GB2399405A - Enhancement of heat transfer - Google Patents

Abstract

A member having an internal channel communicating coolant is delimited by sidewalls comprising a first sidewall 16 or 17 having ribs 47 extending transversely to the longitudinal direction of the channel and a second wall 4a or 6a adjacent the first sidewall 16 or 17 and has roughness elements (figs 5 and 6) distributed over it which are lower in height than the ribs 47. The longitudinal and transverse dimensions of the roughness element maybe equal to the height of the roughness elements. The roughness elements maybe spaced apart in both directions at least twice the dimensions of the longitudinal and transverse dimensions, may have a shape of a cylinder, cone, pyramid or rectangular parallelepiped, and maybe arranged in regular, irregular or random two dimensional arrays. The ribs 47 maybe skewed at angles between 30 and 60 degrees with respect to the longitudinal direction, maybe arcuate or sinuous, maybe equally spaced along the channel, or maybe staggered on one wall relative to the opposite wall. The member maybe a gas turbine blade and sidewalls 16 or 17 maybe webs extending between the second walls 4a and 6a which correspond to the convex suction side and concave pressure side of the blade (fig 2).

Description

Enhancement of Heat Transfer This invention relates to the enhancement of

heat transfer in cooling passages through which a coolant is to flow.

It is well known to cool a member, such as a gas turbine blade, which is in a high-temperature environment by passing a coolant, e.g. air, through at least one cooling passage in the member. It is also known to enhance heat transfer between the member and the coolant by roughening the surface of the cooling passage or providing turbulence-inducing ribs in the cooling passage. Many ways of enhancing heat transfer have been proposed which have concomitant disadvantages, such as difficulty and expense of manufacture, an excessively concentrated or localised cooling effect, or increased weight creating excessive centrifugal stresses in rotating parts.

Figures I and 2 of the accompanying drawing show a known air cooled turbine blade for a gas turbine. The blade includes an aerofoil 1 having a radial axis 2 and is joined to a rotor disk (not shown) by a conventional fir-tree root 3. The rotor disk rotates about its axis 19 in the direction indicated by the arrows 20, resulting in blade motion in the direction indicated by the arrow 21. The aerofoil 1 has a convex sidewall 4 at the leading or suction side and a concave sidewall 6 at the pressure side. The sidewalls 4, 6 extend from a leading edge 7 to a trailing edge 8 of the aerofoil 1 and extend longitudinally from a root 9 to a tip 11.

The turbine blade includes an internal passageway for channelling compressed air as a gaseous coolant to cool the aerofoil 1. The coolant is conventionally conducted from a compressor of the gas turbine through the fir-tree root 3 and radially into the aerofoil 1. The passageway includes a leading edge channel 12a which extends from the root 9 towards the tip I 1, where the coolant turns into a mid-chord channel 12b in which the coolant flows longitudinally towards the root 9, where the coolant turns into a trailing edge channel 12c which extends to the tip 11. The coolant is discharged from the trailing edge channel 12c through trailing edge openings 13 and tip openings 14.

The channels 1 2a to 1 2c are defined by longitudinal webs 16, 17 which extend between the aerofoil sidewalls 4 and 6.

The present invention provides a member having an internal cooling channel along which a coolant is to flow, the cooling channel being delimited by sidewalls including a first sidewall bearing ribs extending transversely to the longitudinal direction of the cooling channel and a second sidewall adjacent to the first sidewall, wherein the second sidewall bears roughness elements which are distributed over at least a given region of the second sidewall and which are lower in height than the ribs.

The invention will be described further, by way of example only, with reference to the accompanying drawings, in which: Figure I is a schematic respective view, partly in section, of a known turbine blade; Figure 2 is a section taken on line II - II in Figure 1; Figure 3A is a diagrammatic section through part of the aerofoil of a turbine blade in accordance with the invention, in a plane normal to the axis of rotation of the rotor disk, with ribs provided on the webs and sweeping toward the concave sidewall of the aerofoil; Figure 3B is a diagrammatic section on line B-B in Figure 3A; Figure 3C is a diagrammatic section on line C-C in Figure 3A; showing the Coriolis and rib-induced forces acting on the coolant flow; Figure 3D is a view similar to Figure 3C but showing the secondary flow field; Figures 4A-D are similar to Figures 3A-D, respectively, but with the ribs sweeping toward the convex sidewall of the aerofoil; Figure 5 is a diagrammatic plan view of part of an array of roughness elements; Figure 6 is view on line VI-VI in Figure 5; and Figure 7 is a graph of the ratio of equivalent sand grain roughness height to actual roughness height plotted against a roughness parameter.

