Radiant tube burner, radiant tube, and design method of radiant tube burner
By using an elliptical opening cross-section and specific air flow distribution in the radiation tube burner to form a circulating flow, the problem of NOx generation is solved, and low NOx emissions and efficient heat recovery are achieved.
Patent Information
- Application Number
- CN202180013590.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Priority Date
- 2020-02-10
- Filing Date
- 2021-02-03
- Publication Date
- 2025-08-15
- Estimated Expiration
- 2041-02-03
AI Technical Summary
The NOx emissions generated by existing radiation tube burners during combustion are high, and prior art solutions such as using fans or catalysts will lead to larger-scale devices or reduced maintenance performance.
A radiation tube burner with an elliptical opening cross section is adopted, and a secondary combustion air nozzle is arranged in the center, and a plurality of primary combustion air and fuel gas nozzles are arranged around it. The circulating flow is formed around the burner by adjusting the air flow ratio to reduce NOx generation.
The effective reduction of NOx under simple structure is achieved, which avoids the device's scale-up and maintenance performance degradation, and maintains the heat recovery efficiency.
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Figure CN115087834B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a technology of radiant tubes. Background Art
[0002] Radiant tubes are devices that supply fuel gas and combustion air through the gas injection port of a radiant tube burner, causing combustion. Heat from the generated combustion gas, heated by the tube, indirectly heats the object outside the tube. Because the combustion space within radiant tubes is limited, radiant tubes alone cannot effectively utilize the heat. Therefore, various waste heat recovery devices, such as recuperators and regenerative burners, are often used to recover heat by preheating the combustion air.
[0003] Radiant tubes present a problem: combustion gases generated within the tubes are exhausted through the tubes, but as the temperature of the combustion gases rises, the production of harmful nitrogen oxides (hereinafter referred to as NOx) increases. Therefore, in order to suppress NOx emissions, the amount of waste heat recovered is sometimes limited.
[0004] Conventionally, as a technology for reducing the generation of NOx in a radiant tube, there are technologies described in Patent Documents 1 and 2, for example.
[0005] Patent Document 1 discloses a technique for reducing NOx generation by mixing exhaust gas with fuel gas or secondary combustion air using a fan to reduce the combustion rate. Patent Document 2 discloses purification of generated NOx using a catalyst.
[0006] Prior art literature
[0007] Patent Literature
[0008] Patent Document 1: Japanese Patent Application Laid-Open No. 63-113206
[0009] Patent Document 2: Japanese Patent Application Laid-Open No. 2017-219235 Summary of the Invention
[0010] Problems to be solved by the invention
[0011] However, Patent Document 1 requires a fan to guide the exhaust gas to the fuel gas or secondary combustion air. For example, installing a fan for each radiant tube would affect maintenance performance. Furthermore, the configuration of Patent Document 1 also presents the problem of increasing the size of the radiant tubes due to the installation of fans.
[0012] Furthermore, Patent Document 2 addresses the significant issue of catalyst degradation due to poisoning in the steel industry, which utilizes by-product gases. Furthermore, the configuration of Patent Document 2 also presents the issue of the radiant tube becoming larger due to the installation of the catalyst.
[0013] The present invention has been made in view of the above-mentioned problems, and its object is to provide a radiant tube burner and a radiant tube that can reduce NOx generation with a simple structure without adversely affecting maintenance performance or reducing the low NOx effect due to poisoning.
[0014] Means for solving problems
[0015] To develop a low-NOx radiant tube burner, the inventors of this application conducted various combustion analyses, including those on NOx generation around the burner, rather than being limited to conventional radiant tube shapes. Based on these results, the inventors discovered that by configuring the radiant tube's opening cross-section to be an ellipse with different major and minor diameters, placing a secondary combustion air nozzle in the center of the tube, and circumferentially surrounding the secondary combustion air nozzle with multiple fuel gas nozzles and multiple primary combustion air nozzles, primary combustion is performed at an air ratio of 1.0 or less. This generates a circulating flow in the primary combustion region around the burner, thereby reducing NOx concentrations in front of the burner. Furthermore, the inventors discovered that by appropriately distributing the flow rate of primary combustion air injected from the multiple primary combustion air nozzles between the major and minor diameters of the tube's ellipse, NOx concentrations can be further reduced. The present invention was completed based on these findings.
