Equation of state

In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensati

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Philipp Kaspar Bättig, Wanhui Liu, Jürg Alexander Schiffmann, Patrick Hubert Wagner

The nonlinear behavior of a rigid rotor supported by herringbone grooved journal gas bearings (HGJBs) was investigated in this study. The two-dimensional narrow groove theory (2D-NGT) was adopted to model the HGJBs. A set of integrated rotor-bearing state equations were built by coupling the rotor motion equations and the bearing Reynolds equation. An implicit integrator with adaptive time step method was used to solve those state equations continuously. Two low-stability HGJBs were implemented to experimentally demonstrate and analyze the appearance of self-excitation motions. The theoretical model was successfully validated by the experimental data on predicting the onset speed of the sub-synchronous vibration of the HGJB-rotor system and the whirl frequency ratio. The predicted limit cycle amplitude increases as the speed increases until the rotor contacts with the bearing surface, which leads to a bearing failure. Forward conical mode dominates the self-excited motion during the whole speed range of self-excited motion. The prediction shows that the HGJB-rotor system can still operate in a stable, even though the rotor is installed vertically, i.e., without static load on the bearings. This is a distinct advantage in comparison to plain bearings. As the static load applies on the bearings increases, the onset speed of sub-synchronous vibration increases as well. For the investigated rotor-bearing system, an increase of the onset speed of sub-synchronous vibration from 36 krpm to 75 krpm is predicted as the static load increases from 0 to 4 times of the rotor weight. This indicates an increased HGJB stability with increased static load. The rotor orbits show complex shapes when the imbalance excitation is considered in the simulation. Both synchronous frequency and whirl frequency are shown in the spectral analysis. Moreover, the speed range of self-excited motion reduces from [38,48] krpm to [40,42] krpm as the imbalance increases from 0 to 40 mgmm.

2021

Constitutive behavior of as-cast magnesium alloy Mg-Al3-Zn1 in the semi-solid state

André Phillion

The first reported tensile semi-solid stress/strain data for as-cast magnesium alloy Mg Al3 Zn1 are provided. The results show that the maximum tensile stress at the solidus temperature (460 degrees C) was 13 MPa. Furthermore, this alloy has no ductility above 540 degrees C. and cannot sustain tensile stresses above 560 degrees C. Based on these tests, an equation relating the maximum tensile stress with temperature was derived. The microstructure of the tested specimens was also examined to link the tensile properties to fraction Solid and microstructure. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

2009

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Philipp Kaspar Bättig, Wanhui Liu, Jürg Alexander Schiffmann, Patrick Hubert Wagner

2021

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Constitutive behavior of as-cast magnesium alloy Mg-Al3-Zn1 in the semi-solid state

Higgs-Dilaton cosmology: Universality versus criticality

Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

Constitutive behavior of as-cast magnesium alloy Mg-Al3-Zn1 in the semi-solid state

Higgs-Dilaton cosmology: Universality versus criticality