EP2103818B1

EP2103818B1 - Friction reducing surface and a mass and heat transfer enhancing surface

Info

Publication number: EP2103818B1
Application number: EP06847404.8A
Authority: EP
Inventors: Gennady Iraklievich Kiknadze
Original assignee: Individual
Current assignee: Individual
Priority date: 2006-08-31
Filing date: 2006-08-31
Publication date: 2013-09-18
Anticipated expiration: 2026-08-31
Also published as: EP2103818A1; WO2008033045A1; EP2103818A4

Description

Field of Invention

The present invention relates to aerohydrodynamics, power generation, and technologies involving flows of various media, to problems associated with raising the efficiency of transport, to medicine and other spheres of scientific-and-technical activities and engineering practice, in which the success of development and realization of continuous-production processes and equipment and their functional and technical-and-economic performance depend on the quality of flows of continuous medium and on the possibility of controlling the process of interaction between flow and surface by and large and, in particular, controlling the boundary layers of flows of gases and liquids and of their two-phase or multicomponent mixtures for the purpose of reducing aerohydrodynamic loss under conditions of relative motion of surface and continuous medium, reducing the cavitation damage to surfaces, and enhancing the exchange processes on these surfaces.

Prior Art

Closest of all to the surfaces disclosed herein is the technical solution under RU Patent 2,020,304 of September 30, 1994 ; this solution relates to surfaces subjected to flow, which are interfaces between a moving continuous medium (gases, liquids, and their two-phase or multicomponent mixtures) and a solid energy-exchange wall which is initially flat, cylindrical, conical, or of any other profile. The shape of surface disclosed in the cited patent, which is a three-dimensional concave or convex relief, makes it possible to enhance the heat transfer between the boundary surface and main flow under conditions of the rate of increase in aerohydrodynamic loss being not faster than the rate of increase in the level of enhancement, owing to formation of vortex structures on such reliefs. The ranges of sizes of the disclosed reliefs are related to the characteristics of boundary layers of flow; in so doing, in accordance with the disclosed solution, the surface subjected to flow contains distributed thereon three-dimensional concave or convex relief elements with rounded transition regions which conjugate these elements with initially smooth surface; any cross section of relief elements, which is parallel to the plane in which three nearest of their peaks lie, has the form of a smooth closed line.
The disadvantage of this prior art patent is that it is unidirectional and largely limited to solving problems of heat transfer; it does not offer optimal solutions for increasing critical heat loads in boiling processes, for reducing the cavitation wear of the surfaces, for reducing the rate deposition of impurities from the flows of energy carriers on the surfaces subjected to flow, for reducing the aerohydrodynamic drag and resistance between friction surfaces in friction pairs etc.; it is further disadvantageous in that no correlations are given between the curvatures of regions of disclosed surface which are opposite in sign on the concave and convex parts of the surface relief, such correlations being absolutely necessary for the design and construction of these parts.
The technical result of realization of the surface for reduction of friction and aerohydrodynamic drag of surfaces includes:

the reduction of aerohydrodynamic drag of energy-exchange channels containing the disclosed curvilinear regions subjected to flows of continuous medium;
the reduction of aerohydrodynamic drag of bodies with surfaces of the same shapes subjected to flow and moving in the air, by water, and by land at a velocity sufficient for self-organization of secondary tornado-like jets; and
the reduction of friction between solid surfaces in gaseous or liquid media or in their mixtures (for example, in friction pairs placed in these media) owing to imparting curvilinear shapes to the friction surfaces to form between these surfaces a vortex boundary layer from the surrounding medium, which serves the function of vortex "bearings".

The technical result of realization of the surface for enhancement of heat and mass transfer includes:

the increase in the rate of heat and mass transfer between the flows of heat-transfer agents and energy-exchange surfaces which contain the disclosed curvilinear regions of double curvature, on which tornado-like jets are formed; the latter jets cause the acceleration of exchange processes in gases, liquids, and their mixtures, with the level of hydraulic loss lagging behind the degree of enhancement;
the increase in critical heat loads on energy-exchange surfaces cooled by liquid heat-transfer agents owing to imparting to these surfaces the disclosed curvilinear shapes which cause a variation of the kinetics of mass transfer in the process of phase transformation in liquid medium;
the prevention of cavitation damage to the surfaces subjected to flows of liquid owing to imparting to these surface the shapes involving curvilinear regions and to developing conditions for the generation on these surfaces of secondary tornado-like jets which suppress the growth on such surfaces of vapor-gas formations (bubbles) and evacuate the nuclei of such formations beyond the surface subjected to flow; and
the reduction of adsorption of contaminants and foreign matter and of growth of deposits from the moving medium on energy-exchange surfaces of the shapes disclosed above owing to the carry-over to the main flow of the impurities from these surfaces, for example, in the form of ashes or substances undergoing phase transformations, including the products of incomplete combustion of fuel, salt deposits, and other adsorbable substances including ice and snow.

Disclosure of the Invention

The technical result is attained owing to the fact that the surface for reduction of friction with gaseous and liquid media or their mixtures is characterized in that recesses of double curvature (dimples) are provided on a smooth surface with or without a protective layer, which are formed by second-order convex and concave surfaces conjugate on common tangents; in so doing, the conjugation of dimples with initially smooth surface is accomplished using convex shapes of surfaces forming slopes, for which the initially smooth surface is tangent at points of conjugation; the concave surface, which forms the bottom part of dimple, is made smooth or with a fairing, the ratios of depths h_c of dimples to dimensions L₁ of dimples along the direction of flow are found in the range $0.001 \leq h_{c} / L_{1} \leq 0.1,$

and the ratio of transverse dimension L₂ of dimple to longitudinal dimension L₁ of dimple is found in the range $0.25 \leq L_{2} / L_{1} < 1$

with the surface density f of dimples found in the range $0.05 \leq f \leq 0.5.$
The dimples may be made with the longitudinal and/or transverse dimensions varying along the flow.
The dimples may be made either mechanically, or electrochemically, or by applying a protective layer to the surface with subsequent polymerization of this layer, or by laser processing of the surface, or by employing combinations of these methods.
The slopes may be formed by a toroidal surface.
The slopes may be formed by a hyperbolic surface.
The slopes may be formed by an elliptic surface.
The surface with curvature radius R_(-) has toroidal slopes; on this surface, the radius r_sp of the concave spherical part of dimple is defined by the relation $r_{sp} = {(2 h_{sp} R_{(-)} - {h_{sp}}^{2})}^{0.5},$

