US20070193726A1

US20070193726A1 - Three-dimensional surface structure for reduced friction resistance and improved heat exchange

Info

Publication number: US20070193726A1
Application number: US11/229,776
Authority: US
Inventors: Nikolaus Vida
Original assignee: Individual
Current assignee: Individual
Priority date: 2003-03-19
Filing date: 2005-09-19
Publication date: 2007-08-23

Abstract

In order to improve the flow properties of a surface, a surface along which a medium flows is provided. The medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases and the surface comprises dimples, the edges of which are rounded, thereby forming a central dimple area and at least one curvature area for each dimple. The at least one curvature area continuously connects the dimple to the surrounding surface.

Description

The invention concerns in general surfaces along which media, e.g. gases, liquids or two-phase mixtures are flowing and especially surfaces as described in EP 92 911 873.5, PCT RU92/00106 or EP 96 927 047.9, PCT/EP96/03200 also termed TLT-reliefs or TLT-surfaces.
It is known that the process when a continuous medium like a gas, a liquid or a two-phase mixture flows along a surface covered with very special three-dimensional concave reliefs, named the TLT-reliefs and being described in more detail in EP 92 911 873.5, PCT RU92/00106 and in EP 96 927 047.9, PCT/EP96/03200, which are completely incorporated here by reference, is accompanied by self-organization of secondary twisted tornado-like jets originating in each concavity of the relief and flowing out of it into the parent flow.
It is known that friction could be reduced by means of dimples located at said surface and that in addition heat transfer between said surface and the streaming media, e.g. gases, liquids and two-phase mixtures containing gases and liquids could be increased.
However, there are special situations in which there is minor interest in drag reduction and major interest in an increased heat transfer, as for instance for heat exchange devices as heat sinks in general, bonnets, chillers and many more. In addition, a huge number of devices demand for drag reduction as vehicles, aircrafts and ships in general. Moreover, any fluid transportation would benefit from a reduced drag resistance as this would decrease energy consumption or increase transportation speed.
Therefore it is an object of the invention to show a new way how the properties of a surface, especially concerning friction resistance and heat exchange with a surrounding medium, can be improved.
The object of the invention is achieved in a surprisingly simple manner by a subject matter of one of the attached independent claims. Advantageous embodiments and refinements are defined in the respective dependent claims.
The inventors surprisingly found that a certain geometry of the TLT-reliefs results in a significant improvement of the flow properties.
Accordingly the invention proposes a surface, which comprises dimples, wherein the edges of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, which continuously connects the dimple to the surrounding surface.
Such a geometry of a surface especially improves the flow properties with respect to friction resistance as also with respect to heat and mass transfer for surfaces, along which a medium flows, which consists of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases.
The underlying principle are secondary vortices, which originate in the dimples and lead to an organized transportation of medium from the surface to the main flow. Due to the reduced pressure inside the vortex flows the boundary layer is sucked in, so that the thickness of the boundary layer does not increase.
Said central dimple preferably area essentially has the form of a section of a sphere or an ellipsoid.
With great advantage said curvature area of the surface comprises at least a first curvature area and a second curvature area, the first curvature area having a different curvature than the second curvature area. Preferably said first curvature area is rounded with a first rounding radius and said second curvature area is rounded with a second rounding radius.
As will also be seen later on, especially suitable for drag reduction, i.e. reduction of friction resistance, and related flow properties like reduced drag vortices and reduced lee waves, is a surface comprising dimples having a relatively low depth in relation to the diameter. In this regime it can be of special advantage to combine two different, consecutive curvature areas to realize different sizes of the central dimple area.
