JP5302852B2 - Reheat boiler - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a reheating boiler, capable of reducing stress generated at a connection part between a header and a heat transfer tube by thermal elongation of a support member. <P>SOLUTION: The reheating boiler includes a main boiler in which main combustion gas generated by burning of a burner flows from a furnace through a superheater and an evaporation pipe group; a reheating furnace disposed on the downstream side of the evaporation pipe group to generate reheating combustion gas by burning of a reheating burner; and a reheater 30 disposed on the upper side of the reheating furnace. As the heat transfer tube 31 of the reheater 30, a folded pipe which is folded in a plurality of lines while reciprocating in a width direction with upper and lower ends being connected to the header 32 is used, and the dead weight load of the heat transfer tube 31 is supported by a plurality of comb-tooth plates 40A in the width direction in which the comb-tooth plates are extended vertically with upper ends being fixed. With respect to a part in which the connection part stress between the header 32 and the heat transfer tube 31 exceeds an allowable value by thermal elongation of the comb-tooth plate 40A of the heat transfer tube support part of the comb-tooth plate 40A, the support structure of the heat transfer tube 31 is a free structure which is free from support or restriction by the comb-tooth plate. <P>COPYRIGHT: (C)2011,JPO&amp;INPIT

Description

    The present invention relates to a reheat boiler provided with a reheat furnace and a reheater on the downstream side of an evaporation tube group.

In a conventional marine boiler, a reheat boiler having a reheat furnace and a reheater on the downstream side of the combustion gas is known.
In such a marine reheat boiler, for example, figure shows how easy it is to repair and maintain, and how to prevent damage to the heat transfer tube when the reheater is not used, that is, when there is no steam flow into the heat transfer tube. As shown in FIG. 4, the reheater is installed in the boiler outlet duct portion where the combustion gas temperature is relatively low.

FIG. 4 is a schematic diagram schematically showing a configuration example of a marine reheat boiler.
A reheat boiler 10 shown in FIG. 4 includes a main boiler 16 including a burner 11, a furnace 12, a front bank tube 13, a superheater (SH) 14 and an evaporation tube group (rear bank tube) 15, and an evaporation tube group 15. A reheating furnace 21 provided on the downstream side and provided with a reheating burner 20 and a reheater 30 provided on the exhaust gas outlet side are provided.

The combustion gas generated by the combustion of the burner 11 flows from the furnace 12 through the front bank tube 13, the superheater 14 and the evaporation tube group 15, and after mixing in the reheating furnace 21 with the reheating combustion gas of the reheating burner 20, It flowed while exchanging heat with the reheater 30 and flowed out of the gas outlet 22 so as to operate efficiently.
In FIG. 4, reference numerals 13H and 14H in the figure indicate headers, 17 indicates a water drum, 18 indicates a steam drum, and 19 indicates a wall tube.

  Since the reheater 30 described above is installed in the outlet duct portion of the main boiler 16, for example, as shown in FIG. 5, a large number of reheaters 30 arranged in the depth direction of the reheater 30 (see the Z direction in FIG. 3). A heat transfer tube 31 is folded in a plurality of rows in the vertical direction (Y-axis direction), and a tube group structure in which both end portions of each heat transfer tube 31 are connected to a header 32 is employed. In the illustrated tube group structure, the flow direction (Y-axis direction) of the reheat combustion gas indicated by an arrow G in the drawing is divided into three stages of tube groups. Comb plates 40 are provided in several places in the width direction (X-axis direction) of the reheater 10, which is the direction in which the combustion gas flows, in 21 for supporting the heat transfer tube with respect to its own load.

For example, as shown in detail in FIG. 6, the comb-tooth plate 40 employs a structure that supports the self-load of the heat transfer tube 31 and suppresses fluid vibration and the like of the heat transfer tube 31.
The illustrated comb-tooth plate 40 is an elongate plate-like member that is fixedly supported at the upper end side and extends downward, as shown in FIG. 6B, for example, as viewed in the direction of arrow C in FIG. 6A. Yes, in order to lock the intersecting heat transfer tubes 31, substantially semicircular recesses 41 are provided at the left and right ends of the plate-like member.
In FIG. 6A, the ends of the heat transfer tube 31 are supported by the joint portions (connection portions) Pa and Pb with the header 32.

