US3817319A - Conduction of heat exchange fluids - Google Patents

Abstract

The heat transfer between a tube and a fluid therein is to be enhanced by providing a tube with helical corrugation having axial crest-to-crest spacing T, crest-to-valley height t, inner diameter d and pitch angle of the helix delta . These parameters are selected as follows: t/5 from 0.01 to 0.5, preferably between 0.1 and 0.2; T/d from 0.01 to 1.0, preferably between 0.03 and 0.3 and helix angle delta from 5* to 20*.

Description

United States Patent [11] 3,817,319 Kauder June 18, 1974 41 CONDUCTION OF HEAT EXCHANGE FLUIDS lnventor: Knut Kauder, Krahenbruch,

Germany Kabel-und Metallwerke Gutehoffnungshutte Aktiengesellschaft, Hannover, Germany Filed: Nov. 14, 1972 Appl. No.: 306,181

Assignee:

Foreign Application Priority Data Nov. 15, 1971 Germany 2156578 US. Cl 165/1, 165/181 Int. Cl F28f l/20 Field of Search 165/], 147, 179, 181

[56] References Cited UNITED STATES PATENTS 3,612,175 10/1971 Ford et al. 165/179 Primary Examiner-Charles Sukalo Attorney, Agent, or Firm-Ralf H. Siegemund [5 7] ABSTRACT The heat transfer between a tube and a fluid therein is to be enhanced by providing a tube with helical corrugation having axial crest-to-crest spacing T, crest-tovalley height I, inner diameter d and pitch angle of the helix 8. These parameters are selected as follows: /5 from 0.01 to 0.5, preferably between 0.1 and 0.2; T/d from 0.01 to 1.0, preferably between 0.03 and 0.3 and helix angle 6 from 5 to 20.

6 Claims, 7 Drawing Figures PATENTEBJuu 18 I974 'sumlnis 0;, f mm M 6 w C CONDUCTION OF HEAT EXCHANGE FLUIDS BACKGROUND OF THE INVENTION The present invention relates to the conduction of fluid through flexible tubes, particularly for purposes of heat exchange. More particularly, the invention relates to improvements involving particulars of helical corrugation for such tubes, with regard to flow characteristics in relation to the tubes wall.

Many fields of art employ tubes which can be described as having wall structure of a regularly repeated geometric contour and configuration pattern. Depending on various factors, including particulars of the pattern, such tubes can be stiff or flexible. However, the tube will be quite flexible where its corrugation crests and valleys loop around the axis and the wall of the tube is not too thick. Tubing with corrugation that loops around the axis along the periphery of the tube, is quite flexible and can be reeled on drums. In fact, the tubing can be installed just like a cable. Such tubes are used as conduit for fluids, either for transporting fluid as such or for using the fluid medium as carrier for thermal energy. Short, metal hose, as well as tubes of medium length, are used particularly in case of heat exchange between the fluid in the tube and the environment, e.g. over the length of the tubing or at the destination point. Long corrugated tubing is used as conduit for fresh or waste water or as conduit for hot water or steam in a central heating system, or for many other purposes. The demand for tubing of this type has steadily increased in recent years. However, corrugated tubes have not always been found satisfactory as carrier for a fluid in a heat exchange device.

A condition is posed usually in the field of heat exchange that the fluids undergoing heat exchange must not come into direct mutual contact, as they should not mix. Thus, tubes are used for heat transfer from one fluid to another one, which tubes maintain physical separation of the fluids but permit heat transfer over short distances of flow. For example, a concentric tube system establishes a flow path for one fluid in an inner tube, while the other fluid passes through the ring space between inner and outer tube. Heat is transferred through the wall of the inner tube.

Considering the heat exchange process in some detail, it involves basically three steps. (1) heat is transferred from the warmer fluid to the surface of the wall separating the fluids, (2) heat is conducted through the wall, (3) heat is transferred from the other wall surface to the cooler fluid. If the wall is made, for example, of copper or any other material having a high coefficient of thermal conductance, the thermal conductance through the wall can be disregarded in the consideration of the overall heat transmission between the two fluids.