where h_sp is the depth of concave spherical part of dimple; in so doing, the curvature radius of the convex part of dimple R₍₊₎ is related to its depth h_c and radius r_c by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
The surface is provided with a fairing which has the shape of a body of revolution with curvilinear base in the form of a part of the concave surface of dimple; in so doing, the projection of fairing onto any plane, in which the symmetry axis of these fairings and the tangent to the point of intersection of their symmetry axis with the concave surface of dimple lie, is defined by the relation ${r_{i}}^{2} h_{i} = const,$

where r_i is the radius of fairing and h_i is its height, which assume their values in the case of selected curvature radius R_(-) in the ranges $10^{- 5} \leq h_{i} / r_{i} \leq 1.$
The technical result is further attained owing to the fact that the surface for enhancement of convective heat and mass transfer with gaseous and liquid media or their mixtures is characterized in that recesses (dimples) are provided on a smooth surface, which are formed by second-order convex and concave surfaces conjugate on common tangents; in so doing, the conjugation of dimples with initially smooth surface is accomplished using convex surfaces forming slopes for which the initially smooth surface is tangent at points of conjugation; the concave surface, which forms the bottom part of dimple, is made smooth or with a fairing, the ratio of depth h_c of dimple to dimension L₁ of dimples along the direction of flow is found in the range $0.05 \leq h_{c} / L_{1} \leq 0.5,$

and the ratio of transverse dimension L₂ of dimple to its longitudinal dimension L₁ is found in the range $0.25 \leq L_{2} / L_{1} < 1,$

with the surface density f of dimples found in the range $0.1 \leq f \leq 0.8.$
The dimples may be made with the longitudinal and/or transverse dimensions varying along the flow.
The dimples may be made either mechanically, or electrochemically, or by laser processing of the surface, or by shaping and polymerization of a surface protective layer, or by employing various combinations of these methods.
The slopes may be formed by a toroidal surface.
The slopes may be formed by a hyperbolic surface.
The slopes may be formed by an elliptic surface.
The surface of dimples with curvature radius R_(-) has toroidal slopes and concave spherical part, the radius r_sp of which is defined by the relation $R_{sp} = {(2 h_{sp} R (-) - {h_{sp}}^{2})}^{0.5},$

where h_sp is the depth of concave spherical part of dimple; in so doing, the curvature radius R₍₊₎ of the convex part of dimple is related to the depth h_c and radius r_c of dimple by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
The surface may be provided with a fairing which has the shape of a body of revolution with curvilinear base in the form of a part of the concave surface of dimple; in so doing, the projection of fairing onto any plane, in which the symmetry axis of these fairings and the tangent to the point of intersection of their symmetry axis with the concave surface of dimple lie, is defined by the relation ${r_{i}}^{2} h_{i} = const,$

where r_i is the radius of fairing and h_i is its height, which assume their values in the case of selected curvature radius R_(-) in the ranges $10^{- 5} \leq h_{i} / r_{i} \leq 1.$
The dimples on the surface of a heat-transfer plate may be arranged in the staggered or in-line order, and the size of dimples and their depth may be increased or reduced in the direction of flow along the plate.
Dimples of smaller longitudinal and transverse dimensions and smaller depth may be located around the main dimples.
Projections reciprocal to recesses are provided on the other side of the surface.
Ribs oriented along the plate in the direction of flow are provided on the other side of the plate surface.
Dimples may be arranged on the other side of the plate symmetrically or asymmetrically with respect to the dimples on the main side of the plate.
The additional surface of the plate, which contains dimples, is located relative to the main surface with the formation of a heat-transfer channel; in so doing, the surfaces of the main and additional plates with dimples are facing each other and are located in parallel owing to spacer elements in the form of projections of spherical, conical, cylindrical, or other shapes.
The surface of a pipe, in which the dimples along the pipe and across the pipe are arranged in the staggered or in-line order.
The size of dimples and their depth are increased or reduced in the direction of flow along or across the pipe.
Projections with second-order surfaces are located on the inner surface of the pipe.
Dimples may be located on the outer surface of the pipe, and projections may be located on its inner surface.
Longitudinal ribs with dimples may be located on the inner surface of the pipe.
Transverse ribs with dimples may be located on the inner surface of the pipe.
A curved twisted tape with dimples may be located within the pipe.
Dimples may be located on the inner surface of the pipe symmetrically or asymmetrically with respect to the dimples on the outer surface.
The longitudinal and transverse dimensions and the depth of dimples made on the inner surface of the pipe are increased or reduced in the direction of flow.
Dimples are located on the inner surface of the pipe, and a curved twisted tape with dimples is placed within the pipe.
The inner surface of the pipe is made without dimples, and a twisted tape with dimples is placed within the pipe.

