Influence of Ideal, Cubic, and Multiparameter Helmholtz Equations of State on the Static and Dynamic Performance of Porous Aerostatic Journal Bearings
Abstract
Porous aerostatic gas bearings are commonly modeled using the ideal-gas law, although non-ideal thermodynamic behavior may become relevant for alternative working fluids. This study quantifies the influence of the thermodynamic closure on the stationary and dynamic response of porous aerostatic journal bearings. A finite-volume formulation couples the compressible Reynolds equation with three-dimensional Darcy flow, retaining transient gas storage in both domains. Density is used as the primary thermodynamic variable, allowing the ideal-gas, van der Waals, Soave--Redlich--Kwong, Peng--Robinson, and multiparameter Helmholtz equations of state to be evaluated within an otherwise unchanged bearing model. Air, R1234yf, and R1234ze(E) are considered. For air, EOS-induced differences remain negligible over the investigated range. For the refrigerants, the ideal-gas approximation produces several-percent deviations, with supplied mass flow and dynamic force response being particularly sensitive. The cubic equations substantially reduce these deviations, with the employed Peng--Robinson formulation providing the closest agreement with the Helmholtz reference for both refrigerants at a computational cost comparable to the other cubic models. The results identify density and differential compressibility as the main thermodynamic quantities governing the propagation of EOS errors into mass transport and transient gas storage.
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BibTeX
@misc{stellmach2026influence,
title = {{Influence of Ideal, Cubic, and Multiparameter Helmholtz Equations of State on the Static and Dynamic Performance of Porous Aerostatic Journal Bearings}},
author = {Laurenz Stellmach and Steffen Nitzschke and Elmar Woschke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27840},
eprint = {2610.27840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27840},
}
RIS
TY - UNPB
TI - Influence of Ideal, Cubic, and Multiparameter Helmholtz Equations of State on the Static and Dynamic Performance of Porous Aerostatic Journal Bearings
AU - Laurenz Stellmach
AU - Steffen Nitzschke
AU - Elmar Woschke
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27840
UR - https://arxiv.org/abs/2610.27840
AB - Porous aerostatic gas bearings are commonly modeled using the ideal-gas law, although non-ideal thermodynamic behavior may become relevant for alternative working fluids. This study quantifies the influence of the thermodynamic closure on the stationary and dynamic response of porous aerostatic journal bearings. A finite-volume formulation couples the compressible Reynolds equation with three-dimensional Darcy flow, retaining transient gas storage in both domains. Density is used as the primary thermodynamic variable, allowing the ideal-gas, van der Waals, Soave--Redlich--Kwong, Peng--Robinson, and multiparameter Helmholtz equations of state to be evaluated within an otherwise unchanged bearing model. Air, R1234yf, and R1234ze(E) are considered. For air, EOS-induced differences remain negligible over the investigated range. For the refrigerants, the ideal-gas approximation produces several-percent deviations, with supplied mass flow and dynamic force response being particularly sensitive. The cubic equations substantially reduce these deviations, with the employed Peng--Robinson formulation providing the closest agreement with the Helmholtz reference for both refrigerants at a computational cost comparable to the other cubic models. The results identify density and differential compressibility as the main thermodynamic quantities governing the propagation of EOS errors into mass transport and transient gas storage.
ER -