In case of a tube, having inner diameter di, outer diameter do, and length L, the surface areas involved in 'the transfer are A, 'rr L di for the inner surface and A 1r L do for the outer surface. Let a, and 01,, be respectively the transfer coefficients at inner and outer surfaces, then the following relation describes the thermal transmission process.

i i' o au i i' o o) (I) wherein K is the particular coefficient of heat transmission, and A is defined by A 1r L (do di)/(lognat do/di) 2 The fraction in the equation being the logarithmic median value for the tube s diameter.

Equation l teaches that the heat transmission coefficient is always smaller than the smallest heat transfer coefficient a of the system because the equation can be written so that such smallest coefficient (a,- or 04,) appears as being multiplied by a factor that is necessarily smaller than unity. The heat transfer coefficients, of course, include the thermal properties of the materials involved. Moreover, the coefficients a are composite parameters which in each system: fluid-wall surface, combine all physical processes that transfer thermal energy from the fluid to the wall (or vice versa). Such processes include molecular conduction, convection, radiation and evaporation or condensation. Evaporation and condensation occur only in special cases. Molecular conduction and radiation are usually determined by the physical properties of the materials involved. The variable parameter in the process is convection, whereby convection is to be understood generally as any flow in any of the fluids which contribute to heat transfer.

In analogy to the known expedient of increasing the effective heat exchange surface, it is, for example, known to place baffles into a smooth wall tube. The baffles differ as to cross section. The baffles so placed in smooth wall tubes may even have rectangular contour, or are discs or rings, or have propeller-like or helical configuration. For similar Reynolds number one can increase heat transfer to about the eightfold value, but up to a ten-thousandfold increase in pressure loss is suffered under such conditions. Thus, the advantage of a better heat transmission process is at least partially offset by high pressure losses requiring increased pumping output.

DESCRIPTION OF THE INVENTION It is an object of the present invention to improve flow conditions in (or on) a tube so as to improve the heat transfer as between fluid and tube wall surface, in either direction and on either side of the tube.

In accordance with the preferred embodiment of the invention, it is suggested to use helically corrugated tubing wherein the ratio of corrugation crest-to-valley height (radial) and corrugation crest-to-crest (axial) distance is from 0.01 to 0.5, preferably from 0.1 to 0.2; the ratio of the crest-to-valley height to smallest inner diameter of the tube is to be about 0.01 to 1.0 and the angle of the corrugation helix is to be between 5 to 20.

The known devices for improving convection are essentially devices which induce and enhance tubulent flow; the more turbulent flow the higher is the heat transfer across the flow into the boundary surface. The penalty, of course, is pressure loss because turbulence enhances both, transfer of momentum and transfer of thermal energy.

Unlike these known methods, applicant suggests to use a tube which imparts rotation upon the flow as a whole. The rotation being defined as the product of circumferential speed and circumference divided by twice the cross section area of the tube. Thus, rotation as defined increases with increasing the product of the speed and the circumference and by reducing the cross section.

As a viscous fluid flows through a tube with helical boundary channels, helical flow adjacent the boundary tends to impart rotation upon the cylindrical, straight axial center flow. Accordingly, the flow has two components, axial and circumferential. The intensity of the latter component depends upon the configuration of the helical channel as it induces, ultimately, the circumferential velocity component. The intensity of the induction of that rotational flow will be higher for larger crest-to-valley height of the corrugation (channel depth). The rotational flow will be lower, the larger is the axial spacing of corrugation crests. Thus, rotational flow will be determined by the ratio of these geometric values as defining the corrugation as well as by the relative channel depth and the pitch of the helix.

DESCRIPTION OF THE DRAWINGS While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter which is regarded as the invention, it is believed that the invention, the objects and features of the invention and further objects, features and advantages thereof will be better understood from the following description taken in connection with the accompanying drawings in which:

FIG. 1 is a three-dimensional velocity profile diagram in a tube to be produced for heat exchange enhancement;

FIGS. 2a and 2b are longitudinal and cross-sectional views through a corrugated tube;

FIGS. 3 and 4 are diagrams for showing kinetic energy of rotational flow and axial flow plotted against corrugation defining tube parameters;

FIG. 5 shows a tube to be used as fluid conduit; and

FIG. 6 is a schematic section diagram through a corrugation valley and adjoining crests to define contour of helical channel flow along a tubes wall.

