Patent Application
20150107206
1. Field of Invention
The present invention relates a porous body, a honeycomb filter, and a manufacturing method of the porous body.
2. Description of Related Art
There are known honeycomb filters and the like to purge exhaust fumes which use porous body. For example, PTL 1 describes a manufacturing method of a porous body, where ceramic particles, fine particles, and a sintering aid are mixed to form a green body, which is formed to yield a compact. The compact is sintered at a predetermined sintering temperature, and thus the porous body is manufactured. PTL 1 describes that, with the described manufacturing method, the pressure drop in a porous body to be manufactured can be suppressed by restricting the average particle size of the ceramic particles.
It is preferable with such porous body that the pressure drop occurring when a fluid passes through is as low as possible, and that the collection performance of particulate matter (PM) in the exhaust fumes is as high as possible. Accordingly, there has been demand for a porous body with which pressure drop is further reduced and collection performance is further improved.
The present invention has been made to solve such problems, and it is a primary object thereof to provide a porous body and a honeycomb filter with which pressure drop is sufficiently reduced and collection performance is sufficiently improved.
The following means were employed for the porous body, honeycomb filter, and manufacturing method of the porous body according to the present invention, to achieve the aforementioned primary object.
A first porous body according to the present invention is a porous body, wherein, when
creating porous body data based on an image obtained by a 3-dimensional scan of the porous body, in which porous body data is correlated position information representing position of a pixel in the image, and pixel type information representing whether a space pixel representing that the pixel is space or a matter pixel representing that the pixel is matter,
performing a processing of placing, as to the porous body data, one parent virtual sphere having the greatest spherical diameter that can be placed so as to fill in the space pixels without overlapping with the matter pixel, placing at least one child virtual sphere such that the center of the child virtual sphere overlaps with the placed parent virtual sphere and pixels occupied by the child virtual sphere fill in the space pixels without overlapping with the matter pixel, and placing one virtual curved surface solid formed of the parent virtual sphere and the child virtual sphere so as to fill in the space pixels with curved surface solid pixels which are pixels occupied by the virtual curved surface solid, and repeating this processing such that pixels occupied by different virtual curved surface solids do not overlap each other, thereby placing a plurality of the virtual curved surface solids,
performing fluid analysis regarding a case of inflow of a fluid from a predetermined inflow face of the porous body by the lattice Boltzmann method based on the porous body data, and thereby deriving a flow velocity vector of the fluid for each space pixel at the time of the fluid passing through the porous body, and
deriving a plurality of in-plane uniformity indices γx of flow velocity at a cross-section on the porous body parallel to the inflow face, by the following Expression (1), based on information relating to the placed virtual curved surface solids and information relating to the derived flow velocity vector for each space pixel, and deriving a spatial uniformity index γ of flow velocity at the porous body by the following Expression (2) using the derived in-plane uniformity indices γx;
the average value of the plurality of in-plane uniformity indices γx is 0.6 or greater, and the spatial uniformity index γ is 0.6 or greater.
where
n: number [count] of virtual curved surface solids within cross-section
x: distance [m] between cross-section and inflow face
ui: average flow velocity (i=1, 2, . . . , n) [m/s] for each of the n virtual curved surface solids at cross-section
umean: average value (=(ui+u2+ . . . +un)/n) [m/s] of average flow velocity ui at cross-section
Ai: cross-sectional area (i=1, 2, . . . , n) [m2] for each virtual curved surface solid within cross-section
A: total cross-sectional area (=A1+A2 . . . An) [m2] of virtual curved surface solids at cross-section
γ=
δγ: standard deviation of γx
The more uniform the flow velocity of the fluid at a cross-section of this porous body is, the greater (closer to 1) the value of the derived in-plane uniformity index γx is, and the more variance there is in the flow velocity of the fluid at the cross-section is, the smaller the value is. Also, the smaller the variance in the in-plane uniformity index γx derived for multiple cross-sections is, the greater the value of the spatial uniformity index γ is, and the greater the variance is, the smaller the value is. The present inventors have found that when using a porous body for a filter, the greater the value of the in-plane uniformity index γx is, the better the power drop properties are, and have found that when using a porous body for a filter, the greater the spatial uniformity index γ is, the better the collection performance is. The present inventors have found that when the condition of the average value of multiple in-plane uniformity indices γx being 0.6 or greater, and the spatial uniformity index γ being 0.6 or greater is satisfied, pressure drop is sufficiently reduced and collection performance is sufficiently improved. The porous body according to the present invention satisfies these conditions so pressure drop is sufficiently reduced and collection performance is sufficiently improved. Portions of the pores (spaces) within the porous body where the flow velocity of the passing fluid is relatively small may not contribute much to transmittance of the fluid, which may lead to increased pressure drop, and deterioration in thermal conductivity and thermal capacity of the material. Also, portions where the velocity of the passing fluid is relatively great may exhibit great flow resistance when the fluid passes through, or the fluid may pass through in a short time and the pores do not contribute much to collecting performance. Accordingly, when the above conditions for the in-plane uniformity index γx and the spatial uniformity index γ are satisfied, there are few such portions where the flow velocity is relatively smaller or portions where the flow velocity is relatively great, so it can be conceived that satisfactory properties can be obtained. Also, with regard to the first porous body according to the present invention, porous body data in which is correlated position information and pixel type information is referenced to place multiple virtual curved surface bodies, made up of parent virtual spheres and child virtual spheres, so as to fill in space pixels with curved surface body pixels occupied by the multiple virtual curved surface bodies that are placed. Thus, spaces (pores) having complicated shapes within the porous body are substituted with virtual curved surface bodies formed by combining multiple shapes, so the space within the porous body can be simulated more precisely as a collection of multiple virtual curved surface bodies. Accordingly, it can be conceived that the precision of correlation between the in-plane uniformity index γx and spatial uniformity index γ derived using the information relating to the placed virtual curved surface bodies, and properties such as pressure drop and collection performance, is further improved.
In this case, with regard to placing one virtual curved surface body, in a case of placing multiple child virtual spheres, the multiple child virtual spheres are preferably permitted to overlap each other. Also, fluid analysis is preferably performed with regard to a fluid flowing from a predetermined inflow face to a predetermined outflow face of the porous body.
The first porous body according to the present invention may be formed such that, when
deriving through-flow volume Q of the fluid per unit time at the virtual curved surface solid for each virtual curved surface solid, based on information relating to the placed virtual curved surface solids and information relating to the flow velocity vector for the each space pixel, and deriving flow-through velocity T of each virtual curved surface solid by T=Q/(πd2/4) based on the derived through-flow volume Q and an equivalent diameter d of the virtual curved surface solid (=6×volume V of virtual curved surface solid/surface area S of virtual curved surface solid), and
deriving a flow velocity ratio Tf (=T/Tin) of the derived flow-through velocity T to an average flow velocity Tin of the fluid at the inflow face in the fluid analysis, and performing classification such that, of the placed virtual curved surface solids, virtual curved surface solids which satisfy Tf<2 are classified as low-flow-velocity curved surface solids, and virtual curved surface solids which satisfy 8≦Tf as high-flow-velocity curved surface solids;
the percentage of the total value of volume of the low-flow-velocity curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 20% or less, and the percentage of the total value of volume of the high-flow-velocity curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 10% or less.