  As a prior art of a heat transfer tube support structure related to a heat recovery device, a heat transfer tube crossing a heat medium flow path between opposed tube plates a plurality of times is constituted by an appropriate number of S-shaped heat transfer tube units (multiple rows of folded tubes). And the structure which supports the inversion part of this heat exchanger tube by the long hole provided in the tube sheet is known. (For example, see Patent Document 1)

Japanese Utility Model Publication No. 60-86773

By the way, the reheater 30 of the reheat boiler mentioned above has many tube rows of the heat exchanger tubes 31 compared with the economizer etc. of a super supercritical pressure (USC) boiler, and also the combustion gas temperature which passes the heat exchanger tube outside Is getting higher due to reheating. For this reason, the comb-tooth plate 40 that supports the upper end side and makes the lower end side free is thermally extended downward, so that the heat transfer tube 31 supported on the lower end portion side of the comb-tooth plate 40 has a larger heat. Under the influence of elongation, it is pushed downward, and as a result, excessive stress is generated at the joint between the heat transfer tube 31 and the header 32.
FIG. 7 shows a modification of the heat transfer tube 31 due to the thermal elongation of the comb tooth plate 40. The heat transfer tube 31 shown by a solid line is in a state before the deformation, and the heat transfer tube 31 'shown by a one-point difference line is the heat of the comb tooth plate. The deformation state due to elongation is shown.

In FIG. 8, the position of the concave portion 41 that supports the heat transfer tube 31 at the lowermost end portion of the comb tooth plate 40 closest to the header 32 is Pc, and the distance Pb / Pc from the coupling portion Pb to the position Pc is plotted on the horizontal axis. Thus, the stress generated in the joint portion Pb is shown on the vertical axis. In FIG. 8, the range of stresses that can be generated is indicated by hatching, and the allowable stress of the coupling portion Pb is indicated by a broken line.
In the support structure (conventional structure) of the heat transfer tube 31 using the comb tooth plate 40 described above, the comb tooth plate 40 is thermally extended to the lower end side in a free state without restraint, so the stress of the joint portion Pb is the joint force. The larger the portion Pa is, and the closer the distance between Pb / Pc is, the greater the stress acts on the joint portion Pb. Therefore, there is a concern that the comb tooth plate 40 having the conventional structure is excessively large in that the stress of the coupling portion Pb exceeds the allowable stress.

From such a background, in a reheat boiler equipped with a reheater with a plurality of folded tube group structures, such as a comb tooth plate that supports the heat transfer tube according to the distance to the header and the distribution of the combustion gas temperature that passes through There is a demand for a heat transfer tube support structure that can suppress or adjust the influence of thermal elongation generated in the support member and can reduce the stress generated at the joint between the header and the heat transfer tube.
The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a reheat boiler that can reduce the stress generated in the joint portion between the header and the heat transfer tube due to the thermal elongation of the support member. There is to do.

In order to solve the above problems, the present invention employs the following means.
A reheat boiler according to claim 1 of the present invention includes a main boiler configured such that main combustion gas generated by combustion of a burner flows from a furnace through a superheater and an evaporation tube group, and after the evaporation tube group A reheat furnace arranged on the flow side and generating reheat combustion gas by combustion of the reheat burner, and a reheater arranged on the upper side of the reheat furnace, and a heat transfer tube of the reheater A plurality of rows of folded tubes connected to the headers at the upper and lower ends and reciprocating in the width direction are used, and the self-weight load of the heat transfer tubes is fixed to the upper end by a plurality of comb teeth plates extending in the vertical direction. In the supported reheat boiler, the portion of the heat transfer tube support portion of the comb tooth plate where the joint stress between the header and the heat transfer tube exceeds the allowable value due to the thermal elongation of the comb tooth plate, The support structure of the heat transfer tube is a free structure without support restriction by the comb tooth plate. It is characterized in.

According to the reheat boiler of claim 1, in the heat transfer tube support portion of the comb tooth plate, the heat transfer tube is provided for a portion where the joint stress between the header and the heat transfer tube exceeds the allowable value due to the thermal elongation of the comb tooth plate. Since it is an unsupported free structure, the heat transfer tube of the free structure portion is not affected by the thermal expansion of the comb tooth plate, and therefore the stress generated at the joint between the header and the heat transfer tube can be reduced. it can. That is, by suppressing the influence of the thermal elongation that occurs in the comb tooth plate that supports the heat transfer tube according to the distance to the header, the stress generated at the joint between the header and the heat transfer tube can be reduced.
Even if such a free structure portion is employed only in the portion that supports the heat transfer tube at the lowest stage of the comb tooth plate where the amount of thermal elongation is the largest, it is possible to greatly reduce the stress.

