The turbo-compound Napier Nomad held the fuel-specific record for years, and is still ahead of straight turbines because the intermittent combustion allows a higher peak temperature, and with it, better Carnot efficiency numbers. It was just considered too complex.
One thing to consider with the automotive application is that when running at part throttle, the exhaust can be just returning to ambient pressure, leaving nothing for the turbo or second cylinder So this would work best on a very low-powered car. I don't think peak temperatures will be a problem in the second cylinder at any point.
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