[0016] Furthermore, in order to solve the problem, one embodiment of the present invention is a radiant tube burner, which is mainly arranged by being inserted into a tube having an elliptical opening cross section, and in a gas injection portion of the radiant tube burner, a secondary combustion air nozzle for injecting secondary combustion air is arranged in a central portion, and a plurality of primary combustion air nozzles for injecting primary combustion air and a plurality of fuel gas nozzles for injecting fuel gas are arranged so as to surround the secondary combustion air nozzle. In the radiant tube burner, the tube is imaginarily divided into four areas using two straight lines obtained by tilting the minor axis of an ellipse, which is the opening cross section shape of the tube, at ±45 degrees with the center of the ellipse as the center as a boundary, as the boundaries, and the primary combustion air injected from the primary combustion air nozzle located in an area containing the minor axis of the ellipse among the four imaginary areas is less than the primary combustion air injected from the primary combustion air nozzle located in an area not containing the minor axis of the ellipse among the four areas.
[0017] Effects of the Invention
[0018] According to the aspects of the present invention, it is possible to provide a radiant tube burner and a radiant tube capable of reducing the generation of NOx with a simple configuration. BRIEF DESCRIPTION OF THE DRAWINGS
[0019] [ Figure 1] is a schematic diagram for explaining the structure of a radiant tube of a radiant tube burner according to an embodiment of the present invention.
[0020] [ Figure 2 ] for Figure 1 FIG. 2 is a diagram illustrating the cross-sectional shape of the opening of the tube, shown in the AA′ cross section.
[0021] [ Figure 3 ] is a schematic three-dimensional diagram showing the relationship between the gas injection part and the tube of the radiant tube burner.
[0022] [ Figure 4 ] is a conceptual diagram showing each nozzle of the gas injection part.
[0023] [ Figure 5 ] is a main view showing the configuration relationship between the four areas and each nozzle.
[0024] [ Figure 6 ] is a graph showing the relationship between the flow rate ratio and the NOx ratio.
[0025] [ Figure 7 ] is a graph showing the relationship between the flow rate ratio and the combustion gas temperature on the short shaft side. DETAILED DESCRIPTION
[0026] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.
[0027] The drawings are schematic, and the sizes and length ratios of the various components may differ from those in reality. The embodiments described below illustrate configurations for embodying the technical concept of the present invention. The materials, shapes, and structures of the components within the technical concept of the present invention are not limited to those described below. Various modifications may be made to the technical concept of the present invention within the technical scope defined by the claims.
[0028] Here, in this specification, an ellipse does not include a perfect circle. The minor diameter of an ellipse refers to the shortest diameter, and the major diameter refers to the diameter in a direction perpendicular to the minor diameter. In addition, the minor axis is the axis extending in the direction of the minor diameter, and the major axis is the axis extending in the direction of the major diameter.
[0029] (constitute)
[0030] like Figure 1 As shown, the radiant tube 100 of this embodiment includes a tube 1 through which combustion gas flows, and a radiant tube burner 2 that generates combustion gas within the tube 1. The radiant tube 100 may also include a heat transfer enhancer 4, various waste heat recovery devices 5 such as a recuperator and a regenerative burner, and other known components, or may not include these components.
[0031] (Tube 1)
[0032] like Figure 1 As shown, the tube 1 of this embodiment has a zigzag shape that is roughly W-shaped in side view. It comprises four straight tube sections 1A to 1D arranged vertically side by side. The ends of adjacent straight tube sections 1A to 1D are connected by curved tube sections 1E to 1G extending in an arcuate shape. Reference numeral 6 denotes a partition member that prevents narrowing between adjacent straight tube sections. Reference numeral 7 denotes a support member that is supported by the extension section 3A and prevents downward displacement of the tube.
[0033] Furthermore, the pipe 1 is supported by the furnace wall 3 by fixing the inlet side of the straight pipe portion 1A at the most upstream position and the outlet side of the straight pipe portion 1D at the most downstream position to the furnace wall 3 .