In an internally ribbed aerofoil 1 of a rotating turbine blade, in a longitudinal cooling channel of basically rectangular cross-section, typified by the channel 1 2b, there occurs the interaction of three flow mechanisms in the cooling stream: the primary flow and two secondary flows (caused by Coriolis acceleration and by ribbed walls). The pressuredriven primary flow 5 is the dominant flow in the cooling channel 1 2b.

The variation of the Coriolis Inertia effect across the cooling channel 1 2b creates secondary flows within that channel. For a particle of cooling gas the Coriolis acceleration component, C, relative to a frame of reference rotating with the rotor, is given by: C = 2 Q v, where Q = the angular velocity of rotor rotation, and v = the local radial component of the cooling flow velocity. Because v is zero in the boundary layer and a maximum within the mainstream, C varies similarly across the stream, resulting in a pump effect forcing the centre of the flow upwards towards the convex sidewall 4.

This creates a pair of counter-rotating vortices with their axes lying along a line parallel with the rotation axis 19. When the pressure-driven primary flow 5 encounters transverse ribs attached to a wall of a cooling channel, in absence of blade rotation, secondary flows near to that wall tend to flow along the ribs (i.e. transversely to the longitudinal direction).

With ribs attached to the aerofoil side walls 4,6 (not as shown), two strong, elongated, counter-rotating vortices are formed with their axes lying one above the other. When the pressure-driven primary flow 5 passes skewed ribs 47 (Figures 3 A-D) or 51 (Figures 4 A-D) attached to a wall, in absence of blade rotation, the flows 10 near to that wall very quickly adopt the skewness of the ribs (i.e. the angle relative to the longitudinal direction). When the ribs 47 or 51 are attached to the webs 16,17 as shown in Figures 4 A-D and 5 A-D, the axes of the vortices lie side by side along a line parallel with the aerofoil faces, but depending on the skew direction, the wall flows are towards the convex or concave aerofoil surfaces 4, 6 respectively. The ribs 47 or 51 are applied to both opposing walls 16, 17 in directly opposing positions and with the same skewness so that when viewed from the side they appear superimposed.

Placing the ribs on the webs 16,17 instead of the aerofoil walls and making the ribs 47 sweep towards the concave aerofoil surface (angle 45), as shown in Figures 3 A- D results in co-Coriolis (49) forces 48 and a smooth merging of both rib streams with Coriolis streams to form a symmetrical pair of elongated vortices 50 without "dead- water" regions noted above. This results in stronger vortices and enhanced heat transfer to the aerofoil walls, as well as lower coolant pumping losses.

Although making the ribs 51 sweep towards the convex aerofoil surface (skew angle 46 in Figure 4 A) creates forces 52 which could be expected to counter the Coriolis forces 49, the configuration switches from two to four vortices, as shown in Figure 4 D, and results in even greater heat transfer, for the same cooling air pumping losses.

In Figures 3A and 4A the skew angles 45 and 46 of the ribs 47 and 51 are approximately 52O, but the skew angles could by greater or less, the preferred range being 30 to 60O, more preferably 35 to 55 . Preferably the ribs are mutually parallel but there may be circumstances in which the skew angle can vary between successive ribs, perhaps decreasing (or increasing) in the direction of the primary flow 5 of coolant.

Although straight ribs have been shown, there may be circumstances in which non- linear ribs (e.g. arcuate or sinuous ribs) may advantageously be used. In a cooling channel delimited by two webs, it is preferable for both webs to be provided with ribs, as described above; however, ribs on only one of the webs would provide some benefit.

At the leading end and trailing end of the aerofoil, a cooling channel is delimited by a single web, which is preferably provided with skewed ribs as described above. The ribs are preferably equally spaced along the cooling channels. A small additional improvement in performance may possibly be achieved by staggering the ribs on one web wall in the longitudinal (radial) direction relative to those on the opposite wall.