Brief Description of the Drawings

Figure 1 gives a fragment of a surface subjected to flow, which contains one dimple; a combination of such dimples forms the surface subjected to flow and realizes the disclosed method. It covers two options demonstrating the fact that geometrical parameters R₍₊₎, R_(-) do not define nether demension L, nor relationships h_c/L, L₂/L₁, nor form of the dimple - rounded, spherical or any other form.
Figure 2 gives the surface of a dimple with a fairing in the form of double dimple made on the surface using one-inside-the-other technique.
Figure 3 gives the surface of a dimple with fairings in the form of a plurality of small dimples on said surface.
Figure 4 gives the surface of a dimple with a fairing in the form of dimple.
Figure 5 gives the scheme of lines of flow of the medium involved in the formation of a secondary swirling structure in a dimple on the surface at low velocities of relative motion of the surface and medium.
Figure 6 shows the same process visualized by photography.
Figure 7 gives the visualization of the process of compression of vortex into a dimple and of suction into the vortex of the medium from the wall layer of flow past the surface with dimples.
Figure 8 gives the visualization of the process of turbulent flow past a relief of three-dimensional dimples.
Figure 9 gives the result of measurement of the thickness of boundary layer on a surface with dimple: 1 - smooth surface, 2 - surface with dimple; the maximum on curve 2 corresponds to the coordinates of the zone of efflux of tornado-like jet from the dimple.
Figure 10 is a three-dimensional pressure profile measured on the surface of a dimple. The lower pressure on the periphery corresponds to suction of the medium from the boundary layer into the dimple, and the zone of higher pressure (dome) in the central part of the dimple defines the pressure at the end face of self-organizing tornado-like jet, which provides for the efflux into the main flow of the mass of medium sucked-in by tornado-like vortex; the zone of location of pressure maximum in the dimple coincides with the zone of location of maximum of boundary layer thickness above the dimple in Fig. 9 and with the coordinates of location of fairing constructed from Görtler surface vortexes in Fig. 11, which is indicative of "extraction" of the tornado-like jet from the dimple by the main flow.
Figure 11 is a photograph of visualization of the process of the main flow of liquid (water) past a dimple of double curvature on the boundary surface, which demonstrates the variation of the structure of boundary layer due to formation of Görtler surface vortexes which have the form of "braids" indicated by arrows. The braids "interwoven" into the boundary layer replace a part of shear stresses in the Prandtl attachment layer by the stresses of rolling of the "braids" on the surface, which is a necessary condition for self-organization of tornado-like vortexes and the basis for the reduction of friction drag on the disclosed surfaces. Recorded in the photograph is a fairing constructed from Görtler surface vortexes by secondary swirling flow in a dimple of selected shape. It follows from the photograph that the trunk of tornado-like vortex is filled with "braids", i.e., Görtler vortexes, sucked off by the tornado-like vortex together with the mass of boundary layer, which provides for its high intensity when such surfaces are employed for heat and mass transfer.
Figure 12 gives the surface of a heat-transfer plate with longitudinal ribs.
Figure 13 shows the arrangement of plates with the formation of heat-transfer channel.
Figure 14 gives the surface of a heat-transfer pipe.
Figure 15 gives the surface of a pipe with longitudinal ribs.
Figure 16 gives the surface of a pipe with transverse ribs therein.
Figure 17 gives examples of view on top of the dimple.

Alternative Embodiments of the Invention

The claimed surfaces subjected to flow intended for reduction of friction drag (TLJS-DR) and for enhancement of heat and mass transfer (TLJS-HMT) provide necessary and sufficient conditions for the development of flows of new class, which offer the possibilities for raising the functional and technical-and-economic efficiency of actually the entire park of processes, apparatuses, and equipment involving flows of various media, and transportation units, which are employed in human research and practical activities.
The TLJS-DR (Tornado-Like Jet Surface-Drag Reduction) surfaces are used for:

reducing the aerohydrodynamic drag of various bodies in the state of relative motion with continuous medium, including aircraft, automobiles, trains, river-going, sea-going, and ocean-going vessels, yachts, and other means of transportation; and
reducing the loss of pressure in pressure channels employed for conveyance of gases, liquids, and/or their mixtures.

The TLJS-HMT (Tornado-Like Jet Surface-Heat and Mass Transfer) surfaces are used for:

raising the functional efficiency of energy-exchange processes and equipment involving flows of various media, including heat and mass transfer equipment;
reducing the cavitation wear of the surfaces of hydraulic turbomachines, propellers of marine propulsion units, hydraulic pumps, and other units subject to the effect of cavitation;
heating and cooling of magneto-thermal units for conversion of low-potential heat fluxes to mechanical and electrical energy; and
raising the functional efficiency of other energy-exchange processes and equipment involving flows of various media.

The spheres of application of the claimed invention define the diversity of its alternative embodiments. However, in formulating the concrete problem, common to all possible embodiments are:

the quantitative determination of the main functional characteristics of processes or equipment, which are to be improved;
the choice of shapes and sizes of reliefs, based on the results of analysis of parameters of the problems; and
the choice of technology of applying reliefs onto the surfaces.

Given by way of example is a relief subjected to a flow of continuous medium, the convex part of whose elements is a segment of a torus of circular cross section, and the concave part - a segment of any second-order surface, for example, spherical. The convex part of the curvilinear surface of the dimples, i.e., slopes, which is external with respect to the geometric center of the dimples, is characterized by the curvature radius R₍₊₎, and the other, or internal, part of this surface, for example, a segment of a sphere, which is located around the geometric center of curvilinear region, is characterized by the curvature radius R _(-); in so doing, the curvature and shape of the convex toroidal part is defined by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}),$

and the shape of the concave part is defined by the relation $R_{(-)} = ({r_{sp}}^{2} + {h_{sp}}^{2}) / 2 h_{sp};$

in so doing, the ratio of the curvature radii of the convex and concave parts of dimple is found from the respective relation of conditions (Q) (see below) in the range $10^{- 6} \leq R_{(+)} / R_{(-)} \leq 1;$

given the validity of conditions which define the limit of stability of the boundary layer of flow on this surface with respect to the emergence of Görtler surface vortexes, we have ${[δ_{2} (x) / R_{(-)}]}^{0.5} U_{\infty} δ_{2} (x) / v \geq 7; {[δ_{2} (x) / R_{(+)}]}^{0.5} U_{\infty} δ_{2} (x) / v \geq 7,$

where U _∞ is the velocity of flow impinging onto the curvilinear surface with curvature radii R₍₊₎ and R_(-), δ ₂(x) is the momentum thickness in the boundary layer formed by the flow of medium on the surface subjected to flow, and v is the velocity of impinging medium; in so doing, it is taken into account that the values of critical velocity U _∞ for isothermal flow are lower for the concave regions of dimples compared to the value of critical velocity for convex regions.
A curvilinear relief is applied onto the surface subjected to flow (Fig. 1) in the form of individual dimples 1 of double curvature, each dimple consisting of a concave part 2 of the inner curvilinear surface of dimple, which has a selected curvilinear shape in the form of a second-order surface without acute angles thereon including, for example, a spherical shape with curvature radius R_(-) or an elliptic shape with curvature radii R_min(-) and R_max(-) , conjugated with an initially smooth surface 3 by convex curvilinear slopes of toroidal shape of round, elliptic, parabolic, or hyperbolic cross sections with curvature radii for which the initially smooth surface is tangent at points of conjugation, and the surfaces of concave and convex shapes have common tangents at points of conjugation. The quantities R_min(-) , R_max(-) , R_min(+), and R_max(+) are determined, as is described above, from relations (Q): $10^{- 6} \leq R_{(+)} / R_{(-)} \leq 1; 10^{- 6} \leq R_{\max (+)} / R_{(-)} \leq 1; 10^{- 6} \leq R_{\min (+)} / R_{(-)};$
$10^{- 6} \leq R_{\min (+)} / R_{\min (-)} \leq 1; 10^{- 6} \leq R_{\max (+)} / R_{\min (-)} \leq 1;$
$10^{- 6} \leq R_{\max (+)} / R_{\max (-)} \leq 1; 10^{- 6} \leq R_{\min (+)} / R_{\max (-)} .$
The surface for reduction of friction with gaseous and liquid media or their mixtures is characterized in that recesses (dimples) 1 are provided on a smooth surface with a protective layer in the form of polymer material applied onto this surface or without such layer; said dimples are formed by second-order convex 4 and concave 2 surfaces conjugate on common tangents; in so doing, the conjugation of dimples with an initially smooth surface 3 is accomplished using convex surfaces forming slopes, for which the initially smooth surface is tangent at points of conjugation; the concave surface, which forms the bottom part of dimple, is made smooth or with a fairing 5, the ratio of depth h_c of dimple to dimension L₁ of dimple along the direction of flow is found in the range: $0.001 \leq h_{c} / L_{1} \leq 0.1,$

