One problem with the perforations in PVs solution is that the freestream velocity, if set to model natural buoyancy, depending on the height of the fagade and the size of the duct behind the panel, can be quite small. The best flow regime for heat transfer is turbulent flow, and so it may be necessary to induce turbulence with other methods. Heat-transfer-enhancing ribs are now routinely employed in blade cooling applications. They are usually employed along two opposite surfaces of internal passages within rotating gas turbine blades [10].

The geometric variables in this case include: Rib height to duct hydraulic diameter (e / Dh ); Rib pitch to height ( P / e ); and Duct aspect ratio ( W/ H ), over a range of Reynolds numbers that encompass those reasonably achieved through flow due to natural buoyancy effects or with the addition of a fan extractor.

Work conducted by Hong and Hseih [11] in 1993 showed that staggered, as opposed to in-line, ribs increase local Nusselt number levels in the developing flow region and that these levels can be maintained for fully developed flow further downstream for certain combinations of duct aspect ratio and Reynolds number.

Fig 2. Square duct with aligned rib turbulators perpendicular to the flow.

Rib roughened duct walls can however, cause localised hot spots to develop along the surface wall in the base region behind the ribs. Hwang and Liou [12] in 1995, published research papers covering their work on the use of perforations in the ribs. They found that having an array of staggered holes in the axial flow direction, in the ribs, has a beneficial effect on heat transfer rates. For their optimal rib configurations, peak heat transfer was observed at a rib open area-to-face area ratio of 0.44. Flow visualisation analysis also showed that incorporating the perforation arrays in the ribs significantly reduced the hot spots in the base region behind the ribs. Changing rib shape to semi-circular or triangular-shaped ribs of the same height was also found to reduce the hot spots, while maintaining Nusselt number distributions. A proposal to include v-notch grooves positioned midway between adjacent square ribs was introduced by Zhang et al [13] in 1994, and proved to improve heat transfers by a factor that can be as high as 3.4 above that for a smooth walled duct, while ribbed walls alone yielded a factor of 2.4, for the same pressure drops.

Recent trends in this area have been to align the ribs at an angle to the main flow direction. The use of inclined ribs induces a secondary motion parallel to the ribs, which is found to improve the thermal performance of the cooling passages. Iacovides et al

[10] published results on their experimental investigations on both local thermal and hydrodynamic data for these internal cooling flows. The secondary flow motion leads to a uniform distribution of the turbulence intensities by causing increased mixing and thus more uniform heat transfers across the duct. Inducing turbulence is relevant in the PV problem, particularly at the lower heights up a fagade, as the air in the duct is relatively cool and the large temperature difference can be fully exploited by the turbulent flow.

The hydraulic diameter for the test rig is initially set to 0.125m, by the constraints of the optimal duct depth to length ratio as described by Brinkworth, 2004. A rib height to hydraulic diameter ratio (e/Dh) of 1.6 will be used, matching those of Hwang, 1998, and Jubran et al., 1996, giving a rib height of 20mm. A rib thickness of 12.5mm will be used giving a height to thickness ratio (e/t) of 1.6, matching that of Cavallero et al., 2002 and again Hwang, 1998 [19]. A pitch of 125mm will be used, giving a pitch to rib height (P/e) ratio of 10 will be used, which a common mid-range parameter used frequently by many researchers, including all those previously mentioned in this field. The use of small P/e ratios is found to decrease overall heat transfer coefficients and promote hot spot development. These parameters will be set to compare the effects of straight ribs, staggered ribs, angled and v-shaped at 60° ribs, and perforated ribs against the Nusselt numbers seen for a smooth duct.

Dimples

In general, internal cooling has been enhanced using rib-turbulators. However, the separated flowfield over discreetly mounted ribs can induce cooling non-uniformity and thermal stresses, along the relatively high pressure drop induced, and the difficulty in manufacture further takes form the ribs attractiveness. In recent years, the concept of using indented (dimpled) surface has attracted attention due to the high heat transfer enhancement and lower pressure loss penalty associated with dimples, with up to 2.5 times greater heat transfer over smooth plates and only 1.6 times the penalty loss or half that of rib turbulators, Acharya et al [20]. Serving as a vortex generator, a concavity promotes turbulent mixing in the flow bulk and enhances the heat transfer. According to Mahmood et al., 2001, these regions of high local heat transfer are a result of vortex

Fig 3 The flow structure showing induced vortices exiting a dimple (Zhou et al., 2000)

pairs and vortical fluid that is shed periodically from each dimple. The outward shedding or ejection of fluid produces heat transfer augmentation from the periodicity and unsteadiness of the vortical fluid, and the strong secondary fluid motions of the vortical fluid and vortex pairs near the surface.

As both Mahmood and Chyu both found that the in dimple heat transfer was not as great as that seen after the dimple, the geometric details used by Chyu et al., 1997, will be adapted as this incorporated a larger pitch. They did however analyse the heat transfers differently, with Chyu et al. using area averaged Nusselt numbers, and Mahmood et al., using the total surface area for this calculation, resulting in lower values. The pitch set to be approximately 2.3 times the diameter of the actual circular opening of the concavity was so chosen as that in heat exchangers arrays, e. g. pin-fins and tube bundles, where this ratio generally optimizes their heat transfer enhancement, if arranged in such a fashion. The dimple profile was manufactured using a 19.1mm ball nose cutter, cutting out an opening of diameter 8.24mm and to a depth of 4.8mm. Given the availability of ball nose cutters of diameter up to 25mm, the Chyu profile will be replicated with both longitudinal and traverse pitches set to be 2.3 times the open cut diameter [20].

Having included the effect of increased area (17% for hemispheric dimple), the level of heat transfer enhancement over a smooth wall of 2.2 to 2.7 was seen, which is comparable to most of rib turbulators but lower than some of the more complex ones, which are ruled out for our purpose due to manufacturing constraints, Han et al.,1995. Chyu et al., noted that the trends observed appeared to be insensitive to channel height, or W/H ratio (W/H was 4 in their case), or the Reynolds numbers they checked for, Chyu et al., which were as low as Re=1250 in the case of Mahmood et al [20].