An improved correlation of the pressure drop in stenotic vessels using Lorentz's reciprocal theorem

A mathematical model of the human cardiovascu lar system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a the oretical relation between pressure drop and flow rate based on Lorentz＇s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxel based simulator VFLOW VOF3D, where the vessel geome try is expressed by using volume of fluid （VOF） functions, is employed to find the flow distribution in an idealized steno sis vessel and the identity was validated numerically. It is revealed from the correlation flow in a stenosis vessel can that the pressure drop of NS be decomposed into a linear term caused by Stokes flow with the same boundary condi tions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication the ory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geomet ric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under dif ferent stenosis conditions by using 1D mathematical model.

Synovial Joint Study

The impact of certain separate characteristics, including the porosity parameter, reaction rate parameter, and viscoelastic parameters of steady convective diffusion across a rectangular channel, has been investigated in this article. The model’s momentum and concentration equations were developed using the similarities technique, and the numerically finite volume method was combined with the Beavers and Joseph slip conditions. Various graphs have been used to get insight into various parameters of the problem on velocity and concentration. The cartilage surfaces are assumed to be porous, and the viscosity of synovial fluid varies with hyaluronate (HA) content.

Saffman–Taylor instability in eccentric cylinders at gaseous cavitation

A flow of silicon fluid in the gap between eccentric cylinders was studied experimentally.The condition of gaseous cavitation inception during the rotation of internal cylinder was considered.It was shown that at reduction of the gap between cylinders Saffman–Taylor instability appeared on surface of the internal cylinder and then gaseous cavitation was observed.Possibility of one uniform gas formation appearance under this type of instability was demonstrated.

HYDRODYNAMIC AND ELASTOHYDRODYNAMIC STUDIES OF A CYLINDRICAL JOURNAL BEARING

In this article,the effect of the bearing elastic deformation on the performance characteristics of a cylindrical journal bearing is analyzed.The variety of simulation models covers hydrodynamic（HD） and elastohydrodynamic（EHD） lubrication theories.The Reynolds equations governing the flow in the clearance space of the journal bearing are obtained by considering the effect of mass transfer across the fluid film.The finite element method with an iteration scheme was employed to solve both the Reynolds equation and the three-dimensional elasticity equation representing the displacement field in the bearing shell.The converged solutions for the lubricant flow and elastic deformation vector are obtained.Dynamic characteristics of the journal bearing are computed for HD and EHD theories.Numerical simulation results show that the flexibility of bearing liner has a significant influence on the performance of a cylindrical journal bearing.Indeed,the elastic deformations of the bearing liner extend the pressure area in the bearing and increase the minimum film thickness.Although,dynamic coefficient,load capacity and attitude angle decrease.