and the ratio of transverse dimension L₂ of dimple to longitudinal dimension L₁ of dimple is found in the range $0.25 \leq L_{2} / L_{1} < 1,$

with the surface density f of dimples being found in the range $0.1 \leq f \leq 0.5.$
The dimples on the surface may be made with their longitudinal and transverse dimensions varying along the flow.
The dimples may be made either mechanically, or electrochemically, or by shaping and polymerization of a protective layer, or by laser processing of the surface, or by employing combinations of these methods.
The slopes may be formed either by a toroidal hyperbolic surface, or by a toroidal parabolic surface, or by a toroidal elliptic surface, or by a toroidal spherical surface.
In the case where the slopes have the shape of a sharp edge, the slope cross section is a circle bounding the dimple and the concave spherical part of this dimple has the curvature 1/R_(-), the dimple radius r_sp is defined by the relation $r_{sp} = {(2 h_{sp} R_{(-)} - {h_{sp}}^{2})}^{0.5},$

where h_sp is the depth of concave spherical part of dimple.
In the case of toroidal spherical shape of the slopes, the cross section of which is a circle of radius R₍₊₎ and the central concave part has a spherical shape, the radius r_c is related to the dimple dimensions by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
The fairings on such surfaces have the shape of a body of revolution, the curvilinear base of which is provided by parts of the concave surface of dimple, and the projection of fairing onto any plane, in which the symmetry axis of the fairing and the tangent to the point of intersection of this axis with the concave surface of dimple lie, is defined by the relation: ${r_{i}}^{2} h_{i} = const,$

where r_i is the radius of fairing and h_i is its height, which assume their values in the case of selected curvature radius R_(-) in the ranges $10^{- 5} \leq h_{i} / r_{i} \leq 1.$
The fairings may be made in the form of dimples, double dimples, or dimples located on the surface of the main dimple (Figs. 2-4).
The surface for enhancement of convective heat and mass transfer with gaseous and liquid media or their mixtures is characterized in that recesses (dimples) 1 are provided on a smooth surface; said dimples are formed by second-order convex 4 and concave 2 surfaces conjugate on common tangents; in so doing, the conjugation of dimples with an initially smooth surface 3 is accomplished using convex surfaces forming slopes, for which the initially smooth surface is tangent at points of conjugation; the concave surface, which forms the bottom part of dimple, is made smooth or with a fairing 5, and the ratio of depth h_c of dimple to dimension L₁ of dimple along the direction of flow is found in the range: $0.1 \leq h_{c} / L_{1} \leq 0.5,$

and the ratio of transverse dimension of dimple to longitudinal dimension of dimple is found in the range $0.25 \leq L_{2} / L_{1} < 1,$

with the surface density f of dimples being found in the range $0.1 \leq f \leq 0.8.$
The dimples on the surface may be made with the longitudinal and/or transverse dimensions varying along the flow.
The dimples may be made either mechanically, or electrochemically, or by shaping and polymerization of a protective layer, or by laser processing of the surface, or by employing combinations of these methods.
The slopes may be formed either by a toroidal hyperbolic surface, or by a toroidal parabolic surface, or by a toroidal elliptic surface, or by a toroidal spherical surface.
The radius r_sp of the concave spherical part of curvilinear surface of the dimple has the curvature radius R_(-) and is defined by the relation $r_{sp} = {(2 h_{sp} R_{(-)} - {h_{sp}}^{2})}^{0.5},$

where h_sp is the depth of concave spherical part of dimple; in so doing, the curvature radius R₍₊₎ of the convex part of dimple is related to the depth h_c and radius r_c of dimple by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
In the case of toroidal spherical shape of the slopes, the cross section of which is a circle of radius R₍₊₎, and the central concave part has a spherical shape, the radius r_c is related to the dimple dimensions by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
The fairings 5 may have the shape of a body of revolution with the curvilinear base in the form of a part of the concave surface of dimple; in so doing, the projection of fairing onto any plane, in which the symmetry axis of the fairing and the tangent to the point of intersection of this symmetry axis with the concave surface of dimple lie, is defined by the relation ${r_{i}}^{2} h_{i} = const,$