Proceeding now to the detailed description of the drawings, FIG. 1 illustrates the velocity profile 15 to be attained. The profile is plotted in three-dimensional diagram. The horizontal plane shown in perspective view is taken in a cross section through a tube, using the same plane to plot azimuthal velocity C along a diameter 10, including circumferential velocity component C,,,,*. The resulting profile curve is denoted with 11.

The axial velocity is plotted along a vertical axis of the drawing, using said diameter 10 as base for each velocity vector. The end points of the vectors follow a profile 12 for the axial component of fluid velocity. The character c denotes a vector on that diameter as foot point of the actual composite velocity resulting in a profile curve 15.

This then is the velocity distribution found desirable. That this distribution improves, in fact, the heat transfer between fluid and boundary will be justified next, the generation of that profile will be discussed thereafter.

The fluid flow in a tube according to the profile 15 causes transportation of kinetic energy and momentum in accordance with density and velocity. That energy transport can be divided into an axial component and an azimuthal or rotational component. The relative energy inherent in the axial component of flow and integrated over the cross section of the conduit, may be designated E and the rotational component, integrated analogously, may be called E Fluid increments carrying this kinetic energy of flow are also the carrier of the thermal energy. Thus, a high energy component for the rotational (kinetic) flow inherently enhances the heat transfer into the wall. Therefore, the fluid flows in axial direction pursuant to the regular axial extension of the conduit; a rotational velocity field is superimposed upon the axial component, circulating around the circumference and imparting its thermal energy to (or receiving thermal energy from) the wall of the tube.

The mechanism for setting up the rotational flow of the type plotted in FIG. 1 is explained now with reference to FIG. 2. The FIG. shows a tube made, for example, from thin metal strip. The strip has been folded longitudinally into a split tube, the joint being established by and along the previously opposite edges of the strip which now abut or overlap. The joint is closed through longitudinal seam welding, and the resulting tube is provided with helical corrugation. The corrugation in cross section appears as a wave-like pattern of alternating crests and grooves or valleys. Corrugated tubing is, of course, known per se, but the corrugation is provided under observation of specific rules so that the rotational component of flow is obtained by forcing the fluid to follow particular channels as defined by the corrugation grooves or valleys as seen from the interior of the tube.

The (axial) crest-to-crest distance T and the (internal, radial) crest-to-valley height I define the corrugation pattern. Of further relevancy is the smallest inner diameter d which is the diameter of a cylinder 20 that is tangent to all inwardly directed crests. T/n'd defines the tangent function of the helix angle 5 of the corrugation.

The largest outer diameter D of the tube, measured on a cylinder 21, is tangent to the outer apeces of the radially outwardly directed crests. If the tubes wall has thickness S, one can also define a cylinder that is tangent to the apex of the inner valleys, that cylinder has diameter D-2S.

In order to practice the invention, the parameters are selected as follows. For t/T to range from 0.01 to 0.5 (preferably 0.1 to 0.2); t/d to be within the range from 0.01 to 1.0 (preferably 0.03 to 0.3); and helix angle 8 5 to 20. It can readily be seen that these corrugation parameters define the intensity of compelling a peripheral portion of the fluid to flow in a helical channel, and viscosity causes the fluid outside of the helical channel, closer to the interior of the tube, to still have a rotational component. The parameters determine also the number of loops in the flow path per axial unit length.

FIG. 3 illustrates the relationship between corrugation helix angle 8 and the ratio of the two kinetic energies E and E as defined above. The solid dots are measured values for !/d= 0.0455, the circles have been measured for t/d 0.635. The angle 8 has to be varied through variation of T, and curve 30 has been calculated.

FIG. 4 illustrates the energy ratio E /E, plotted against t/d for T/d 0.3 which is between 5 and 6. As stated, it was found in practice that for best results t/T 0.1 to 0.2 and t/d= 0.03 to 0.3. This way one obtains best conditions for heat transfer as between fluid and wall, so that these parameters are deemed preferred for heat exchange tubing. As the channel flow includes a rotational component, little actual pressure loss occurs as a result of this deviation from straight axial flow, because rotational flow (ideally) produces no pressure gradient.

