on a front-end-surface-27side) of the inflow-side cells33is open, whereas the other end (on a rear-end-surface-28side) thereof is plugged with the rear-side plugging portion38. The outflow-side cells34have a quadrangular cross-section. One end of the outflow-side cells34is plugged with the front-side plugging portion37, whereas the other end thereof is open. An inner circumferential surface of each of the inflow-side cells33among the surface of the partition portions22is referred to as an inflow-side inner circumferential surface23. An inner circumferential surface of each of the outflow-side cells34among the surface of the partition portions22is referred to as an outflow-side inner circumferential surface24. The inflow-side cells33are adjacent to and on the right, left, upper, and lower sides of each of the outflow-side cells34. Surfaces extending in the X direction and surfaces extending in the Y direction among the inflow-side inner circumferential surfaces23face the outflow-side inner circumferential surfaces24. In addition, surfaces of the inflow-side inner circumferential surfaces23of the plurality of inflow-side cells33inclined from the X direction and the Y direction face each other. A portion of the inflow-side inner circumferential surface23that faces the inflow-side inner circumferential surface23of another inflow-side cell33(but does not face the outflow-side inner circumferential surface24) is referred to as an inflow-inflow facing surface23a. In an enlarged view on the right inFIG. 3, the inflow-inflow facing surface23ais represented by a thick line among the inflow-side inner circumferential surface23of the inflow-side cell33located at the center. In this honeycomb structure20, when a fluid flows from the front side, the fluid flows into the inflow-side cells33from the inlet side (a front end surface27), passes through the partition portions22from the inflow-side cells33and flows into the outflow-side cells34, and flows out from the outlet side (a rear end surface28) of the outflow-side cells34to the rear side. Note that the fluid that flows into portions of the inflow-side inner circumferential surface23other than the inflow-inflow facing surface23amainly passes through the partition portion22toward the outflow-side inner circumferential surface24, and flows out to the outflow-side cell34as indicated by arrows in the enlarged view on the right side inFIG. 3. In addition, the fluid that flows into the inflow-inflow facing surface23aflows out to the outflow-side cell34after changing its flow direction at the partition portion22together with the flow from its opposing inflow-inflow facing surface23a. As described above, the flow of the fluid that has passed through the inflow-inflow facing surface23ais different from the flow of the fluid that has passed through the other portion of the inflow-side inner circumferential surface23of the inflow-side cell33in the honeycomb structure20. Note that when a fluid flows through the inflow-side inner circumferential surface23, particulate matter contained in the fluid is collected by the partition portions22and accumulates on the inflow-side inner circumferential surface23because the particulate matter cannot pass through the partition portions22. In addition, the honeycomb structure20has an area ratio A of 15% or greater. The area ratio A is a ratio of an inflow-inflow facing area to an area of the inflow-side inner circumferential surface23, and the inflow-inflow facing area is an area of the inflow-inflow facing surface23a. The area ratio A according to this embodiment is equal to a ratio of the sum of lengths of sides inclined from the X direction and the Y direction (four sides denoted by thick lines in the enlarged view on the right side inFIG. 3) of the hexagonal cross-section of one inflow-side cell33to the sum of lengths of sides (six sides) of the hexagonal cross-section of the inflow-side cell33. Note that since the external shape of the honeycomb structure20is circular cylindrical, the inflow-side cells33having a shape different from that of the other inflow-side cells33are located near the periphery of the honeycomb structure20. However, the area ratio A is assumed to be a value derived based on the smallest unit (one inflow-side cell33in this embodiment) of an iterative structure of the inflow-side cells33without taking into account such an exceptional shape of some of the inflow-side cells33.

The object information19stored on the HDD15of the analysis apparatus10is information that simulates the honeycomb structure20illustrated inFIGS. 2 and 3by using a plurality of mesh portions.FIG. 4is a conceptual diagram of a model21of the honeycomb structure20simulated by the object information19. In this embodiment, the object information19is information that simulates the model21representing the shape of the smallest unit of the iterative structure of the honeycomb structure20. An upper portion ofFIG. 4is a partially enlarged view of the front end surface27of the honeycomb structure20. A portion within a dotted line triangular frame denotes the smallest unit of the iterative structure of the honeycomb structure20. As illustrated in a lower portion ofFIG. 4, the model21represents the structure of a portion from the front end surface27to the rear end surface28(triangular-cylindrical portion) within the dotted-line frame illustrated in the upper portion ofFIG. 4extracted from the honeycomb structure20. The model21includes one quarter of the inflow-side cell33and one eighth of the outflow-side cell34at the cross section along the X-Y plane. In addition, the model21may include a space on the front side of the front end surface27or a space on the rear side of the rear end surface28. In the lower portion ofFIG. 4, the outflow-side cell34in the model21is not illustrated; only the front-side plugging portion37is illustrated. In the lower portion ofFIG. 4, a particulate layer40, which is a layer formed as a result of particulate matter contained in a fluid accumulating on the inflow-side inner circumferential surface23, is also illustrated. Note that the object information19yet to be subjected to an analysis process (described later) simulates a state where the particulate layer40has not yet accumulated on the inflow-side inner circumferential surface23. Further, in the lower portion ofFIG. 4, open arrows indicate the flow of the fluid that flows from the front end surface27, the flow of the fluid that flows from the inflow-side cell33to the partition portion22(the inflow-side inner circumferential surface23), and the flow of the fluid that flows from the rear end surface (the outflow-side cell34). Each side of the dotted-line triangular frame in the upper portion ofFIG. 4or the periphery of the triangular column of the model21corresponds to a structural symmetry plane of of the honeycomb structure20. By configuring the object information19to be information that simulates the smallest unit (the model21) of the iterative structure of the honeycomb structure20in this way, a decrease in the accuracy of the analysis process (described later) is successfully suppressed and a time taken for the analysis process is successfully reduced. Note that the object information19is not limited to the above-described information and may be information that simulates the shape including a plurality of smallest units of the iterative structure of the honeycomb structure20or information that simulates the whole honeycomb structure20.