where r_i is the radius of fairing and h_i is its height, which assume their values in the case of selected curvature radius R_(-) in the ranges $10^{- 5} \leq h_{i} / r_{i} \leq 1.$
The dimples 1 on the surface of heat-transfer plate 6 may be arranged in the staggered or in-line order.
The size of dimples and their depth may be increased or decreased in the direction of flow along the plate.
Dimples of smaller dimensions and smaller depth may be symmetrically located around dimples of larger size. Projections reciprocal to recesses may be located on the other side of plate 6. Ribs 7 oriented along the plate in the direction of flow may be located on the other side of the plate.
Dimples on the other side of the plate may be arranged symmetrically or asymmetrically with respect to the dimples on the main side.
The additional surface of plate 12 may be located relative to the main surface of plate 6 with the formation of a heat-transfer channel; in so doing, the surfaces of the main and additional plates with dimples are facing each other and are located in parallel owing to spacer elements 8 in the form of projections of spherical, conical, cylindrical, or other shapes.
The dimples on the surface of pipe 9 may be arranged in the staggered or in-line order along the pipe and across the pipe.
The size of dimples and their depth may be increase or reduced in the direction of flow or across the flow.
Spherical projections (not shown in the drawing), longitudinal ribs 10 or transverse ribs 11, or a twisted tape 13 with dimples may be located on the inner surface of pipe 9.
Dimples on the inner surface of the pipe may be located symmetrically or asymmetrically with respect to the dimples on the outer surface.
Dimples may be located on the inner surface of the pipe, the size and depth of which are increased or reduced in the direction of flow along the pipe.
Dimples may be located on the inner surface of the pipe, and a curved twisted tape with dimples is placed within the pipe.
The curvature radii of relief, the radii of traces of dimples on the surface being shaped, the depths of relief, and the parameters of fairing in the case where the latter is located in dimples are determined by the foregoing relations and ranges lettered (A), (B), (C), (D), (E), (F), (G), (H), (I), (J), (K), and (Q). For example, a channel or a body is selected, the functioning of which is associated with the relative motion of their surface and continuous medium. The basic aerohydrodynamic characteristics are determined of flows of gases, liquids, or their two-phase mixtures in the case of formation of disclosed flow with built-in tornado-like jets in channels, or analogous characteristics for a body moving in the above-said media. The ranges are established of possible variation of the thermal properties of working medium, the characteristic dimension is determined which defines the conditions of relative motion of continuous medium and surface, the Reynolds number (Re) is calculated and possible ranges of variation of its values are determined. The results of analysis are used for varying the values of Re for the purpose of fitting possible values of radii (dimensions) of the trace of dimples on the surface being shaped with a view to accommodating their integral-valued amounts along and across the flow and in the direction of motion of the body. In accordance with the problem to be solved by forming a flow with built-in tornado-like jets, the shape of dimples, their curvature radii, and the density of relief f are selected using the ranges of their variation lettered (A), (B), (C), (E), and (Q). In view of the fact that $f = {πr}_{c}^{2} / t_{1} t_{2},$

t₁ and t₂, i.e., the transverse and longitudinal spacings between dimples on an initially smooth surface, respectively, are fitted such that, given the optimal closeness to the preassigned value of f, the number of dimples along and across the surface being shaped would be integral-valued. After fitting the values of f, t₁ , and t₂, the radius of trace of dimple on the surface is determined from the relation $r_{c} = {({ft}_{1} t_{2} / π)}^{0.5} .$
The range of values of h_c/r_c , which is lettered (A) or (H) depending on the problem being solved, is used to calculate the depth h_c of the relief being constructed. In accordance with the selected curvature radii, density of dimples, sizes of traces, and depths of relief, the surface shaping technology is developed, the appropriate tools are prepared, and channels or supporting surfaces are manufactured.
The disclosed invention is based on the phenomenon discovered by the authors approximately 30 years ago, namely, the phenomenon of self-organization of quasi-potential tornado-like jets of gases, liquids, and/or their two-phase mixtures in recesses with second-order boundary surface and of rearrangement of the boundary layer on such surfaces under conditions of flows of said media past surfaces with recesses. This phenomenon was experimentally investigated, theoretically described, visualized, and tested under laboratory and full-scale conditions in a wide range of velocities and pressures, including the ranges of subsonic and supersonic velocities of air flows, and at critical and supercritical parameters of liquid heat-transfer agents.
The velocity and pressure fields in the discovered tornado-like jets are described by exact solutions of basic unsteady-state equations of hydrodynamics of viscous liquid (Navier-Stokes and continuity equations); the knowledge and experience, which were gained from the investigation and development of shaped surfaces, provided for finding the necessary and sufficient conditions for their formation, which is the subject of invention.
We gave the discovered jets and the process of their self-organization the names of Tornado-Like Jet (TLJ) and Tornado-Like Jet Self-Organization (TLJSOP), respectively; the surface on which the TLJSOP arises received the name of TLJ-Surface (TLJS), and the technologies utilizing such jets - Tornado-Like Jet Technologies (TLJT).
The results of numerous aerohydrodynamic and thermophysical experiments and of development and testing of prototypes and full-scale samples of relevant equipment and transportation units highly reliably indicate the reduction, owing to the use of TLJT, of friction drag on surfaces subjected to flow (see Figs. 8-10) and the enhancement of heat and mass transfer with hydraulic loss lagging behind the rate of this enhancement. In so doing, TLJs are formed in flows of gases, liquids, and their mixtures under conditions of practical importance of motion of continuous medium, which correspond to Reynolds number values of Re ≥ 5 10² calculated by geometric dimensions of the selected curvilinear relief, for example, by the diameter of symmetric dimples d_c or by their depth h_c, which define the characteristics of secondary flow in the dimple.
The visualization of the process of formation of TLJ flows, as is given in the photographs in Figs. 5, 6, 7, and 8, enables one to see a radially divergent tornado-like jet drawn out from a dimple and built into an incoming flow; the longitudinal dimension of said tornado-like jet significantly exceeds its transverse dimension, and its spatial orientation in the flow points to the interfacing of one end of the jet with the curvilinear surface of the dimple, from which the jet sucks off the mass of continuous medium and flows out, and to the interfacing of the other end of the jet either with the curvilinear surface of the neighboring dimple located downstream, into which the tornado-like jet injects the mass of continuous medium sucked off from the former dimple, or with the respective zone of the main flow, which receives this mass, where the pressures and velocities of swirling jet join with the pressure and velocity of the flow.
It has been experimentally proved that tornado-like jets (TLJ) are self-organized on TLJS in dimples of special relief described below under conditions of relative motion of formed boundary surface and viscous continuous medium.
In so doing, the flow of medium or motion of bodies in the medium are characterized by Reynolds number values of Re ≥ 500 calculated by the size of dimples along the flow or in the directions of motion of the body; the selected shapes and dimensions of curvature of the convex and concave parts of relief initiate the impact, which is made on the flow by the field of forces absent in the case of flow past smooth surfaces, and the restructuring of the boundary layer of flow from shear layer in its initially smooth regions to three-dimensional vortex boundary layer on curvilinear surface consisting of surface vortexes such as Görtler vortexes or their ensembles.
The dimensionless relation (K), which involves the radius vector of surface curvature R₍₊₎ or R_(-) (hereinafter referred to as radius), the viscosity of the medium v, the velocity vector of unperturbed flow of continuous medium U _∞, and the momentum thickness δ ₂(x) in the boundary layer of flow, is the criterion of stability with respect to emergence in the boundary layer of surface vortexes such as Görtler vortexes and points to the possibility of controlling the vortex boundary layer with the aid of the parameters of flow of continuous medium and the curvature radius of the surface subjected to flow. In a boundary layer of this type, which we refer to as Finely Divided Moving Boundary Layer (FDMBL), the pattern of friction stresses on curvilinear surfaces varies from shear stress to that defined by rolling friction. This property is one of the main advantages of the disclosed TLJS, the necessary condition for self-organization of TLJ, and one of the main reasons for reduction of friction drag in the case of flow past concave curvilinear reliefs. The presence of three-dimensional vortex boundary layer (FDMBL) provides conditions for conjugation of TLJ with the concave surface of dimples without resulting in dissipation of energy in rotational flow, which is known to destroy vortex systems formed on smooth surfaces where the Prandtl "attachment" conditions are valid, which require that the velocity of flow be equated to the velocity of surface subjected to flow, and no FDMBL is present. In the case of three-dimensional vortex flow, this condition is met through the intermediary of surface vortexes arising at the ends of the tornado-like jet being formed which "straddles" these surface structures (see Fig. 11). Surface FDMBL vortexes move on the curvilinear relief like a roller or a wheel and exhibit at points of contact with the surface or on the line of conjugation therewith a velocity which, as was stated above, is equal to the surface velocity; in the case of TLJS of stationary channels or plates the velocity is equal to zero, and in the case of TLJS moving at preassigned velocity U _∞ - equal to this latter velocity, which corresponds to the "attachment" conditions. The remaining points of the surface of these vortexes move at other-than-zero velocities which correspond to the velocity of tornado-like swirling flow generating these vortexes and joined with them (see the photograph in Fig. 11). In the case of TLJ, the ensemble of vortexes which make up the FDMBL is formed by the swirling flow proper at the ends of the jet on curvilinear surface and is, figuratively speaking, utilized by tornado-like vortex for rolling on the vortexes of said ensemble over the surface of dimple. This explains the mechanism of reduction of dissipation of energy in self-organizing tornado-like jets. In addition to this process, the boundary layer on curvilinear surface is structured into large formations consisting of vortexes in the form of macroscopic "braids" visualized in the photograph of Fig. 11. As was observed above, the self-organizing vortex jets suck off the boundary layer consisting of such "braids" from the dimple surface and from the smooth part of relief surrounding the dimple and transfer the sucked-off mass to the main flow. Each one of such "braids" significantly exceeds in mass and volume the turbulent moles which define the efficiency of the mechanisms of heat and mass transfer in turbulent flows; this explains the advantages of TLJS compared to other shapes of reliefs which are traditionally employed for enhancement of heat and mass transfer.
The three-dimensional relief of dimples and the TLJs which are self-organized therein transform the shaped surface subjected to flow into:

a system of sink of the working continuous medium from the boundary layer of flow into dimples, with the sink provided by the acceleration of flow on the convex slopes of relief, which causes the decrease in static pressure in this zone of jet formation, and the rate of sink is defined by the selected shape and curvatures of the boundary surface; and
a system of sources of tornado-like jets, which flow out and suck from the dimples the surface vortexes and vorticity from the FDMBL formed on the region of curvilinear surface, and transfer to the main flow (as was stated above) masses of continuous medium flowing down into the dimples in the form of large formations, i.e., macroscopic "braids" visualized in the photograph of Fig. 11.

As was observed above, the mechanisms of these processes cause the reduction of friction stress on shaped surfaces and enhance the processes of heat and mass transfer thereon; in so doing, the regularities of these processes on surfaces with convexo-concave reliefs significantly differ from the regularities describing the processes of friction and exchange under conditions of flow of conventionally smooth and rough surfaces which "generate" turbulence in the wall layers of flow, for example, owing to natural or artificial roughness.
The tornado-like jets are formed, as was observed above, in dimples on the "surface-moving medium" interface under the effect of forces caused by the shapes of selected relief, including:

braking forces arising under the effect of dynamic pressure of flow on downstream slopes of dimples, which cause (to the extent of the square of velocity of incoming flow U _in ²) an elastic reflection of flow from the concave slopes and the emergence in the concave part of dimples of a return flow moving in the bottom part of dimple at a velocity differing little from U_in . (U is the velocity of flow flowing into a dimple, which is measured at the boundary of conjugation of the dimple with initially smooth surface at a point 0.1 mm above said surface and in the return flow within the dimple at a point lying on the central meridian on downstream slopes.) On the slopes which meet the main flow coming to the dimples, said flow is joined with the return flow to generate within the dimples a vortex structure with circulation of the medium Γ ₀ ≈ 2πRUϕ; in so doing, the azimuthal velocity of such circulation is U _ϕ ≈ U_in ≈ kU _∞, where k < 1 reflects the features of the velocity profile of flow above the initially smooth and curvilinear surfaces subjected to flow. Because of the small difference in the velocities of the incoming flow and of the return flow it generates (according to experimental data, the difference in k in the return and incoming flows is ±4%, i.e., not more than 8%), the vortex jet formed in the dimple is acted upon by a pair of forces which cause its additional swirling and self-similarly turn the tornado-like vortex in the dimple through angle β ∼ 45° relative to the direction of main flow;
mass inertial forces which are directed along the curvature radii of dimples towards their center and form on convex slopes of relief in the moving medium a two-dimensional velocity field containing radial U_r and azimuthal U _ϕ (with respect to the central axis of dimple) components of velocity. In so doing, the motion of the medium on curvilinear convex slopes causes a decrease in the probability of separation of flow and, as was observed above, the formation of FDMBL three-dimensional vortex boundary layer on said slopes. It is known that the characteristics of surface vortexes arising in such a layer on curvilinear surface depend on the velocity U_in, on the state of the boundary layer (laminar, turbulent), on the momentum thickness in said layer, and on the curvature radii of convexo-concave relief R₍₊₎ and R_(-), respectively. As was stated above, such a boundary layer causes a decrease in the level of dissipation of energy in the flow, thereby reducing the probability of the separation of flow from the convex surface of slopes, and imparts high dynamism to the flow in the dimple owing to the transformation of the shear boundary layer into three-dimensional vortex one with which the swirling flow being formed is joined. Further forming of tornado-like jets occurs on concave slopes of dimples likewise under the effect of mass inertial forces directed in this zone from the surface to the main flow along the curvature radii towards its center. The choice of geometric shape of convexo-concave regions of boundary surface and of corresponding curvature radii of the relief of dimples defines the impact made on the swirling jet being formed by the inertial forces which impart the longitudinal component of velocity U_z to this secondary flow. This component arises owing to the impact made on the flow flowing down into dimples at velocity U = (U _ϕ ² + U_r ²)^0.5 by accelerations a = U²/R which are directed along the curvature radii R away from the concave surface to the flow, impart additional radial convergence to the jet, and cause an increase, with decreasing jet radius r_i, in the azimuthal velocity of secondary flow U _ϕ and in the longitudinal pressure gradient defined by this latter velocity and by the longitudinal velocity U_z. This mechanism provides in the TLJ a pressure profile required for transfer and injection of the mass of medium sucked off by tornado-like jets onto the surface downstream of the flow or into the main flow; and - forces of the type of Magnus force, which arise because of interaction between the main flow to dimples and the tornado-like vortex; the circulation Γ ₀ in the dimple generates the lifting force F dependent on the velocity of incoming flow U_in and on the effective dimension of vortex structure across the flow L, $F \approx {ρU}_{in} Γ_{0} L,$

