Turbulence plate and stacked disk heat exchanger

Abstract

A turbulence-inducing sheet for a stacked disk heat exchanger may include a plurality of a plurality of parallel rows each including a plurality of wave crests and a plurality of wave troughs alternately adjoining one another in a longitudinal direction of the plurality of rows. Three directly adjacent rows of the plurality of rows may be arranged offset from one another in the longitudinal direction such that the plurality of wave crests and the plurality of wave troughs of the three adjacent rows are arranged on a respectively associated straight line extending obliquely to the longitudinal direction.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to German Patent Application No. DE 10 2023 211 570.0, filed on Nov. 21, 2023, the contents of which is hereby incorporated by reference in its entirety.TECHNICAL FIELD

[0002] The present invention relates to a turbulence-inducing plate for a stacked disk heat exchanger. The invention also relates to a stacked disk heat exchanger with at least one such turbulence-inducing sheet.BACKGROUND

[0003] Turbulence-inducing sheets are already well known and serve to enlarge a heat transfer surface between two stacked disks of a stacked disk heat exchanger and to swirl a cooling fluid or a fluid to be cooled. On the one hand, such turbulence-inducing sheets increase the surface area available for heat transfer and improve mixing, especially of a coolant. On the other hand, however, they also increase pressure loss, which means, for example, that pumps have to be designed to be stronger and therefore often also more expensive, which in turn requires more electrical energy, which should be kept as low as possible, especially in electric vehicles.

[0004] With turbulence-inducing sheets designed in accordance with the type, there is thus always a conflict of objectives between the heat-transferring surface and mixing of a coolant on the one hand and the pressure loss on the other.SUMMARY

[0005] The present invention is therefore concerned with the problem of providing an improved or at least an alternative embodiment of a turbulence-inducing sheet of the type according to the prior art, which in particular helps to better manage the conflict of objectives between cooling capacity and pressure loss.

[0006] According to the invention, this problem is solved by the subject matter of the independent claim(s). Advantageous embodiments are the subject matter of the dependent claim(s).

[0007] The present invention is based on the general idea of forming a turbulence-inducing sheet for heat transfer, for example from a coolant to an oil in a stacked disk heat exchanger of an electric vehicle, with differently shaped and differently arranged wave crests and wave troughs, wherein the wave crests and the wave troughs of the turbulence-inducing sheet according to the invention are configured and arranged relative to one another in such a way that both a high heat transfer and a good mixing of the oil or coolant and a comparatively low pressure loss can be achieved. The turbulence-inducing sheet according to the invention has several parallel rows with wave crests and wave troughs that adjoin one another in the longitudinal direction of the row. At least three directly adjacent rows are staggered in relation to one another, viewed in the longitudinal direction of the row, such that the wave crests and the wave troughs of the three adjacent rows are arranged on a respectively associated straight line running obliquely to the longitudinal direction of the rows. This represents a complete departure from the previous arrangement of wave crests and wave troughs in the case of turbulence-inducing sheets known from the prior art, and for the first time enables improved heat transfer, improved mixing of the fluid flowing through the turbulence-inducing sheet, and a lower pressure drop. According to the invention, this is achieved by the open cross-section available for the flow being larger, but the turbulence and thus the heat transfer can be maintained at at least the same high level.

[0008] In a favorable further development of the turbulence-inducing sheet according to the invention, the wave crests and wave troughs of all rows are arranged on a respective associated zigzag line running transversely to the longitudinal direction of the row. The zigzag line runs parallel to the flow direction of the fluid flowing through the turbulence-inducing sheet, providing a comparatively large open flow cross-section and minimizing pressure loss. Tests have shown that the wave crests and wave troughs arranged on a zigzag line with three wave crests or wave troughs arranged in a row on each flank of the zigzag line enable a particularly high heat transfer and thus a particularly high cooling capacity and a comparatively low pressure loss to be achieved. Due to the improved, increased heat transfer, it is also possible to make the stacked disk heat exchanger smaller and therefore more compact overall, which is a great advantage, especially in the particularly cramped installation space conditions in modern motor vehicles, particularly in modern electric vehicles.

[0009] In another advantageous embodiment of the turbulence-inducing sheet according to the invention, it is produced by means of deep drawing. Using a deep-drawing method of this kind, which has been tried and tested for many years in the sheet metal processing industry, particularly in the automotive industry, a large number of wave troughs and wave crests can be introduced into the turbulence-inducing sheet to be formed in a single punching and deep-drawing process, so that it can be produced faster and thus more cost-effectively.

