Effects of humid air on aerodynamic journal bearings

The development of aerodynamic bearings applications where ambient conditions cannot be controlled (e.g., for automotive fuel cell compressor) raises the question of the effects of condensation in the humid air on performance. A modified Reynolds equation is obtained in relation to humid air thermodynamic equations, accounting for the variation of compressibility and viscosity in the gas mixture. The load capacity and stability of plain and herringbone-grooved journal bearings is computed on a wide range of operating and ambient conditions. In general, performance metrics show an independence on humid-air effects at moderated temperature, although the stability of the grooved journal bearing exhibits strong variations in particular conditions. In consequence, a safety margin of 25% is suggested for the critical mass.


Roman symbols a
Groove length b Ridge However, the existing literature on the HA-lubricated bearings is limited 24 to slider geometries with ultra-thin film lubrication, with no application to 25 journal bearings. 26

Goals and objectives 27
The present work investigates the HA effects on the performance of plain 28 journal bearings (PJB) and of herringbone-grooved journal bearings (HGJB).

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The objectives are to: (1) Since the practical problem targeted in the present work involves an atmospheric pressure, both gases (air and water vapor) are considered as ideal.

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However, for an isothermal gas, the saturation partial pressure of water can 67 be reached within the film as mixture pressure increases. At this point (dew 68 point), water vapor starts condensing and limits its contribution to the mix-69 ture pressure build-up on which the bearing relies to serve its purpose. At 70 this point, the behavior of the mixture deviates from an ideal gas, namely: where r a is the specific gas constant of the ambient HA. In order to account Where (∂ ρ P ) T is associated to the bulk modulus β of the lubricant gas: The following normalization is performed on Equation 1 to express it in 77 cylindrical coordinates (Equation 6): In order to obtain the dynamic coefficients and to compute the critical mass, the clearance is perturbed by an infinitesimal harmonic motion 1x and 1y ( x/y = e x/y /h 0 ) in the x and y directions respectively [7]: where 0x and 0y are the static equilibrium eccentricity ratios. The other 81 perturbed terms involved in Equation 7 are: Only terms of order 0 and 1 with respect to 1x and 1y are retained 83 and grouped in Equations 14 and 15 respectively. The same procedure is 84 reiterated in the y direction without being repeated here.  The same method can be applied to the HGJB using the Narrow Groove pairs over the bearing domain, smoothing the local pressure variation over a ridge-groove pair. Only the resulting differential equation is displayed here: where the geometry is presented in Figure A.2 and functions f i are sum-97 marized in the Appendix. A first-order perturbation is applied to this equa-98 tion following Equations 9 to 13 and zeroth-and first-order equations are 99 segregated to be solved successively.

100
The problem of HA lubrication consists in the expression of (∂ρP ) T . As 101 long as the saturation partial pressure of water vapor is not locally reached, 102 the mixture is assumed to be an ideal gas. Thus, the term (∂ρP ) T , encapsu-103 lated in the bulk modulus, is equal to unity: Only when the saturation pressure is met, condensing water will stop 105 building up pressure, leading to (∂ρP ) T < 1, thus, departing from the ideal-106 gas behavior.

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The ideal-gas equation for the gas mixture is: The value of (∂ ρ P ) T is simply: where r is the mixture specific gas constant and w is the humidity ratio defined as the ratio of mass water vapor per unit 111 mass of dry air: The value of w of the gas phase is defined locally depending on whether the 113 saturation conditions are met or not: w * is the saturation humidity ratio, which is a function of the ambient tem-115 perature and local pressure as follows: where P * vap is the saturation pressure of water that depends on the tempera- 23 and w * is isolated: If saturation is reached and the water content in the gas phase decreases, 123 the mixture viscosity evolves accordingly. It is expressed from [11] as follows:    assumption, the void fraction gets the following expression: The minimum value barely reaches 99% for T just below 100 • C, which is 235 suggested to be sufficiently small to discard any risk linked to the formation 236 of a local liquid film in the bearing clearance.