Also two curvature areas are very advantageous in order to achieve a gentle transition from the dimple to the surrounding surface, thereby reducing the probability of destruction of the advantageous secondary vortices, which originate in the dimples.
With advantage the dimples are arranged periodically on the surface. In order to realize a good coverage of the surface, the centers of three adjoining dimples preferably form a triangle, the distance between two neighboring dimples having a constant value t₁and the distance between two rows of dimples having a constant value t₂.
The maximum coverage can be reached in this kind of arrangement when the curvature areas of said three adjoining dimples are in contact with each other.
Even in this arrangement a small area of flat surface remains in the center of three respective adjoining dimples. In this location preferably additional smaller-sized dimples are provided, by which the flow properties can be further improved.
The inventors also surprisingly found that there are regimes of significantly increased heat exchange and regimes of strongly reduced drag resistance.
Accordingly a surface, along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, with dimples having a diameter d and a depth h with a ratio between said depth and said diameter of h/d≦0.1, also lies within the scope of the invention. In this geometrical regime the surface shows an especially low friction resistance.
With a ratio of h/d≧0.1 the surface shows an especially high heat transfer between said surface and said flowing medium.
The dimpled surfaces or reliefs with small relative depth of h/d≦0.1, where h is the concavity depth and d is the concavity diameter, significantly reduce the friction resistance of the shaped surfaces, as well as intensify the heat and mass transfer, to a lesser extend, however, as compared with the friction resistance of a smooth surface.
The dimpled surfaces or reliefs with a larger relative depth of h/d≧0,1 significantly intensify the heat and mass transfer with the aerohydrodynamic losses being constant or lagging behind the rate of intensification, with considerable disturbance of Reynolds in favorite to heat transfer.
Also within the scope of the invention lies a means for locomotion with at least one surface, along which a medium flows when said means for locomotion is in movement, wherein the at least one surface is provided with dimples as described above, in particular provided as a car, a truck, a train, an airplane, a helicopter or a ship.
In comparison to an otherwise identical means for locomotion or vehicle with a flat surface certain flow properties are improved, especially the drag resistance is reduced, the forming of drag vortices is reduced, the forming of lee waves is reduced, and the separation point of the flow is moved further downstream.
Further a device for transportation of a medium lies within the scope of the invention, which comprises at least one surface with dimples as described above. With advantage the surface with dimples is provided as an inner surface of a transport channel, in particular a pipe, of the device, in which the medium is transported. The implementation in such a device is of advantage due to a further result of the described surface structure found by the inventors, consisting in a reduced deposition of particles on the surface compared to a flat surface.
Further a device for heat exchange between a flowing medium and at least one surface of the device, in particular an air-conditioning system or part thereof, is proposed, wherein the at least one surface is provided with dimples. Here it can be taken advantage of the effect of reduced ice-forming on a surface, which comprises the described dimples, in comparison to a flat surface.
The invention further proposes a container for cooking and/or for keeping warm, wherein the outside surface of the bottom wall of the container and/or the outside surface of the side walls of the container comprise a surface with the described dimples.
Also a layer or coating for applying on a surface is proposed, which-comprises a surface with the described dimples. By use of such a layer, a device or vehicle having a surface along which a medium flows can be upgraded for improved flow properties, such as reduced friction resistance or improved heat or mass transfer or a combination thereof.
For this purpose the layer can advantageously be provided with a first side and a second side, wherein said first side comprises dimples as described above and said second side comprises a self-adhesive coating.
Accordingly the invention proposes a method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the step of applying a described layer onto said surface.
Also a method is proposed for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, which comprises the steps of

