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the ending angle of the involute and it affects the built in volume ratio of the expander. During the inlet condition the fluid enters in the centre of the scroll expander where there is a space between the two mated scrolls. The pocket size increases as the scroll orbits and after a certain angle the intake process ends and the initial pocket is divided into two small pockets. This process is modeled by the equation below. () = h ∗ ( − − + 3) (5.2) This is valid for angles ranging from 0 ≤ < 2. The expander’s expansion volume is given by the equation below which is valid for angles between 2 ≤ ≤ − 2. () = 2h(2 − ( − − )) (5.3) The last relation for modeling the volumes during orbiting is the discharge process. This happens during orbiting angles of − 2 ≤ < and is shown below. (,)=h((2 −2) −( −) −( −)( + +)+2(1− cos( − )) − 2( − ) sin( − ) − sin2( − )) (5.4) The built in volume ratio of the expander is the ratio of the expansion volume at the end of expansion over the value of the expansion volume at the beginning of the expansion process. Equations 5.1-5.4 are used in the relation of the ratio which is shown below: = () = (5.5) () 36PDF Image | Exergoeconomic Analysis and Optimization of ORC
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