Although the illustration is omitted, the object information19is information that simulates the model21using a plurality of mesh portions by dividing the model21into a plurality of portions in the X, Y, and Z directions. The object information19includes, for each of the plurality of mesh portions, type information indicating which part of the honeycomb structure20the mesh portion corresponds to and position information (X, Y, and Z coordinates) of the mesh portion, for example. The type information is information indicating which of the space in front of the front end surface27, the space behind the rear end surface28, the partition portion22, the inflow-side cell33, the outflow-side cell34, the front-side plugging portion37, and the rear-side plugging portion38the mesh portion corresponds to. How many portions into which the model21is divided in the X, Y, and Z directions can be appropriately set by taking into account the required analysis accuracy and the time taken for the analysis (calculation time). In addition, the object information19may include various parameters regarding the honeycomb structure20used in the analysis process (described later), such as permeability αw [μm2] of the partition portion22and dimensions (dimensions in the X, Y, and Z directions) of each mesh portion.

The cells32and the partition portions22having shapes different from those of the smallest unit (the model21) of the iterative structure are located near the periphery of the honeycomb structure20. Accordingly, the object information19may include information that simulates such shapes different from those of the model21separately from the information that simulates the model21.

The analysis process performed by the analysis apparatus10will be described next. The analysis process is a process for analyzing a pressure loss in the honeycomb structure20by taking into account a distribution of the particulate layer40that has accumulated on the inflow-side inner circumferential surface23in response to inflow of a fluid when the fluid flows inside the honeycomb structure20.FIG. 5is a flowchart illustrating an example of an analysis process routine. This analysis process routine starts as a result of the CPU12executing an analysis process program stored on the HDD15upon the user inputting an instruction to perform the analysis process via the input device17.

Upon the start of the analysis process routine, the CPU12performs an object information setting process in which the object information19to be subjected to the analysis process is set as the processing target (step S100). In this process, the CPU12receives an instruction to perform an analysis based on the object information19from the user via the input device17and sets the object information19as a target subjected to the analysis process on the basis of the received instruction. The object information19is stored on the HDD15in advance in this embodiment; however, the CPU12may obtain the object information19from an external recording medium readable by the analysis apparatus10or from another computer or the like, store the obtained object information19on the HDD15, and set the stored object information19as the analysis target. In addition, the CPU12may receive an instruction to modify data of the object information19stored on the HDD15from the user via the input device17and modify the data of the object information19on the basis of the received instruction. The following description will be given of the case where the object information19that simulates the model21described usingFIG. 4is set as the target subjected to the analysis process.

Subsequent to step S100, the CPU12performs an analysis condition setting process in which analysis conditions are set (step S110). The CPU12sets, for example, information stored on the HDD15in advance or information received from the user via the input device17as the analysis conditions. In this embodiment, conditions such as fluid inflow conditions, physical property value conditions of the fluid, physical property value conditions of the particulate layer40, boundary conditions, and a target amount Mg [kg] of particulate matter that has accumulated on the inflow-side inner circumferential surface23are set as the analysis conditions. Examples of the fluid inflow conditions include a flow rate Q [m3/s] of a fluid that flows in from the front side of the front end surface27. Examples of the physical property value conditions of the fluid include a fluid density ρg [kg/m3], a fluid viscosity μ [Pa·s], and a concentration of particulate matter in the fluid. The concentration of particulate matter in the fluid may be, for example, a mass/volume concentration Ds1[kg/m3] or a volume concentration Ds2[vol %]. Examples of the physical property value conditions of the particulate layer40include a permeability αs [μm2] of the particulate layer40and a density ds [kg/m3] of the particulate layer40. Examples of the boundary conditions include a fluid pressure Pin [Pa] at the inlet of the model21or a fluid pressure Pout [Pa] at the outlet of the model21. Note that the fluid inflow conditions may change depending on the time t or the position on the X-Y plane. The physical property value conditions of the fluid may change depending on the time t.

Subsequent to step S110, the CPU12performs a process (transient analysis process) including steps S120to S160. Note that the CPU12performs the transient analysis process while appropriately reading and obtaining (referring to) the object information19and the analysis conditions respectively set (stored on the HDD15) in steps S100and S110. Upon the start of the transient analysis process, the CPU12first sets time t to the analysis start time (value of 0) (step S120). Then, the CPU12performs a fluid analysis for the case where a fluid flows inside the honeycomb structure20on the basis of the object information19and derives, for each of the mesh portions corresponding to the inflow-side inner circumferential surface23, a state of the particulate layer40, which is the accumulation of particulate matter contained in the fluid, after a short time interval Δt. In this way, the CPU12performs a particulate-layer-distribution deriving process for deriving transient distribution information that indicates the state of the particulate layer40that has accumulated on the inflow-side inner circumferential surface23(step S130). In the particulate-layer-distribution deriving process, any known fluid analysis using the finite element method, the finite volume method, or the like can be used. It is assumed that the finite volume method is used in this embodiment.

