• The KSFM Journal of Fluid Machinery
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• v.3 no.2 s.7
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• pp.50-56
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• 2000

The effects of lobe shapes on the leak flow conductance of Roots-type vacuum pump are studied numerically and experimentally. The modelled lobe shape of Roots-type vacuum pump is two-lobe spur gear. The numerical analyses are performed on leak flows in Roots-type vacuum pump. It is numerically calculated using a 4th-order Runge-Kutta method and is compared with experimental results. Results show that for the case of involute lobe shape the total amount of the leak flow conductance is greater than that of cycloid and Cassini oval lobe shapes.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.6
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• pp.101-110
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• 2000

A Computer program is developed for creation of a new lobe shaper for Roots-type supercharger. Numerical analyses are preformed for the flowfields in the pocket volumes formed by various lobe shapes. The governing equations for the two-dimensional, turbulent, operational processes in the housing are discretized by the control volume approach that insures the conservative characteristics to be satisfied in the calculation domain, and they are solved by a modified SIMPLE algorithm. Numerical results show that the effects of secondary flow on the leakage flow rate with the Cassini(B) lobe shape is smaller than that of Cassini(A) rotor. But the pocket volume of Cassine(B) lobe is larger than the other lobe shapes.

• Tunnel and Underground Space
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• v.27 no.4
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• pp.243-252
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• 2017

Since the failure behavior of transversely isotropic rocks is significantly different from that of isotropic rocks, it is necessary to develop a transversely isotropic rock failure function in order to evaluate the stability of rock structures constructed in transversely isotropic rock masses. In this study, a spatial distribution function for strength parameters of transversely isotropic rocks is proposed, which is based on the Cassini oval curve proposed by 17th century astronomer Giovanni Domenico Cassini to model the orbit of the Sun around the Earth. The proposed distribution function consists of two model parameters which could be identified through triaxial compression tests on transversely isotropic rock samples. The original Mohr-Coulomb (M-C) failure function is extended to a three-dimensional transversely isotropic M-C failure function by employing the proposed strength parameter distribution function for the spatial distributions of the friction angle and cohesion. In order to verify the suitability of the transversely isotropic M-C failure function, both the conventional triaxial compression and true triaxial compression tests of transversely isotropic rock samples are simulated. The predicted results from the numerical experiments are consistent with the failure behavior of transversely isotropic rocks observed in the actual laboratory tests. In addition, the simulated result of true triaxial compression tests hints that the dependence of rock strength on intermediate principal stress may be closely related to the distribution of the microstructures included in the rock samples.