[0034] like Figure 2 As shown, the cross-sectional opening of at least the most upstream straight tube portion 1A of the tube 1 has an elliptical shape, with a minor diameter La and a major diameter Lb that are different. Specifically, the cross-sectional opening of the most upstream straight tube portion 1A of the radiant tube burner 2, where the gas injection portion 2A is located, has an elliptical shape with a minor diameter La and a major diameter Lb that are different. In this embodiment, the tube 1 has an elliptical shape with the major axis Y oriented in the vertical direction along its entire length.
[0035] Specifically, the tube 1 is positioned so that the major axis Y, which is the axis of the major diameter perpendicular to the minor diameter of the ellipse, faces the vertical direction. By arranging the tube 1 with the major axis Y facing the vertical direction, the rigidity of the tube 1 is improved compared to a case where the opening cross-section of the tube 1 is a true circle, and downward displacement of the straight tube portions 1A to 1D constituting the tube 1 due to their own weight or thermal load can be suppressed.
[0036] The ellipse defining the cross section of the tube is not particularly limited as long as the minor diameter La and the major diameter Lb are different in length, since the rigidity is improved compared to a perfect circle. For example, the ratio (major diameter Lb / minor diameter La) can be set to 1.1 or more and 1.4 or less.
[0037] Here, this embodiment has a configuration in which an object to be heated (not shown) is moved up and down in front of and behind the tube 1 , thereby heating the object to be heated by radiant heat from the radiant tube 100 . Figure 2 In FIG. 1 , reference numeral 50 indicates an example of the moving direction of the object to be heated.
[0038] (Radiant tube burner 2)
[0039] like Figure 1 As shown, in the radiant tube burner 2, a gas injection portion 2A is inserted coaxially with the upstream end of the straight tube portion 1A into the most upstream straight tube portion 1A. The gas injection portion 2A is a header formed with nozzles for injecting combustion air and fuel gas.
[0040] like Figure 3 As shown, the gas ejection portion 2A of the present embodiment has a main body with a cylindrical outer shape, and is arranged so that the central axis P of the cylindrical shape is coaxial with the central axis P of the tube 1 .
[0041] The front end of the gas injection section 2A is provided with a secondary combustion air nozzle 21, a plurality of primary combustion air nozzles 22, and a plurality of fuel gas nozzles 23. The surface of the front end of the gas injection section 2A is also referred to as a gas injection surface. Figure 4 As shown, the gas injection axis of each nozzle is set parallel to the center P axis of the gas injection portion 2A, and the gas can be injected in the same direction as the extending direction of the tube 1.
[0042] Here, the secondary combustion air nozzle 21 is a nozzle for injecting secondary combustion air, the primary combustion air nozzle 22 is a nozzle for injecting primary combustion air, and the fuel gas nozzle 23 is a nozzle for injecting fuel gas.
[0043] like Figures 3 to 5 As shown, the secondary combustion air nozzle 21 is arranged in the center of the circular gas injection surface and is composed of a cylindrical portion extending forward (in the gas injection direction) from the gas injection surface. The secondary combustion air nozzle 21 of this embodiment is set coaxially with the gas injection portion 2A.
[0044] Furthermore, on the gas injection surface, a plurality of primary combustion air nozzles 22 and a plurality of fuel gas nozzles 23 are arranged radially outward of the secondary combustion air nozzle 21 so as to surround the outer circumference of the secondary combustion air nozzle 21. Furthermore, holes are formed on the gas injection surface to form openings at the distal ends of the plurality of primary combustion air nozzles 22 and the plurality of fuel gas nozzles 23.
[0045] This embodiment illustrates a case where a plurality of primary combustion air nozzles 22 are arranged in a point-symmetrical pattern about the center of the gas injection surface (center P of the ellipse), with two nozzles on the left and right and two on the top and bottom, for a total of four. Furthermore, fuel gas nozzles 23 are disposed circumferentially between adjacent primary combustion air nozzles 22.
[0046] It should be noted that reference numeral 24 denotes a back plate, and the shape of the back plate 24 is an elliptical shape similar to the elliptical shape of the tube 1 .
[0047] (Regarding primary combustion air)
[0048] The flow rate of the total amount of air mx of the primary combustion air injected from all the primary combustion air nozzles 22 is set so that primary combustion is performed at an air ratio of 1.0 or less.