In this particulate-layer-distribution deriving process, the CPU12assumes each one of the mesh portions of the model21included in the object information19as a small element in the finite volume method. Then, the CPU12derives setting condition values of the fluid analysis, such as a flow resistance Ri [Pa·s/m] between adjacent mesh portions, on the basis of the object information19and the analysis conditions respectively set in steps S100and S110. Then, the CPU12derives, for each of the small elements, an equation regarding the flow of the fluid by using the state of the small element at the time t and determines a solution with which the equations hold true for all the small elements (fluid analysis). In this way, the CPU12derives a flow velocity Vi [m/s] of the fluid that flows between the adjacent mesh portions, a flow rate Qi [m3/s] of the fluid that flows between the adjacent mesh portions, an absolute pressure Pi [Pa] (total pressure) at each mesh portion, a dynamic pressure [Pa] at each mesh portion, and a static pressure [Pa] at each mesh portion as values regarding the state of each small element (mesh portion) after the short time interval Δt from the time t. The CPU12stores these derived values on the HDD15in association with the corresponding time (the time t+Δt) and the corresponding mesh portion. Note that the CPU12performs the fluid analysis in a state where the particulate layer40has not accumulated on the inflow-side inner circumferential surface23(without taking into account the particulate layer40) during the first particulate-layer-distribution deriving process (process performed at the time t=0) of the analysis process.

The CPU12then derives, for each of the mesh portions corresponding to the inflow-side inner circumferential surface23among the plurality of mesh portions of the model21, the state of the particulate layer40after the short time interval Δt on the basis of the values derived through the fluid analysis. Note that the mesh portions corresponding to the inflow-side inner circumferential surface23are mesh portions adjacent to mesh portions corresponding to the inflow-side cell33, among mesh portions corresponding to the partition portions22. It is assumed that a thickness Ts [μm] of the particulate layer40is derived as the state of the particulate layer40in this embodiment. For example, the CPU12first sets one of the mesh portions corresponding to the inflow-side inner circumferential surface23as a target for which the values are to be derived, and then derives, for the target mesh portion, a product (=a weight Mi [kg] of the particulate matter that has accumulated) of the concentration of the particulate matter in the fluid (e.g., the mass/volume concentration Ds1[kg/m3] set in step S110), the flow rate Qi [m3/s] of the fluid that flows from the adjacent mesh portion (mesh portion corresponding to the inflow-side cell33) to the target mesh portion, which is a value derived through the fluid analysis performed this time, and the short time interval Δt [s], at a time point after the short time interval (at time t+Δt). The CPU12then divides the obtained weight of the particulate matter by the density ds [kg/m3] of the particulate layer40set in step S110and by an area (area of the inflow-side inner circumferential surface23) of a portion of the target mesh portion facing the inflow-side cell33to derive the thickness Ts [μm] of the particulate layer40. In this way, the CPU12derives the state (thickness Ts) of the particulate layer40after the short time interval Δt by using the values derived through the fluid analysis on the assumption that an amount of particulate matter corresponding to the flow rate Qi of the fluid that has passed through the target mesh portion (the inflow-side inner circumferential surface23) over the short time interval Δt and the concentration (the mass/volume concentration Ds1) of the particulate matter contained in the fluid accumulates at (is collected by) the target mesh portion (the inflow-side inner circumferential surface23). The CPU12then changes the target mesh portion and performs the similar process to derive the thickness Ts of the particulate layer40after the short time interval Δt for each of the mesh portions corresponding to the inflow-side inner circumferential surface23of the model21. The values of the thickness Ts of the particulate layer40thus derived for the respective mesh portions corresponding to the inflow-side inner circumferential surface23represent the distribution of the particulate layer40that has accumulated on the inflow-side inner circumferential surface23. The CPU12stores the derived values of the thickness Ts of the particulate layer40on the HDD15as transient distribution information in association with the respective mesh portions corresponding to the inflow-side inner circumferential surface23and the time (the time t+Δt). Note that the analysis is performed in this embodiment on the assumption that all the particulate matter contained in the fluid is collected when the fluid passes through the inflow-side inner circumferential surface23; however, the assumption is not limited to this one. For example, the distribution of the particulate layer40that has accumulated after the short time interval Δt may be derived by taking into account a parameter indicating a collection rate associated with the partition portion22.

After performing the particulate-layer-distribution deriving process in step S130in a manner as described above, the CPU12increments the time t by the short time interval Δt (step S140) and determines whether the total amount M [kg] of the particulate matter that has accumulated on the inflow-side inner circumferential surface23at the time t becomes greater than or equal to the target amount Mg (step S150). That is, the CPU12determines whether the total amount M has reached the target amount Mg. Note that the CPU12is able to easily derive the total amount M of the particulate matter contained in the particulate layer40at each mesh portion on the basis of the thickness Ts of the particulate layer40of the mesh portion included in the transient distribution information derived through the immediately preceding particulate layer distribution deriving process, for example. The CPU12may store the above-described weights Mi derived for the respective mesh portions corresponding to the inflow-side cell33through the immediately preceding particulate-layer-distribution deriving process and may derive the sum of the weights Mi as the total amount M. If the total amount M is not greater than or equal to the target amount Mg, the CPU12performs the processing of step S130and the following steps. That is, the CPU12repeatedly performs the particulate-layer-distribution deriving process and a process of incrementing the time t by the short time interval Δt, until the total amount M becomes greater than or equal to the target amount Mg.

