Unsteady Flow of Shear-Thinning non-Newtonian Incompressible Fluid Through a Twin-Screw Extruder

The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed bound- ary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it con- tains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

Energy flow characteristics of friction-induced nonlinear vibrations in a water-lubricated bearing-shaft coupled system

Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.