The present inventors have found that upon having derived the flow velocity ratio Tf regarding each virtual curved surface body, the smaller the volume of a virtual curved surface body where the flow velocity ratio Tf is relatively small, and the smaller the volume of a virtual curved surface body where the flow velocity ratio Tf is relatively great, the better the pressure drop properties and collection performance is. The present inventors have also found that when the percentage by volume of low-flow-velocity curved surface solids which satisfy flow velocity ratio Tf of Tf<2 is 20% or less, and the percentage by volume of high-flow-velocity curved surface solids which satisfy flow velocity ratio Tf of 8≦Tf is 10% or less, the pressure drop is sufficiently reduced and collection performance is sufficiently improved. The porous body according to the present invention satisfies these conditions, so pressure drop is sufficiently reduced and collection performance is sufficiently improved. Now, pores of the porous body simulated with virtual curved surface solids of which the flow velocity ratio Tf is relatively small may not contribute much to transmittance of the fluid, leading increased pressure drop, and deterioration in thermal conductivity and thermal capacity of the material. Also, pores of the porous body simulated with virtual curved surface solids of which the flow velocity ratio Tf is great, may exhibit great flow resistance when the fluid passes through, or the fluid may pass through in a short time and the pores do not contribute much to collecting performance. When the percentage by volume of the total value of low-flow-velocity curved surface solids and the percentage by volume of the total value of high-flow-velocity curved surface solids satisfy the above conditions, such portions with relatively small flow velocity and relatively great flow velocity are few, which can be conceived to yield good properties.
The first porous body according to the present invention may be formed such that, when deriving an equivalent diameter d of each virtual curved surface solid by d=6×(volume V of virtual curved surface solid)/(surface area S of virtual curved surface solid) based on information relating to the placed virtual curved surface solids, and classifying virtual curved surface solids where the value of the derived equivalent diameter d satisfies 10 μm≦d≦25 μm as mid-diameter curved surface solids;
the percentage of the total value of volume of the mid-diameter curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 60% or greater.
The present inventors have found that upon deriving the equivalent diameter d for each virtual sphere, the smaller the percentage by volume of small-diameter curved surface bodies where the equivalent diameter d is small and large-diameter curved surface bodies where the equivalent diameter d is great, that is to say, the greater the percentage by volume of mid-diameter curved surface bodies which are neither small-diameter curved surface bodies nor large-diameter curved surface bodies, the better the pressure drop properties and collection performance of the porous body tends to be. The present invention have also found that when the percentage by volume of mid-diameter curved surface solids satisfying 10 μm≦d≦25 μm for the equivalent diameter d is 60% or more, pressure drop is sufficiently reduced and collection performance is sufficiently improved. The porous body according to the present invention satisfies these conditions so pressure drop is sufficiently reduced and collection performance is sufficiently improved. Now, regarding pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is small, the flow velocity of the fluid passing through may be small, leading to increased pressure drop, or the catalyst applied to the walls of the pores to use the porous body as a filter may not be appropriately applied, or the like. Also, pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is great, may result in the flow velocity of the fluid passing through being great to the point of not contributing to collecting performance very much when using the porous body as a filter. When the percentage of the total value of volume of mid-diameter curved surface solids satisfies the above condition, pores with such small equivalent diameters d and great equivalent diameters d are few, which can be conceived to yield good properties. In this case, the percentage of the total value of volume of the mid-diameter curved surface solids as to the total value of volume of the multiple virtual curved surface solids may be 70% or more. This further reduces pressure drop and further improves collection performance.
A second porous body according to the present invention is a porous body, wherein, when
creating porous body data based on an image obtained by a 3-dimensional scan of the porous body, in which porous body data is correlated position information representing position of a pixel in the image, and pixel type information representing whether a space pixel representing that the pixel is space or a matter pixel representing that the pixel is matter,
performing a processing of placing, as to the porous body data, one parent virtual sphere having the greatest spherical diameter that can be placed so as to fill in the space pixels without overlapping with the matter pixel, placing at least one child virtual sphere such that the center of the child virtual sphere overlaps with the placed parent virtual sphere and pixels occupied by the child virtual sphere fill in the space pixels without overlapping with the matter pixel, and placing one virtual curved surface solid formed of the parent virtual sphere and the child virtual sphere so as to fill in the space pixels with curved surface solid pixels which are pixels occupied by the virtual curved surface solid, and repeating this processing such that pixels occupied by different virtual curved surface solids do not overlap each other, thereby placing a plurality of the virtual curved surface solids,
performing fluid analysis regarding a case of inflow of a fluid from a predetermined inflow face of the porous body by the lattice Boltzmann method based on the porous body data, and thereby deriving a flow velocity vector of the fluid for each space pixel at the time of the fluid passing through the porous body,
deriving through-flow volume Q of the fluid per unit time at the virtual curved surface solid for each virtual curved surface solid, based on information relating to the placed virtual curved surface solids and information relating to the flow velocity vector for the each space pixel, and deriving flow-through velocity T of each virtual curved surface solid by T=Q/(πd2/4) based on the derived through-flow volume Q and an equivalent diameter d of the virtual curved surface solid (=6×volume V of virtual curved surface solid/surface area S of virtual curved surface solid),
deriving a flow velocity ratio Tf (=T/Tin) of the derived flow-through velocity T to an average flow velocity Tin of the fluid at the inflow face in the fluid analysis, and performing classification such that, of the placed virtual curved surface solids, virtual curved surface solids where Tf<2 are classified as low-flow-velocity curved surface solids, and virtual curved surface solids where 8 Tf as high-flow-velocity curved surface solids;
the percentage of the total value of volume of the low-flow-velocity curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 20% or less, and the percentage of the total value of volume of the high-flow-velocity curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 10% or less.
In this porous body, the percentage by volume of low-flow-velocity curved surface solids which satisfy flow velocity ratio Tf of Tf<2 is 20% or less, and the percentage by volume of high-flow-velocity curved surface solids which satisfy flow velocity ratio Tf of 8≦Tf is 10% or less. Therefore, for reasons described above, the pressure drop is sufficiently reduced and collection performance is sufficiently improved.
