Influence of Thermodynamic Models in Two-Dimensional Flow Simulations of Turboexpanders

Abstract

This paper presents a quantitative comparison of the effect of using thermodynamic models of various degrees of complexity if applied to fluid-dynamic simulations of turboexpanders operated at conditions affected by strong real-gas effects. The 2D flow field of a standard transonic turbine stator is simulated using the state-of-the-art inviscid ZFLOW computational fluid-dynamic solver coupled with a fluid property library containing the thermodynamic models. The considered thermodynamic models are, in order of increasing complexity, the polytropic ideal-gas (PIG) law, the Peng–Robinson–Stryjek–Vera (PRSV) cubic equation of state, and the highly accurate multiparameter equations of state (MPEoSs), which are adopted as benchmark reference. The fluids are steam, toluene, and R245fa. The two processes under scrutiny are a moderately nonideal subcritical expansion and a highly nonideal supercritical expansion characterized by the same pressure ratio. Using the PIG model for moderately nonideal subcritical expansions leads to large deviations with magnitudes of up to 18–25% in density, sound speed, velocity, and total pressure loss, and up to 4–10% in Mach number, pressure, temperature, and mass flow rate. The PIG model applied to highly nonideal supercritical expansions leads to a doubling of the deviations’ magnitudes. The advantage of the PIG model is that its computational cost is roughly 1/11 (or 1/3 if saturation-checks in the MPEoS are omitted) of the cost of the MPEoSs. For the subcritical expansion, adopting the physically more correct cubic PRSV model leads to comparatively smaller deviations, namely, <2% (toluene and R245fa) and <4% (steam) in all flow parameters, except for the total pressure loss error, which is comparable to that of the PIG model. The PRSV model is reasonably accurate even for the highly nonideal supercritical expansion, for which the errors are at most 4%. The computational cost of the PRSV model is roughly nine times higher than the cost of the PIG model (or twice as high if saturation-checks in the PRSV are omitted). Contrary to low-complexity fluids like water, for complex fluids like toluene and R245fa the deviations in density, speed of sound, and velocity ensuing from the use of the PIG model vary strongly along the isentropic expansions. This invalidates the approach commonly used in practice of correcting the PIG model with a properly chosen constant compressibility factor.