EP1317648B1 - Heat exchanger and heating system equipped therewith - Google Patents

Abstract

The invention relates to a heat exchanger (1) with a number of first ducts (2) for a first medium and a number of second ducts (4) for a second medium in heat-exchanging contact therewith via partition walls (5). The dimensions of the first ducts (2) in the flow direction of the first medium and perpendicularly thereof are herein chosen such that boundary layers (11) formed along the walls of the duct and developing in the flow direction meet each other in each case close to the downstream ends of the ducts (2). A very compact heat exchanger (1) is thus obtained.

Description

• The invention relates to a method of manufacturing a heat exchanger that comprises at least one first duct for a first medium and at least one second duct for a second medium in heat-exchanging contact therewith via at least one wall, said method including choosing the dimensions of at least the first duct in the flow direction of the first medium and perpendicularly thereof. Such a method is generally used for manufacturing.
• In the past, many efforts have been made to optimize the design of heat exchangers, the aim being to provide maximum heat exchanging capacity in a compact heat exchanger.
• An example of such an earlier attempt is to be found in DE-A-22 54 851, which discloses a stepped heat exchanger design. The steps in the heat exchanger ducts are intended to periodically break down the boundary layer developing on the heat-exchanging wall between two ducts, in order to optimize heat transfer through that wall. Alternatively, this prior art document proposes to use ribs or other transverse obstacles for breaking down the boundary layer.
• US-A-5 121 792 proposes a heat exchanger design having narrow ducts that converge in the inflow direction and diverge in the outflow direction. These ducts are intended at some point to become narrower than the thickness of the boundary layer developing therein.
• Yet another heat exchanger design is disclosed in SU-A-992 993. This prior art document shows a concentric heat exchanger comprising an inner tube consisting of spring connected parts having stepped diameters and an outer tube also consisting of parts having stepped diameters, the outer tube parts however being fixed. This stepped arrangement would serve to breakdown the boundary layer, while the spring induced movement of the inner tube parts would create turbulence.
• The invention has for its object to provide a manufacturing method that will yield a heat exchanger with an increased efficiency. An improved heat exchanger as manufactured using this method can take a more compact form compared to known heat exchangers as described above and still have the same heat transfer capacity.
• According to the invention this is achieved in a method of manufacturing a heat exchanger as described above in that the dimensions of the first duct are chosen such as to satisfy the relation: $$L=\frac{0.25D^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}\ast \frac{V}{\nu }$$

  