A third porous body according to the present invention is a porous body, wherein, when
creating porous body data based on an image obtained by a 3-dimensional scan of the porous body, in which porous body data is correlated position information representing position of a pixel in the image, and pixel type information representing whether a space pixel representing that the pixel is space or a matter pixel representing that the pixel is matter,
performing a processing of placing, as to the porous body data, one parent virtual sphere having the greatest spherical diameter that can be placed so as to fill in the space pixels without overlapping with the matter pixel, placing at least one child virtual spheres such that the center of the child virtual sphere overlaps with the placed parent virtual sphere and pixels occupied by the child virtual sphere fill in the space pixels without overlapping with the matter pixel, and placing one virtual curved surface solid formed of the parent virtual sphere and the child virtual sphere so as to fill in the space pixels with curved surface solid pixels which are pixels occupied by the virtual curved surface solid, and repeating this processing such that pixels occupied by different virtual curved surface solids do not overlap each other, thereby placing a plurality of the virtual curved surface solids,
deriving an equivalent diameter d of each virtual curved surface solid by 6×(volume V of virtual curved surface solid)/(surface area S of virtual curved surface solid) based on information relating to the placed virtual curved surface solids, and classifying virtual curved surface solids where the value of the derived equivalent diameter d satisfies 10 μm≦d≦25 μm as mid-diameter curved surface solids;
the percentage of the total value of volume of the mid-diameter curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 60% or greater.
In this porous body, the percentage of the total value of volume of the mid-diameter curved surface solids as to the total value of volume of the plurality of virtual curved surface solids is 60% or greater. Therefore, for reasons described above, the pressure drop is sufficiently reduced and collection performance is sufficiently improved. In this case, the percentage of the total value of volume of the mid-diameter curved surface solids as to the total value of volume of the plurality of virtual curved surface solids may be 70% or greater. With such structure, the pressure drop is further reduced and collection performance is further improved.
A honeycomb filter according to the present invention comprises a partition formed of the porous body according to the present invention of any structure described above, forming a plurality of cells of which one end is open and the other end is sealed and which serve as channels for a fluid.
In the porous body forming the honeycomb filter, the pressure drop is sufficiently reduced and collection performance is sufficiently improved. Therefore, the pressure drop is sufficiently reduced and collection performance is sufficiently improved when a fluid flows through the honeycomb filter.
A method according to the present invention is a method for manufacturing a porous body, comprising:
a raw material mixing step of mixing a base material made up of an inorganic material, and a pore-forming agent, to yield a green body; and
a molding-and-sintering step of obtaining a compact by molding the green body, and sintering the compact;
wherein a (D90−D10)/D50 value of the base material is 2 or less, and a (D90−D10)/D50 value of the pore-forming agent is 2 or less, where D10 represents particle diameter that is 10% by volume, D50 represents particle diameter that is 50% by volume, and D90 represents particle diameter that is 90% by volume.
The present inventors have found that when manufacturing the porous body, the closer the particle diameter of the base material and the pore-forming agent is, i.e., the smaller the variance in the particle diameter of the base material and the pore-forming agent is, the further the pressure drop in the manufactured porous body is reduced and the greater the improvement in collection performance is. The present inventors have also found that by the value of (D90−D10)/D50 of the base material being 2 or smaller, and value of (D90−D10)/D50 of the pore-forming agent being 2 or smaller, the pressure drop in the manufactured porous body is sufficiently reduced and collection performance is sufficiently improved. The manufacturing method of the porous body according to the present invention satisfies these conditions, so a porous body with sufficiently reduced pressure drop and sufficiently improved collection properties can be obtained. Manufacturing the porous body by this manufacturing method enables manufacturing of a porous body which satisfies at least one condition of the three conditions of “the average value of multiple in-plane uniformity indices γx is 0.6 or greater, and the spatial uniformity index γ is 0.6 or greater”, “the percentage of the total value of volume of low-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 20% or less, and the percentage of the total value of volume of high-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 10% or less”, and “the percentage of the total value of volume of mid-diameter curved surface solids as to the total value of volume of multiple virtual curved surface solids is 60% or more”. In this case, a dispersant may be mixed in the raw ingredient mixing procedure. The value of (D90−D10)/D50 of the base material is preferably as small as possible, and for example is preferably 1.5 or smaller. The value of (D90−D10)/D50 of the pore-forming agent also is preferably as small as possible, and for example is preferably 1.5 or smaller. Now, the term that D10 of the base material, which is to say the particle diameter that is 10% by volume, is a value 20 μm, means that the total volume of particles of which the particle diameter is 20 μm or smaller occupies 10% of the total volume of all particles of the base material. This is the same for D50 and D90 as well. Note that D50 is a value equivalent to the average particle diameter.
Next, an embodiment of the present invention will be described with reference to the drawings.
This honeycomb filter 30 is installed downstream of a diesel engine not illustrated in the drawings, for example, and is used to purge exhaust gas including PM so as to be discharged into the atmosphere. Note that the arrow in
The porous partition 44 according to the present embodiment satisfies at least one of the following three conditions when the later-described microstructure of the porous body making up the porous partition 44 is analyzed; “the average value of multiple in-plane uniformity indices γx is 0.6 or greater, and the spatial uniformity index γ is 0.6 or greater”, “the percentage of the total value of volume of low-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 20% or less, and the percentage of the total value of volume of high-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 10% or less”, and “the percentage of the total value of volume of mid-diameter curved surface solids as to the total value of volume of multiple virtual curved surface solids is 60% or more”. A method to analyze the microstructure will be described next.
The HDD 25 of the user PC 20 stores 3-dimensional pixel data of the porous partitions 44 obtained by performing a CT scan on this honeycomb filter 30, as porous body data 60. With the present embodiment, an X-Y plane indicated by the X direction and Y direction in
The analysis processing program 25a includes a virtual curved surface solid placement module 25b, a fluid analyzing module 25c, an in-plane uniformity index evaluation module 25d, a spatial uniformity index evaluation module 25e, a pressure drop evaluation module 25f, a flow-through velocity evaluation module 25g, an equivalent diameter evaluation module 25h, and an analysis result output module 25i. The virtual curved surface solid placement module 25b has a function of referencing the porous body data 80, taking a curved surface solid including a parent virtual sphere and one or more child virtual spheres partially overlapping the parent virtual sphere with regard to occupied pixels, as a virtual curved surface solid, and placing multiple virtual curved surface solids so as to fill in space pixels with curved surface solid pixels which are pixels occupied by virtual curved surface solids. The fluid analyzing module 25c has a function of deriving information relating to the flow of fluid for each space pixel at the time of the fluid passing through the interior of the porous body, by performing fluid analysis based on the porous body data 80. The in-plane uniformity index evaluation module 25d has a function of deriving one or more in-plane uniformity index γx of flow velocity at a cross-section parallel to the inflow face 61 of the porous body data 80, based on information relating to the virtual curved surface solid placed by the virtual curved surface solid placement module 25b and information relating to flow that has been derived by the fluid analyzing module 25c, and evaluating the porous body based on the in-plane uniformity index γx. The spatial uniformity index evaluation module 25e has a function of deriving a spatial uniformity index γ of the flow velocity at the porous body using the in-plane uniformity index γx derived by the in-plane uniformity index evaluation module 25d, and evaluating the porous body based on the in-plane uniformity index γx. The pressure drop evaluation module 25f has functions of deriving pressure drop P per unit thickness of the porous body using the in-plane uniformity index γx derived by the in-plane uniformity index evaluation module 25d, and evaluating the porous body based on the pressure drop P. The flow-through velocity evaluation module 25g has functions of deriving flow-through velocity T and flow velocity ratio Tf for each virtual curved surface solid, based on information relating to position of virtual curved surface solids placed by the virtual curved surface solid placement module 25b and information relating to the flow derived by the fluid analyzing module 25c, classifying the virtual curved surface solids based on the flow-through velocity T and flow velocity ratio Tf, and evaluating the porous body based on the classification results. The equivalent diameter evaluation module 25h has functions of deriving equivalent diameter d of the virtual curved surface solids placed by the virtual curved surface solid placement module 25b, classifying the virtual curved surface solids based on the equivalent diameter d, and evaluating the porous body based on the classification results. The analysis result output module 25i has a function of compiling the various types of values and evaluation results and so forth that have been derived, and outputting to store such values and evaluation results in the HDD 25 as analysis result data. The controller 21 executing the analysis processing program 25a realizes the above-described functions of the virtual curved surface solid placement module 25b, fluid analyzing module 25c, in-plane uniformity index evaluation module 25d, spatial uniformity index evaluation module 25e, pressure drop evaluation module 25f, flow-through velocity evaluation module 25g, equivalent diameter evaluation module 25h, and analysis result output module 25i.