[0010] In a further advantageous embodiment of the turbulence-inducing sheet according to the invention, this has a height H between 0.9 and 1.3 mm, preferably a height H of about 1.1 mm. Compared to the turbulence-inducing sheets known from the prior art, a significantly lower component height can be achieved, which has a positive effect on the component height of a stacked disk heat exchanger equipped with such a turbulence-inducing sheet.

[0011] In addition or as an alternative, the turbulence-inducing sheet can have a material thickness of approx. 0.1 mm. The thickness of the turbulence-inducing sheet according to the invention is significantly lower than that of conventional turbulence-inducing sheets. This makes it possible to produce the turbulence-inducing plate according to the invention not only in a resource-saving manner and with comparatively little effort in a forming tool, but also in a cost-effective and weight-optimized manner, which is a great advantage, especially for electric vehicles.

[0012] The present invention is further based on the general idea of specifying a stacked disk heat exchanger with several stacked disks, each with a bottom and a peripheral edge, wherein a turbulence-inducing sheet is arranged between at least two adjacent stacked disks in accordance with the previous paragraphs. This means that, for example, in the case of the stacked disk heat exchanger according to the invention, turbulence-inducing sheets according to the invention can be arranged alternately with conventional, i.e., further, turbulence-inducing sheets in the cavities arranged in between. The advantages described with regard to the turbulence-inducing sheet can be transferred to the stacked disk heat exchanger according to the invention by means of the turbulence-inducing sheet according to the invention, these advantages specifically being a higher cooling capacity due to improved turbulence and a lower pressure drop. Another major advantage is that, due to the increased heat transfer capability of the turbulence-inducing sheet according to the invention and the lower pressure loss of the same, the stacked disk heat exchanger according to the invention can be built smaller and thus more compact to provide the same cooling capacity, as can other components, such as a coolant pump.

[0013] In a particularly preferred embodiment of the invention, the stacked disk heat exchanger has the stacked disks of the same, each with an inlet opening and an outlet opening, which are designed like a parallelogram and each have two long sides and two short sides. The transitions from the long sides to the adjacent short sides and vice versa are rounded, i.e., they are designed differently from the actual shape of a parallelogram. The two long sides can also be angled at an angle to each other. In addition, the stacked disks can also have nubs that either protrude inwards or outwards from the bottom of the respective stacked disk. The inlet and outlet openings designed according to the invention allow them to be moved close to one edge of the short sides, whereby a comparatively long distance is available for heat transfer between the diagonally opposite inlet and outlet openings. The inlet and outlet openings are designed to follow the contour of the edge, which allows the comparatively dense arrangement of the inlet and outlet openings on the associated edge. The individual stacked disks are soldered together at the edges. The surface area available for heat transfer can be increased further by means of the nubs that protrude inwards or outwards from the bottom, and these nubs can also be arranged in such a way that they have a pressure-reducing effect. It is also possible to use such nubs to fix the turbulence-inducing sheets arranged between two adjacent stacked disks, by making the nubs fit the turbulence-inducing sheets in a form-fitting manner.

[0014] In a particularly preferred embodiment of the invention stacked disk heat exchanger, the stacked disks each have an inlet opening and an outlet opening, each of which is oval in shape, the stacked disks also having nubs that project either inwardly or outwardly from the bottom of the respective stacked disks. The same advantages can be achieved with the nubs arranged on these stacked disks as with the stacked disks with the parallelogram-like inlet and outlet openings. Specifically, these advantages lie in the possible fixation of a turbulence-inducing sheet by means of such cams, an increase in the surface area available for heat transfer, and the possibility of reducing pressure loss.

[0015] The stacked disk heat exchanger is advantageously designed as an oil-coolant heat exchanger with a coolant side and an oil side, with the turbulence-inducing sheet being arranged on the coolant side and a further turbulence-inducing sheet, which may be designed according to the state of the art, being arranged on the oil side. A stacked disk heat exchanger of this kind, designed as an oil-coolant heat exchanger, can be of great advantage in particular for electric vehicles, as it can be designed to be more compact overall due to the increased cooling capacity and is therefore not only more compact but also lighter in terms of weight, which has a positive effect on the range of the electric vehicle. In combination with the stacked disk heat exchanger designed as an oil-coolant heat exchanger according to the invention, other components, such as a coolant pump, can be made smaller, with lower performance and thus not only optimized in terms of installation space, but also more cost-effectively.

