WO1996012151A1

WO1996012151A1 - Heat transfer tube

Info

Publication number: WO1996012151A1
Application number: PCT/GB1995/002443
Authority: WO
Inventors: Brian Edward Launder; Timothy John Craft
Original assignee: The University Of Manchester Institute Of Science And Technology
Priority date: 1994-10-18
Filing date: 1995-10-17
Publication date: 1996-04-25
Also published as: GB9420946D0; AU3658795A

Abstract

A heat transfer tube (1) for effecting heat transfer between a wall (2) of the tube (1) and a fluid flowing through said tube (1) has an internal spirally fluted surface (3). Each flute (4) is at a common helix angle relative to the axis of the tube and each is asymmetrical in cross section. The asymmetry of the flutes (4) provides for high heat transfer coefficients with a reduction in the friction factor. Thus high performance heat exchange is possible with a reduced loss of pressure in the fluid as it flows through the tube (1).

Description

HEAT TRANSFER TUBE

The present invention relates to a heat transfer tube and more particularly to such a tube for use in a heat exchanger

Tubular heat exchangers have widespread applications in many industries. In an effort to minimise the costs of such exchangers it is desirable to minimise the amount of tubing required per heat exchanger and to improve the efficiency of heat transfer surfaces.

It is generally recognised that roughening the surface of a heat transfer tube can greatly increase the heat transfer coefficient but that there is an attendant increase in wall friction and therefore pressure loss in fluid passing down the tube

US Patent Number 4305460 describes a spirally fluted heat transfer tube in which a significant improvement in heat transfer coefficient over that for pπor heat tubes was achieved without any increase in fπctional flow loss (pressure drop). The heat transfer coefficient increased by a factor of 1.6 when compared to a smooth tube. In this tube the flute contour has a symmetrical sine wave profile and the helix angle of the flute relative to a longitudinal axis of the tube is in the range 25 to 50 degrees.

It is an object of the present invention to provide a heat transfer tube with an improved heat transfer coefficient with a decrease in or without an increase in the fnctional coefficient or pressure drop

According to the present invention there is provided a heat transfer tube for effecting heat transfer between a wall of the tube and a fluid flowing through said tube, the tube having an internal surface comprising flutes formed along its length in a helical formation, said flutes each having a common helix angle relative to a longitudinal axis of the tube and each being asymmetrical in cross- section.

The fluted internal surface comprises a plurality of peaks and troughs The ratio of the circumferential distance between an adjacent peak and trough to the distance between two successive peaks is beneficially in the range 0 2 to 0.5 and is preferably 0.25. The asymmetry results in each flute having a relatively steep face and a relatively shallow face.

The helix angle of the flutes relative to the longitudinal axis of the tube is preferably in the range 20 to 40 degrees and is most preferably 25 degrees.

Preferably the ratio ot the flute height to the mean diameter of the tube is in the range 0.02 to 0.08 and is most preferably 0.07. A specific embodiment of the present inv ention w ill now be described, by way of example only, w ith reference to the accompanying drawings in which:

Figure 1 is a transverse sectioned view through a tube according to the present invention:

Figure 2 is an longitudinal sectioned view of the tube of Figure 1 along line X-X;

Figure 3 is a scrap view of part of Figure 1 show ing flute profiles in detail;

Figure 4 is a graph showing computed and experimental friction factors for a prior art tube, a smooth tube and a tube according to the present invention at a range of Reynolds numbers;

Figures 5- 10 show graphs of various flow parameters tor a prior art tube and a tube according to the present invention at different

nolds numbers.

Figure 1 1 is a graph showing computed Nusselt numbers against Reynolds number at a Prandtl number of 0.71 for a prior art tube, a smooth tube and a tube according to the present invention;

Figure 12 is a graph showing computed Nusselt numbers against Reynolds number at a Prandtl number of 5 for a prior art tube, a smooth tube and a tube according to the present invention;

Figure 13 is a table of computed friction factors and Nusselt numbers at different Reynolds numbers for a prior art tube and a tube according to the present invention;

Figure 14 shows graphs of computed Nusselt numbers normalised with respect to a smooth tube plotted against Reynolds number at Prandtl numbers of 0.71 and 5;

Figure 15 shows graphs of the variation of friction factor and Nusselt number with respect to flute angle of the tube of the present invention;

Figure 16 shows graphs of the variation of friction factor and Nusselt number with respect to flute height; and

Figure 17 shows graphs of the variation of friction factor and Nusselt number with respect to flute asymmetry.

Referring now to the drawings, Figures 1 and 2 show a heat transfer tube 1 in accordance with the present invention. The tube has a smooth outer circumferential wall 2 and an interior circumferential wall 3 having a plurality of flutes 4. The flutes 4 extend in parallel along the length of the tube 1 in a helical formation.