When performing the particulate-layer-distribution deriving process for the second or subsequent time, the CPU12performs the fluid analysis using the result of the fluid analysis performed in the immediately preceding particulate-layer-distribution deriving process. The CPU12performs the fluid analysis also by taking into account the transient distribution information derived through the immediately preceding particulate-layer-distribution deriving process. That is, the CPU12performs the fluid analysis for the state where the particulate layer40has accumulated on the inflow-side inner circumferential surface23as illustrated inFIG. 4. For example, the CPU12performs the fluid analysis on the assumption that it becomes more difficult for the fluid to pass through the mesh portion having a larger value of the thickness Ts of the particulate layer40among the mesh portions corresponding to the inflow-side inner circumferential surface23. For example, the CPU12derives, for each of the mesh portions corresponding to the inflow-side inner circumferential surface23, a flow resistance of the particulate layer40on the basis of the thickness Ts of the particulate layer40, the viscosity μ of the fluid, and the permeability αs of the particulate layer40, and updates the setting condition values (e.g., the flow resistance Ri) of the fluid analysis by taking this result into account. The CPU12performs the fluid analysis on the basis of the updated setting condition values. The CPU12then derives current transient distribution information, on the basis of the fluid analysis performed by taking into account the transient distribution information derived previous time.

If the total amount M becomes greater than or equal to the target amount Mg in step S150, the CPU12derives transient distribution information derived through the last particulate-layer-distribution deriving process as the post-transient-analysis distribution information and stores the post-transient-analysis distribution information on the HDD15(step S160). The CPU12then ends the transient analysis process, and the routine proceeds to the following step. In this embodiment, the CPU12uses the transient distribution information as the post-transient-analysis distribution information without any processing; however, the CPU12may use, as the post-transient-analysis distribution information, information obtained by performing processing, such as converting a value included in the transient distribution information. As described above, the CPU12repeatedly analyzes a distribution of the accumulated particulate layer40after the short time interval Δt (derives the transient distribution information) and derives the post-transient-analysis distribution information that represents the distribution of the accumulated particulate layer40when the total amount M has reached the target amount Mg during the transient analysis process. From the viewpoint of the accuracy of the derived post-transient-analysis distribution information, the particulate-layer-distribution deriving process is performed preferably three times or more, more preferably ten times or more, and further more preferably a hundred times or more during the transient analysis process. The number of times the particulate-layer-distribution deriving process is performed during the transient analysis process can be adjusted by appropriately setting the short time interval Δt in accordance with the concentration of the particulate matter in the fluid or the value of the target amount Mg.

After performing the transient analysis process, the CPU12performs a fluid analysis based on the object information19and the post-transient-analysis distribution information to perform a pressure loss deriving process in which a pressure loss that occurs when the fluid flows inside the honeycomb structure20is derived (step S170). Specifically, the CPU12performs the fluid analysis by taking into account not only the object information19but also the accumulation state (accumulation distribution) of the particulate layer40simulated by the post-transient-analysis distribution information to derive a pressure loss (a difference between the pressure at the front end surface27and the pressure at the rear end surface28of the model21). This fluid analysis can be performed in a manner similar to the fluid analysis performed during the particulate-layer-distribution deriving process in step S130, for example. For example, the CPU12successfully derives a pressure loss on the basis of the absolute pressure Pi at each mesh portion derived through the fluid analysis and the boundary conditions set in step S110. Note that the CPU12may perform the pressure loss deriving process by using analysis conditions different from those used in step S130. The CPU12stores the derived value of the pressure loss on the HDD15as the result of this pressure loss deriving process. Note that each value obtained through the fluid analysis performed during the pressure loss deriving process may be stored on the HDD15.

If the object information19includes information regarding the structure (e.g., information that simulates the structure near the periphery of the honeycomb structure20) other than the smallest unit (the model21) of the iterative structure, the CPU12may perform the transient analysis process and the pressure loss deriving process also for the structure in a manner similar to the above one. The CPU12may derive a pressure loss in the whole honeycomb structure20by also taking into account a pressure loss at such a structure different from the smallest unit of the iterative structure.

After performing the pressure loss deriving process, the CPU12performs an analysis result output process in which the results of the transient analysis process and the pressure loss analysis process described above are output as analysis result data (step S180). Then, the CPU12ends this routine. The analysis result data includes, for example, the post-transient-analysis distribution information and the value of the pressure loss. The analysis result data may also include the transient distribution information at the respective time points from the time point of t=0 to the time point at which the total amount M has become greater than or equal to the target amount Mg. The analysis result data may be output by storing the data on the HDD15, an external storage medium, or the like or by outputting the analysis results to the display16on the basis of the a user instruction received via the input device17. The pressure loss in the honeycomb structure20can be evaluated using this analysis result data in terms of whether the pressure loss in the honeycomb structure20is within a permissive range, for example.