[0016] In another advantageous embodiment of the stacked disk heat exchanger according to the invention, the further turbulence-inducing sheet surrounds the inlet opening and the outlet opening. In particular, in the case of a stacked disk with an oval inlet and outlet opening, these can be arranged at a distance from the edge of the respective stacked disk, resulting in a shorter distance between the associated inlet and outlet openings and thus a lower pressure loss. In order to ensure a high level of heat transfer despite this, it may be necessary to ensure that the additional turbulence-inducing sheet completely surrounds the inlet and outlet openings. This not only allows the additional turbulence-inducing sheet to be reliably fixed in place, but also significantly increases the surface area available for heat transfer.

[0017] It is advisable for the further turbulence-inducing sheet to have a height H between 2.9 mm and 3.1 mm, preferably a height H of approx. 3.0 mm. The additional turbulence-inducing sheet, which is usually located on the oil side, can be designed according to the state of the art.

[0018] In a particularly preferred embodiment, the turbulence-inducing sheet according to the invention and / or the further turbulence-inducing sheet has / have recesses in which the nubs engage for fixing the respective turbulence-inducing sheet according to the invention or the further turbulence-inducing sheet relative to the stacked disk. The following advantages can be achieved with the recesses or nubs according to the invention: A larger surface area available for heat transfer, a fixing of the turbulence-inducing sheet according to the invention or of the further turbulence-inducing sheet, and a reduction of a possible pressure loss.

[0019] Further important features and advantages of the invention are apparent from the sub-claims, from the drawings, and from the associated description of the figures with reference to the drawings.

[0020] It is understood that the above-mentioned features and those yet to be explained below can be used not only in the combination indicated in each case, but also in other combinations or on their own, without deviating from the scope of the present invention. The above-mentioned components of a superordinate unit, such as a device, an apparatus, or an arrangement, which are designated separately, can form separate parts or components of this unit or be integral areas or sections of this unit, even if this is shown differently in the drawings.

[0021] Preferred exemplary embodiments of the invention are shown in the drawings by way of example and will be explained in more detail in the following description, wherein identical reference numbers refer to identical or similar or functionally identical elements.BRIEF DESCRIPTION OF THE DRAWINGS

[0022] They show, each schematically,

[0023] FIG. 1 shows a view of a turbulence-inducing sheet according to the invention,

[0024] FIG. 2 shows a view of the turbulence-inducing sheet according to the invention in the direction of flow,

[0025] FIG. 3 shows a top view of the turbulence-inducing sheet according to the invention

[0026] FIG. 4 shows a view from above onto a turbulence-inducing sheet according to the invention.

[0027] FIG. 5 shows an exploded view of a stacked disk heat exchanger according to the invention in a first embodiment.

[0028] FIG. 6 shows an angled view of another turbulence-reducing sheet.

[0029] FIGS. 7 and 8 show views of stacked disks of the stacked disk heat exchanger according to the invention, as shown in FIG. 5.

[0030] FIG. 9 shows a representation as in FIG. 5, but with different stacked disks.

[0031] FIGS. 10 and 11 show views of the stacked disks used in the stacked disk heat exchanger according to FIG. 9.DETAILED DESCRIPTION

[0032] According to FIGS. 1-5 and 9, a turbulence-inducing sheet 1 for a stacked disk heat exchanger 2 according to the invention (see in particular FIGS. 5 and 9) has several parallel rows 3 with wave crests 5 and wave troughs 6 adjoining one another in the longitudinal direction of the rows 4. Three directly adjacent rows 3 are offset in relation to one another in the longitudinal direction of the row 4 in such a way that the wave crests 5 and wave troughs 6 are arranged on a respectively associated straight line 7 running obliquely to the longitudinal direction of the row 4. In a total of five neighboring rows 3, the middle row 3 belongs both to the straight line 7 of the row 3 arranged to the right, and to the straight line 7, running orthogonally to it, of the row 3 arranged to the left.