  According to a second aspect of the present invention, there is provided a reheat boiler comprising: a main boiler configured such that a main combustion gas generated by combustion of a burner flows from a furnace through a superheater and an evaporation tube group; A reheat furnace arranged on the flow side and generating reheat combustion gas by combustion of the reheat burner, and a reheater arranged on the upper side of the reheat furnace, and a heat transfer tube of the reheater A plurality of rows of folded tubes connected to the headers at the upper and lower ends and reciprocating in the width direction are used, and the self-weight load of the heat transfer tubes is fixed to the upper end by a plurality of comb teeth plates extending in the vertical direction. In the reheat boiler that is supported, the comb tooth plate uses a material having a smaller linear expansion coefficient as the distance from the header becomes shorter.

  According to the reheat boiler of claim 2, since the comb tooth plate uses a material having a smaller linear expansion coefficient as the distance from the header is shorter, the heat received by the heat transfer tube in a region where the influence of the thermal expansion is large. The influence of expansion can be reduced, and therefore the stress generated at the joint between the header and the heat transfer tube can be suppressed. That is, by adjusting the influence of the thermal elongation generated in the comb tooth plate that supports the heat transfer tube according to the distance from the header, the stress generated at the joint between the header and the heat transfer tube can be reduced.

  The reheat boiler according to claim 1 or 2, wherein the heat transfer tube support portion has a free structure as the comb tooth plate existing in a high temperature region of the combustion gas temperature distribution in the reheater inlet cross section, or a material It is preferable to use one having a smaller coefficient of linear expansion, so that it is possible to suppress or adjust the influence of thermal expansion even in a region where the thermal expansion of the comb tooth plate increases due to high combustion gas temperature. Therefore, the stress generated at the joint between the header and the heat transfer tube can be reduced.

  According to the above-described present invention, in the reheat boiler provided with the reheater having a plurality of folded tube group structures, the comb tooth plate that supports the heat transfer tube according to the distance to the header and the distribution of the temperature of the passing combustion gas. The amount of thermal elongation generated in the support member can be suppressed or adjusted, and the stress generated at the joint between the header and the heat transfer tube can be reduced. As a result, the reheater of the reheat boiler has a remarkable effect that durability and reliability are improved.

It is a figure which shows 1st Embodiment which concerns on a heat exchanger tube support structure about the reheat boiler of this invention, (a) is the schematic diagram which looked at the heat exchanger tube support structure from the front of the width direction, (b) is (a). FIG. It is explanatory drawing which shows 2nd Embodiment which concerns on the heat exchanger tube support structure about the reheat boiler of this invention. It is a figure which shows the example of combustion gas temperature distribution in the reheater inlet cross section (BB cross section of FIG. 4). It is a longitudinal cross-sectional view which shows the structural example of a reheat boiler. It is a longitudinal cross-sectional view which shows the schematic structural example which concerns on the heat exchanger tube support structure of a reheater. It is a figure which shows the conventional heat exchanger tube support structure, (a) is the schematic diagram which looked at the heat exchanger tube support structure from the front of the width direction, (b) is C arrow directional view of (a). It is a figure which shows the modification of the heat exchanger tube by the thermal elongation of a comb-tooth board. It is explanatory drawing which shows the relationship between the distance (distance between Pb / Pc) from the coupling part Pb of a header to the position Pc which is supporting the heat exchanger tube with a comb-tooth board, and the stress which acts on the coupling part Pb.

Hereinafter, one embodiment of a reheat boiler concerning the present invention is described based on a drawing.
For example, as shown in FIG. 4, the reheat boiler 10 of the present embodiment is configured such that the main combustion gas generated by the combustion of the burner 11 flows from the furnace 12 through the superheater 14 and the evaporation tube group 15. A reheat furnace 21 disposed on the downstream side of the main boiler 16 and the evaporator tube group 15 and generating reheat combustion gas by combustion of the reheat burner 20, and a reheat disposed on the upper side of the reheat furnace 21 Device 30.