Figure 3 shows in cross-section the detail of two adjacent flutes 4. The contour of the flutes 4 comprises alternating peaks 5 and troughs 6 and each flute 4 is asymmetrical in profile, having a steep pressure face 7 and a relatively shallow leeward face 8. When fluid flows through the tube 1 it impinges on the pressure face 7 which induces a swirling motion.

In the exemplary embodiment shown in Figure 3, each peak 5 is a circular arc of radius 0.019R, where R is the mean interior radius of the tube 1. The distance between adjacent peaks 5 or adjacent troughs 6 is denoted by S and the distance between an adjacent peak 5 and trough 6 is indicated by the letter L. The height of the peak 5 above the trough 6 (in the radial direction) is denoted by 2h.

The flutes 4 are inclined to the longitudinal axis A of the tube by a helix angle represented by Φ (see Figure 2).

Evidence of the improved behaviour of the heat transfer tube described above has been obtained empirically and by means of newly developed computational techniques as described below.

Experiments were conducted on large-sections of tubing using hot-wire anemometry. This technique enabled detailed measurements to be made in the region near the wall between adjacent flutes. A comparison was made of the performance of spirally fluted heat transfer tubes made in accordance with the present invention with the performance of the tube described in US4305460 (hereinafter referred to as the "Yampolsky Tube"). In both cases a sufficiently long length of tubing was used to ensure that the measured profiles corresponded to essentially fully developed flow.

The computations were also based on the fully developed flow through the tubes. A modified version of the STREAM computer code was used as described in "Second-moment modelling of recirculating flow w ith a non-orthogonal collocated finite algorithm" by F.S. Lien and M . A. Leschziner published by Springer in 1993. To account for the turbulence, the widely used Gibson Launder Reynolds stress model (described in "Fluid Mech. " by M.M. Gibson and B.E. Launder) was used over the majority of the flow, with the simpler Launder Sharma low-Reynolds number k-e model (described in "Heat Mass Transfer" by B.E. Launder and B.I. Sharma) applied in the near-wall region.

Figure 4 shows the computed and experimentally measured friction factors for the original Yampolsky tube and the modified tube according to the present invention together with the measurements reported by Yampolsky for his tube design. Friction factor f is plotted against Reynolds number Re (the ratio of inertia] forces to viscous forces) for each of the tubes and are compared to the results for a smooth tube. It can be seen that the measurements taken in relation to the original tube (denoted by "ong tube" in Figure 4) are very close to those reported b> Yampolsky.

For the modified geometry of the tube of the present invention, the computations show that the friction factor is further reduced, being some 14-20% lower than in the original tubing. This trend is confirmed by the experimental measurements, although the reduction in this case is slightls lower at around 10%.

Figures 5 to 10 show profiles of mean streamw ise velocity, swirl velocity, normal stresses, turbulent kinetic energy, and Reynolds shear stress at three different Reynolds numbers for both the Yampolsky (original) tube and the (modified) tube according to the present invention It will be seen that there is a good level of agreement between the computations and the experimental measurements, giving confidence that the main features of the flow are being reproduced in the computations. The levels of swirl velocity and turbulent kinetic energy in the core region of the fluid are similar for the two geometries but the modified tubing returns a lower friction factor because of its smaller flute angle and shallower slope on the downstream side of the flute which reduces the tendency of the flow to separate behind the flute. The nomenclature used on these graphs is as follows: k = turbulent kinetic energy r = radius

R = mean radius of pipe

U = axial velocity

U = centreline axial velocity

W = circumferential velocity uv = turbulent shear stress A comparison of the heat transfer efficiencies is shown in Figures 1 1 and 12. The graphs show calculated values only of the Nusselt numbers against Reynolds numbers for both tubes at Prandtl numbers of 0.71 (Figure 1 1) and 5 (Figure 12). The Nusselt number is a measure of the rate of heat transfer by convection and the Prandtl number is a property of the fluid necessary to account for differences in the properties in the fluids used w hich are assumed constant in the computations. The values 0.71 and 5 correspond to air and water flows respectively. In this case the Nusselt number is defined as:

Nu = _ <Λ_ P where: P - perimeter of the tubing q_^ - wall heat transfer rate per unit area

D^ - hydraulic diameter of tube a - thermal conductivity

T_Λ - local wall temperature

T_bUι - bulk temperature of fluid The factor P/27rR is included to account for the increase in surface area as a result of the fluting.

It can be seen that there is surprisingly very little difference between the heat-transfer levels using the two tubes, despite the lower friction factor in the modified tube of the present invention.

The table in Figure 13 shows the precise computed results of both friction factors and Nusselt numbers and Figure 14 shows the Nusselt numbers normalised by those found in a smooth tube. This clearly shows the enhancement in heat- transfer as the Prandtl number increases.