Next, the analysis processing which the user PC 20 performs with regard to the porous body data 60 will be described.
Upon the analysis processing routine being executed, the CPU 22 first executes curved surface solid placement processing, which is processing to place virtual curved surface solids so as to fill in space pixels in the porous body data 60 (step S100).
Now, we will depart from description of the analysis processing routine to describe the virtual curved surface solid placement processing.
Next, the virtual curved surface solid placement module 25b sets a maximum value Ramax for the diameter Ra of the parent virtual sphere (step S220), and determines whether or not a parent virtual sphere of diameter Ra can be placed in the space pixels on the inner side of the virtual wall face set in step S210 (step S230). A parent virtual sphere with a diameter Ra is a virtual sphere having a size of a diameter of Ra (μm), with the center thereof at the center of one of the pixels. Whether or not this parent virtual sphere of diameter Ra can be placed is determined as follows, for example. First, any one pixel of space pixels (pixels of which the type information is value 0) at that point-in-time is selected. In the event that placing the parent virtual sphere of diameter Ra centered on the selected pixel causes the parent virtual sphere to overlap with a matter pixel or a virtual curved surface solid already placed, another space pixel is selected again as the center. One space pixel after another is selected, and in the event that the parent virtual sphere does not overlap a matter pixel or a virtual curved surface solid already placed, it is determined that the parent virtual sphere of diameter Ra can be placed at that position. In the event that the parent virtual sphere overlaps a matter pixel or a virtual curved surface solid already placed regardless of every space pixel being selected as the center at that point-in-time, it is determined that the parent virtual sphere of diameter Ra cannot be placed. Note that the order of selecting pixels to serve as a center may be random, or may be performed in order from pixels on the inflow face 61 toward pixels on the outflow face 62. Also, the value of the maximum value Ramax may be any value as long as a value equal to or greater than the maximum value of the diameter of pores normally present in the porous partition 44, and for example, the value can be set by reference to a value obtained beforehand by experiment. When it is determined in step S230 that the parent virtual sphere cannot be placed, the value of diameter R is decremented by 1 (step S240), and the processing of step S230 and thereafter is performed. Note that while the value to be decremented is 1 with the present embodiment, this may be set as appropriate according to the allowable calculation load and so forth.
When it is determined in step S230 that the parent virtual sphere can be placed, one parent virtual sphere of diameter Ra is placed at that position (step S250). Specifically, the type information corresponding to the pixel occupied by the parent virtual sphere when the parent virtual sphere of diameter Ra is placed, in the porous body table 71 of the porous body data 80 stored in the RAM 24 in step S200, is updated to a value 3 which represents a pixel occupied by a parent virtual sphere. Note that the type information of a pixel, the center of which is included in the parent virtual sphere, is updated to the value 3 with the present embodiment. This holds true for pixels occupied by later-described child virtual spheres as well.
Next, the virtual curved surface solid placement module 25b sets a diameter Rb of a child virtual sphere to the same value as the diameter Ra (step S260), and determines whether or not a child virtual sphere of a diameter Rb can be placed in the space pixels on the inner side of the virtual wall face set in step S210 (step S270). A child virtual sphere with a diameter Rb is a virtual sphere having a size of a diameter of Rb (μm), with the center thereof at the center of one of the pixels, and with a part of the occupied pixels overlapping pixels of the parent virtual sphere. Also, the placement of the child virtual spheres is performed such that the center of the child virtual sphere overlaps the parent virtual sphere placed in step S250. Determination of whether or not this child virtual sphere of a diameter Rb can be placed is performed as follows, for example. First, any one pixel of pixels which the parent virtual sphere occupies at that point-in-time (a pixel with a type information value is 3) is selected. In the event that placing the child virtual sphere of diameter Rb centered on the selected pixel causes the child virtual sphere to overlap with a matter pixel or a virtual curved surface solid already placed, another pixel occupied by the parent virtual sphere is selected again as the center. One pixel after another is selected, and in the event that the child virtual sphere does not overlap a matter pixel or a virtual curved surface solid already placed, it is determined that the child virtual sphere of diameter Rb can be placed at that position. In the event that the child virtual sphere overlaps a matter pixel or a virtual curved surface solid already placed regardless of every pixel occupied by the parent virtual sphere being selected as the center at that point-in-time, it is determined that the child virtual sphere of diameter Rb cannot be placed.
When it is determined in step S270 that the child virtual sphere can be placed, one child virtual sphere of diameter Rb is placed at that position (step S280). Specifically, of the porous body table 81 of the porous body data 80 stored in the RAM 24 in step S200, the type information corresponding to the pixel occupied by the child virtual sphere when the child virtual sphere of diameter Rb is placed is updated to a value 4 which represents a pixel being occupied by a child virtual sphere. Note that no updating of type information is performed for pixels with type information of value 3, which are pixels occupied by the parent virtual sphere. That is to say, pixels where the parent virtual sphere and child virtual sphere overlap are correlated with the type information of the parent virtual sphere. Upon having placed one child virtual sphere, the processing of step S270 and thereafter is performed, and step S280 is repeated and child virtual spheres of diameter Rb are placed until it is determined that no child virtual sphere of diameter Rb can be placed. Note that mutual overlapping of child virtual spheres is permitted. That is to say, overlapping of pixels which one child virtual sphere occupies and pixels which another child virtual sphere occupies is permitted.
