Non-circular exhaust sections
In one of the previous articles, the discussion points were on the traditional methods of manufacture, and this month we shall look in more depth at non-circular sections in exhausts.
In the article dated June 14, we mentioned pressed mends as a means of being able to produce very tight radii where space constraints require this. Of course, there are other applications of pressed parts in exhausts, especially where the space envelope is tight. As we know, the aero departments have a great influence on the design of the car and the tight spaces left after they have draped their desired bodywork shapes over the chassis, engine and gearbox mean that our pipes are often, by necessity, quite contorted. In this case, pressed and welded exhaust sections can offer us the chance to use different cross-sectional shapes. By flattening the exhaust pipes locally we are able to fit within spaces where a number of round-section pipes might not. In view of non-circular pipes, we need to be careful not to flatten the profile too much without consideration of the results. If we don’t have the luxury of CFD analysis, then here we need to consider hydraulic diameter. Many people are not familiar with the concept of hydraulic diameter. It takes into consideration the flows in non-circular ducts and equates this to the behaviour of flows in a circular duct. This circular duct has a smaller cross-sectional area than the non-circular pipe and therefore has higher pressure losses. The calculations are based on the diameter of this analogous duct – the hydraulic diameter.
If we take a circular pipe and compress it in one direction between two flat plates, it distorts to form a shape that is often called a ‘racetrack’ (more like Indianapolis than Spa!), similar to the profile of the pressed sections we have discussed. Whilst we would all accept that the internal cross-sectional area of the pipe remains pretty constant, the effective flow area does not behave as such. For regular polygons (equal sides and angles), the hydraulic diameter is taken to be the diameter of a circle inscribed inside the wetted perimeter of the section. For other irregular sections there is a (thankfully simple) formula to allow us to calculate this:
Dh = 4A/P
Dh = hydraulic diameter
A = measured cross-sectional area of the duct in question
P = wetted perimeter of the duct
Let us work through a trivial example of a circular tube of 50 mm inside diameter and compare this to rectangular section duct with an aspect ratio of 2:1 of the same area. The cross-sectional area in both cases is 1963 mm2. We can therefore calculate that the sides of the rectangle are 31.33 mm x 62.66 mm. The perimeter of the rectangular section is 2 x (31.33 + 62.66 mm) = 188 mm.
The hydraulic diameter is then 41.76 mm, which is only 83.5% of the diameter of a circular pipe of the same cross-sectional area. We can make an estimate of flow-losses from textbooks on fluid flow due to this decreased equivalent diameter. It should be noted that this effect is not always negative, and irregular cross-sections have been used to control and mitigate the effects of other flow phenomena….
The June 14 article also implied that the section of the pipes would be round immediately after the cast flange which joins the primaries to the header pipes. This again isn’t necessarily the case, and a number of teams use quite a length of fabricated transition on each primary before finally coming to the round section. Too quick a change of section can lead to separation of the flow from the walls, and hence to higher pressure losses in the system. The result here is the same as having a section of pipe of smaller cross-sectional area.
Written by Wayne Ward