  
  in which:
• L = length of the duct (in flow direction),
• D = (hydraulic) diameter of the duct (perpendicularly of flow direction),
• k = constant depending on the velocity curve in the boundary layer
• V = intended flow velocity of the first medium to be used, and
• ν = kinematic viscosity of the first medium to be used,
such that boundary layers formed along the opposite walls of the duct and developing in the flow direction meet each other at a downstream end of the duct.
• By selecting the length of the duct such that the boundary layers meet each other precisely at the end thereof and a fully laminar flow is thus established, optimum use is made of the transport of the medium transversely of the flow direction during the development of the boundary layer. This medium transport transversely of the main direction of the flow results in a very good heat exchange, whereby the efficiency of the heat exchanger corresponds to that of an exchanger with turbulent flow, even when the exchanger is used with media which in principle have a fully laminar flow pattern.
• The method of manufacturing the heat exchanger advantageously includes placing a plurality of first ducts in series as seen in the flow direction, and arranging means in each case between successive ducts for enhancing the heat transfer inside the first medium. The transfer-enhancing means can herein comprise a space with an enlarged cross-section compared to the first ducts.
• When as first medium a medium having a relatively high kinematic viscosity is chosen, the length of the first ducts can be kept relatively short.
• The invention also relates to a method of manufacturing a heating system incorporating a heat exchanger manufactured by the above described method, as well as a method of using such a heat exchanger.
• The invention will now be elucidated with reference to the drawing, in which:
• Fig. 1 shows a partly broken-away perspective view of a heat exchanger according to the invention,
• Fig. 2 is a schematic cross-sectional view of a duct showing the development of the boundary layers and the associated velocity curves, and
• Fig. 3 shows a diagram in which, for a number of different media, the optimum length of an exchanger duct is plotted as a function of the flow velocity.
• A heat exchanger 1 (fig. 1) according to the invention comprises a number of first ducts 2 for a first medium, for instance flue gas from a burner 7, and a number of second ducts 4 for a second medium which is in heat-exchanging contact with the first medium, for instance water intended for radiators of a heating system (not shown here). Ducts 2 and 4 are physically separated from each other by walls 5 which are readily permeable to heat and are for instance manufactured from a metal.
• The first ducts 2 are connected on one side to a space 6 in which a burner 7 Is arranged, and on the other side to an outlet 8. Ducts 4 are included in a closed circuit of the heating system and connected to an inlet 9 and an outlet 10.
• According to the invention the dimensions L, D of first ducts 2 in the flow direction of the medium (arrow F) and perpendicularly thereof are chosen such that the boundary layers 11 formed along walls 5 of these ducts 2 just make mutual contact at the end of each duct 2. Optimum benefit is in this way gained from the transport of the medium transversely of its main flow direction during the creation and development of boundary layers 11. Means are herein preferably present at the end of each duct 2 for enhancing the heat transfer inside the medium, for instance in the form of a part 12 with enlarged cross-section. In the shown embodiment this part 12 forms a bend between two successive ducts 2 as seen in the flow direction. Owing to the enlarged cross-section of part 12 and the flow phenomena resulting therefrom, additional movement components are introduced into the flow which enhance the heat transfer.
• As seen in flow direction F the boundary layers 11 (fig. 2) thus develop along walls 5 of each duct 2 from the inflow side, whereby the effective surface area of each duct 2 becomes increasingly smaller. The medium flowing therethrough is hereby urged toward the middle of duct 2, and this forced transport transversely of flow direction F causes a heat transport in the same direction, whereby the efficiency of heat exchanger 1 is greatly increased. The velocity curve in transverse direction of duct 2 herein changes from a completely uniform velocity over the whole surface into a parabolic velocity distribution with a low speed (practically zero) along walls 5 and a higher speed in the middle of duct 2.
• The thickness δ of each boundary layer 11 at any point of duct 2 is related to the distance x from the inflow side of duct 2, and can be expressed as: $$\mathrm{\delta }=\mathrm{k}\ast \mathrm{x}/\sqrt{{\mathrm{R}}_{\mathrm{x}}},$$

  

  
  in which k is a constant which is related to the velocity distribution inside the boundary layer and R_x is the Reynolds number relating to the distance x. This Reynolds number is herein defined as: $${\mathrm{R}}_{\mathrm{x}}=\mathrm{\rho }\ast \mathrm{V}\ast \mathrm{x}/\mathrm{\mu },$$

  

  
  wherein ρ and µ represent the density and the dynamic viscosity of the medium, and V represents the flow velocity thereof.
• The boundary layers 11 along two opposite walls 5 of each duct 2 make mutual contact when the thickness δ of each boundary layer 11 amounts to half the distance D between these walls 5. For the distance x from the inflow side where this occurs there applies: $$\mathrm{x}=0.5\ast \mathrm{D}\ast \sqrt{{\mathrm{R}}_{\mathrm{x}}}/\mathrm{k},$$

  

  
  or, by substituting the value of the Reynolds number: $$x=\frac{0.25D^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}\ast \frac{V}{\nu }$$