  In the reheat boiler 10 configured as described above, the main combustion gas generated by the combustion of the burner 11 passes from the furnace 12 through the front bank tube 13, the superheater 14, and the evaporation tube group 15 in the main boiler 16. It flows to the reheating furnace 21 downstream. Thereafter, the main combustion gas flowing into the reheating furnace 21 from the main boiler 16 flows out to the reheater 30 together with the reheat combustion gas generated by the reheating burner 20. The main combustion gas and the reheat combustion gas that pass through the reheater 30 are used as a heat source for heat exchange when passing through the reheater 30, and then the gas outlet 22 that opens to the top of the reheat boiler 10. It flows out to the outside.

<First Embodiment>
Below, 1st Embodiment is described based on FIG. 1 about the heat exchanger tube support structure which supports many heat exchanger tubes 31 arrange | positioned inside the reheater 30 mentioned above.
A large number of heat transfer tubes 31 are arranged inside the reheater 30. The heat transfer tubes 31 are connected to the headers 32 at both upper and lower ends, and in the vertical direction (Y in the illustrated configuration example) while reciprocating multiple times in the width direction (X direction) of the reheater 30 (four times in the illustrated configuration example). A folded tube extending in the axial direction is used. The heat transfer tube 31 formed as such a folded tube has a tube group structure in which a large number (a plurality) are connected to the header 32 and arranged substantially in parallel to the depth direction of the reheater 30 (see the Z direction in FIG. 3). Is adopted. The combustion gas flow direction in the reheater 30 is the vertical direction (Y-axis direction) in FIG. 1, and the above-described tube group structure is divided into a plurality of tube groups in the vertical direction as necessary. .

The heat transfer tubes 31 having such a tube group structure are arranged at several positions in the width direction (X-axis direction) of the reheater 30 at each stage of the tube group, and the vertical comb tooth plates 40A are used for supporting the heat transfer tubes 31. Is provided. The comb-tooth plate 40A is a member in which a recess (heat transfer tube support portion) 41 for supporting the heat transfer tube 31 is formed on a rectangular plate material made of an elongated metal (for example, stainless steel). The illustrated comb tooth plate 40 </ b> A has substantially semicircular recesses 41 formed on both sides in the longitudinal direction, and the pitch in the vertical direction forming the recesses 41 coincides with the folding pitch of the heat transfer tubes 31.
The above-described comb tooth plate 40A is fixed at an appropriate position in the reheater 30 and supports the self-load of the heat transfer tube 31 extending from the header 32 in the horizontal direction.
In FIG. 1A, symbol Pa in the drawing is a joint (connection portion) between the upper header 32 and the upper end of the heat transfer tube 31, and symbol Pb is the lower header 32 and the lower end of the heat transfer tube 31. The symbol Pc ′ is a position that intersects the heat transfer tube 31 in a free state at the lowest end of the comb tooth plate 40A closest to the header 32.

In such a comb-tooth plate 40A, in this embodiment, the stress at the joint portion between the header 32 and the heat-transfer tube 31 in the recess 41 serving as the heat-transfer tube support portion exceeds the allowable value due to the thermal elongation of the comb-tooth plate 40A. About the part, the free structure which makes the heat exchanger tube 31 unsupported is employ | adopted.
That is, in this embodiment, since the comb-tooth plate 40A is thermally extended downward, the recess 41 that supports the heat transfer tube 31 is not provided on the lower end side of the comb-tooth plate 40A, and the heat transfer tube 31 is not supported. It has become. Further, as apparent from the deformation of the heat transfer tube 31 shown in FIG. 7 and the stress of the coupling portion Pb shown in FIG. 8, the stress acting on the coupling portion Pb is close to the header 32 (the distance between Pb / Pc is small). The comb tooth plate 40A becomes larger. As a result, the portion where the joint stress between the header 32 and the heat transfer tube 31 is most likely to exceed the allowable value due to the thermal elongation of the comb tooth plate 40 </ b> A is in the lower end side region of the comb tooth plate 40 </ b> A closest to the header 32. It becomes a heat pipe support part.

