In this sixth and final lesson we introduce a couple of alternative cycle arrangements that pocketORC is able to deal with. We also recast one of our cycle variables into a form that allows these different cycle arrangements to be easily modelled.
The potential benefits from these alternative cycle stems from their potential to facilitate large heat source temperature drops, and therefore extract more heat. This allows us to produce more power from the heat source.
In lesson 1, we revised the concept of saturation properties, and introduced the condensation and evaporation temperatures and pressures. Such a cycle, where we have both condensation and evaporation, is referred to as a subcritical cycle since both pressure levels are below the critical pressure of the working fluid.
However, in a transcritical cycle, the pressure rise in our pump increases the high pressure of our system to a value that is above the critical pressure. Such a fluid state is referred to as a supercritical state, and for such a state there is no longer a distinction between separate liquid and vapour states.
For the cycle below, try varying the pressure ratio to see what our subcritical and transcritical cycles looks like in the temperature-entropy diagram.
Another alternative cycle is a cycle involving two-phase expansion. In this cycle, instead of having saturated or superheated vapour at the inlet of our expander, we admit a two-phase mixture (i.e., a mixture of saturated liquid and saturated vapour) into our expander.
We can define the two-phase mixture using the vapour quality, which is defined as the ratio of the mass of the vapour to the mass of the two-phase mixture as a whole. If the vapour quality is 0, then we saturated liquid, whilst if it is 1 we have completely saturated vapour. If it was set to 0.3, we have 30% vapour, and 70% liquid.
Try varying the expander inlet vapour quality below to see what a cycle operating with two-phase expansion looks like in the temperature-entropy plane. Try varying the vapour quality below.
In our earlier lessons, we have explicitly defined the degree of superheat at the expander inlet as an input into our calculations. However, doing this introduces some challenges when we want to have a single model that is capable of modelling subcritical cycles, transcritical cycles, and cycles operating with two-phase expansion.
For this reason, our degree of superheat variable is recast in a different form which easily allows all of these cycles to be modelled using a single parameter. This parameter is referred to as the expander inlet parameter.
The expander inlet parameter can take any value between the limits of 0 and 2, and is defined as follows:
Input values between 0 and 1 can be used to model two-phase expansion, and the input value for the expander inlet parameter is linked directly to the expander inlet vapour quality. So, expander inlet parameters of 0, 0.5 and 1 would correspond to expander inlet vapour qualities of 0%, 50% and 100% respectively.
Input values between 1 and 2 can be used to model expansion from superheated vapour, and the degree of superheat is defined as a fraction of the maximum possible superheat. The definition takes the form:
T = TA + (x - 1)(Thi - TA)
where TA is a reference temperature, x is the expander inlet parameter, and Thi is the heat source inlet temperature. The reference temperature TA is taken as the evaporation temperature for subcritical cycles, and the critical temperature for transcritical cycles. Therefore, if x = 1 then the expander inlet temperature is equal to the evaporation (or critical temperature), and if x = 2, then the expander inlet temperature is equal to the heat source temperature.