Now, the accumulation state of the particulate layer40derived through the transient analysis process will be described.FIG. 6is a conceptual diagram illustrating an example of the accumulation distribution of the particulate layer40represented by the post-transient-analysis distribution information.FIG. 7is a conceptual diagram illustrating an example of a state where the particulate layer40is distributed evenly. As described usingFIG. 3, the flow of the fluid that has passed through the inflow-inflow facing surface23aof the inflow-side inner circumferential surface23differs from that of the fluid that has passed through the other portion of the inflow-side inner circumferential surface23in the honeycomb structure20according to the embodiment. Specifically, the fluid tends to more easily flow through (the flow resistance is small at) the other portion of the inflow-side inner circumferential surface23than at the inflow-inflow facing surface23aof the inflow-side inner circumferential surface23. For this reason, the flow rate of the fluid that passes through the inflow-inflow facing surface23atends to be small, and consequently the particulate layer40is less likely to accumulate on the inflow-inflow facing surface23a(the thickness Ts is less likely to be large). Since the accumulation distribution of the particulate layer40after the short time interval Δt is repeatedly analyzed by repeatedly performing the particulate-layer-distribution deriving process in this embodiment, a transient change in the accumulation distribution of the particulate layer40over time can be accurately analyzed. Thus, the accumulation state (accumulation distribution) of the particulate layer40after the short time interval Δ has passed a plurality of times is accurately simulated by the post-transient-analysis distribution information. That is, the accumulation state of the particulate layer40simulated by the derived post-transient-analysis distribution information is uneven as illustrated inFIG. 6, and a relatively small amount of particulate layer40has accumulated on the inflow-inflow facing surface23. It is confirmed that the accumulation distribution of the particulate layer40obtained when the fluid actually flows inside the honeycomb structure20is similar to the state illustrated inFIG. 6, and the state closer to the actual accumulation state of the particulate layer40can be simulated through the transient analysis process according to this embodiment. Since the a pressure loss that occurs when the fluid flows inside the honeycomb structure20in this state is derived in the analysis process according to this embodiment, the pressure loss can be analyzed by more accurately simulating the accumulation state of the particulate matter. As a method for simulating the state of the particulate layer40without performing the transient analysis process, the state where the particulate layer40has accumulated evenly at every position on the inflow-side inner circumferential surface23as illustrated inFIG. 7(the state where the particulate layer40is distributed evenly) may be simulated. However, since this state differs from the actual accumulation state of the particulate layer40, a deviation from the actually measured value tends to be large when the pressure loss is analyzed in this state, and the analysis accuracy tends to decrease.

FIG. 6illustrates an example of the accumulation distribution of the particulate layer40on a cross-section perpendicular to the front-rear direction of the honeycomb structure20; however, the accumulation state of the particulate layer40may be uneven also depending on the position in the front-rear direction of the honeycomb structure20. The post-transient-analysis distribution information determined through the transient analysis process according to this embodiment is information also simulating such an accumulation distribution in the front-rear direction.

Now, correspondences each between an element of this embodiment and an element of an aspect of the present invention will be clarified. The analysis apparatus10according to this embodiment corresponds to a pressure loss analysis apparatus according to an aspect of the present invention. The CPU12corresponds to transient analysis device and pressure loss deriving device. Note that this embodiment also discloses an example of a pressure loss analysis method and an example of a program for executing the pressure loss analysis method according to aspects of the present invention by describing the operation of the analysis apparatus10.

According to the analysis apparatus10according to this embodiment described in detail above, the CPU12derives transient distribution information that represents an accumulation distribution of the particulate layer40on the inflow-side inner circumferential surface23of the honeycomb structure20(the model21) at a time point after the short time interval Δt by performing a fluid analysis. The CPU12then repeatedly derives transient distribution information by performing a fluid analysis while taking into account the transient distribution information derived previous time, and consequently derives post-transient-analysis distribution information that represents the accumulation distribution of the particulate layer40at a later time point. By repeatedly analyzing the distribution of the accumulated particulate layer40at each time point after the short time interval Δt in this way, a transient change in the accumulation distribution of the particulate layer40over time can be accurately analyzed. Thus, the accumulation state (accumulation distribution) of the particulate layer40at a time point after the short time interval Δt has passed a plurality of times is accurately simulated by the post-transient-analysis distribution information. For example, the state closer to the actual accumulation state of the particulate layer40can be simulated compared with the case of simulating a state where the particulate layer40has accumulated evenly at every position on the inflow-side inner circumferential surface23(state where the particulate layer40is distributed evenly). Since a pressure loss for the case where the fluid flows inside the honeycomb structure20is derived on the basis of this post-transient-analysis distribution information, the pressure loss can be analyzed by more accurately simulating the accumulation state of the particulate matter.

In addition, during a particulate-layer-distribution deriving process, the CPU12derives the transient distribution information on the basis of information regarding a concentration of the particulate matter in the fluid (mass/volume concentration Ds1) and information regarding a flow rate of the fluid that flows into each of the mesh portions corresponding to the inflow-side inner circumferential surface23(flow rate Qi), information regarding a flow rate being a value derived through the fluid analysis performed during the particulate-layer-distribution deriving process. Here, the higher the concentration of the particulate matter in the fluid and the larger the flow rate of the fluid that flows through the inflow-side inner circumferential surface23, the more the particulate matter accumulates. Accordingly, the transient distribution information can be appropriately derived by using the information regarding the concentration of the particulate matter in the fluid and the information regarding the flow rate of the fluid. That is, the accumulation state of the particulate layer40can be appropriately simulated.

Further, each of the transient distribution information and the post-transient-analysis distribution information is information including at least one of a distribution of the thickness Ts of the particulate layer40, a distribution of permeability of the particulate layer40, and a distribution of flow resistance of the particulate layer40. More specifically, each of the transient distribution information and the post-transient-analysis distribution information is information including a distribution of the thickness Ts of the particulate layer40. Since the thickness Ts is information that influences a pressure loss that occurs when the fluid passes through the particulate layer40, it is suitable as information representing the accumulation distribution of the particulate layer40(the transient distribution information and the post-transient-analysis distribution information).