The illustrated comb-tooth plate 40A has no recess 41 for supporting the lowermost heat transfer tube 31 by cutting out the member in the region where the recess 41 for supporting the lowermost heat transfer tube 31 is formed. The free state is not affected by the thermal elongation of the comb tooth plate 40A. Here, the region where the comb-tooth plate 40A is not cut and the concave portion 41 is not formed is not particularly limited in the number of steps from the lowest step, but a large effect can be obtained only by making only the lowest step free.
Further, the support of the heat transfer tube 31 by the comb tooth plate 40A described above has the purpose of preventing fluid vibration and drift in addition to supporting its own weight load. It is desirable to keep it to a minimum.

  In the support structure of the heat transfer tube 31 using the above-described comb tooth plate 40A, that is, in the heat transfer tube support structure in which the heat transfer tube 31 is free on the lower end portion side of the comb tooth plate 40A, the comb tooth plate having the greatest influence of thermal elongation. Since the deformation of the heat transfer tube 31 is eliminated or minimized at the lower end portion side of 40A, the stress acting on the coupling portion Pb can be reduced below the allowable stress (see FIG. 8). In such a heat transfer tube support structure using the comb tooth plate 40A, the heat transfer tube support portion located on the lower end side of the comb tooth plate 40A closest to the header 32 is affected by the thermal elongation, and the stress of the coupling portion Pb is increased. Since it is easy to exceed the allowable value, the heat transfer tube 31 only needs to have an unsupported free structure only for the heat transfer tube support portion in this region.

In other words, depending on the distance between the header 32 and the heat transfer tube support portion, the heat transfer tube support portion closer to the distance suppresses the influence of the thermal elongation generated in the comb tooth plate 40A that supports the heat transfer tube 31 and becomes smaller. By doing, the stress which generate | occur | produces in the joint part Pb of the header 32 and the heat exchanger tube 31 can be reduced.
In addition, such a heat transfer tube support structure may be simply changed in structure by cutting out a necessary portion from the comb tooth plate 40 described in the conventional structure, and accordingly, the dimensions and specifications of the reheater 30 are changed. Without this, the stress of the joint portion Pb can be reduced below the allowable value.

<Second Embodiment>
Then, 2nd Embodiment is described based on FIG. 2 about the heat exchanger tube support structure which supports many heat exchanger tubes 31 arrange | positioned inside the reheater 30 mentioned above. In addition, the same code | symbol is attached | subjected to the part similar to embodiment mentioned above, and the detailed description is abbreviate | omitted.
In this embodiment, a comb tooth plate 40B manufactured using a material having a smaller linear expansion coefficient is used as the distance from the header 32 (distance between Pb / Pc) is shorter. That is, in the present embodiment, the material of the comb tooth plate 40B is changed to a material having a small linear expansion coefficient according to the distance from the header 32, and the generated stress due to the thermal elongation of the comb tooth plate 40B is reduced.

As a specific example, the comb tooth plate 40B closest to the header 32 is made of a material having a small linear expansion coefficient, such as Inconel. For this reason, the heat transfer tube support portion in the region where the deformation due to the influence of the thermal expansion maximizes the stress of the coupling portion Pb is the heat of the comb tooth plate 40B at the position Pc of the lowermost end portion that is most affected by the thermal elongation. Elongation decreases. That is, the position Pc after the thermal elongation rises to the position Pc ′ by changing the material of the comb tooth plate 40B to a material having a small linear expansion coefficient, and thus the amount of decrease in thermal elongation is δ.
Therefore, since the stress generated in the joint portion Pb between the header 32 and the heat transfer tube 31 is proportional to the thermal expansion amount of the comb tooth plate, the deformation of the heat transfer tube 31 is reduced by the thermal expansion reduction amount δ. It is suppressed. In other words, the material of the comb tooth plate 40B that supports the heat transfer tube 31 is changed according to the distance to the header 32, and the influence of the thermal elongation generated in the comb tooth plate 40B is adjusted. The stress which generate | occur | produces in the joint part Pb of can be reduced.

