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A direct numerical method for the anisotropic diffusion equation is presented and the balancepoint method and adaptive method are also derived. All these methods are formulated and implemented in the in-house fluid flow solver GTEA. Two test cases, an isotropic problem and an anisotropic problem with exact solution on a skewed mesh, are chosen for comparison and validation. The error and computation time are illustrated. It is concluded that the direct method has the least computation time among all the diffusion problems and that all the methods meet the precision requirement in engineering computation even on skewed meshes.

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Rotary compressors are designed more and more compact and the compressor cylinder's ambient pressure is designed very high to facilitate oil separation and improve efficiency. However, these designs cause the working condition of the thrust bearing becoming harsher, and severe wear may occur. The present study is aimed at mitigating its wear condition through surface texturing. Based on a transient tribo-dynamics model considering the coupling effect of the journal and thrust bearings, a texture optimization study for the thrust bearing is conducted, in which three different stochastic optimization algorithms are utilized. The results show that thrust bearings with optimized textures have significantly reduced contact forces and wear under a high working frequency due to an extra hydrodynamic support around the texture dimples. The optimized texture designs are fabricated on the thrust bearing surfaces by a high-accurate picosecond laser machine and their performance is assessed through experiments using a compressor performance test platform. The experiment results confirm that the textured thrust bearing has a lower wear depth. Moreover, the coefficient of performance (COP) of the testing compressor with textured thrust bearing is increased while its input power decreases, which implies a reduced friction force and a higher energy efficiency.

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