Furthermore, during the transient analysis process, the CPU12repeatedly performs the particulate-layer-distribution deriving process until the total amount M of the particulate matter that has accumulated on the inflow-side inner circumferential surface23reaches the predetermined target amount Mg. Accordingly, the accumulation state of the particulate layer40in a state for which analysis of the pressure loss is desired (state where the target amount Mg has been reached) can be simulated relatively easily, and the pressure loss in that state can be derived easily.

The object information19is information that simulates the honeycomb structure20having the area ratio A of 15% or greater, the area ratio A being a ratio of the inflow-inflow facing area to an area of the inflow-side inner circumferential surface23, the inflow-inflow facing area being an area of a portion (the inflow-inflow facing surface23a) of the inflow-side inner circumferential surface23facing the inflow-side inner circumferential surface23of another inflow-side cell33. When a fluid containing particulate matter passes through the honeycomb structure20, the particulate matter is unlikely to accumulate evenly on the inflow-side inner circumferential surface23in the honeycomb structure20having the area ratio A of 15% or greater. Accordingly, the value of the pressure loss derived by simulating the state where the particulate layer40is distributed evenly tends to deviate from the actually measured value of the pressure loss measured using the honeycomb structure20in which the same amount of particulate matter has accumulated. That is, the accuracy of the pressure loss analysis tends to decrease. In contrast, a deviation of the value derived through the analysis process according to the above-described embodiment from the actually measured value is small also for the honeycomb structure20having the area ratio A of 15% or greater, and thus the pressure loss analysis can be performed more accurately. Therefore, it is beneficial to employ the present invention when the pressure loss analysis is performed for the honeycomb structure20having the area ratio A of 15% or greater.

The present invention is by no means limited to the embodiments described above, and can be carried out in various ways within the technical scope of the present invention.

For example, it is assumed in the above-described embodiment that the honeycomb structure20has the shape illustrated inFIGS. 2 and 3; however, the shape is not limited to this one. Whatever shape the honeycomb structure has, a pressure loss can be analyzed by more accurately simulating the accumulation state of the particulate matter by using object information that simulates the honeycomb structure, as in the embodiment described above.FIGS. 8 to 14are cross-sectional diagrams illustrating the cell structure (positional relationships between the inflow-side cells33and the outflow-side cells34) in honeycomb structures according to modifications. InFIGS. 8 to 14, the outflow-side cells34are hatched so as to be easily distinguished from the others. For example, the cross-sectional shape of the cells32can be polygonal such as triangular, quadrangular (e.g.,FIGS. 8 to 10 and 12 to 14), hexagonal (e.g.,FIG. 11), or octagonal (e.g.,FIGS. 9 and 10); circular; or elliptical. The inflow-side cells33and the outflow-side cells34have different shapes in the above-described embodiment; however, they may have the same shape (e.g.,FIGS. 8 and 11). In addition, the plurality of inflow-side cells33have the same shape and the plurality of outflow-side cells34have the same shape in the above-described embodiment; however, at least the inflow-side cells33or the outflow-side cells34may have two or more shapes (e.g.,FIGS. 10 and 12). For example, the inflow-side cells33illustrated inFIG. 10have two cross-sectional shapes, i.e., quadrangular and octagonal shapes. The inflow-side cells33illustrated inFIG. 12have two cross-sectional shapes, i.e., square and rectangular shapes. In addition, the honeycomb structure20structured such that the inflow-side cells33and the outflow-side cells34described in the above-described embodiment andFIGS. 8 to 14are arranged oppositely may be employed. In addition, the inflow-side cells33are plugged with the rear-side plugging portion38and the outflow-side cells34are plugged with the front-side plugging portion37in the above-described embodiment; however, the configuration is not limited to this one. For example, the inflow-side cells33need not be plugged with the rear-side plugging portion38.

It is assumed in the above-described embodiment that the object information19is information that simulates the honeycomb structure20having the area ratio A of 15% or greater; however, the object information19is not limited to this one. Even when an analysis is performed on the basis of the object information19that simulates the honeycomb structure20having the area ratio A greater than or equal to 0% and less than 15%, a pressure loss can be analyzed by more accurately simulating the accumulation state of the particulate matter as in the above-described embodiment. However, since the value of the pressure loss derived by simulating the state where the particulate layer40is evenly distributed without performing the transient analysis process tends to deviate from the actual measured value as the value of the area ratio A becomes larger, particularly, the area ratio A becomes larger than or equal to 15%, it is beneficial to employ the present invention. Although the upper limit of the area ratio A is 100%, the area ratio A of the honeycomb structure is practically less than or equal to 90%, for example.

The particulate-layer-distribution deriving process is repeatedly performed during the transient analysis process until the total amount M of the particulate matter that has accumulated on the inflow-side inner circumferential surface23reaches the predetermined target amount Mg in the above-described embodiment; however, the configuration is not limited to this one. For example, the CPU12may repeatedly perform the particulate-layer-distribution deriving process until the sum of the short time intervals Δt reaches a predetermined target period tg [s]. With this configuration, the accumulation state of the particulate layer40in a state for which analysis of the pressure loss is desired (state the target period tg has been reached) can be simulated relatively easily, and a pressure loss in that state can be derived easily. In addition, the CPU12may repeatedly perform the particulate-layer-distribution deriving process until at least one of the total amount M of the particulate matter reaches the predetermined target amount Mg or the sum of the short time intervals Δt reaches the predetermined target period tg. In addition, the total amount M and the target amount Mg are represented by weight [kg] in the above-described embodiment; however, they may be represented as a weight of particulate matter per unit volume of the honeycomb structure (the model21) [g/L] or a volume [m3] of the particulate matter. Alternatively, the CPU12may repeatedly perform the particulate-layer-distribution deriving process until it receives an end instruction from the user.

Each of the transient distribution information and the post-transient-analysis distribution information is information including a distribution of the thickness Ts of the particulate layer40in the above-described embodiment; however, the information is not limited to this one. Each of the transient distribution information and the post-transient-analysis distribution information may be information including at least one of the distribution of thickness of the particulate layer40, the distribution of permeability of the particulate layer40, and the distribution of flow resistance of the particulate layer40. Since the permeability and the flow resistance of the particulate layer40as well as the thickness are information that influences the pressure loss that occurs when the fluid passes through the particulate layer40, they are suitably used as the information representing the accumulation distribution of the particulate layer40(the transient distribution information and the post-transient-analysis distribution information). In the case where each of the transient distribution information and the post-transient-analysis distribution information is information including the distribution of permeability of the particulate layer40, for example, the value of the permeability αs [μm2] of the particulate layer40may be derived for each of the mesh portions corresponding to the inflow-side inner circumferential surface23during the particulate-layer-distribution deriving process in step S130by setting the thickness of the particulate layer40to be constant (does not change over time) for all the mesh portions corresponding to the inflow-side inner circumferential surface23by using the physical property conditions of the particulate layer40. In addition, any other information may be used as the transient distribution information and the post-transient-analysis distribution information if the information is capable of simulating the accumulation state (accumulation distribution) of the particulate layer40.

The CPU12derives the transient distribution information during the particulate-layer-distribution deriving process on the basis of the concentration (mass/volume concentration Ds1) of the particulate matter in the fluid and the flow rate Qi of the fluid that flows into each of the mesh portions corresponding to the inflow-side inner circumferential surface23, the flow rate Qi being a value derived through the fluid analysis performed during the particulate-layer-distribution deriving process, in the above-described embodiment; however, the configuration is not limited to this one. The transient distribution information may be derived on the basis of any information regarding the concentration of the particulate matter in the fluid (e.g., information convertible into the concentration, information from which the concentration can be derived, information equivalent to the concentration, etc.) and any information regarding the flow rate of the fluid that flows into each of the mesh portions corresponding to the inflow-side inner circumferential surface23(e.g., information convertible into the flow rate, information from which the flow rate can be derived, or information equivalent to the flow rate). For example, the volume concentration Ds2[vol%] may be used as the information regarding the concentration. For example, a flow velocity Vi of the fluid that flows from a mesh portion corresponding to the adjacent inflow-side cell33to the mesh portion corresponding to the inflow-side inner circumferential surface23may be used as the information regarding the flow rate. Alternatively, any other value may be used as long as the transient distribution information can be derived based on the fluid analysis.

The object information19may simulate the honeycomb structure in which the partition portions22include a collection layer in the above-described embodiment. Specifically, the honeycomb structure20illustrated inFIGS. 2 and 3may include the partition portions22each including a partition wall (corresponding to the partition portion22in the above-described embodiment) and a collection layer. In this case, mesh portions corresponding to the partition portions22may be further classified into mesh portions corresponding to the partition wall and mesh portions corresponding to the collection layer in the object information19. The object information19may also include information regarding permeability of the partition wall (equivalent to the permeability αw [μm2] in the above-described embodiment) and information regarding permeability of the collection layer. When the partition portion22includes a collection layer, the surface of the collection layer serves as the inflow-side inner circumferential surface23.

The pressure loss value predicted for the state where the predetermined total amount M of particulate matter has accumulated is derived by performing the pressure loss deriving process in step S170after performing the transient analysis process in the above-described embodiment; however, the configuration is not limited to this one. For example, a relationship between the total amount M of particulate matter and the pressure loss may be derived a plurality of times from a state where the total amount M is equal to 0 to a state where the total amount M is equal to the final accumulation amount (e.g., the target amount Mg). For example, the CPU12can derive the pressure loss on the basis of the absolute pressure Pi at each mesh portion derived in an n-th particulate-layer-distribution deriving process performed during the transient analysis process as in the pressure loss deriving process performed in step S170. The resultant pressure loss is a value taking into account the transient distribution information derived through an (n−1)-th particulate-layer-distribution deriving process and corresponds to a pressure loss for the accumulation state of the particulate layer40represented by the (n−1)-th transient distribution information. Accordingly, the CPU12may store the pressure loss derived through the n-th particulate-layer-distribution deriving process in association with the total amount M based on the transient distribution information derived in the (n−1)-th particulate-layer-distribution deriving process (i.e., the total amount M obtained in step S150performed for the (n−1)-th time) on the HDD15every time the CPU12performs the particulate-layer-distribution deriving process. In addition, the CPU12may include such a correspondence between the pressure loss and the total amount M in the analysis result data output in step S180. In this way, the user can grasp not only the ultimate pressure loss derived in step S170but also the pressure loss during accumulation of the particulate layer40and a change in the pressure loss.

