It's a great concept, only:

1) the pressure behind the disc would have to be tremendous to hold up to the compression cycle.

2) making a good reliable seal around the moving parts is always an issue with alternative engine designs / gizmos.

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1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma