Figure 1.
Ideal Rankine power cycle with one open feed water heater redrawn as energy flow networks following thermodynamic network theory [26].
Note that the link between the condenser (Node vi) and Pump 1 (Node i) is not a physical flow of energy. Since State 1 acts as an energetic reference state for the network, working fluid returning to that reference state only closes the material loop; energy embodied in the working fluid leaving the condenser is rejected to the surroundings.) (a) Energy, in the form of heat and work and carried by the working fluid, flows to and from the mechanical components of the idealized equipment diagram for a power cycle. (b) The system is simplified with the mechanical components modeled as ‘nodes’ connected by flows of energy in the energy flow diagram.
Figure 2.
The process for calculating the cyclicity of the 6 component Rankine cycle from Figure 1.
(a) Labeled adjacency matrix for the ideal Rankine cycle with one open feed water heater – rows represent flow to a node, columns from a node. (b) Equation for the calculation of the eigenvalues for the adjacency matrix. (c) Eigenvalues. (d) Maximum real eigenvalue, or the cyclicity, of the cycle.
Figure 3.
Examples of the three types of internal structural cycling based on cyclicity (eigenvalues).
(a) No cycling λmax = 0, (b) weak cycling λmax = 1, (c) and strong cycling λmax>1 [10].
Table 1.
Specified state point data for all ideal Rankine and Brayton cycle analyses.
Table 2.
Thermal efficiency and cyclicity values for 20 (R1–R20) Ideal Rankine power cycles evaluated under the same conditions.
Table 3.
Thermal Efficiency And Cyclicity Values 8 (B1–B8) Ideal Brayton Power Cycles Evaluated Under The Same Conditions [27].
Figure 4.
Maximum Thermal Efficiency vs. Cyclicity for all 28 Power Cycles with linear trend lines.
Note: All cycles described here are ideal and optimized for maximum thermal efficiency; changes in kinetic and potential energy from one point to another have been neglected as well as losses in connections between components, such as friction losses in pipes, turbulence, and flow separation.