and directed away from the concave part of curvilinear surface into the flow on a normal to the plane which accommodates the velocity vector of the main flow and the vector defined by the direction of circulation in vortex structures, where U_in and Γ ₀ are determined above, and ρ is the density of continuous medium in the vortex.

These forces, along with the mass inertial forces acting on the concave part of relief, provide for the "incorporation" of tornado-like vortexes into the incoming flow and draw out one of the ends of the vortex and its "trunk" into the main flow.
As was indicated above, the values of the above-said forces and the directions of their action on the structure of flow being formed are controlled by the preassigned shapes of dimples of double curvature, by the density of distribution of dimples with respect to the area of initially smooth surface, and by the modes of motion of flow of medium. For example, in the process of flow past dimples whose shape exhibits central axial symmetry and is defined by the curvature radii R₍₊₎ and R_(-), the flow of continuous medium, which is characterized by Reynolds number values of Re ≥ 500 calculated by the diameter d_c = 2r of the trace of dimple on the surface being shaped and moves above convex slopes of dimples at velocity U_in, is acted upon by mass inertial forces which urge the flow against convex slopes in accordance with the sign of curvature R₍₊₎ . These forces cause a decrease in the probability of separation of flow from the curvilinear surface of dimple and impart to the flow coming into the dimple a higher or lower (depending on the selected curvature radii) radial convergence and azimuthal velocity U _ϕ . As was observed above, such motion causes the formation of FDMBL between the curvilinear surface and tornado-like flow; in so doing, such a boundary layer accompanies the flow being formed on the concave part of dimple as well. Surface vortexes such as Görtler vortexes impart to the swirling jet in the dimple the dynamism relative to the curvilinear surface, stabilize the efflux of said jet into the main flow, and make up a fairing formed by the structure of swirling tornado-like flow and curvilinear shape of dimple (see photograph in Fig. 11).
In accordance with the foregoing, the "continuous medium-surface subjected to flow" interface is imparted a curvilinear shape in the form of regularly alternating dimples of double curvature which develop force action to provide in the flow the self-organization in these zones of FDBML and secondary swirling jets directed away from said surface zone of flow into the main flow. In so doing, the arising forces cause an independent force action on the moving medium, which results in the curvature of shapes of lines of flow and, as a consequence, in the self-organization of tornado-like jets.
As was found in theoretical and experimental investigations, the dimple relief made on surfaces subjected to flow causes the variation of the structure of boundary layer of flow on the boundary surfaces and gives rise to the self-organization of tornado-like jets which suck off a part of continuous medium concentrated in the zone of location of dimples on the surface subjected to flow, thereby affecting the level of dissipation of energy of the flow and intensifying the exchange processes between swirling jet and surface. The choice of curvature radii and dimensions of curvilinear regions of the surface subjected to flow is based on the results of theoretical calculations supported by experimental results, the technology of producing dimples on the surface is developed, and provision is made for the validity of the conditions of self-organization of secondary tornado-like jets built in the flow past the surface. The flow of working continuous medium is directed to the surface shaped with dimples, or a relief of desired shape is made on the surface of bodies moving in a medium of gases, liquids, or their two-phase mixtures to attain the reduction of friction drag on shaped surfaces and enhance the processes of heat and mass transfer between the energy-exchange surface and flows of continuous medium.

Industrial Use of Invention

The disclosed surfaces are employed for reducing aerohydrodynamic drag of pressure channels and various bodies in the state of relative motion with continuous medium and/or for raising the functional efficiency of energy-exchange processes and equipment, including heat-transfer and mass-transfer processes, as well as in all other spheres where, compared to the conventional methods of heat and mass transfer, it is necessary to intensify exchange processes under conditions of restricted rise or reduction of hydraulic drag and reduce the cavitation wear of the surfaces of hydraulic turbines, hydraulic pumps, propellers of marine propulsion units, and other units operating in liquid medium. In particular, the present invention finds application in various means of transportation including aircraft, automobiles, high-speed railroad trains, sea-going and river-going vessels; in gas-turbine units with cooled blades, in nuclear-power uranium assemblies, in steam generators, in various heat-exchangers, in recuperators and other energy-exchange apparatuses and devices; in household appliances such as air conditioners, fans, heating equipment and in kitchen appliances such as tea kettles, pots, fiying pans etc.; in sports goods of various kinds including sports cars, motorcycles, bicycles, sportswear for motor sports, bicycle racing, swimming, running etc.; in various biochemical processes involving the motion of gaseous or liquid reagents, as well as in developing apparatuses and prostheses for blood circulation systems, in medical devices for artificial blood supply and for purifying blood from harmful impurities, in artificial respiration equipment, and so on; in other words, in technologies involving flows of various media, in which the process efficiency is defined by the motion of gases, liquids and their two-phase and/or multicomponent mixtures.
The above-said spheres of utilization of the disclosed invention define the diversity of its embodiments. However, common to all possible embodiments in formulating the concrete problem are the determination of the basis functional characteristics of processes or equipment to be improved and the choice of shapes, sizes, and the technology of making of reliefs on the surface.

