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In a radial compressor, the air enters centrally and passes outwards, aided by centrifugal force. But, as the diagram shows, in piston-engine superchargers the driving exhaust gas flows inwards through a radial turbine. This has to fight against centrifugal force instead of leveraging it. So why is it done?

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This has to fight against centrifugal force instead of leveraging it.

In fact, the opposite is true. The arrangement shown actually helps to extract energy, perhaps counterintuitively. A typical example of this arrangement is the Francis turbine.

A high flow speed plus high tangential velocity input, fed through to a low flow speed/low tangential velocity exit, will create the maximum energy differential for extraction. And that describes inwards flow.

There are a few ways of looking at this. One is to look at the exit velocity of the fluid. In a compressor, it's okay if the fluid has some leftover velocity as it will by converted to static pressure when slowed down by Bernoulli's law. For a turbine, the exit velocity should be as low as possible, as kinetic energy of the exhaust flow is 'wasted' energy. So it makes sense to place the exit at the inner radius of the turbine, where the radial velocity component is lowest.

Another way of looking at it is pressure. Centrifugal force creates a pressure gradient across the turbine in radial direction. As a 'packet' of air moves inwards, its pressure becomes lower. By conservation of energy, this must mean that it is expending work on its surroundings. The turbine extracts this work done from the packet of air moving inside.

Another intuitive explanation involves an ice skater retracting their arms in a pirouette (or a bored office worker on a swivelling chair). By conservation of angular momentum, their angular velocity increases. A packet of air would 'like' to increase its angular velocity, but this is kept fixed by the turbine rotating at a fixed velocity. The packet of air must thus be slowed down moving inwards, and as a result exerts a pressure on the turbine blade in front of it.

The choice between axial, centrifugal or mixed-flow is done based on the flow conditions, with high-flow low pressure differential favouring axial design and lower flow or higher pressure differential favouring the radial setup as shown. A more compact design means fewer turbine or compressor stages, which results in a higher pressure differential across the single stage. Thus, a radial setup is preferred.

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  • $\begingroup$ Thank you. I have some observations. If the exit velocity of a compressor can be manipulated by design, so can that of a turbine. Then, whichever way the air flows its angular momentum will change, it doesn't matter which direction it pushes on the blades. So those points are not significant. But as you say, "The turbine extracts [the] work done from the packet of air moving inside." A high flow speed plus high tangential velocity input, fed through to a low flow speed/low tangential velocity exit, will create the maximum energy differential for extraction. And that describes inwards flow. $\endgroup$ – Guy Inchbald Sep 21 at 16:30
  • $\begingroup$ Exactly. Indeed you could swirl the turbine blades such that the flow is slowed down towards the outer perimeter but then you are limited by practical engineering (a larger blade so more wetted=draggy area). The reverse is just easier. $\endgroup$ – Sanchises Sep 21 at 17:08
  • $\begingroup$ It's not obvious why the radial flow speed is lowest at the axis. In fact, due to the constricting effect (less volume near the axis), by Bernoulli we'd expect a higher radial speed. $\endgroup$ – MSalters Sep 22 at 7:44
  • $\begingroup$ @MSalters For most rotating devices, it is obvious that radial speed is greatest at the perimeter, lowest at the axle. You are right that, for turbomachinery, you could indeed find that the channels are directed forward or aft, effectively changing the radial speed. Your intuition is precisely the reason why this turbine is so effective: we would expect by Bernoulli (which is really conservation of energy) that the radial speed is higher, but instead the turbine slows down the radial speed and thus extracts work. See also my last comment. $\endgroup$ – Sanchises Sep 22 at 7:50
  • $\begingroup$ @Sanchises: I still find it non-obvious. The radial velocity at a distance R by definition needs to be the volume flow divided by the cross-section at distance R. That cross-section, for a radial flow in a cylinder of length L, has an area 2πRL. For a constant volume flow, that means the radial velocity is proportional to 1/R. I.e. the velocity goes up. Of course, this is under the assumption of a constant volume flow. In reality, the mass flow is constant, and the pressure drops, so the volume flow only increases going inward. Hence the increase in radial velocity has to exceed 1/R. $\endgroup$ – MSalters Sep 22 at 7:57
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It does seem counterintuitive to arrange the flow as it has been done in turbochargers, but this arrangement is the best compromise for harnessing kinetic energy from exhaust gasses of a reciprocating engine.

Design goals are

  • compact size
  • small backpressure
  • simplicity of construction (build and maintenance cost)
  • ability to utilize "traditional" materials and manufacturing tehcniques.

The turbine housing is formed in such a way, that it dimishimes in size as it circles the turbine wheel. Thus the exhaus gasses travelling throug the chamber eventually (rather quickly in fact) run out of space, and are pushed into the exhaust outlet by the following exhaust pulses.

As such, the exhaust gasses do not need to overcome or fight centrifugal forces, as the housing provides a path that guides the gasses along.

This arrangement, as opposed to reversing the flow, allows for a simplier and less critical turbine wheel profile, and much higher efficiency across flow rate range (iirc I try to dig up the reference) Compared to an axial turbine this construction is less efficient, but it also is so much more simple and compact, that it by far outweights the smaller efficiency.

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  • $\begingroup$ Thank you. A couple of problems I have with that. 1) Does not the circling air path still create a centrifugal force and hence an unwelcome backpressure component? 2) If this is all so great for the turbine, why is it not equally great for the compressor? $\endgroup$ – Guy Inchbald Sep 21 at 11:58
  • $\begingroup$ One way to look at it is that the logic is similar for a regular fan. If you want the fan to blow air the curved (concave) part of the fan should be behind the fan. If you want to blow air into the fan the curved part of the fan should be in front of the fan. Your question is analogous to asking if it's so great for the fan to blow in the direction of the curve why is it less efficient for a windmill to receive wind in the same direction? $\endgroup$ – slebetman Sep 22 at 7:14

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