- providing a workpiece with at least one surface and
- imprinting into said at least one surface a structure comprising dimples.

Another inventive method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprises the steps of

- providing a casting mold with at least one structured surface and
- molding, in particular injection molding, of a workpiece with at least one surface comprising dimples by means of said casting mold.

The invention is not limited to the described production methods, but shall also encompass any other method, which is suitable to produce a surface comprising the above described dimples.
Also within the scope of the invention lies the usage of a surface with dimples as described above as a surface of

- a means for locomotion or
- a device for transportation of a medium or
- a device for heat exchange or
- a container for cooking and/or for keeping warm.

In the following the invention is described exemplary in more detail on the basis of preferred embodiments and with reference to the enclosed drawings. Therein same reference marks in the drawings indicate same or similar parts.

BRIEF DESCRIPTION OF THE FIGURES

It is shown in:
FIG. 1: a schematic diagram of a first distribution of dimples,
FIG. 2: a schematic diagram of a cross section through a dimple according to a first preferred embodiment,
FIG. 1: a schematic diagram of a second distribution of dimples,
FIG. 4: a schematic diagram of a cross section through a dimple according to a second preferred embodiment,
FIG. 5: a schematic diagram of a train with an inventive surface,
FIG. 6: schematically a comparison of two wing profiles,
FIG. 7: a schematic diagram of a container immersed in a flowing fluid,
FIG. 8: schematically a transport channel, the inner surface of which being provided with dimples,
FIG. 9: a schematic diagram of a measurement arrangement for measuring the velocity profiles over different investigated plates comprising a laser Doppler anemometer (LDA),
FIG. 10: a schematic diagram of a metal plate with TLT relieves or dimples,
FIG. 11: a schematic diagram of a plate with variable TLT relieves or dimples,
FIG. 12: a schematic diagram of a plate with TLT relieves showing the points, at which the velocity was measured.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows schematically a preferred distribution of dimples 10 on a surface. The dimples 10 are arranged periodically, wherein the centers of three directly adjoining dimples 10 form an equilateral triangle. The angle α therefore has a value of 60°. The distance between the centers of two adjoining dimples 10, which is equal to the length of a side of the triangle, has a constant value t₁. The distance between two rows of dimples 10, which equals the height of the triangle, has a constant value t₂. The parameters t₁and t₂can have different values depending on the purpose for which the surface shall be utilized.
FIG. 2 shows a cross section through the center of one of the dimples 10 shown in FIG. 1, perpendicular to the surface. In this embodiment the dimple essentially has the form of a calotte with radius R_ahp, height h_cand diameter d_c. Further the dimple 10 is rounded at the edges with a rounding radius R_S. Thereby in this example the dimple is symmetrical with respect to rotation around an axis through the center of the dimple and perpendicular to the surface.
FIG. 3 shows schematically a top view of a distribution of dimples comprising a central dimple area 110, a first curvature area 120 and a second curvature area 130, the named areas being arranged consecutively from the center of the dimple to the outside.
The central dimple area has a diameter of d₁, the first curvature area has an diameter of d₂and the second curvature area has a diameter of t₁. The dimples are arranged similar to FIG. 1, but in this preferred embodiment the outer rims of two adjoining dimples are in contact with each other for a maximum surface coverage.
Again, the centers of three adjoining dimples form an equilateral triangle, the distance between the centers of two adjoining dimples having the constant value t₁and the distance between two rows of dimples having the constant value t₂. In this embodiment therefore the diameter of the second curvature area equals the distance between two adjoining dimples t₁.
A small area of surface remains in the center between three adjoining dimples. In this location preferably additional smaller-sized dimples 200 can be provided, thereby further improving the flow properties of the surface.
The cross section AA′ through the center of a dimple perpendicular to the surface is shown in more detail in FIG. 4.
The central dimple area 110 essentially has the form of a section of a sphere, followed in the outward direction by two consecutive curvature areas. Since the curvature areas can be described as an arc, which is rotated in space, they have a surface formed as a part of a torus or similar thereto.
The form of the central dimple area, of the first curvature area and of the second curvature area in the shown cross section perpendicular to the surface and through the center of the dimple is defined by the following parameters:

d₁: Diameter of the central dimple area,
d₂: Outer diameter of the first curvature area,
t₁: Outer diameter of the second curvature area,
R₁, C₁: Radius and center point of the sphere, the section of which forms the surface of the central dimple area,
R₂, C₂: Radius and center point of the rounding radius of the first curvature area,
R₃, C₃: Radius and center point of the rounding radius of the second curvature area,
P₁: Transition point from the central dimple area to the first curvature area,
P₂: Transition point from the first curvature area to the second curvature area,
P₃: Transition point from the second curvature area to the surrounding surface,
h₁: Difference in height between the lowest point of the central dimple area and the outer rim of the central dimple area,
h₂: Difference in height between the inner rim of the first curvature area and the outer rim of the first curvature area,
h₃: Difference in height between the inner rim of the second curvature area and the outer rim of the second curvature area,
α₁: Angle between the y-axis and a line connecting C₂and C₃,
α₂: Angle between the x-axis and a line connecting C₁and C₂,
f: Parameter related to the portion of the surface covered by the central dimple area in relation to the combined area of central dimple area and curvature areas.

