Page 237 - 48Fundamentals of Compressible Fluid Mechanics

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This chapter is the second on the section dealing with filling and evacuating cham-
bers. Here the model deals with the case where the volume is controlled by exter-
nal forces. This kind of model is applicable to many manufacturing processes such
as die casting, extraction etc. In general the process of the displacing the gas (in
many cases air) with a liquid is a very common process. For example, in die cast-
ing process liquid metal is injected to a cavity and after the cooling/solidification
period a part is obtained in near the final shape. One can also view the exhaust
systems of internal combustion engine in the same manner. In these processes,
sometime is vital to obtain a proper evacuation of the gas (air) from the cavity.

12.1 Model

In this analysis, in order to obtain the essence of the process, some simplified
assumptions are made. It simplest model of such process is when a piston is
displacing the gas though a long tube. It assumed that no chemical reaction (or
1
condensation/evaporation) occur in the piston or the tube . It is further assumed
that the process is relatively fast. The last assumption is a appropriate assumption
in process such as die casting.
Two extreme possibilities again suggest themselves: rapid and slow pro-
cesses. The two different connections, direct and through reduced area are com- again to add the dimensional
bined in this analysis. analysis what is rapid and
what is slow.
1 such reaction are possible and expected to be part of process but the complicates the analysis and
do not contribute to understand to the compressibility effects.

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