Research of particle movement on rough surface formed by screw movement of sinusoid under action of own weight

The differential equations of particle movement on a rough surface which is formed by the helical motion of a sinusoid under the action of the force of own weight were obtained in the article. The sinusoid is the axial cross-section curve of the helical surface and is located in the vertical plane. The obtained equations were solved by numerical methods and the trajectories of the particle on the helical surface were constructed. In addition, graphs of the change in the particle velocity and its distance from the axis of the surface were found, as a result of which the conditions when stabilization of the particle movement is possible were found. It is shown that in the general case, as a result of acceleration, the particle moves away from the axis of the surface and stops in one of its gutters. The depth and density of the gutters are controlled by changing the constant coefficients parameters. Also, a partial case at zero depths of the gutter, when the sinusoid turns into a straight line and the particle moves on the surface of the helical conoid, were considered.

Air Distribution Over a Combustor Liner

The splitting of the airflow that passes through the openings in the combustor liner is vital to its performance. Traditionally, numerical simulations of the gas turbine combustor have limited the computational domain to only the flow field inside the liner, while the airflow distribution over the liner is estimated based on semi-empirical correlations. In addition, the airflow rates are assumed to be the same through the identical open passages at each combustor axial cross-section. In the present study, the internal and external flow fields of a practical gas turbine combustor liner are directly coupled, so the air splitting is determined by comprehensive simulations. The predicted results for the air distribution are closely correlated to the dataset estimated from recently improved semi-empirical correlations for passage discharge-coefficients. The simulations also show that the effects of the combustion process on the air splitting can be neglected. Lastly, the results reveal that the airflow through identical passages at the same axial cross-section are not equal, and can vary by up to ±25% of the mean. In summary, the present study suggests that when performing computational models of gas turbine combustor flows, the simulations should couple the liner’s internal and external air splits whenever possible.

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.