Under-Compression (Over-Expansion) – An Isochoric Or Adiabatic Process?

Paul Xiubao Huang


It has long been established that for a Positive Displacement (PD) compressor or expander such as reciprocating or rotary screw type, the thermodynamic process is adiabatic when compressor or expander discharge pressure is equal to system back pressure (or 100% internal compression or expansion). At this design point, compressor or expander efficiency and noise are most desirable. But more often, PD compressor or expander operates at off-design points where the discharge pressure is either lower or higher than the system back pressure caused by the inherent nature of possessing a fixed built-in volume ratio. The resulting processes are often called an Under-Compression abbreviated as UC (or Over-Expansion, OE) and an Over-Compression, OC (or Under-Expansion, UE), and the thermodynamic process suddenly changes to iso-choric (constant volume). The compressor or expander efficiency and noise become worse at these off-design conditions and some type of controls are always desired such as a variable geometry in order to minimize the losses. On the other hand, there have been test observations that seem to contradict the conventional theory, pointing to the dramatic difference of the thermodynamic processes between an UC and internal compression. So questions arise: What is the true thermodynamic process of an UC? What really does the compression at the instant when the gas is exposed to higher system pressure? How is energy exchanged during an UC cycle? And why does UC possess the unique self-adjusting capability to different system pressures? This paper attempts to re-exam these questions by applying the 1st Law of Thermodynamics to UC (or OE) mode. It will be demonstrated that an UC (or OE) may inherently be an adiabatic process with compression achieved by a “flexible” backflow rather than a “rigid” piston or lobe. The energy exchange, in addition to work input from shaft to gas, is assisted by a dynamic process of “borrow and return” with the discharge system. It will be further explored that the mechanism of backflow compression is in essence a wave compression as illustrated by the Shock Tube Theory. Potential efficiency of an UC or OE could be close to the classical internal compression if the high velocity backflow is managed properly. But the best or maybe the most overlooked property seems to be its “feedback” capability, that is, an UC is a self-correcting, negative feedback control loop capable of meeting different system back pressures without using any variable geometry. A Roots type blower is used as an extreme example of UC to illustrate the new theory.