Claims

A surface for reduction of friction with gaseous and liquid media or with their mixtures, characterized in that recesses (dimples) are provided on a smooth surface with or without a protective layer, which are formed by second-order convex and concave surfaces conjugate on common tangents; in so doing, the mating of a dimple with initially smooth surface is accomplished using convex surfaces that form slopes, for which the initially smooth surface is tangent at points of mating; the concave surface, which forms the bottom part of dimple, is made smooth or with a fairing, the ratio of depth h_c of dimple to dimension L₁ of dimple along the direction of flow is in the range 0.001 ≤ h_c /L₁ ≤ 0.1, and the ratio of transverse dimension L₂ of dimple to longitudinal dimension L₁ of dimple is in the range 0.25 ≤ L₂/L₁ < 1, with the surface density f of dimples being in the range 0.05 ≤ f ≤ 0.5.
The surface as claimed in the Claim 1, on which the dimples are made with the longitudinal and/or transverse dimensions varying along the flow and are made either mechanically, or electrochemically, or by shaping and polymerization of the protective layer, or by laser processing of the surface; in so doing, the slopes of the dimples are formed by a toroidal spherical surface, or by a hyperbolic surface, or by an elliptic surface.
The surface as claimed in the Claim 1, on which the radius r_sp of the concave spherical part of dimple, which has the curvature radius R_(-), is defined by the relation $r_{sp} = {(2 h_{sp} R_{(-)} - {h_{sp}}^{2})}^{0.5},$

where h_sp is the depth of concave spherical part of dimple; in so doing, the curvature radius of the convex part of dimple is related to the dimple depth h_c and radius r_c by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
The surface as claimed in the Claim 1, on which the dimples have fairings in the form of bodies of revolution with a curvilinear base lying on the concave surface of dimple, and the projection of fairing onto any plane, in which the symmetry axis of the fairing and the tangent to the point of intersection of said symmetry axis with the concave surface of dimple lie, is defined by the relation ${r_{i}}^{2} h_{i} = const,$

where r_i is the radius of fairing and h_i is its height, which assume their values in the case of selected curvature radius R_(-), in the ranges $10^{- 5} \leq h_{i} / r_{i} \leq 1.$
A surface for enhancement of convective heat and mass transfer with gaseous and liquid media or their mixtures, characterized in that recesses (dimples) are provided on a smooth surface, which are formed by second-order convex and concave surfaces mating on common tangents; in so doing, the mating of dimples with initially smooth surface is accomplished using convex surfaces that form slopes for which the initially smooth surface is tangent at points of mating; the concave surface, which forms the bottom part of dimple, is made smooth or with a fairing, the ratio of depth h_c of dimple to dimension L₁ of dimples along the direction of flow is found in the range 0.05 ≤ h_c/L₁ ≤ 0.5, and the ratio of transverse dimension L₂ of dimple to longitudinal dimension L₁ of dimple is in the range 0.25 ≤ L₂/L₁ < 1, with the surface density f of dimples being in the range 0.1 ≤ f ≤ 0.8.
The surface as claimed in the Claim 5, on which the dimples are made with the longitudinal and/or transverse dimensions varying along the flow; in so doing, the dimples are made either mechanically, or electrochemically, or by laser processing of the surface, or by shaping and polymerization of the surface protective layer, or by employing various combinations of said methods, with the slopes being formed by a toroidal surface, or by a hyperbolic surface, or by an elliptic surface.
The surface as claimed in the Claim 5, on which the radius r_sp of the concave spherical part of dimple, which has the curvature radius R_(-), is defined by the relation $r_{sp} = {(2 h_{sp} R_{(-)} - {h_{sp}}^{2})}^{0.5},$

where h_sp is the depth of concave spherical part of dimple; in so doing, the curvature radius R₍₊₎ of the convex part of dimple is related to the dimple depth h_c and radius r_c by the relation $R_{(+)} = [{(r_{c} - r_{sp})}^{2} + {(h_{c} - h_{sp})}^{2}] / 2 (h_{c} - h_{sp}) .$
The surface as claimed in the Claim 5, on which the fairings have the shape of bodies of revolution which have a curvilinear base in the form of a part of the concave surface of dimple and the projection of fairing onto any plane in which the symmetry axis of said fairings and the tangent to the point of intersection of their symmetry axis with the concave surface of dimple lie; in so doing, the shape of said projection is defined by the relation ${r_{i}}^{2} h_{i} = const,$

where r_i is the radius of fairing and h_i is its height, which assume their values in the case of selected curvature radius R_(-) in the ranges $10^{- 5} \leq h_{i} / r_{i} \leq 1.$
The surface of heat-transfer plate as claimed in Claim 5, on which the dimples are arranged in the staggered or in-line order, and the size of dimples and their depth are increased or reduced in the direction of flow along the plate.
The surface as claimed in Claim 9, on which dimples of smaller longitudinal and transverse dimensions and smaller depth are located around the dimples.
The surface as claimed in Claim 9, wherein projections reciprocal to recesses are provided on the other side of said surface, or ribs oriented along the plate in the direction of flow are provided on the other side of said surface, or dimples are arranged on the other side symmetrically or asymmetrically with respect to the dimples on the main side.
The surface as claimed in Claim 9, which contains an additional surface of the plate with dimples, which is located relative to the main surface with the formation of a heat-transfer channel; in so doing, the surfaces of the plates with dimples are facing each other and are arranged in parallel owing to spacer elements in the form of projections of hemispherical, conical, cylindrical, or other shapes.
The surface of pipe as claimed in Claim 5, on which the dimples along the pipe and across the pipe are arranged in the staggered or in-line order, and the size of dimples and their depth are increased or reduced in the direction of flow along or across the pipe.
The surface as claimed in Claim 13, on which projections with second-order surfaces are located on the inner surface of the pipe; or dimples are located on the inner surface of the pipe, the size and depth of which are increased or reduced in the direction of flow along or across the pipe; or longitudinal ribs with dimples on their surface are located on the inner surface of the pipe; or transverse ribs with dimples are located on the inner surface of the pipe; or a curved twisted tape with dimples is located within the pipe; or dimples are located on the inner surface of the pipe symmetrically or asymmetrically with respect to the dimples on the outer surface.