Effect of environmental pressure enhanced by a booster on the load capacity of the aerodynamic gas bearing of a turbo expander
Introduction
The turbo expander is an equipment utilized to obtain low temperature and recycle energy. In the cryogenic turbo expander, the temperature of the inlet medium is low, the expansion ratio is high, and the specific enthalpy drop of the expansion medium is large. Generally, the rotor speed of the turbo expander is very high that it exceeds 104 r/min [1], [2], [3], e.g., the rotation speed of turbo expander reaches 196 kr/min in the literature [4]; a high speed turbo expander with gas bearing has been studied in literature [5], [6], the design rotation speed is 300 kr/min and the maximum rotation speed is 342 kr/min. The operation requirements of an equipment are difficult to achieve with oil-lubricated bearing under such a high speed. Gas bearing has the advantages of light weight, high speed, frictionless, non-polluting, and it can be steady running at the high and ultra-speed [7], [8], [9]. Recent years have seen an increasing number of researchers to explore aerodynamic gas bearing. Such as active lubrication applied to gas bearings is presented [10], [11]. They proved that it is possible to avoid common drawbacks associated with gas bearings, namely poor carrying capacity and low damping properties, which often lead to a reduced stability range. Xuedong Chen and Xueming He studied the effects of the recess shape of the gas-lubricated bearing on the performance analysis through numerical method [12], they found that the rectangular recess can provide larger load capacity than the spherical recess. Jianjun Du et al. studied the influences of structural parameters of pressure-equalizing grooves (PEGs) on the load capacity and stiffness of externally pressurized gas journal bearings and found that opening the axial PEGs is more helpful to improve the load capacity than opening the circumferential PEGs [13]. Yu Hou et al. analyzed the static and dynamic characteristics of a new type of foil journal bearings with protuberant foil structure and indicated that the bearing characteristics are significantly affected by the increase of bearing number and eccentricity ratio, particularly with respect to small bearing number [14]. Kai Feng et al. proposed a comprehensive theoretical model of flexure pivot tilting pad gas bearings (FPTPGBs) with metal mesh dampers (MMDs) in parallel by coupling the FPTPGB model and MMD model [15].
The lubrication medium of an aerodynamic gas bearing is compressible fluid. The flowing pressure of the compressible lubricating film is related to the environmental pressure. The supporting properties of aerodynamic gas bearing have been investigated extensively, but the effect of the environmental pressure of the bearing end on gas bearing properties has not been reported.
This study focuses on the bump foil gas aerodynamic bearing to analyze the effect of the environmental pressure of the bearing end on the gas bearing properties. The finite difference method and Newton-Raphson iteration method are adopted to solve Reynolds equation and gas film thickness equation.
In addition, for several turbo expanders that employ a fan brake (e.g., small cryogenic turbo expander), the fan sucks and discharges air from and to the atmosphere directly; hence, the power provided by the turbo expander is wasted completely. To recycle this part of energy, we recommend replacing the fan impeller with a booster and supplying pressurized gas to the gas bearing to enhance the environmental pressure at both ends of the bearing. As a result, the load capacity of the aerodynamic bearing can be improved. The design of the fan brake often focuses on simplified structure and improved mechanical strength; efficiency is often a secondary consideration. This study investigates the fan impeller as a booster, which not only consume the mechanical work of the turbo expander but also compresses the gas and does work on it to increase the gas pressure from the outlet nozzle. The flow in the internal mechanical part of the impeller is a highly complicated viscous and compressible unsteady 3D flow. The FINE/Turbo solver of the NUMECA software employs the time marching method to solve Reynolds averaged N–S equations and is applied to compressible and incompressible flows across a range of low, transonic, and hypersonic speeds. In this paper, the internal flow of the booster impeller is numerically analyzed with the NUMECA software to provide a theoretical foundation for the feasibility of improving the environmental pressure of the aerodynamic gas bearing through a booster.
Section snippets
Mathematical model
Fig. 1 shows a schematic of a bump foil gas aerodynamic bearing. φ is attitude angle of the bearing.
- (1)
Reynolds equation
In this paper, the N-S equation for three-dimensional compressible flow is solved for numerical simulations. The dimensionless form of compressible gas static Reynolds equation at the isothermal condition is:
The dimensionless parameters are:Where: P—dimensionless gas film pressure;
Pa— environmental pressure (Pa);
R
Acknowledgements
The authors are grateful for the support of Natural Science Foundation of China (Grant no. 51276016) and the Foundation of China State Key Laboratory of Technologies in Space Cryogenic Propellants (Grant no. SKLTSCP1201).
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