There is one point, in which the circle with radius R₁, being part of the sphere that forms the central dimple area, and the circle with radius R₂, defining the curvature of the first curvature area, have a mutual tangent. Further, there is another point, in which the circle with radius R₂and the circle with radius R₃have a mutual tangent.
To completely describe the form of the dimple a set of parameters, in particular the parameters d₁, α₁, α₂, R₂/R₁and f, are chosen according to the necessities of the specific purpose the surface shall be used for and depending on whether drag reduction or improved heat exchange has priority. For most purposes the coverage of the surface by the central dimple areas lies below 70%, but also a greater coverage falls within the scope of the present invention.
The remaining of the named parameters can be calculated by means of the following equations: $R_{1} = \frac{d_{1}}{2 \cdot \sin α_{1}}, R_{2} = \frac{R_{2}}{R_{1}} \cdot \frac{d_{1}}{2 \cdot \sin α_{1}}, R_{2} = \frac{t_{1} - \frac{d_{1}}{2} \cdot \frac{R_{2}}{R_{1}} \cdot \frac{(1 - \sin α_{1})}{\sin α_{2}}}{\sin α_{2}}, h_{1} = \frac{d_{1}}{2} \cdot \frac{(1 - \cos α_{1})}{\sin α_{1}}, h_{2} = R_{2} \cdot (\cos α_{2} - \cos α_{1}), h_{3} = R_{3} \cdot (1 - \cos α_{2}), H = h_{1} + h_{2} + h_{3}, t_{1} = \sqrt{\frac{π}{6 \cdot f}} \cdot d_{1}, C_{1} = (X_{C 1}, Y_{C 1}) with X_{C 1} = 0, Y_{C 1} = R_{1} - H, C_{2} = (X_{C 2}, Y_{C 2}) with X_{C 2} = \frac{d_{1}}{2} \cdot (1 + \frac{R_{2}}{R_{1}}), Y_{C 2} = R_{3} + \frac{X_{C 3} - X_{C 2}}{tg α_{2}}, C_{3} = (X_{C 3}, Y_{C 3}) with X_{C 3} = \frac{t_{1}}{2}, Y_{C 3} = - R_{3}, P_{1} = (X_{P 1}, Y_{P 1}) with X_{P 1} = \frac{d_{1}}{2}, Y_{P 1} = H - h_{1}, P_{2} = (X_{P 2}, Y_{P 2}) with X_{P 2} = \frac{t_{1}}{2} - R_{3} \cdot \sin α_{2}, Y_{P 2} = R_{3} \cdot (\cos α_{2} - 1), P_{3} = (X_{P 3}, Y_{P 3}) with X_{P 3} = \frac{t_{1}}{2}, Y_{P 3} = 0,$
said equations being defined in a two-dimensional coordinate-system with the x-axis in the plane of the surface and with the y-axis through the center of the dimple and perpendicular to the surface.
In FIGS. 5 to 8 various preferred embodiments of the invention are shown, thereby demonstrating the broad range of applications, for which an inventive surface with dimples as described above can be utilized. The shown embodiments are only exemplary and do not limit the scope of the invention, as numerous other applications could be named.
In FIG. 5 a high-speed train 300 is shown schematically, which is provided with an inventive outer surface 310, which comprises a multitude of dimples, the form, size and distribution of which is adapted according to speed and geometry of the train 300.
A train as shown in FIG. 5 is characterized by improved flow properties in comparison to a similar train with a flat surface. In particular the forming of drag vortices is reduced as also the forming of lee wave in case of side winds. Consequently the overall friction resistance is also reduced.
A further effect of the inventive surface lies in the separation point of the flow being moved further downstream or in certain circumstances the complete disappearance of a separation point. This effect allows for instance for providing completely new wing profiles. In FIG. 6 a conventional wing profile 400 is shown in comparison with a modified wing profile 410, the use of which becomes possible for example as a wing of an airplane, when the surface is provided with an inventive dimple structure.
FIG. 7 shows a further utilization of an inventive surface for a container usable for cooking or for keeping some substance at a desired temperature. The container schematically shown in FIG. 7 is immersed in a flowing fluid 510. The outside surface of the bottom wall 520 of the container and/or the outside surface of the side walls 530 of the container comprise a surface with periodically arranged dimples.
In this embodiment the dimples are of the type shown in FIG. 1 and FIG. 2, preferably with the following values:

t₁=28.6 mm,
t₂=33.0 mm,
d_c=20.0 mm,
h_c=3.0 mm,
R_ahp=68.2 mm,
R_S=5.0 mm,
or scaled up or down keeping essentially the ratios $\frac{t_{1}}{t_{2}} = \frac{28.6}{33.0}, \frac{R_{ahp}}{R_{S}} = \frac{68.2}{3.0}, \frac{R_{S}}{h_{c}} = \frac{5.0}{3.0}$

The above named values result in a fraction of the surface, which is covered by the dimples, of about 0.3.
FIG. 8 schematically shows a pipe 600, the inner surface 610 of which is provided with dimples 630. This pipe can be utilized as a transport channel for transportation of a medium. The significant improvement achieved by using the inventive surface in this embodiment lies in a reduced deposition of particles on the surface due to the suction of the boundary layer from the surface into the main flow by means of the self-organizing vortex flows originating in the dimples.
Furthermore, because of the same reasons the forming of ice on the surface is reduced, so that such a pipe can also be utilized with great advantage in a device, in which a medium is to be cooled, like an air-conditioning system, especially an air-conditioning system used in an airplane.
The inventors have studied the phenomenon of friction resistance reduction on the TLT-relief surfaces using a laser Doppler anemometer (LDA) to measure velocity profiles formed over the surfaces being flowed around, and the theorem of momentum to process the obtained results. The experimental setup is schematically illustrated in FIG. 9.
The investigated plate 704 is positioned in the test section 710 of the cavitation tunnel. By means of a laser 706 arranged on an optical bench 708 and a signal control and preliminary processing unit 702 as parts of the laser Doppler anemometer (LDA) the flow properties are measured.
The test specimens, which were examined by the inventors, were thin flat plates of the following two types:

metal plates 800 of size 378×679 mm²either having a smooth surface or a TLT-relief formed surface provided with dimples 802 as shown in FIG. 10,
plates 810 of the same size with an elastic rubber coating 820 applied onto a flat plate with either a continuous surface or a surface provided with the regular grid of axially symmetrical holes connecting the elastic coating 820 above them with the pressure-tight chamber beneath the plate 810 as shown in FIG. 11.

By varying the pressure in the pressure-tight chamber, the experimentalist can form on the flowed-around surface the TLT relief with various depth of the concavities by retracting the elastic coating 820 inside the hole in the plate. When the pressure above and beneath the plate is the same, the surface being flowed around represents a grid of rubber membranes covering the holes in the plate and interacting with the ambient flow. Reducing the pressure beneath the plate, one can control the TLT relief with the depth of the relief concavities varying almost from zero to the depths corresponding to the radius of the hole in the support plate.
FIG. 11 further shows bearing cylinders 830, the vacuum cover 850, which seals the air-tight chamber and a vacuum union 840.
A similar arrangement as the one shown in FIG. 11 can also be used in a device or a vehicle to change the size, the form and/or the number of the dimples on the surface during operation of said device or vehicle. That way the flow properties of the device or vehicle can be flexibly adapted to changing operating conditions.
During the experiment performed by the inventors the hydrodynamic characteristics of the following objects were compared:

- the TLT-relief metal plate with the smooth surface metal plate;
- the adjustable elastic TLT-relief plate with the smooth plate with no holes on the support plate having the same elastic coating;
- the plates with various TLT reliefs on the metal surface with the plates with membranes and different TLT reliefs on the elastic surface.