By the way, the comb tooth plates 40A and 40B described in the first and second embodiments described above have a high combustion gas temperature distribution in the reheater inlet cross section of the reheat boiler 30 (BB cross section in FIG. 4). It is also possible to apply to the following areas.
FIG. 3 is a diagram showing an example of the combustion gas temperature distribution at the reheater inlet cross section. In this combustion gas temperature distribution example, the combustion gas flow flowing in from the main boiler 16 on the right side of the paper and the reheat combustion gas flow generated by the reheating burner 20 installed on the lower side of the paper merge to form a reheater. 30. For this reason, an area where the gas temperature becomes high is formed in the area close to the header 32 on the downstream side (upper left in the drawing) in the reheat combustion gas flow direction from the reheat burner 20.

Since such a high temperature region is close to the hedder 32, the thermal expansion of the comb tooth plate 40 increases, and accordingly, a large stress acts on the joint portion Pb between the heat transfer tube 31 and the hedder 32.
Therefore, it is preferable to change the comb tooth plate 40 in the high temperature region described above to the comb tooth plates 40A and 40B described in the first and second embodiments. That is, the comb-tooth plate 40 in the high temperature region can be changed to either the comb-tooth plate 40A having a heat transfer tube support portion having a free structure or the comb-tooth plate 40B having a reduced linear expansion coefficient of the material. desirable.

  In this way, the influence of the thermal expansion of the comb teeth plates 40A and 40B can be suppressed or adjusted even in a high temperature region where the combustion gas temperature becomes high and the stress of the coupling portion Pb increases due to the influence of thermal expansion. Therefore, the stress generated in the joint portion Pb between the header 32 and the heat transfer tube 31 can be reduced.

As described above, according to the reheat boiler 10 of the present embodiment described above, in the reheater 30 having a plurality of rows of folded tube group structures, the heat transfer tubes 31 according to the distance from the header 32 and the passing combustion gas temperature distribution. Since the comb-tooth plates 40A and 40B that can suppress or adjust the amount of thermal elongation generated in the supporting member are employed, the stress generated in the joint portion Pb between the header 32 and the heat transfer tube 31 can be reduced. As a result, the durability and reliability of the reheater 30 of the reheat boiler 10 are improved.
In addition, this invention is not limited to embodiment mentioned above, In the range which does not deviate from the summary, it can change suitably.

10 Reheat boiler 11 Burner 12 Furnace 13 Front bank tube 14 Superheater (SH)
15 Evaporation tube group (rear bank tube)
16 main boiler 20 reheat burner 21 reheat furnace 22 gas outlet 30 reheater 31 heat transfer tube 40A, 40B comb tooth plate 41 recess

Claims (3)

The main combustion gas generated by the burner combustion is arranged on the downstream side of the main boiler configured to flow from the furnace through the superheater and the evaporator tube group, and is regenerated by the combustion of the reheat burner. A reheat furnace for generating thermal combustion gas, and a reheater disposed on the upper side of the reheat furnace,
The reheater uses a plurality of rows of folded tubes connected to the headers at both upper and lower ends to the heat transfer tubes and reciprocates in the width direction, and the self-load load of the heat transfer tubes has a width that extends in the vertical direction with the upper end fixed. In the reheat boiler supported by a plurality of comb teeth plates in the direction,
Of the heat transfer tube support portion of the comb tooth plate, the heat transfer tube support structure is a comb tooth plate for a portion where the joint stress between the header and the heat transfer tube exceeds an allowable value due to thermal expansion of the comb tooth plate. A reheat boiler characterized by having a free structure without support restraint. The main combustion gas generated by the burner combustion is arranged on the downstream side of the main boiler configured to flow from the furnace through the superheater and the evaporator tube group, and is regenerated by the combustion of the reheat burner. A reheat furnace for generating thermal combustion gas, and a reheater disposed on the upper side of the reheat furnace,
The reheater uses a plurality of rows of folded tubes connected to the headers at both upper and lower ends to the heat transfer tubes and reciprocates in the width direction, and the self-load load of the heat transfer tubes has a width that extends in the vertical direction with the upper end fixed. In the reheat boiler supported by a plurality of comb teeth plates in the direction,
The reheat boiler, wherein the comb tooth plate uses a material having a smaller linear expansion coefficient as the distance from the header is shorter. As the comb tooth plate present in the high temperature region of the combustion gas temperature distribution in the reheater inlet cross section, the support structure of the heat transfer tube is a free structure without support restriction by the comb tooth plate, or the linear expansion coefficient of the material The reheat boiler according to claim 1 or 2, wherein any one of those having a smaller size is used.

Images