When it is determined in step S270 that no child virtual sphere can be placed, the value of diameter Rb is decremented by 1 (step S290), and it is determined whether or not the diameter Rb is smaller than the minimum value Rbmin (step S300). When the diameter Rb is equal to or greater than the minimum value Rbmin, the processing of step S270 and thereafter is performed. The minimum value Rbmin is the lower limit value of the diameter Rb of the child virtual sphere, and is a threshold determined to prevent placement of child virtual spheres with relatively small diameters that would not affect the analysis results very much, for example. With the present embodiment, Rbmin is 2 μm.
When the diameter Rb is smaller than the minimum value Rbmin in step S300, a virtual curved surface solid formed of the parent virtual sphere placed in step S250 and child virtual spheres placed in step S280 (step S310). Specifically, of the porous body table 81 of the porous body data 80 stored in the RAM 24 in step S200, the type information corresponding to the pixels occupied by the parent virtual sphere (pixels of type information is value 3) and the pixels occupied by the child virtual sphere (pixels of type information is value 4) are updated to a value 5 which represents a pixel of a curved surface solid pixel occupied by the virtual curved surface solid. Also, an identification symbol of the virtual curved surface solid is correlated with the position information of the curved surface solid pixels updated to the value 5 this time. The identification symbol of the virtual curved surface solid is a value given to each virtual curved surface solid in accordance with the order of being placed, for example, and curved surface solid pixels configuring one virtual curved surface solid have the same identification symbol correlated therewith. Information relating to this virtual curved surface solid is stored in the RAM 24 (step S320), it is determined whether or not 99% or more of space pixels have been replaced with the curved surface solid (step S330). This determination is made specifically by referencing the type information of each pixel included in the porous body table 71 stored in the RAM 24, and determining whether or not the number of pixels of which the type information of value 5 is 99% or more of the total number of pixels, of the number of pixels of which the type information is of value 0 and the number of pixels of which the type information is of value 5. The determination threshold is not restricted to 99%, and that other values may be used. When it is determined in step S330 that less than 99% of space pixels have been replaced with the curved surface solid, processing of step SS230 and thereafter is performed, so as to place the next virtual curved surface solid. On the other hand, when it is determined in step S330 that 99% or more of space pixels have been replaced with the curved surface solid, the virtual curved surface solid placement processing ends.
Note that in step S320, a virtual curved surface solid table 83 is stored in the RAM 24, as part of the porous body data 80. In the virtual curved surface solid table 83, as information relating to the virtual curved surface solid, an identification symbol identifying the virtual curved surface solid, the center coordinates (X, Y, Z) and diameter of the parent virtual sphere configuring the virtual curved surface solid, and the center coordinates and diameter of the one or more child virtual spheres configuring the virtual curved surface solid, are correlated.
According to this virtual curved surface solid placement processing, the virtual curved surface solid table 83 is stored in the RAM 24, and also the space pixels are replaced with curved surface solid pixels by the virtual curved surface solid that has been placed. Now, the way in which one virtual curved surface solid made up of a parent virtual sphere and child virtual spheres is placed by the virtual curved surface solid placing processing will be described.
The description now returns to the analysis processing routine in
Next, the in-plane uniformity index evaluation module 25d performs in-plane uniformity index evaluation processing (step S120). In the in-plane uniformity index evaluation processing, an in-plane uniformity index γx is derived, and acceptability determination is made based on the derived value to evaluate the porous body. The in-plane uniformity index γx is derived from the following Expression (1) as a value at a section specified as a cross-section parallel to the inflow face 61. Note that an n number of average flow velocities ui at the cross-section described below, and cross-sectional area Ai of each virtual curved surface solid within the cross-section, are derived as follows, for example. First, curved surface solid pixels included in a cross-section from which the in-plane uniformity index γx is to be derived are identified based on a distance x between cross-section and the inflow face 61, and the position information and type information in the porous body table 81 stored in the RAM 24. Next how many types of identification symbols there are in virtual curved surface solids correlated with the identified curved surface solid pixels is counted, and this number is taken as the number n of virtual curved surface solids within the cross-section. Next, one of the identification symbols of the virtual curved surface solids within the cross-section is selected. Next, with regard to the curved surface solid pixel correlated with the selected identification symbol, i.e., the curved surface solid pixels configuring one virtual curved surface solid, the flow velocity vector correlated with each curved surface solid pixel in the fluid analysis processing is found, the average value of the flow velocity components in a direction perpendicular to the cross-section for each curved surface solid pixel is derived, and this is taken as average flow velocity u1. The number of pixels is also counted for the curved surface solid pixels correlated with the selected identification symbol, and the product of the number of pixels and the area of the curved surface solid pixels following the cross-section (=1.44 μm2) is taken as cross-section area A1. The selected identification symbol is sequentially changed, whereby the average flow velocity u2, u3, . . . , un, and cross-section area A2, A3, . . . , An can be derived in the same way for the n virtual curved surface solids within the cross-section. The in-plane uniformity index evaluation module 25d then derives the in-plane uniformity index γx for multiple cross-sections, e.g., 250 (=300 μm/1.2 μm) cross-sections with the distance x changed 1.2 μm (the same value as the length of a pixel in the x direction) at a time for example. It is determined that the pressure drop property of the porous body is acceptable when the average value of the in-plane uniformity index γx is 0.6 or greater, and unacceptable when smaller than 0.6.
[Math. 1]
where
n: number [count] of virtual curved surface solids within cross-section
x: distance [m] between cross-section and inflow face
ui: average flow velocity (i=1, 2, . . . , n) [m/s] for each of the n virtual curved surface solids at cross-section
umean: average value (=(ui+u2+ . . . +un)/n) [m/s] of average flow velocity ui at cross-section
Ai: cross-sectional area (i=1, 2, . . . , n) [m2] for each virtual curved surface solid within cross-section
A: total cross-sectional area (=A1+A2 . . . An) [m2] of virtual curved surface solids at cross-section
Next, the spatial uniformity index evaluation module 25e performs spatial uniformity index evaluation processing (step S130). In the spatial uniformity index evaluation processing, a spatial uniformity index γ is derived, and acceptability determination is made based on the derived value to evaluate the porous body. The spatial uniformity index γ is derived by the following Expression (2) using multiple in-plane uniformity indices γx derived in the in-plane uniformity index evaluation processing. It is determined that the collection performance of the porous body is acceptable when the derived spatial uniformity index γ is 0.6 or greater, and unacceptable when smaller than 0.6.
