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Why is the surge line of an aeroengine curved? Why is it not a straight line? Surge diagram of an aeroengine

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    $\begingroup$ The surge line is valid for the compressor as a whole. This surge line is compromised of the stall lines for each compressor stage. In the lower-left corner, the surge happens due to a stall in the first stages; In the top-right corner, the surge happens due to a stall in the last stages. For a more detailed understanding, please refer to pertinent literature about speed lines and the flow around blades. $\endgroup$ – user12485 Jan 31 '16 at 10:50
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    $\begingroup$ Please provide the source for your image $\endgroup$ – TomMcW Jan 31 '16 at 19:57
  • $\begingroup$ Surge is a very complex phenomena, coming for flow going in opposite direction to the main flow. That's is a very complex phenomena, the question is why do you think a such a complex phenomena is having a linera behaviour $\endgroup$ – Trebia Project. Jan 31 '16 at 21:36
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Simply put, it's supposed to follow a constant flow/fanspeed curve but multiple stages and the mechanics of surging make it a lot more complex in practice.

The surge line slope on multistage compressors can range from a simple, single-parabolical [sic] relationship to a complex curve containing several break-points or even 'notches.' The complexity of the surge line shape depends on whether or not the flow limiting stage changes with operating speed from one compression stage to another; in particular, very closely matched stage combinations frequently exhibit complex surge lines... The surge line in many cases has an approximately constant value of Q/N [mass flow/fan speed]. In many multi-stage units, and especially in units which are controlled by variable inlet guide vanes, the surge line curves bend dramatically at higher flows and speeds.
Source: "Practical Aspects of Centrifugal Compressor Surge and Surge Control" by Meherwan P. Boyce (pdf)

So some of the shape comes from the curvature and irregular spacing of the constant speed lines, and some of the curve comes from adding in different stages.

Unfortunately, exact surge conditions are not easy to describe mathematically even if we know the properties of each stage in the compressor. There are things like multi-blade interactions and boundary layer effect that make things difficult really fast. These factors are so important because surge is not quite the same as a stall on compressor blades. Surge is a more complex unstable compressor flow resulting from stalls. Single blade stall, which isn't observed much in practice, will not cause a surge. Surge happens when the stall propagates across several blades due to blocked incoming air. There aren't easy,exact, and universal equations for this complex behavior unfortunately.

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    $\begingroup$ I "quotified" the quote to make it easier to identify. Feel free to revert or adjust if I missed some of it. $\endgroup$ – FreeMan May 6 '16 at 15:45

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