The measurements were carried out in a cavitational tunnel, which was the cavitational tunnel of the Hamburgische Schiffbau-Versuchsanstalt GmbH (HSVA), in which the flow was characterized by the Reynolds numbers defined as follows:

- along the plate length considering the preliminary section within the range:
  9×10⁵ ≦Re≦7,5×10⁶;
- along the TLT relief concavity diameter within the range:
  2.5×10⁴ ≦Re≦6×10⁵.
  The onflowing stream turbulence rate was high and according to the laser measurements comprised:
  0.1≦σ≈√(u′²)/u∞≦0.3

The water temperature in the flow was measured within the range:
15° C.≦T≦ 22° C.
The velocity profiles were measured at thirty points 930 arranged on the surface of the plate 910 shown in FIG. 12. The profile speed measurements on the ambient surfaces of the flat plates and the plates with TLT relief comprising dimples 920 were performed at these points 930, which are indicated by crosses.
The measurements were processed using the theorem of momentum in accordance with the procedure suggested by I.Nikuradze in “Turbulente Reibungsschichten an der Platte”, ZWB, R.Oldenbourg, Muenchen und Berlin, 1942, and comprised determination of the values of the local and full friction resistance coefficients C′ and C_F. The experimental data are represented in the table shown below.
It follows from the table that the friction resistance of the metallic surface with the TLT relief is ˜22% lower than that of the smooth metallic surfaces. The friction resistance of the surface with elastic rough rubber coating and the TLT relief on it is ˜34% lower than that of the smooth elastic rough rubber coated surface.

Claims

1. A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, said surface comprising:

dimples, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.

2. The surface according to claim 1, wherein said central dimple area essentially has the form of a section of a sphere or an ellipsoid.

3. (canceled)

4. The surface according to claim 1, wherein said first curvature area is rounded with a first rounding radius and said second curvature area is rounded with a second rounding radius.

5. The surface according to claim 4, wherein said central dimple area essentially has the form of a section of a sphere, and the form of the central dimple area, of the first curvature area and of the second curvature area in a cross section perpendicular to said surrounding surface and through a center of the dimple is defined by the following parameters:

d₁: Diameter of the central dimple area,

d₂: Outer diameter of the first curvature area,

t₁: Outer diameter of the second curvature area,

R₁, C₁: Radius and center point of the sphere, the section of which forms the surface of the central dimple area,

R₂, C₂: Radius and center point of the rounding radius of the first curvature area,

R₃, C₃: Radius and center point of the rounding radius of the second curvature area,

P₁: Transition point from the central dimple area to the first curvature area,

P₂: Transition point from the first curvature area to the second curvature area,

P₃: Transition point from the second curvature area to the surrounding surface,

h₁: Difference in height between the lowest point of the central dimple area and the outer rim of the central dimple area,

h₂: Difference in height between the inner rim of the first curvature area and the outer rim of the first curvature area,

h₃: Difference in height between the inner rim of the second curvature area and the outer rim of the second curvature area,

α₁: Angle between the y-axis and a line connecting C₂and C₃,

α₂: Angle between the x-axis and a line connecting C₁and C₂,

f: Parameter related to the portion of the surface covered by the central dimple area in relation to the combined area of central dimple area and curvature areas,

wherein a set of parameters, in particular the parameters comprising d₁, α₁, α₂, R₂/R₁and f, are chosen and a remaining set of parameters are calculated by the following equations with a tolerance of ±10% for each parameter:

R_{1} = \frac{d_{1}}{2 \cdot \sin α_{1}}, R_{2} = \frac{R_{2}}{R_{1}} \cdot \frac{d_{1}}{2 \cdot \sin α_{1}}, R_{2} = \frac{t_{1} - \frac{d_{1}}{2} \cdot \frac{R_{2}}{R_{1}} \cdot \frac{(1 - \sin α_{1})}{\sin α_{2}}}{\sin α_{2}}, h_{1} = \frac{d_{1}}{2} \cdot \frac{(1 - \cos α_{1})}{\sin α_{1}}, h_{2} = R_{2} \cdot (\cos α_{2} - \cos α_{1}), h_{3} = R_{3} \cdot (1 - \cos α_{2}), H = h_{1} + h_{2} + h_{3}, t_{1} = \sqrt{\frac{π}{6 \cdot f}} \cdot d_{1}, C_{1} = (X_{C 1}, Y_{C 1}) with X_{C 1} = 0, Y_{C 1} = R_{1} - H, C_{2} = (X_{C 2}, Y_{C 2}) with X_{C 2} = \frac{d_{1}}{2} \cdot (1 + \frac{R_{2}}{R_{1}}), Y_{C 2} = R_{3} + \frac{X_{C 3} - X_{C 2}}{tg α_{2}}, C_{3} = (X_{C 3}, Y_{C 3}) with X_{C 3} = \frac{t_{1}}{2}, Y_{C 3} = - R_{3}, P_{1} = (X_{P 1}, Y_{P 1}) with X_{P 1} = \frac{d_{1}}{2}, Y_{P 1} = H - h_{1}, P_{2} = (X_{P 2}, Y_{P 2}) with X_{P 2} = \frac{t_{1}}{2} - R_{3} \cdot \sin α_{2}, Y_{P 2} = R_{3} \cdot (\cos α_{2} - 1), P_{3} = (X_{P 3}, Y_{P 3}) with X_{P 3} = \frac{t_{1}}{2}, Y_{P 3} = 0,

said equations being defined in a two-dimensional coordinate-system with an x-axis in the plane of said surrounding surface and with the a y-axis through the center of the dimple and perpendicular to said surrounding surface.

6. The surface according to claim 1, wherein said dimples are arranged periodically on said surrounding surface.

7. The surface according to claim 5, wherein the centers of three adjoining dimples form a triangle, a first distance between two neighboring dimples of said triangle having a constant value t₁, and a second distance between two rows of the dimples having a constant value t₂.

8. The surface according to claim 7, wherein the at least one curvature areas of said three adjoining dimples are in contact with each other.

9. The surface according to claim 7, further comprising additional dimples of a different size than said dimples, which are located in the center of three respective adjoining dimples.

10. A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, comprising:

dimples having a diameter of d and a depth of h with a ratio between said depth and said diameter of h/d less than or equal to 0.1, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface.

11. A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, said surface comprising:

dimples having a diameter of d and a depth of h with a ratio between said depth and said diameter of h/d greater than or equal to 0.1, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface.

12 and 13. (canceled).

14. The surface according to claim 1, wherein said surrounding surface comprises a locomotive device selected from the group consisting of a car, a truck, a train, an airplane, a helicopter and a ship.

15 and 16. (canceled).

17. The surface according to claim 1, wherein said surrounding surface comprises an inner surface of a transport channel.

18. The surface according to claim 17, wherein said transport channel is a pipe.

19. (canceled)

20. The surface according to claim 1, wherein said surrounding surface comprises a device for heat exchange between a the medium and at least one surface of the device.

21. (canceled)

22. The surface according to claim 1, wherein said surrounding surface comprises a container for cooking and/or for keeping warm, said surrounding surface being located at an outside surface of a bottom wall of the container and/or an outside surface of side walls of the container.

23. A layer for applying on a surface, comprising:

a surface with dimples wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface, and wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.

24. The layer according to claim 23, further comprising a first side and a second side, wherein said first side comprises said surface and said second side is self-adhesive.

25. A method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the step of:

forming a layer having a first side with dimples and a second side with an adhesive, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimples to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area; and

applying a said second side of said layer onto said surface.

26. The method according to claim 25, further comprising the steps of:

imprinting said dimples into said first side.

27. A method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the steps of:

providing a casting mold with at least one structured surface; and

molding a workpiece with at least one surface in contact with said at least one structured surface to define comprising dimples, on the workpiece, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimples to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.

28. (canceled)