[Math. 2]
γ=
δγ: standard deviation of γx
Next, the pressure drop evaluation module 25f performs pressure drop evaluation processing (step S140). In the pressure drop evaluation processing, the pressure drop P per unit thickness is derived, and acceptability determination is made based on the derived value to evaluate the porous body. The pressure drop P is derived by the following Expression (3) using multiple in-plane uniformity indices γx derived in the in-plane uniformity index evaluation processing. This Expression (3) is one where a known Ergun's Equation representing pressure drop properties at the time of a fluid passing through a porous body has been revised using the in-plane uniformity index γx. Note that the representative hydraulic diameter Dhx of the space (pores) at the cross-section at distance x is obtained as follows with the present embodiment. First, a total area Ax as the total area of space portions at the cross-section x is derived. This is derived as the product of the number of pixels of the space pixels (including curved surface solid pixels) at the cross-section at distance x, and the cross-sectional area of each pixel (1.44 μm2 with the present embodiment). Next, the total wetted perimeter Lx as the total of wetted perimeters at the cross-section at distance x as Lx is derived. This is derived as the total of the length of boundary lines between space pixels (including curved surface solid pixels) and matter pixels. The representative hydraulic diameter Dhx is then derived from representative hydraulic diameter Dhx=4×total area Ax/total wetted perimeter Lx. A flow velocity average value Ux for every space pixel at the cross-section at the distance x described below may be derived by, for example, finding the flow velocity vectors correlated with each space pixel in the fluid analysis processing for the space pixels (including curved surface solid pixels) at the cross-section at the distance x, deriving the flow velocity component in a direction perpendicular to the cross-section of each space pixel, and deriving the flow velocity average value as the average value thereof. Note that a constant k can be obtained beforehand by experiment, for example, so that the correlation between the pressure drop P and the actual pressure drop of the porous body is higher. With the present embodiment, the constant k is set to the value “−2”. The acceptability determination based on pressure drop P is performed as follows, for example. First, the pressure drop P is derived for each of the multiple in-plane uniformity indices γx, and the average value of the multiple pressure drops P is derived. When the average value of the pressure drops P is at or below a predetermined threshold (e.g., allowable upper limit value of pressure drop), it is determined that the pressure drop of the porous body is acceptable, while it is determined to be unacceptable when the predetermined threshold is exceeded. At the time of deriving the multiple pressure drops P with the present embodiment, the distance x is changed by a value the same as the X direction length of the pixels (1.2 μm with the present embodiment), i.e., shifting the cross-section which is the object of derivation one pixel at a time, and pressure drops P of a number corresponding to as many in-plane uniformity indices γx as there are pixels in the X direction are derived. However, the method for deriving the average value of pressure drops P is not restricted to this, and any method will suffice as long as pressure drops P corresponding to multiple in-plane uniformity indices are derived while changing the distance x and the average thereof is derived.
Δx: cross-sectional thickness [m] at cross-section at distance x
ΔPX: pressure drop [Pa] at cross-section at distance x
Dhx: representative hydraulic diameter [m] of space (pores) at cross-section at distance x
εx: voidage (=number of space pixels/(number of space pixels+number of matter pixels)) at cross-section at distance x
μ: viscosity [Pa·s] of fluid
Ux: flow velocity average value [m/s] at each space pixel at cross-section at distance x
ρ: density of fluid [kg/m3]
k: constant
Next, the flow-through velocity evaluation module 25g performs flow-through velocity evaluation processing (step S150). In the flow-through velocity evaluation processing, the flow-through velocity T at each virtual curved surface solid is derived, the virtual curved surface solids are classified based on the derived values, and the porous body is evaluated based on the classification results. The flow-through velocity T at each virtual curved surface solid is derived as follows. First, a through-flow volume Q of the fluid per unit time is derived for each virtual curved surface solid. The flow-through velocity T of each virtual curved surface solid is then derived by T=Q/(πd2/4), based on the derived through-flow volume Q and an equivalent diameter d of the virtual curved surface solid (=6×volume V of virtual curved surface solid/surface area S of virtual curved surface solid). The through-flow volume Q, volume V, and surface area S of each virtual sphere is derived as follows. First, one virtual curved surface solid is selected, and the curved surface solid pixels corresponding to the identification symbols of the selected virtual curved surface solid are found from the porous body table 81 in the RAM 24. The number of pixels of the curved surface solid pixels configuring the selected virtual curved surface solid is derived, and the product of the number of pixels and the volume of one curved surface solid pixel (1.728 μm3 with the present embodiment) is taken as the volume V. The surface area S of the selected virtual curved surface solid is derived based on information (center coordinates and diameters of parent virtual sphere and child virtual spheres) included in the virtual curved surface solid table 83. Next, of the curved surface solid pixels configuring the selected virtual curved surface solid, the curved surface solid pixel configuring the surface of the virtual curved surface solid are identified based on the information included in the virtual curved surface solid table 83. The flow vectors correlated with the curved surface solid pixels configuring the surface are found using the porous body table 81 in the RAM 24, the curved surface solid pixels of which the flow velocity vector heads toward the inside of the virtual curved surface solid are identified, the magnitude of the flow velocity vectors of the identified curved surface solid pixels is obtained for each curved surface solid pixel, and through-flow volume Q per unit time is derived by the through-flow volume Q per unit time=(sum of magnitude of flow velocity vectors)×(number of identified curved surface solid pixels)×(area of one face of a curved surface solid pixel (=1.44 μm2)). Thus, the flow-through velocity T of the selected curved surface solid pixel can be derived. In the same way, the flow-through velocity T is derived for each of the multiple virtual curved surface solids.
Classification of each of virtual curved surface solids in the flow-through velocity evaluation processing is performed as follows. First, one virtual curved surface solid is selected, and a flow velocity ratio Tf (=T/Tin) is derived from the flow-through velocity T of the selected virtual curved surface solid and the average flow velocity Tin in fluid analysis. A virtual curved surface solid having a flow velocity ratio within the range of Tf<2 is classified as being a low-flow-velocity curved surface solid, a virtual curved surface solid having a flow velocity ratio within the range of 2≦Tf<8 is classified as being a mid-flow-velocity curved surface solid, and a virtual curved surface solid having a flow velocity ratio within the range of 8≦Tf is classified as being a high-flow-velocity curved surface solid. Each of the virtual curved surface solids are classified in the same way. It is determined that the performance of the porous body is acceptable when the percentage of the total value of volume V of the low-flow-velocity curved surface solid is 20% or less as to the total value of volume V of the multiple virtual curved surface solids, and at the same time the percentage of the total value of volume V of the high-flow-velocity curved surface solid is 10% or less. On the other hand, it is determined that the performance of the porous body is unacceptable when the percentage of the total value of volume V of the low-flow-velocity curved surface solid is greater than 20%, or when the percentage of the total value of volume V of the high-flow-velocity curved surface solid is greater than 10%.