The CPU12uses a product of the concentration (mass/volume concentration Ds1) of particulate matter in the fluid, the flow rate Qi of the fluid that flows into each of the mesh portions corresponding to the inflow-side inner circumferential surface23, and the short time interval Δt as the weight Mi of the accumulated particulate matter when deriving the transient distribution information; however, the configuration is not limited to this one. For example, a value obtained by multiplying “Ds1×Qi×Δt” by a calculation acceleration factor Ac may be used as the weight Mi (where Ac>1). In this way, the mass/volume concentration Ds1can be made Ac times as large as the actual value (value for the fluid used for simulation), and the calculation can be performed by increasing the amount of particulate matter that accumulates over the short time interval Δt. Accordingly, the number of times the particulate-layer-distribution deriving process is performed during the transient analysis process until the total amount M reaches the target amount Mg can be reduced, and consequently time taken for the transient analysis process can be reduced. For example, when the value of the mass/volume concentration Ds1is very small, formation of the particulate layer40takes time, which may require the particulate-layer-distribution deriving process to be repeatedly performed many times during the transient analysis process until the total amount M reaches the target amount Mg, and consequently, the calculation may take long. In such a case, the use of the calculation acceleration factor Ac can reduce the time taken for the transient analysis process. Note that when the calculation acceleration factor Ac is used, the product of the short time interval Δt and the calculation acceleration factor Ac can be construed as the time in reality. For example, when the particulate-layer-distribution deriving process is repeatedly performed n times during the transient analysis process, the analysis is performed from a time point of t=0 to a time point of t=n×Δt. This can be construed as the analysis being performed from a time point of tR=0 to a time point of TR=n×Δt×Ac in reality. The time period and the time point included in the analysis result data output in step S180may be the time period and the time point tRobtained by such a conversion.

EXAMPLES

The case where the analysis process program and the pressure loss analysis apparatus described above were actually created will be described as an example below. Note that the present invention is not limited to the example below.

Example and Comparative Example

As an example, an analysis process program implementing the functions according to the above-described embodiment was created. This program was stored on an HDD of a computer including the HDD and a controller including a CPU, a ROM, and a RAM, whereby a pressure loss analysis apparatus according to the example was created. In addition, an analysis process program for performing the pressure loss deriving process of step S170without performing the transient analysis process illustrated inFIG. 5was stored on an HDD of a computer, whereby a pressure loss analysis apparatus according to a comparative example was created.

[Pressure Loss Analysis of Honeycomb Structures1to4]

Object information simulating each of honeycomb structures1to4was created. The pressure loss analysis apparatuses according to the example and the comparative example were caused to execute the respective analysis process programs on the basis of this object information to derive the pressure loss. The honeycomb structure1is structured such that both the inflow-side cells33and the outflow-side cells34have quadrangular cross-sectional shapes and are alternately arranged as illustrated inFIG. 8. Since the honeycomb structure1does not have the inflow-inflow facing surface23a, its area ratio A is 0%. The honeycomb structure2is structured such that the inflow-side cells33have an octagonal shape and the outflow-side cells34have a quadrangular shape and are alternately arranged as illustrated inFIG. 9. In the honeycomb structure2, four sides inclined from the up-down and right-left directions of the octagonal shape of the inflow-side cells33illustrated inFIG. 9serve as the inflow-inflow facing surface23a, and thus its area ratio A is 10%. The honeycomb structure3is structured in the same manner as the honeycomb structure2except for the area ratio A, which is 15%. The honeycomb structure4is structured as illustrated inFIGS. 2 and 3, and its area ratio A is 63%. In addition, in the example, the transient analysis process was performed until the total amount M [g/L] of particulate matter per unit volume of the honeycomb structure (the model21) has reached the target amount Mg (=4 g/L). In the example, the particulate-layer-distribution deriving process was performed 200 times (until the total amount M has reached the target amount Mg). In the comparative example, the pressure loss was derived using object information simulating the state where the target amount Mg (=4 g/L) of particulate matter (the particulate layer40) has evenly accumulated in the inflow-side cells33. In addition, the honeycomb structures1to4were actually produced, and values of the pressure loss that occurs when the fluid passes were measured in the following manner. First, the honeycomb structures1to4having a diameter of 144 mm and a length of 152 mm were produced by joining together 16 plugged honeycomb structure segments (having a quadrangular cylindrical shape of a 36 mm×36 mm quadrangle and a length of 152 mm) composed of porous Si-bond SiC (Si—SiC) and by processing the periphery of the resultant structure. The honeycomb structures1to4were installed in an exhaust system of a 2.0 L diesel engine, and the diesel engine was operated at conditions of an engine speed of 2000 rpm, an engine torque of 60 Nm, an exhaust temperature of 250° C., and an exhaust flow rate of 2.5 m3/min. The pressure loss was measured when 4g/L of particulate matter (such as soot) has accumulated. Then, an error (%) of the derived pressure loss from the actually measured value was derived for each of the example and the comparative example.

Table 1 collectively shows the structures of the cells and the area ratio A of the honeycomb structures1to4, the error in the comparative example from the actually measured value, and the error in the example from the actually measured value. As shown in Table 1, the error in the example was smaller than or equal to the error in the comparative example for all of the honeycomb structures1to4. In addition, the error of the pressure loss derived in the comparative example for the honeycomb structures3and4having the area ratio A of 15% or greater from the actually measured value was greater than or equal to 15%, which was large and exceeded the permissible margin of error. In contrast, in the example, the error for the honeycomb structures3and4was substantially the same as that for the honeycomb structures1and2and was within the permissive range.

The present application claims priority of Japanese Patent Application No. 2015-202114 filed on Oct. 13, 2015, the entire contents of which are incorporated herein by reference.