[0049] In addition, if Figure 5As shown, in this embodiment, the opening cross-section of the straight tube portion at the most upstream position is virtually divided into four areas ARA-1 to ARA-4 using as boundaries two straight lines X1 and X2, which are obtained by tilting the short axis X, which is the axis of the short diameter of the ellipse, at ±45 degrees in the circumferential direction about the center P of the ellipse, as the center.
[0050] Furthermore, the flow rate mt of the primary combustion air ejected from the primary combustion air nozzles 22A and 22B located in regions ARA-1 and ARA-2 that include the minor axis X of the ellipse is set to be less than the flow rate of the primary combustion air ejected from the primary combustion air nozzles 22C and 22D located in regions ARA-3 and ARA-4 that do not include the minor axis X of the ellipse (hereinafter also referred to as the region that includes the major axis Y). Specifically, the flow rate ratio (mt / mx), which is the ratio of the flow rate mt of the primary combustion air ejected from the primary combustion air nozzles 22A and 22B located in regions ARA-1 and ARA-2 that include the minor axis X of the ellipse to the total amount mx of primary combustion air ejected from all primary combustion air nozzles 22, is set to be less than 0.5. The flow rate ratio (mt / mx) is preferably set to be 0.45 or less.
[0051] In this embodiment, the flow rate ratio (mt / mx) is La 2 / (La 2 +Lb 2 It is preferable to set the flow rate ratio (mt / mx) to be La / (La+Lb) or more.
[0052] That is, in this embodiment, the flow rate distribution of the primary combustion air is designed so as to satisfy the following formula (1).
[0053] La 2 / (La 2 +Lb 2 )≤(mt / mx)<0.5···(1)
[0054] Here, in this embodiment, the flow rate mt of the primary combustion air from the primary combustion air nozzles 22A and 22B on the side of the short axis X is set to be smaller than the flow rate of the primary combustion air from the primary combustion air nozzles 22C and 22D on the side of the long axis Y, and the total opening cross-sectional area of the primary combustion air nozzles 22 located in the area ARA-1 and ARA-2 including the short axis X of the ellipse is set to be smaller than the total opening cross-sectional area of the secondary combustion air nozzles located in the area ARA-3 and ARA-4 including the long axis Y of the ellipse, so as to be adjusted so that the ratio of these two total opening areas becomes a flow rate ratio that satisfies formula (1).
[0055] Alternatively, the flow rate mt of the primary combustion air from the primary combustion air nozzles 22A and 22B on the minor axis X side is set to be smaller than the flow rate of the primary combustion air from the primary combustion air nozzles 22C and 22D on the major axis Y side. Alternatively, separate combustion air supply paths are provided on the minor axis X side and the major axis Y side to supply combustion air separately, or flow rate control valves are provided midway through the flow paths to adjust the mixing ratio. However, the aforementioned method of adjusting the ratio of the opening areas of the two nozzles is a simpler configuration.
[0056] Furthermore, it is preferable that the flow rates of primary combustion air from the areas ARA-1 to ARA-4 (upper and lower areas, and left and right areas) that are point-symmetrical with respect to the center P of the ellipse be the same. Specifically, the flow rate of primary combustion air supplied from the upper area ARA-4 is set to be the same as the flow rate of primary combustion air supplied from the lower area ARA-3. Furthermore, the flow rate of primary combustion air supplied from the left area ARA-1 is set to be the same as the flow rate of primary combustion air supplied from the right area ARA-2.
[0057] (About nozzle configuration)
[0058] Here, Figure 5 In the example above, one primary combustion air nozzle 22 is arranged in each of the four areas ARA-1 to ARA-4, but the present invention is not limited thereto. For example, two or more primary combustion air nozzles 22 may be arranged in each of the areas ARA-1 to ARA-4.
[0059] in addition, Figure 5 In the example, the primary combustion air nozzles 22 are arranged on the major axis Y or the minor axis X of the ellipse, but the present invention is not limited thereto. For example, the primary combustion air nozzles 22 may not be arranged so as to overlap on the major axis Y or the minor axis X.
