Airflow around bends
As with other pieces of ducting, the loss incurred when air flows around a bend is expressed as a fraction of the mean velocity pressure in the bend, provided that the section is constant. If the section varies, precise calculations are not possible but, with a bit of common sense, a good approximation can frequently be obtained.
For a normal bend of constant cross-sectional area, the loss depends on three structural properties:
(i) The curvature of the throat.
(ii) The shape of the section.
(iii) The angle through which the airstream is turned.
It is customary to express the curvature of the throat either in terms of the ratio of the throat radius Rt to the dimension W, parallel to the radius, or, in terms of the ratio of the centre-line radius Rc to the dimension W. Figure 15.13(a) illustrates these two methods. The mode using the centre-line radius is the more common and the one adopted by the CIBSE. A very large value of RJW implies that the air is only very gradually turned and that, turbulence having little opportunity to form, the loss is small. It is evident, however, that not only will skin friction play an increasing part if the bend is excessively gradual, but that the bend will be expensive to make and unsightly in appearance, occupying as it does a very large amount of space. A good practical value for RJW is 1.0.
Case 2 Large aspect ratio
Small aspect ratio
Fig. 15.13 (a) and (b) Airflow around a bend, (c) Bends of different aspect ratios.
The loss through a bend is approximately proportional to the angle turned through, with bends of 45° having ^-values of 0.6 times those of similar 90° bends. When a pair of 90° bends with smoothly curved throats forms an off-set (Figure 15.14) the i^-value for the combination is about 1.8 times that of a single 90° bend. Tsai (1989) and CIBSE (1986a) provide comprehensive information.
The shape of the section, or the aspect ratio, has an effect which is shown by Figure 15.13(c). Case 1 illustrates a duct where the aspect ratio, W/h, is small and the curvature
Fig. 15.14 Duct bends in series.
Of the throat is also small. Case 2 shows the reverse situation: W/h is large, the curvature of the throat is great, and the loss is comparatively large.
There are two methods of minimizing the energy loss round a bend: the use of splitters or the use of turning vanes.
Splitters are only of value when the aspect ratio (W/h) is large and Rt/W is small. They divide the duct into several sub-sections, reducing the turbulence, the noise and the pressure drop. Extensive information on the loss through bends fitted with splitters is provided in ASHRAE (1993) but none is given in CIBSE (1986a). It is usual to arrange the positioning of the splitters so that they cluster near to the throat of the bend. Experiment suggests that it is the curve ratio, defined as throat radius/heel radius, which determines the energy loss, rather than the aspect ratio directly. The consequence is that the splitters should be arranged to produce a number of sub-sections of the duct, each having the same curve ratio.
An expression for the curve ratio, C, in terms of the number of splitters, n, the throat radius, R0, and the heel radius, Rn+l, can be obtained. The following statements hold good for the bend shown in Figure 15.15:
Fig. 15.15 The location of splitters in a bend.
R0 throat radius of the bend without splitters
= K = — — “■" — —
Rn+[ heel radius of the bend without splitters
C = ^- = §- = etc…. = — jЈ=- (15.36)
*M K2 Kn+]
Thus Ri = Rq/C, R2 = R/C = Rq/C2, etc___ Rn+l = R()/Cn+’
= AT1/(n+,) (15.37)
Note also that
Dividing above and below by /?n+1, this becomes
W ~ (1-/0
Applying equations (15.36) to (15.38) shows that a single splitter would be closer to the throat than the centre-line. It is seldom necessary to use more than two splitters. The method is expensive in manufacturing cost.
One of the most effective bends, both from the point of view of accommodating the ductwork neatly and minimising the energy loss, is the mitred bend containing turning vanes. There are two types of turning vane, the simple kind and the so-called aerofoil sort. Of these, the former have an energy loss which is about double that of a conventional bend with RJW equal to unity, and the latter a loss somewhat less than the conventional bend. To achieve a fairly low pressure drop, the ratio of the height of the vanes to their spacing should be six, or greater.
Reference should be made to manufacturers’ data for the loss through turning vanes.
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