Q: How does reversible adiabatic efficiency apply in the context of compressors and turbines compared with your reciprocating machine?
In large turbo machinery, you would expect to see reversible adiabatic efficiencies for compressors around 93% and for turbines around 94%. These will be large machines operating in an almost adiabatic regime. Consequently, the reversible adiabatic efficiency is a measure of the irreversibility of the gas process, principally kinetic and friction heating of the gas by the blades.
However, reciprocating machinery can operate with far lower flow velocities than turbo machinery, so these losses are far less significant. The gas flows are only exposed to passage through valves during inlet and egress from compression and expansion processes, with compression and expansion forces being applied by the piston rather than a multiplicity of aerodynamic devices.
Reversible adiabatic efficiency has little relevance to a reciprocating compressor, as the only area to which it can be directly applied is the dissipation of turbulence after passage of the gas through valves. Parasitic heat transfer over the duration of the process is of much greater significance and is manifested as a heat flow in opposition to the normal heat flow direction within the device.
Q: How does the Carnot cycle efficiency apply?
A: The second law of thermodynamics places a fundamental limit on the thermal efficiency of all heat engines. This limiting value is called the Carnot cycle efficiency, because no engine can convert 100% of its heat into work. The Carnot cycle is reversible and represents the upper limit of an engine cycle’s efficiency for an engine in which heat is supplied at a constant temperature and rejected at a constant, but lower temperature. One of the factors determining engine efficiency is therefore how heat is added to the working fluid in the cycle and how it is removed.
The Carnot efficiency is really an availability ratio, not an efficiency, that is, heat pump COP of an ideal engine is the inverse of its engine availability. “Availability” in this context may therefore be defined as the ratio of mechanical work to heat processed.
What is important in terms of our system is that the engine cycle is reversible, not that it is a Carnot-equivalent cycle. “Reversible” means that, for the idealised cycle, the heat moved to the hot store during charging is energy input through the shaft divided by the availability ratio, whereas the mechanical power released upon discharge is equal to the availability multiplied by the heat energy taken from the hot store. As this heat transfer involves varying the temperature of the store material between two reference temperatures, this is not a Carnot- equivalent situation. The essence of our system is therefore the achievement of a real cycle that is as close as possible to the idealised cycle, not a Carnot-equivalent cycle.
Q: How does your system use a Brayton cycle to achieve high reversibility?
A: In its ideal form, a Brayton cycle is reversible, that is, constant entropy compression and expansion are coupled with isobaric heat transfer, but not Carnot-equivalent. A Brayton cycle in its purest form is actually the First Ericsson Cycle.
The reason that we can show high reversibility is that isobaric heat transfer in the constant pressure stores can take place slowly under drifting flow conditions. Adiabatic compression and expansion take place rapidly in our very carefully designed cylinders and can approach the ideal constant entropy condition.
The transfer valves in our system are also an example of extremely careful design with exceptionally low pressure losses. Parasitic heat transfer within the cylinders is very carefully controlled, resulting in very high thermodynamic reversibility. Dead volume must also be minimised since it thermally pollutes the gas charge by mixing the new charge of gas with the gas remaining in the cylinder at the end of the stroke.
Small irreversibilities manifest themselves as waste heat which, if no further steps were taken, would result in an overall rise in mean cycle temperature over several charge-discharge cycles. We remove this heat of irreversibility (also known as generated entropy) via heat exchange to atmosphere on the two datum temperature limbs of the gas circuit. This is a non-critical part of the operation since we are creating a thermal split around this datum temperature. If the datum temperature is slightly above ambient (as it has to be to reject the heat of irreversibility), then it has an inconsequential effect on the system’s performance.
Q: Why not use a Stirling engine?
A: The Stirling cycle is often presented as having the potential to deliver the Carnot efficiency, but this is misleading. A Stirling engine combines a cold space, a hot space, and an interconnecting regenerator.
The theoretical Stirling cycle is reversible, but to achieve high reversibility in a real engine, the real engine would need to operate in a manner close to the theoretical cycle. No real Stirling engine has an operating cycle anything like the theoretical ideal.
Another fundamental problem with the Stirling engine as a prime mover is the need to transfer heat to and from the gas through a wall and over a short portion of each cycle. The wall limits temperature to that which the wall can withstand and the duration of heat transfer is typically one quarter of a cycle. Since heat transfer by conduction is by definition a time-based flow of energy, attempting to perform conductive heat transfer rapidly is always problematic.
Although Stirling engines can be useful in certain roles, for example, cryocoolers and space applications, they should never be confused with engines having a potential Carnot efficiency.
The Stirling cycle is not suitable for PHES as, quite apart from the problems of realising it as a highly reversible cycle, it requires heat to be added and rejected at constant temperatures. This is incompatible with near-reversible cooling or heating a store material between two reference temperatures.