As shown diagrammatically in Figures 3 A-D and 4 A-D the sidewalls not bearing the ribs 47 or 51, i.e. the adjacent sidewalls 4 and 6, are provided with arrays 4a and 6a of roughness elements, giving a roughness equivalent to that which would be achieved by distributing sand grains over the sidewalls (referred to as equivalent sand grain roughness or ESGR). The ribs create thin turbulence-, thermal-, and momentum boundarylayers (due to the secondary flows), and then shed turbulent free-shear layers which wash through the roughness, producing additional smallerscale vertical structures and yet more turbulence, thus increasing the heat transfer. An additional enhancing effect on the Coriolis-pressure surfaces is the destabilising influence of the Coriolis force on the boundary-layer turbulence.

The cooling channel 12b may have an average width of from about 10 mm to about 50 rnm for example. The ribs 47 or 5 l may, for example, have a height in the range of 2 mm to 4 mm and be spaced 10 mm to 30 mm apart. The roughness elements of the array 4a or 6a are lower in height than the ribs, preferably 4% to 20% of the rib height, the roughness element height typically being in the range from about 0.1 rum to about 0.5 mm, preferably between 0.1 mm and 0.5 mm.

With a typical gas turbine engine cooling channel, any array of roughness elements which gives an ESGR of 0.45 mm should give an increase in heat transfer coefficient of 100% (relative to that with ribs only) together with an increase in heat transfer efficiency. There are many surface shapes which could give a suitable ESGR: cylinders (attached by their ends), cones, pyramids (attached by their bases, which may be of any regular or irregular polygonal shape), spherical segments (in particular hemispheres), and rectangular parallelepipeds (in particular cubes). Each variant can have a different height and aspect ratio, and the spacing can be either close-packed or sparse. Two or more different shapes may be mixed in the array, which may be regular, irregular, or random. Constraints imposed by operating conditions of a gas turbine blade are that the elements should not be too high (to reduce centrifugal bending stresses) and there should be a smoothly-blended land between the elements (to reduce the risk of stress-concentration and crack- propagation).

There are many methods of manufacture which could be used to form the array of roughness elements but casting (usually investment or lost-wax casting) will usually the most suitable. Other possible methods are e] ectro-chemical machining (ECM), electrical discharge machining (EDM or spark-erosion), coating (co-depositing with inclusions), shot-peening, abrasive-flow, grit-blasting, and etching.

Figures 5 and 6 show a representative surface roughness in the form of uniformly-distributed roughness elements in the form of rectangular pyramids. Owing to symmetry the whole surface can be represented by the domain shown inside the rectangle marked with the chain line in Figure 5.

e = pyramid height; p = pitch transverse to nominal coolant flow direction; q = pitch in nominal flow direction; a = pyramid base length transverse to nominal flow direction; b = pyramid base length in nominal flow direction; S is the planar area not occupied by the roughness elements and is shown shaded in Figure 5; Sf is the total area of the roughness elements projected onto a plane normal to the nominal flow direction; As is the windward wetted surface area of a single roughness element; At is the surface area of a single roughness element projected onto a plane ! norma] to the nominal flow direction; A roughness (spacing / shape) parameter As is defined as: As = (S / Sf) (As / AM 6; --Equation 1 ks = equivalent sand grain surface roughness height (defined as the height of sand grains which give the same skin friction coefficients in internal passages as the roughness being evaluated); and k = actual roughness height.

By experiment (Sigal and Danberg, 1988 and 1990) it has been found that ks / k = 1.583 x 10-5x Ass683 for As < 7.842) = 1.802 x A 0.03O3g for 7.842 < As < 28.12) --- Equation 2 = 255.5 x AM 4s4 for 28.12 < As) Figure 7 shows a plot of this function.

The present inventor suggests a geometry for application to a gas turbine engine cooling passage having the following proportions: p = q = 4e, p'= q' = 2e, a = b = e, giving: S= 14e2 Sf= e2 As = e2 5 5/ 4 At =e2/2 From Equation l: As = 16.73.

From Equation 2: k5 / k = 1.963.

This value can be seen from Figure 7 to give be near to the maximum, and is therefore a good value for a rotating turbine blade from the point of view of roughness weight.