Next, the equivalent diameter evaluation module 25h performs equivalent diameter evaluation processing (step S160). In the equivalent diameter evaluation processing, the equivalent diameter d of each virtual sphere is derived, the virtual curved surface solids are classified based on the equivalent diameter d, and the porous body is evaluated based on the classification results. In classification of the virtual curved surface solids based on the equivalent diameter d, a virtual curved surface solid having an equivalent diameter within the range of d<10 μm is classified as being a small-diameter curved surface solid, a virtual curved surface solid having an equivalent diameter within the range of 10 μm≦d≦25 μm is classified as being a mid-diameter curved surface solid, and a virtual curved surface solid having an equivalent diameter within the range of 25 μm<d is classified as being a large-diameter curved surface solid. It is determined that the performance of the porous body is acceptable when the percentage of the total value of volume V of mid-diameter curved surface solids as to the total value of volume V of the multiple virtual curved surface solids is 60% or more, and unacceptable when the percentage is less than 60%. Note that the equivalent diameter d and the volume V may be derived in the same way as with the flow-through velocity evaluation processing described above, or values derived in the flow-through velocity evaluation processing may be used without change.
Upon performing each evaluation processing of steps S120 through S160, the analysis result output module 25i performs analysis result output processing in which the information and the like stored in the RAM 24 in the above processing is output as analysis result data and stored in the HDD 25 (step S170), and the present routine ends. The analysis result data includes, for example, the porous body data 80 including the porous body table 81, inflow/outflow table 82, and virtual curved surface solid table 83, stored in the RAM 24, the values of the in-plane uniformity index γx and the results of acceptability determination in the in-plane uniformity index evaluation processing, the values of the spatial uniformity index γ and the results of acceptability determination in the spatial uniformity index evaluation processing, the values of the pressure drop P and the results of acceptability determination in the pressure drop evaluation processing, the values of the flow-through velocity T and flow velocity ratio Tf in the flow-through velocity evaluation processing, percentages of the total value of volume V of low-flow-velocity curved surface solids and the total value of volume V of high-flow-velocity curved surface solids and the results of acceptability determination, the values of equivalent diameter d in the equivalent diameter evaluation processing, and percentage of the total value of volume V of mid-diameter curved surface solids and the results of acceptability determination, and so forth. Values used for the fluid analysis processing, such as average flow velocity Tin, fluid viscosity μ, fluid density ρ, and so forth may also be included.
The results of analysis of the microstructure of the porous partition 44 according to the present embodiment, performed as described above, satisfy at least one of the following three conditions; “the average value of multiple in-plane uniformity indices γx is 0.6 or greater, and the spatial uniformity index γ is 0.6 or greater” (that is, the evaluation results of in-plane uniformity index evaluation processing and spatial uniformity index evaluation processing are both good), “the percentage of the total value of volume of low-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 20% or less, and the percentage of the total value of volume of high-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 10% or less” (that is, the evaluation results of flow-through velocity evaluation processing are good), and “the percentage of the total value of volume of mid-diameter curved surface solids as to the total value of volume of multiple virtual curved surface solids is 60% or more” (that is, the evaluation results of equivalent diameter evaluation processing are good). Preferably, two or more conditions are satisfied, and more preferably, all three conditions are satisfied.
Next, a method of manufacturing the honeycomb filter 30 including the porous partition 44 according to the present embodiment will be described. The porous partition 44 of the honeycomb filter 30 can be manufactured by way of a raw material mixing process where a base material and a pore-forming agent are mixed to form a green body, and a molding-and-sintering process where the green body is formed to yield a compact, and the compact is sintered. The aforementioned inorganic material can be used for the base material. For example, a mixture of 80:20 by mass of Sic powder and metal Si powder can be used for a substrate of SiC. The pore-forming agent preferably burns away in the later sintering, examples thereof including starch, coke, foamed resin, or the like. The average particle size of the base material is 5 to 50 μm, for example, but is not restricted in particular. The average particle size of the pore-forming agent is 5 to 50 μm, for example, but is not restricted in particular. A base material where the value of (D90−D10)/D50 is 2 or smaller is used, where D10 represents particle diameter that is 10% by volume, D50 represents particle diameter that is 50% by volume, and D90 represents particle diameter that is 90% by volume. The smaller the (D90−D10)/D50 of the base material is, the more preferable, and preferably is a value 1.5 or smaller, for example. In the same way, the smaller the (D90−D10)/D50 of the pore-forming agent is, the more preferable, and preferably is a value 1.5 or smaller. Now, the term that D10 of the base material, which is to say particle diameter that is 10% by volume, is a value 20 μm, means that the total volume of particles of which the particle diameter is 20 μm or smaller occupies 10% of the total volume of all particles of the base material. This is the same for D50 and D90 as well. D10, D50, and D90 are values of D10, D50, and D90 obtained by measuring raw material particles using a laser diffraction/scattering particle size distribution measurement device, with water as a dispersant. In the raw material mixing process a binder such as methyl cellulose and hydroxypropoxyl methyl cellulose, and water may be added, and dispersant further mixed in. A surfactant such as ethylene glycol or the like can be used for the dispersant. The means for preparing the green body are not restricted in particular, examples thereof including methods using a kneader, a vacuum kneading machine, and so forth. In the molding-and-sintering process, for example, this green body is molded by extrusion into the shape with cells 34 arrayed as illustrated in
According to the present embodiment described in detail above, the porous partition 44 serving as the porous body satisfies at least one of the three conditions when the microstructure is analyzed using the user PC 20; “the average value of multiple in-plane uniformity indices γx is 0.6 or greater, and the spatial uniformity index γ is 0.6 or greater”, “the percentage of the total value of volume of low-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 20% or less, and the percentage of the total value of volume of high-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 10% or less”, and “the percentage of the total value of volume of mid-diameter curved surface solids as to the total value of volume of multiple virtual curved surface solids is 60% or more”. Accordingly, pressure drop has been sufficiently reduced and also collection performance has been sufficiently improved.
Now, the more uniform the flow velocity of the fluid at a cross-section of the porous body is, the greater (closer to 1) the value of the in-plane uniformity index γx is, and the more variance there is in the flow velocity of the fluid at the cross-section is, the smaller the value is. Also, the smaller the variance in the in-plane uniformity index γx derived for multiple cross-sections is, the greater the value of the spatial uniformity index γ is, and the greater the variance is, the smaller the value is. Portions of the pores (spaces) within the porous body where the flow velocity of the passing fluid is relatively small may not contribute much to transmittance of the fluid, which may lead to increased pressure drop, and deterioration in thermal conductivity and thermal capacity of the material. Also, portions of the pores where the flow velocity of the passing fluid is relatively great may exhibit great flow resistance when the fluid passes through, or may not contribute much to collecting performance because the fluid passes through in a short time. Accordingly, when the condition of the in-plane uniformity index γx being 0.6 or greater, and the spatial uniformity index γ being 0.6 or greater is satisfied, there are few such portions where the flow velocity is relatively smaller or portions where the flow velocity is relatively great, so it can be conceived that the pressure drop is sufficiently reduced and collection performance is sufficiently improved thereby.