The preferred form of constructing a heat exchange tube is actually shown in FIG. 5. FIG. 2 has served primarily for defining the relevant parameters. The grooves or valleys in FIG. 5 are rather shallow, followed in each instance by a pronounced crest. The selection of tube corrugation is preferably tightened additionally as follows.

The corrugation has been described in terms of the parameters T, t and d. However, this does not completely described the corrugation contour as can readily be seen by comparing FIGS. 2 and 5. FIG. 6 shows particularly a variety of curves, each outlining the corrugation for the same set of parameters T, t and d, including even an asymmetric pattern as shown-in dotted lines. Not all of these contours give equally favorable results. It can readily be seen that, for example, trace a outlines a corrugation which, in fact, establishes a deep, narrow channel separated by crests with rather shallow apex as extending into the flow, so that a predominant portion of the inner surface is defined by almost cylindrical sections, separated by the narrow spiral channel. On the other hand, trace b outlines a contour of a rather wide channel separated axially by steep ridges (such as shown in FIG. 5).

It was found that best results are obtained if the channel area is selected as follows. One can see that wavelength T/2 and corrugation depths t define a rectangle. Part of this rectangle is occupied by two subareas, each being half of a cross section area of an inwardly directed corrugation crest (e.g., as hatched), the remainder being the channel cross section area. That area is to be about two-thirds less of the rectangle T/2-t. To state it differently, half of the cross section of the helical channel as defined by the corrugation, is at most twice as large as half of the cross section of the helical ridge that separates the loops of the spiral channel. Under these conditions, optimum heat transfer coeffi cients are obtained as between fluid and the tubes wall. This is approximately curve c in FIG. 6.

Tubes meeting these requirements are well suited as fluid conductors in long paths for heat exchange such as required, for example, in desalination plants. It may be desirable here to provide stretches of the tube with smooth wall to facilitate installation in heat exchange planes.

It should also be mentioned that the helical corrugation having the stated parameters do, in fact, provide for rotational flow at optimum heat transfer characteristics as been fluid and wall. Tubes having annular corrugation at similar parameters provide baffles in the flow resulting in backwater zones adjacent the annular corrugation ridges with no rotational flow and provide for considerably inferior heat transfer.

The invention is not limited to the embodiments described above but all changes and modifications thereof not constituting departures from the spirit and scope of the invention are intended to be included.

1 claim:

1. Method for conducting fluids through a tube for heat transfer as between tube and fluid. comprising the step of:

using a helically corrugated tube;

the corrugation having axially alternating crests and valleys;

the axial distance T from crest-to-crest, the crest-tovalley t, the inner tube diameter d and the helix angle 8 of the corrugation selected so that t/T is from 0.01 to 0.5, t/d from 0.01 to 1.0; and 8 from 5 to 20.

2. Method as in claim 1, wherein t/T is from 0.1 to 0.2.

3. Method as in claim 1, wherein t/d is from 0.03 to 0.3.

4. Method as in claim 1, wherein t/Tis from 0.1 to 0.2 and t/d from 0.03 to 0.3.

5. Method as in claim 1, wherein half the cross section of a fluidflow channel defined by the helical corrugation valleys is not larger than twice half of the cross section of the crests as separating axially sequential channel loops.

6. Method as in claim 1, using the tube in a heat exchanger.

Claims (6)

1. Method for conducting fluids through a tube for heat transfer as between tube and fluid, comprising the step of: using a helically corrugated tube; the corrugation having axially alternating crests and valleys; the axial distance T from crest-to-crest, the crest-to-valley t, the inner tube diameter d and the helix angle delta of the corrugation selected so that t/T is from 0.01 to 0.5, t/d from 0.01 to 1.0; and delta from 5* to 20*.

2. Method as in claim 1, wherein t/T is from 0.1 to 0.2.

3. Method as in claim 1, wherein t/d is from 0.03 to 0.3.

4. Method as in claim 1, wherein t/T is from 0.1 to 0.2 and t/d from 0.03 to 0.3.

5. Method as in claim 1, wherein half the cross section of a fluid flow channel defined by the helical corrugation valleys is not larger than twice half of the cross section of the crests as separating axially sequential channel loops.

6. Method as in claim 1, using the tube in a heat exchanger.

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