- For a gas turbine blade cooling-channel with a 25.4 mm square crosssection, with ribs of 2.54 mm square cross-section at 45 skew attached to the webs at a pitch of 25.4 mm and the roughness elements on the inner-aerofoil surfaces, for a channel Reynolds number of 30000 and a rotation number of 0.3, the present inventor has computed that the following dimensions would close to optimum heat transfer coefficient, efficiency, and structural properties: e = 0.45 mm, a = b = 0.45mm, p=q = 1.8mm.

It should be understood that Figures 5 and 6 are a stylised and idealised representation of the arrangement of peaks constituting the roughness of the surface region. The array is not necessarily regular, the pyramids are not necessarily right pyramids and their bases are not necessarily squares, equilateral triangles, or regular polygons. Pyramids of different shape may be mixed. The peaks are not necessarily all of the same height. All of the parameters may be varied, deliberately, randomly, or pseudo-randomly. In practice the peaks may resemble the corners of the sand grains, distributed all over the surface region.

The projection of many peaks through a laminar sub-layer and into a transition region or fully turbulent region of a flowing coolant ensures an extremely effective transfer of heat from the surface region to the main coolant stream. The roughness is easy and cheap to manufacture, requiring only simple additions to the surface of the casting mould. Roughening only one or some of the sidewalls of a cooling channel minimises pressure loss and maximises heat transfer efficiency.

It is possible to tailor the distribution and height of the roughness elements to the local heat transfer requirements, thereby giving the opportunity of avoiding concentration of the cooling effect, in order to reduce thermal stresses in the cooled member.

The cooling channel described above with reference to Figures 3 A-D and 4 A-D corresponds to the channel 12b shown in Figure 2, with ribs on the web walls and roughness elements on the aerofoil walls. Similarly, each of the other two channels 12a and 1 2c, which are generally triangular in cross-section, would be provided with ribs on the single web wall and roughness elements on the aerofoil walls.

Although the cooling channel has been described in its application to a gas turbine blade, the cooling channel could be used in any member which is subjected to a high-temperature environment. The cooling channel may be of any convenient cross- sectional shape, with ribs on at least one wall and roughness elements on at least one adjacent wall. The or each region occupied by the roughness elements and/or the ribs may be a portion of the area of a wall.

Claims (14)

1. CLAIMS: 1. A member having an internal cooling channel along which a

   coolant is to flow, the cooling channel being delimited by sidewalls including a first sidewall bearing ribs extending transversely to the longitudinal direction of the cooling channel and a second sidewall adjacent to the first sidewall, wherein the second sidewall bears roughness elements which are distributed over at least a given region of the second sidewall and which are lower in height than the ribs.
2. 2. A member as claimed in claim I, wherein the height of the roughness elements is 4% to 20% of the height of the ribs.
3. 3. A member as claimed in claim I or 2, wherein the dimensions of the roughness elements in the said longitudinal direction and in the transverse direction at right angles to the said longitudinal direction are substantially equal to the height of the roughness elements.
4. 4. A member as claimed in any preceding claim, wherein the roughness elements are spaced apart both in the said longitudinal direction and in the transverse direction at right angles to the said longitudinal direction at pitches that are at least twice the respective dimensions of the roughness elements in the respective directions.
5. 5. A member as claimed in any preceding, wherein the roughness elements are selected from cylinders, cones, pyramids, and rectangular parallelepipeds.
6. 6. A member as claimed in any preceding claim, wherein the roughness elements constitute a substantially regular two-dimensional array.
7. 7. A member as claimed in claim 6, wherein the roughness elements are square pyramids.
8. 8. A member as claimed in any preceding claim, wherein the second sidewall is an external wall of the member.
9. 9. A member as claimed in any preceding claim, wherein the ribs on the first sidewall are skewed in the same sense with respect to the said longitudinal direction.
10. 10. A member as claimed in claim 9, wherein the skewed ribs are at 30 60 to the said longitudinal direction.
11. A member as claimed in any preceding claim, being a gas turbine blade.
12. 12. A member as claimed in claim 1 1, wherein the height of the roughness elements is in the range from 0.1 mm to 0.5 mm.
13. 13. A member as claimed in claim 1 l or 12, wherein the height of the ribs is in the range from 2 mm to 4 mm. t
14. 14. A member having an internal cooling channel substantially as described with reference to Figures 3 A-D or Figures 4 A-D of the accompanying drawings.