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Accelerating Iterative Equation of State Calculations With Superancillary Phase Boundaries



Ian Bell


Iterative calculations are needed to obtain the natural variables of an equation of state from the given state variables when analyzing thermal systems (machinery, systems, even simple cycle analysis). When the given state variables are entropy and enthalpy, which arise naturally in turbomachinery, this problem is particularly challenging due to the range of shapes of the phase boundary possible in these coordinates. The iterative calculation of temperature and density from entropy and enthalpy represents a computational bottleneck in many cases. In recent studies it has been shown how superancillary equations (sets of one-dimensional Chebyshev expansions) can be generated that represent the phase boundary of the equation of state to approximately numerical precision. These functions are a few hundred times faster to obtain than the full equation of state. This work shows that if the phase boundary is expressed as superancillary curves, the enthalpy-entropy calculations can be accelerated, particularly near the phase boundary, and made simultaneously more reliable than the existing approaches. The approach is applied to two pure fluids with differing phase boundary shapes.
Proceedings Title
6th International Seminar on ORC Power Systems
Conference Dates
October 11-13, 2021
Conference Location
Munich, DE


Chebyshev expansion, equation of state, iterative, phase equillibria


Bell, I. (2021), Accelerating Iterative Equation of State Calculations With Superancillary Phase Boundaries, 6th International Seminar on ORC Power Systems, Munich, DE, [online], (Accessed April 21, 2024)
Created October 11, 2021, Updated November 29, 2022