  

  
  in which ν represents the kinematic velocity of the medium, defined as ν = µ / ρ.
• This distance x therefore forms in principle the optimal length of duct 2 with an eye to the heat transfer inside one of the media themselves. In addition however, the length of duct 2 must also be sufficient to enable the intended heat transfer between the two media flowing through the exchanger. The choice of the length of duct 2 will therefore often have to be slightly larger in practice than would follow from the above relation. This length may not however become so great as to result in the danger of transition of the flow from laminar to turbulent, since the flow losses in heat exchanger 1 would thereby increase greatly. When a plurality of ducts 2 are placed in series as seen in the flow direction, with bends 12 therebetween as shown here, an optimal ratio must be found between the length of ducts 2 and the number of bends 12, since these bends will of course also entail flow losses.
• The duct length wherein the boundary layers 11 just make mutual contact, expressed as multiple of the hydraulic cross-section D_hydr (flow surface area divided by circumference) of duct 2, is shown (fig. 3) as a function of the undisturbed flow velocity of the medium for a number of different media. As expected, the progression of the relevant curves is found to depend on the nature of the medium, wherein the kinematic viscosity determines the gradient of the curves. For media with a relatively high kinematic viscosity, particularly gases, such as flue gases and thermal oil, a relatively short length of the ducts 2 is found to be ideal over a wide range of flow velocities.
• Although the invention is elucidated above with reference to one embodiment, it will be apparent that it is not limited thereto. The structure of the heat exchanger could thus be other than shown here, with a differing number of ducts which could also take another form. The means connected between the ducts for enhancing the heat transfer could also take a form differing from the bends shown here. The scope of the invention is therefore defined solely by the appended claims.

Claims (6)

1. Method of manufacturing a heat exchanger (1) that comprises at least one first duct (2) for a first medium and at least one second duct (4) for a second medium in heat-exchanging contact therewith via at least one wall (5), said method including choosing the dimensions (L, D) of at least the first duct (2) in the flow direction (F) of the first medium and perpendicularly thereof,
   characterized in that the dimensions of the first duct (2) are chosen such as to satisfy the relation: $$L=\frac{{0.25}^2{D}^2}{k^2}\ast \frac{V}{\nu }$$

   

   
   in which:

   L = length of the duct (in flow direction),

   D = (hydraulic) diameter of the duct (perpendicularly of flow direction),

   k = constant depending on the velocity curve in the boundary layer,

   V = intended flow velocity of the first medium to be used, and

   ν = kinematic viscosity of the first medium to be used,

   such that boundary layers (11) formed along the opposite walls (5) of the duct (2) and developing in the flow direction (F) meet each other at a downstream end of the duct (2).
2. Method of manufacturing a heat exchanger as claimed in claim 1, characterized in that a plurality of first ducts (2) are placed in series as seen in the flow direction (F), and in that means are in each case arranged between successive ducts (2) for enhancing the heat transfer inside the first medium.
3. Method of manufacturing a heat exchanger as claimed in claim 2, characterized in that the transfer-enhancing means comprise a space (12) with an enlarged cross-section compared to the first ducts (2).
4. Method of manufacturing a heat exchanger as claimed in any of the foregoing claims, characterized in that as first medium a medium having a relatively high kinematic viscosity (ν) is chosen.
5. Method of manufacturing a heating system, comprising providing at least one heat source (7), providing at least one heating element and arranging a heat exchanger (1) manufactured by the method as claimed in any of the foregoing claims therebetween.
6. Method of using a heat exchanger (1) for bringing two media in heat-exchanging contact, the heat exchanger (1) comprising at least one first duct (2) for a first medium, at least one second duct (4) for a second medium an at least one heat-permeable wall (5) separating the first and second ducts (2,4), at least the first duct (2) having a dimension (D) perpendicularly thereof, the method being characterized in that the first medium and its flow velocity (V) are chosen such as to satisfy the relation: $$\frac{V}{\nu }=\frac{k^2\ast L}{0.25D^2}$$

   

   
   in which:

   L = length of the duct (in flow direction),

   D = (hydraulic) diameter of the duct (perpendicularly of flow direction),

   k = constant depending on the velocity curve in the boundary layer,

   V = flow velocity of the first medium, and

   ν = kinematic viscosity of the first medium,

   such that boundary layers (11) formed along the opposite walls (5) of the duct (2) and developing in the flow direction (F) meet each other at a downstream end of the duct (2).

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