Great article, Marty. Thank you for sharing your thoughts. Unfortunately it stopped without sharing the math for the design of this Laval TP, how to create one in an existing airgun, or how to install it. The concept makes a lot of sense but implementation could be a real challenge - great information, though.
The Walther LGV belongs to Hector. He custom-tuned it with an anti-bounce piston (ABP). The ABP has a cavity in an enlarged piston stem that holds a non-Newtonian fluid steel. The enlarged stem also functions as a spring guide, it just happens to be inside the piston, not at the rear, as usual. The fluid steel holds a shape (behaves like a solid) when accelerated or under pressure, but when acceleration becomes zero (as when the bounce cycle starts), then the steel becomes fluid again and tries to remain in position by its internal inertia. So the piston is stopped from bouncing and the piston, by holding the position in the compression chamber, maintains the pressure behind the pellet, so that with the same energy input, it can achieve almost 10% more muzzle energy.
Adiabatic heating during springer compression is important. It is also "mostly" conserved and used during the brief expansion (with adiabatic cooling) time behind the pellet. Of course SOME heat is lost to the rifle and the surrounding air, but in the short time frame involved it is a trivial amount of lost energy. This is oversimplifying the process, but I think it is basically "good enough" for this discussion.Before the pellet moves the piston is compressing the air in the compression tube and the transfer port and there is no air "flow" through the transfer port. Maybe the air molecules are crowding into the transfer port at some "effective velocity", but I can't see why that velocity would be faster than the piston velocity (~15 m/s max in my simulation).I think it is important to mention that the pellet typically doesn't start to move until the piston is 0.1"-0.2" away from slamming into the end wall.Once the pellet starts to move down the barrel the air pushing it cannot be traveling any faster than the pellet itself. Most folks seem to agree that airgun pellet (diabolo shape) accuracy is best when muzzle velocity is sub-sonic. That means the maximum air velocity behind the pellet is also subsonic. Once the pellet leaves the muzzle that airflow velocity might increase to supersonic as the "cork leaves the bottle". Except for excessive NOISE and some small amount of wasted potential energy, I don't see how that exit airflow matters once the pellet is in free flight.IMO the air flow through a "springer" transfer port is not fast like flow through a rocket/jet nozzle. That is why a transfer port shaped like a rocket nozzle will not provide any significant performance boost.I can't PROVE that without performing advanced math and expensive time consuming experiments with measurements. A project I don't have the resources to tackle.If you still feel that great improvements can be made in springer TP design, please continue until you find the answers to your questions.