[0033] The wave crests 5 and wave troughs 6 of all rows 3 are arranged on a corresponding zigzag line 8 running transversely to the longitudinal direction of the rows 4, as can be seen from FIGS. 1 and 3. A flow direction 9 of the turbulence-inducing sheet 1 according to the invention also runs transversely to the longitudinal direction of the rows 4. In FIG. 2, the longitudinal direction of the rows 4 is in the plane of the leaf, while the flow direction 9 is perpendicular to the plane of the leaf.

[0034] The turbulence-inducing sheet 1 according to the invention can be used to achieve a particularly high heat transfer and a particularly effective swirling, for example of a coolant flowing through the turbulence-inducing sheet 1, while at the same time a pressure loss can be reduced due to the comparatively large open cross-section in the flow direction 9. By reducing such pressure losses, it is possible to use smaller coolant pumps that are not only more compact and less expensive to produce, but also require less electrical energy to operate. The increased heat transfer due to the wave crests 5 and wave troughs 6 being arranged in a zigzag line 8 in the flow direction 9 also allows the complete stacked disk heat exchanger 2 to be manufactured in a compact way that optimizes the overall installation space.

[0035] The turbulence-inducing sheet 1 can be manufactured by means of deep drawing in a joint deep drawing and punching process, whereby a cost-effective production is possible.

[0036] In general, the term “turbulence-inducing sheet” is used to represent a turbulence-inducing insert, so that the turbulence-inducing sheet 1 described in the present application and also another turbulence-inducing sheet 10 (see FIGS. 5, 6, and 9) can also be made of a material other than sheet metal, in particular of aluminum, plastic, etc.

[0037] The turbulence-generating sheet 1 may have a height H between 0.9 and 1.3 mm, preferably a height H of about 1.1 mm (see FIG. 2). The material thickness of the turbulence-inducing sheet 1 is approx. 0.1 to 0.3 mm. Due to the improved heat transfer capability of the turbulence-inducing sheet 1 according to the invention, the height H of the turbulence-inducing sheet can also be reduced, which also allows the total height of the stacked disk heat exchanger 2 according to the invention to be reduced. The webs 11 connecting the wave crests 5 with the wave troughs 6 (compare FIG. 2) can be angled at an angle of up to 78° to the respective wave crest 5 or wave trough 6. This results in an almost sinusoidal curve from the wave crests 5 over the webs 11 to the wave troughs 6. A width B of a respective row 3, i.e., for example a wave crest 5, can be 0.8 mm.

[0038] According to FIGS. 5 and 9, a stacked disk heat exchanger according to the invention has two stacked disks 12 (see FIGS. 5, 7 and 8) or stacked disks 12′ (see FIGS. 9-11), each of which has a bottom 13 and a peripheral edge 14, via which they are tightly connected to one another, for example soldered together. A turbulence-inducing sheet 1 according to the invention and a further turbulence-inducing sheet 10 or only turbulence-inducing sheets 1 are arranged alternately between two adjacent stacked disks 12, 12′.

[0039] If one now looks at the stacked disks 12 corresponding to FIGS. 5, 7, and 8, one can see that these each have an inlet opening 15 and an outlet opening 16, as well as two through openings 24. It is of course clear that only one inlet opening 15 and one associated outlet opening 16 are used per stacked disk level for the flow through a space located between two adjacent stacked disks 12. No fluid enters or leaves this space through the through openings 24, but only into the space above or below. If you now look at the inlet openings 15 and the outlet openings 16 of the stacked disks 12 corresponding to FIGS. 5, 7, and 8, you can see that these are designed like a parallelogram and have two long sides 17 and two short sides 18, with transitions 19 from a long side 17 to an associated and adjacent short side 18 and vice versa being rounded / rounded off. The two long sides 17 are also angled to each other and are therefore not parallel. In addition, there may be nubs 20 that either project inwards (see FIG. 7), i.e., upwards, or outwards (see FIG. 8), i.e., downwards, from the bottom 13 when installed. The nubs 20 serve both to increase the surface area available for heat transfer and to reduce pressure loss when flowing through the space between two neighboring stacked disks 12.

[0040] In contrast to the stacked disks 12 corresponding to the FIGS. 5, 7 and 8, the stacked disks 12′ corresponding to the FIGS. 9, 10, and 11 each also have an inlet opening 15′ and an outlet opening 16′, which, however, are oval in shape. Here, too, there is an inlet 15′ and an outlet 16′ diagonally opposite for each (flow) space bounded by two adjacent stacked disks 12′. The through openings 24′ are used to supply or dispose of fluid to or from the adjacent room. As can be seen from FIGS. 9-11, the stacked disks 12′ shown there also have nubs 20′ which project either inwards from the bottom 13, i.e., upwards in the installed state (see FIG. 11), or downwards, i.e., outwards in the installed state (see FIG. 10). The respective nubs 20, 20′ can have a height of approx. 1.4 mm.

[0041] In the case of two adjacent stacked disks 12, 12′, it is conceivable that two nubs 20, 20′ of two adjacent stacked disks 12, 12′ touch each other and are even soldered together.

[0042] A stacked disk heat exchanger 2 according to the invention can be designed as an oil-coolant heat exchanger with a coolant side 21 and an oil side 22, with the turbulence-inducing sheet 1 according to the invention preferably being arranged on the coolant side 21 and the other turbulence-inducing sheet 10 being arranged on the oil side 22.

[0043] If one now looks at the further turbulence-inducing sheet 10 according to FIG. 9, one can see that it surrounds the inlet opening 15′, the outlet opening 16′ and the through openings 24′ of the associated stacked disks 12′. The inlet opening 15′, the outlet opening 16′, and the through openings 24′ are not arranged directly on the edge 14 in the stacked disks 12′, but at a distance from it, which results in a shorter distance between the respective inlet openings 15′ and outlet openings 16′, which contributes to a reduction in pressure loss. In order to increase the heat transfer despite this, the additional turbulence-inducing sheet 10 surrounds the inlet opening 15′, the outlet opening 16′ and the through openings 24′.

[0044] The turbulence-inducing sheet 1 according to the invention, like the further turbulence-inducing sheet 10, can have recesses 23, in which the nubs 20, 20′ of an associated stacked disk 12, 12′ engage and thereby fix the turbulence-inducing sheet 1 according to the invention or the further turbulence-inducing sheet 10. The size of the turbulence-inducing sheet 1 according to the invention can also be adapted in such a way that it is arranged at the edge between the nubs 20 or 20′ and held above them.

[0045] The further turbulence-inducing sheet 10 can have a height H between 2.9 mm and 3.1 mm, or a height H of about 3 mm, whereby it is also or alternatively conceivable that the further turbulence-inducing sheet 10 has a material thickness of about 0.2 mm. The other turbulence-inducing sheet 10 has webs 11 aligned orthogonally to the respective wave crests 5 and wave troughs 6, as shown in FIG. 6. Of course, it is also possible to arrange the turbulence-inducing sheet 1 according to the invention on the oil side 22.

[0046] The stacked disks 12, 12′ have a wall thickness of approx. 0.4 mm and can therefore not only be produced in a cost-effective, resource-saving, and simple manner, but are also comparatively light in weight.

[0047] All in all, the stacked disk heat exchanger 2 according to the invention and the turbulence-inducing sheet 1 used in it can achieve a high level of heat transfer, a low pressure loss, and a particularly compact design. This is particularly advantageous for use in electric vehicles.

Claims

1. A turbulence-inducing sheet for a stacked disk heat exchanger, comprising:a plurality of parallel rows each including a plurality of wave crests and a plurality of wave troughs alternately adjoining one another in a longitudinal direction of the plurality of rows;wherein three directly adjacent rows of the plurality of rows are arranged offset from one another in the longitudinal direction such that the plurality of wave crests and the plurality of wave troughs of the three adjacent rows are arranged on a respectively associated straight line extending obliquely to the longitudinal direction.

2. The turbulence-inducing sheet according to claim 1, wherein the plurality of wave crests and the plurality of wave troughs of all of the plurality of rows are arranged on a respective associated zigzag line extending transversely to the longitudinal direction.

3. The turbulence-inducing sheet according to claim 1, wherein the turbulence-inducing sheet is manufactured via deep drawing.

4. The turbulence-inducing sheet according to claim 1, wherein the turbulence-inducing sheet has a height of 0.9 mm to 1.3 mm.

5. A stacked disk heat exchanger, comprising:a plurality of stacked disks each having a bottom and a peripheral edge; anda turbulence-inducing sheet according to claim 1 arranged between the bottom and the peripheral edge of an associated disk of the plurality of stacked disks.