[0060] in addition, Figure 5 In the figure, the opening shape of each hole constituting the primary combustion air nozzle 22 is exemplified by a fan-shaped shape in which the circumferential distance increases as the distance from the center P of the ellipse in the outer radial direction increases, but the present invention is not limited to this. For example, the opening shape of the hole constituting the primary combustion air nozzle 22 is not particularly limited and may be a shape other than a fan-shaped shape.
[0061] In addition, the distance from the center P of the ellipse to each primary combustion air nozzle 22 can be set to different distances from the center P of the ellipse to the primary combustion air nozzles 22A, 22B on the short axis X side and from the center P of the ellipse to the primary combustion air nozzles 22C, 22D on the long axis Y side.
[0062] (Other operations)
[0063] In the radiant tube 100 of this embodiment, combustion air and fuel gas are injected (discharged) and supplied from the radiant tube burner 2 through each nozzle in a direction parallel to the axis of the straight tube portion 1A constituting the most upstream position of the tube 1 .
[0064] This embodiment employs a two-stage combustion system: fuel gas injected from the fuel gas nozzle 23 is mixed with primary combustion air injected from the primary combustion air nozzle 22, partially combusting the mixture. The secondary combustion air discharged from the secondary combustion air nozzle 21 then completely combusts the partially combusted combustion gas, thereby reducing NOx. The generated combustion gas flows along the pipe 1.
[0065] In addition, in the present embodiment, with respect to the total amount of primary combustion air supplied, the generation of NOx caused by combustion can be further suppressed by making the flow rate mt of the primary combustion air from the primary combustion air nozzles 22A and 22B on the side of the axis of the short diameter, i.e., the short axis X, relatively less than the flow rate of the primary combustion air from the primary combustion air nozzles 22C and 22D on the side of the axis of the long diameter orthogonal to the short diameter, i.e., the long axis Y.
[0066] Here, the opening cross-sectional shape of the pipe 1 was set to an ellipse (minor diameter La: 188 mm, major diameter Lb: 236 mm), and the relationship between the flow rate ratio (mt / mx) and NOx was analyzed by NOx generation prediction simulation using the finite volume method. The results are shown in Figure 6 .
[0067] Figure 6 The NOx ratio (NOx generation amount) is shown when the flow rate ratio (mx / mt) is represented on the horizontal axis and the NOx generation amount when mx / mt=0.5 on the vertical axis is normalized to 1.
[0068] Depend on Figure 6 It can be seen that NOx decreases as the flow rate mt of the primary combustion air from the primary combustion air nozzles 22A and 22B on the minor axis X side decreases relative to the flow rate of the primary combustion air from the primary combustion air nozzles 22C and 22D on the major axis Y side.
[0069] The reason for this is presumably that the discharge amounts of primary combustion air from adjacent areas ARA-1 to ARA-4 are different, so that the ratio of air blown into each area ARA-1 to ARA-4 is adjusted to form an appropriate N2 concentration distribution, thereby suppressing the generation of NOx.
[0070] On the other hand, when the radiant tube 100 is elliptical, it is preferable to orient the surface on the shorter diameter La side, which has a relatively large area, toward the heated object, taking into account the radiation area with respect to the object. As in this embodiment, the amount of air injected toward the shorter diameter La side is reduced because the surface temperature of the radiant tube 100 on the shorter diameter La side decreases due to the increase in non-combustible matter in regions ARA-1 and ARA-2 on the shorter diameter La side, potentially reducing heat transfer efficiency.
[0071] Therefore, the relationship between the flow rate ratio and the average combustion gas temperature on the short axis X is obtained, and the result is Figure 7 The results shown.
[0072] Figure 7 The result is the average temperature on the minor axis X of the ellipse of the cross section perpendicular to the flow direction at a point 2000 mm away from the primary combustion air nozzle 22 and the fuel gas nozzle 23 in the injection direction from the ejection surface.
[0073] Depend on Figure 7 It can be seen that the smaller the flow rate ratio (mx / mt) is than 0.5, the lower the average gas temperature on the minor axis X side is.
[0074] According to the above results, in order to achieve the low NOx effect and prevent the decrease in heat transfer efficiency, it is preferable to set the flow ratio (mx / mt) to La 2 / (La 2 +Lb 2 ) or above, and it is further preferred that the flow ratio (mx / mt) is La / (La+Lb) or above.