In the same way, pores of the porous body simulated with virtual curved surface solids of which the flow velocity ratio Tf is relatively small may not contribute much to transmittance of the fluid, leading increased pressure drop, and deterioration in thermal conductivity and thermal capacity of the material. Also, pores of the porous body simulated with virtual curved surface solids of which the flow velocity ratio Tf is relatively great may exhibit great flow resistance when the fluid passes through, or may not contribute much to collecting performance because the fluid passese through in a short time. Accordingly, when the condition of “the percentage of the total value of volume of low-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 20% or less, and the percentage of the total value of volume of high-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 10% or less” is satisfied, there are few such portions where the flow velocity is relatively smaller or portions where the flow velocity is relatively great, so it can be conceived that the pressure drop is sufficiently reduced and collection performance is sufficiently improved thereby.
Also, with pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is small, the flow velocity of the fluid passing through may be small, leading to increased pressure drop, or the catalyst applied to the walls of the pores to use the porous body as a filter may not be appropriately applied, or the like. Also, pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d great, may result in the flow velocity of the fluid passing through being great to the point of not contributing to collecting performance very much when using the porous body as a filter. Accordingly, when the condition of “the percentage of the total value of volume of mid-diameter curved surface solids as to the total value of volume of multiple virtual curved surface solids is 60% or more” is satisfied, it can be conceived that the pressure drop is sufficiently reduced and collection performance is sufficiently improved by there being few such pores where the equivalent diameter d is small and pores where the equivalent diameter d is great.
Also, when manufacturing the porous partition 44, the value of (D90−D10)/D50 for the base material is 2 or smaller, and the value of the (D90−D10)/D50 for the pore-forming agent is 2 or smaller. Such a small variance in the particle diameter of the base material and pore-forming agent enables a porous body to be obtained with sufficiently reduced pressure drop and sufficiently improved collection performance.
Note that the present invention is by no way restricted to the above-described embodiment, and it is clearly understood that various forms may be realized as long as within the technical scope of the present invention.
For example, in the above-described embodiment, the performance of the porous body is determined to be good in a case where, in the equivalent diameter evaluation processing, the percentage of the total value of volume V of mid-diameter curved surface solids as to the total value of volume V of multiple virtual curved surface solids is 60% or more. But performance of the porous body may be determined to be good when the percentage is 70% or more. When the condition of “the percentage of the total value of volume V of mid-diameter curved surface solids as to the total value of volume V of multiple virtual curved surface solids is 70% or more” is satisfied for the porous body, pressure drop is further reduced and collection performance is further improved.
In the above-described embodiment, the results of analyzing the above-described microstructure of the porous partition 44 satisfy at least one of the following three conditions; “the average value of multiple in-plane uniformity indices γx is 0.6 or greater, and the spatial uniformity index γ is 0.6 or greater”, “the percentage of the total value of volume of low-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 20% or less, and the percentage of the total value of volume of high-flow-velocity curved surface solids as to the total value of volume of multiple virtual curved surface solids is 10% or less”, and “the percentage of the total value of volume of mid-diameter curved surface solids as to the total value of volume of multiple virtual curved surface solids is 60% or more”. However, porous partition 44 manufactured by the above-described manufacturing method satisfying the conditions where the value of (D90−D10)/D50 for the base material is 2 or smaller, and the value of the (D90−D10)/D50 for the pore-forming agent is 2 or smaller need not satisfy any of these three conditions. Further, an arrangement may be made where none of these three conditions are satisfied, but the condition of “the average value of multiple in-plane uniformity indices γx is 0.6 or greater” is satisfied.
A honeycomb filter according to Example 1 was fabricated as follows. First, SiC powder, having an average particle diameter of 40 μm and a value for (D90−D10)/D50 of 1.9, and metal Si powder, having an average particle diameter of 4 μm and a value for (D90−D10)/D50 of 1.8, were mixed at a ratio of 80:20 by mass, to serve as a base material. This base material, and a pore-forming agent (starch) having an average particle diameter of 30 μm and a value for (D90−D10)/D50 of 1.7, were mixed at a ratio of 100:30 by mass, to which methylcellulose serving as an organic binder and an appropriate amount of water were added and mixed, thereby yielding a green body. The SiC powder, metal Si powder, and pore-forming agent, were subjected to sieving using a screen with a predetermined sieve opening, thereby suppressing variance in particle diameter and obtaining those where the values of (D90−D10)/D50 are as described above. Next, a predetermined mold was used to extrude the green body, thus forming a compact having the form of the porous partition 44 illustrated in
A honeycomb filter according to Example 2 was fabricated in the same way as Example 1, except that the value for (D90−D10)/D50 of the Sic powder was 1.3, the value for (D90−D10)/D50 of the metal Si powder was 1.3, and the value for (D90−D10)/D50 of the pore-forming agent was 1.2.
Creating Microstructure Analysis Device
A microstructure analysis device was created to evaluate Examples 1 and 2. First, an analysis processing program 25a having the functions of the above-described embodiment was created. This program was then stored in the HDD of a computer having a controller including a CPU, ROM, and RAM, and a HDD, thereby creating a microstructure analysis device.
Evaluation by Microstructure Analysis Device
Porous partitions (porous bodies) of the honeycomb filters according to Examples 1 and 2 were CT-scanned, and of pixel data obtained thereby, one data was extracted where the X direction is 300 μm (=1.2 μm×250 pixels), which is the same value as the thickness in the direction of passage of the exhaust gas, the Y direction is 480 μl (=1.2 μm×400 pixels), and the Z direction is 480 μm (=1.2 μm×400 pixels), which was stored in the HDD as the above-described porous body data 60, and the above-described analysis processing routine was executed regarding this porous body data 60. Analysis result data of the Examples 1 and 2 was obtained, including the above-described porous body table, virtual curved surface solid table, average value of in-plane uniformity index γx, spatial uniformity index γ, average value of pressure drop P, flow velocity ratio Tf (=T/Tin) of each virtual curved surface solid, equivalent diameter d of each virtual curved surface solid, volume V, and so forth.
In-Plane Uniformity Index γx
Spatial Uniformity Index γ
Results of Classification by Flow Velocity Ratio Tf
Tabulation Results of Pore Diameter
Results of Classification by Equivalent Diameter d
The (D90−D10)/D50 values for the base material and pore-forming agent, average values of in-plane uniformity indices γx, values of spatial uniformity indices γ, percentage of low-flow-velocity curved surface solids by volume, percentage of high-flow-velocity curved surface solids by volume, percentage of mid-diameter curved surface solids by volume, leaked particle count, and actual pressure drop, of Examples 1 and 2, which have been described above, are shown together in Table 1.
The present application claims priority from Japanese Patent Application No. 2012-082500 filed on Mar. 30, 2012, the entire contents of which are incorporated herein by reference.
The present invention is applicable to the manufacturing industry of porous bodies used as filters for purging exhaust gas emitted from stationary engines and burning appliances and the like for automobiles, construction equipment, and industrial use.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2012-082500 | Mar 2012 | JP | national |
| Number | Date | Country | |
|---|---|---|---|
| Parent | PCT/JP2013/057974 | Mar 2013 | US |
| Child | 14499750 | US |