6. The stacked disk heat exchanger according to claim 5, wherein:the plurality of stacked disks each include an inlet opening and an outlet opening disposed in the bottom, the inlet opening and the outlet opening each having a parallelogram like shape with two long sides, two short sides, and a plurality of rounded transitions between the two long sides to the two short sides;the two long sides are arranged at an angle to each other; andthe plurality of stacked disks each have a plurality of nubs that project at least one of inwards and outwards from the bottom.

7. The stacked disk heat exchanger according to claim 5, wherein:the plurality of stacked disks each include an inlet opening and an associated outlet opening that are oval in shape; andthe plurality of stacked disks each further include a plurality of nubs that protrude at least one of inwards and outwards from the bottom.

8. The stacked disk heat exchanger according to claim 5, further comprising a further turbulence-inducing sheet, wherein:the stacked disk heat exchanger is an oil-coolant heat exchanger with a coolant side and an oil side; andthe turbulence-inducing sheet is arranged on the coolant side and the further turbulence-inducing sheet is arranged on the oil side.

9. The stacked disk heat exchanger according to claim 8, wherein:the plurality of stacked disks each include an inlet opening and an associated outlet opening that are oval in shape;the plurality of stacked disks each further include a plurality of nubs that protrude at least one of inwards and outwards from the bottom; andthe further turbulence-inducing sheet surrounds the inlet opening and the outlet opening of at least one disk of the plurality of stacked disks.

10. The stacked disk heat exchanger according to claim 8, wherein the further turbulence-inducing sheet has a height of 2.9 mm to 3.1 mm.

11. The stacked disk heat exchanger according to claim 8, wherein:the plurality of stacked disks each further include a plurality of nubs that protrude at least one of inwards and outwards from the bottom; andthe further turbulence-inducing sheet includes a plurality of recesses engaged with the plurality of nubs of at least one disk of the plurality of stacked disks fixing the further turbulence-inducing sheet and the at least one disk together.

12. The stacked disk heat exchanger according to claim 5, wherein the plurality of stacked disks each have a wall thickness of approximately 0.4 mm.

13. The stacked disk heat exchanger according to claim 5, wherein:the plurality of stacked disks each further include a plurality of nubs that protrude at least one of inwards and outwards from the bottom; andthe turbulence-inducing sheet includes a plurality of recesses engaged with the plurality of nubs of at least one disk of the plurality of stacked disks fixing the turbulence-inducing sheet and the at least one disk together.

14. The stacked disk heat exchanger according to claim 8, wherein the further turbulence-inducing sheet has a material thickness of approximately 0.2 mm.

15. The stacked disk heat exchanger according to claim 10, wherein the further turbulence-inducing sheet has a height of approximately 3.0 mm.

16. The turbulence-inducing sheet according to claim 1, further comprising a plurality of recesses configured to receive and engage a plurality of nubs of at least one disk of the stacked disk heat exchanger to couple the turbulence-inducing sheet and the at least one disk together.

17. The turbulence-inducing sheet according to claim 1, wherein the turbulence-inducing sheet has a material thickness of approximately 0.1 mm.

18. The turbulence-inducing sheet according to claim 4, wherein the turbulence-inducing sheet has a height of approximately 1.1 mm.

19. A turbulence-inducing sheet for a stacked disk heat exchanger, comprising a plurality of parallel rows extending in a longitudinal direction, wherein:each of the plurality of rows include a plurality of wave crests and a plurality of wave troughs alternately adjoining one another in the longitudinal direction;the plurality of wave crests include a first wave crest, a second wave crest, and a third wave crest;the plurality of wave troughs include a first wave trough and a second wave trough;a set of directly adjacent rows of the plurality of rows are arranged offset from one another in the longitudinal direction such that:the first wave crests of the adjacent rows are arranged along a first imaginary straight line extending obliquely to the longitudinal direction;the first wave troughs of the adjacent rows are arranged along a second imaginary straight line extending obliquely to the longitudinal direction;the second wave crests of the adjacent rows are arranged along a third imaginary straight line extending obliquely to the longitudinal direction;the second wave troughs of the adjacent rows are arranged along a fourth imaginary straight line extending obliquely to the longitudinal direction; andthe third wave crests of the adjacent rows are arranged along a fifth imaginary straight line extending obliquely to the longitudinal direction.

20. The turbulence-inducing sheet according to claim 19, wherein the first wave crests, the first wave troughs, the second wave crests, the second wave troughs, and the third wave crests of the plurality of rows are each arranged to define a respective zigzag line extending transversely to the longitudinal direction.

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