[0075] As described above, the present embodiment provides a radiant tube burner 2 and a radiant tube 100 capable of reducing NOx generation with a simple configuration without adversely affecting maintenance performance or reducing the low NOx effect due to poisoning or the like.
[0076] This application claims priority and incorporates the entire contents of Japanese Patent Application No. 2020-020549 (filed on February 10, 2020) into this disclosure by reference. While the present invention is described with reference to a limited number of embodiments, the scope of the invention is not limited thereto, and modifications based on the embodiments disclosed above will be apparent to those skilled in the art.
[0077] Reference numerals
[0078] 1 tube
[0079] 1A Straight pipe section at the most upstream position
[0080] 2 Radiant tube burners
[0081] 2A Gas injection unit
[0082] 3 Furnace wall
[0083] 21 Air nozzle for secondary combustion
[0084] 22 Primary combustion air nozzle
[0085] 22A, 22B Primary combustion air nozzle on the short shaft side
[0086] 22C, 22D Primary combustion air nozzle on the long axis side
[0087] 23 Fuel gas nozzle
[0088] ARA-1~ARA-4 region
[0089] La Short Path
[0090] Lb long diameter
[0091] X minor axis
[0092] Y-long axis
Claims
1. Radiant tube burner, characterized in that, The radiant tube burner is inserted into a tube having an elliptical opening cross section, and a secondary combustion air nozzle for injecting secondary combustion air is arranged at the center of the gas injection portion of the radiant tube burner, and a plurality of primary combustion air nozzles for injecting primary combustion air and a plurality of fuel gas nozzles for injecting fuel gas are arranged so as to surround the secondary combustion air nozzle. The opening cross section of the tube is virtually divided into four regions using two straight lines obtained by tilting the short axis of an ellipse, which is the shape of the opening cross section of the tube, at ±45 degrees with the center of the ellipse as the center. The flow rate of the primary combustion air injected from the primary combustion air nozzle in the area including the short axis of the ellipse among the four areas divided hypothetically is less than the flow rate of the primary combustion air injected from the primary combustion air nozzle in the area not including the short axis of the ellipse among the four areas divided hypothetically.
2. The radiant tube burner according to claim 1, wherein: When the short axis of the ellipse is La and the long axis perpendicular to the short axis is Lb, The ratio of the flow rate mt of the primary combustion air injected from the primary combustion air nozzle located in the region including the minor axis to the total amount mx of the primary combustion air injected from all the primary combustion air nozzles, that is, the flow rate ratio (mt / mx) is La 2 / (La 2 +Lb 2 )above.
3. The radiant tube burner according to claim 1 or 2, characterized in that: The flow rate of the primary combustion air ejected from the primary combustion air nozzle is regulated by making the total opening cross-sectional area of the primary combustion air nozzle located in the area including the above-mentioned short axis smaller than the total opening cross-sectional area of the primary combustion air nozzle located in the area not including the short axis of the above-mentioned ellipse.
4. Radiant tubes, where The tube has an elliptical opening cross section and comprises the radiant tube burner according to any one of claims 1 to 3.
5. A design method for a radiant tube burner, characterized in that: The radiant tube burner is inserted into a tube having an elliptical opening cross section. A secondary combustion air nozzle for injecting secondary combustion air is arranged at the center of the gas injection portion of the radiant tube burner. A plurality of primary combustion air nozzles for injecting primary combustion air and a plurality of fuel gas nozzles for injecting fuel gas are arranged to surround the secondary combustion air nozzle. The opening cross section of the tube is virtually divided into four regions using two straight lines obtained by tilting the short axis of an ellipse, which is the shape of the opening cross section of the tube, at ±45 degrees with the center of the ellipse as the center. When the short axis of the ellipse is La and the long axis perpendicular to the short axis is Lb, The amount of primary combustion air blown from each primary combustion air nozzle is set so that the ratio of the flow rate mt of the primary combustion air injected from the primary combustion air nozzle located in the area including the minor axis to the total amount of primary combustion air injected from all primary combustion air nozzles, that is, the flow rate ratio (mt / mx), satisfies the following formula (1). <h2 style=";text-align:left;direction:ltr">No<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / (La<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +Lb<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> )≤(mt / mx)<0.5···(1)。
Citation Information
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