It will be appreciated from the aforedescπbed graphs that the experimental and computational results have confirmed the reported friction factors in the Yampolsky tubing and that the modified tube of the present invention provides friction factors of the order of 10- 15 % lower than the Yampolsky tubing with negligible reduction in the heat-transfer coefficients.

The improved friction factor results are attributable to the asymmetric design of the flutes. The pressure face on which the fluid impinges imparts a strong swirling motion to the core fluid which is responsible for reducing the turbulence energy and keeping the friction factor low. The steeper pressure face in the modified tube is more efficient at inducing the swirling motion than is the original Yampolsky tube and hence a smaller flute angle can be used to generate roughly the same level of swirl. The shallower leeward flute face also contributes to a reduction in the friction factor as it reduces the tendency of the fluid to separate on the downstream side of the flute. The steep pressure face permits more heat transfer so that the modified tube has heat-transfer coefficients comparable to the original tube.

Figures 15 to 17 show the results of investigations into the sensitivity of the modified tube performance to variations in geometrical parameters.

Figure 15 shows the effect on the friction factor (f/fsm) and heat transfer (Nu/Nusm) characteristics of varying the flute angle Φ whilst keeping the flute height constant at h/R = 0.06 and the asymmetry constant at L/S=0.3. In the graph, friction factors and Nusselt numbers are normalised by corresponding to smooth-tube values The results are shown tor Reynolds numbers of 10,000 and 50,400 with the flute angle Φ being \ aπed between 20 and 40 degrees It can be seen that as the flute angle is increased the f riction factor rises from 73 % of the smooth tube value at Φ = 20 degrees to 120% at Φ = 40 degrees ( tor Re = 50,400) At the lower Reynolds number the increase is slightly less The heat transfer results are shown for both air and water at the two Reynolds numbers The results for air are not greatly different from the smooth tube values However, the results for water show a greater effect, with an increase from 130% to 175 % at Re =50,400

Figure 16 shows the effect of varying the flute height to mean radius ratio (h/R) on the normalised friction factor (t/tsm) and the normalised Nusselt number (Nu/Nusm) The flute height was varied from h/R = 0 02 to h/R = 0 08 whilst keeping the helix angle constant at Φ = 25 degrees and the asy mmetry constant at L/S =0.3 The results are shown for the friction factor tor a Reynolds number Re=50,400 and the Nusselt number results are shown for Prandtl numbers of 5 corresponding to water and 0 71 corresponding to air As h/R increases the friction factor shows a decrease, falling from 96% of its smooth tube v alue at h/R=0.02 to 69% at h/R=0 08 At the same time, the Nusselt number shows an increase as h/R is increased For air the increase is quite modest, but for water it is more pronounced with a sharp rise betw een h/R = 0 045 and 0 06

Figure 17 shows the effect of varying the asymmetrv L/S of the flute on the fπction factor and Nusselt number The asymmetry w as v aried betw een L/S =0.5 (symmetrical flute) and 0 2 At lower values than this the numerical scheme becomes less stable (and less accurate) as a result of the greater difficulties in obtaining an adequate grid resolution of the steep pressure face ot the flute Results were obtained at Re = 50 400 using h/R = 0 06 and a flute angle Φ=25 degrees.

As L/S is decreased, the fπction factor shows a small decrease, which appears to be getting steeper as L/S becomes smaller There is a corresponding increase in the heat-transfer as the as mmetry is increased This is particularly noticeable for the water results which rise from 142 % of the smooth tube value when L/S =0.5 to 154% at L/S =0.25

Claims

1 . A heat transfer tube for effecting heat transfer between a wall of the tube and a fluid flowing through said tube, the tube having an internal surface comprising flutes formed along its length in a helical formation, said flutes each forming a common helix angle relative to a longitudinal axis of the tube and each being asymmetrical in cross-section.

2. A heat transfer tube according to claim 1 , wherein the fluted internal surface comprises a plurality of peaks and troughs and the ratio of the circumferential distance between an adjacent peak and trough to the distance between two successive peaks is in the range 0.2 to 0.5.

3. A heat transfer tube according to claim 2, wherein the ratio of the distance between an adjacent peak and trough to the distance between two successive peaks is 0.25

4. A heat transfer tube according to any preceding claim, wherein the helix angle of the flutes relative to the longitudinal axis of the tube is in the range 20 to 40 degrees.

5. A heat transfer tube according to claim 4, wherein the helix angle is 25 degrees.

6. A heat transfer tube according to any preceding claim, wherein the ratio of the flute height to the mean diameter of the tube is in the range 0.02 to 0.08.

7. A heat transfer tube according to claim 6, wherein the ratio of flute height to mean diameter of the tube is 0.07.

8. A heat transfer tube substantially as hereinbefore described with reference to the accompanying drawings.