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It seems like a rotary vane compressors have ideal characteristics for a jet engine. They can generate high pressure ratios (up to maybe 10-12) compared to older axial compressors and I think they can have a high flow rate at ~90% energy efficiency. They also seem simpler to construct/cheaper than axial compressors.

I understand that modern axial compressors can generate a higher pressure ratio, but historically why didn't rotary vane compressors have a place over at least centrifugal compressors in earlier jet engines?

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    $\begingroup$ They really can't face the on coming air and keep the flow linear, and they're heavy. In a jet engine, the exhaust turns the turbine in the aft to re-energize the compressor. I can't see that kind of feedback happening in a rotary vane pump. But don't take my word for it just yet. $\endgroup$ – ymb1 Jun 29 '16 at 20:32
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The most important characteristic for a jet engine compressor is high mass flow rate with light weight and if possible small size. For the same size, the flow rate can be increased by operating the compressor at higher rpm. But sliding components don't allow that.

Only the axial and centrifugal compressors can achieve sufficient flow rates, so they are used. Centrifugal compressors achieve higher pressure ratio for weight, but are larger, so they were used in many early designs and now remain in small turboprops while larger engines use axial compressors for their compactness.

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