Elastoplastic deformation of a rotating hollow cylinder with a rigid casing

A rotating hollow cylinder with fixed ends is considered, the inner surface of which is free of stresses, and the outer one is fixed from radial movements. It is assumed that the cylinder is made of an ideal isotropic elastoplastic material, and the deformations in it are small and represent the sum of elastic and plastic deformations. Stresses are associated with elastic deformations by Hooke's law. Plastic deformations are determined using the Tresca - Saint-Venant condition and the plastic flow rule associated with it. The cylinder rotation speed first monotonically increases to a maximum value, and then decreases to zero. By using the elastic solution, the dependence is found for the critical rotation speed at which the plastic flow begins. It is established that, depending on the thickness of the cylinder and the Poisson's ratio, plastic flow can begin, either on the inner or on the outer surface of the cylinder. In addition, 3 plastic regions appear in the cylinder at the loading stage, and 4 plastic regions appear at the unloading stage. These regions correspond to two faces and two edges of the Treska prism. For each plastic region, an exact analytical solution of the determining system of equations is found. The system of conditions at the boundaries between the regions providing continuity of the obtained solutions throughout the cylinder is given. Two cases are considered, i.e. the case with a plastic flow which starts first on the inner, and then on the outer surface of the cylinder. Analytical expressions are obtained for rotational speeds at which new regions appear. The relationship between the nucleation rates of the secondary and primary plastic flow is established. The value of the maximum rotation speed sufficient for a complete transition of the cylinder to the state of the secondary plastic flow was also found. It has been revealed that the adding of a rigid casing can significantly increase the resource of an exploited part.

Thermo-Elastic Analysis Of A Rotating Hollow Cylinder Made Of Arbitrary Functionally Graded Materials

Thermo-mechanical analysis of the functionally graded orthotropic rotating hollow structures, subjected to thermo-mechanical loadings is studied in this paper. The relations were derived for both plane strain and plane stress conditions as a cylinder and disk, respectively. Non homogeneity was considered arbitrary through thickness direction for all mechanical and thermal properties. The responses of the system including temperature distribution, radial displacement and radial and circumferential stresses were derived in the general state. As case study, power law gradation was assumed for functionally graded cylinder and the mentioned results were evaluated in terms of parameters of the system such as non-homogeneous index and angular velocity.

Levitation of a drop over a moving surface

We investigate the levitation of a drop gently deposited onto the inner wall of a rotating hollow cylinder. For a sufficiently large velocity of the wall, the drop steadily levitates over a thin air film and reaches a stable angular position in the cylinder, where the drag and lift balance the weight of the drop. Interferometric measurements yield the three-dimensional (3D) air film thickness under the drop and reveal the asymmetry of the profile along the direction of the wall motion. A two-dimensional (2D) model is presented which explains the levitation mechanism, captures the main characteristics of the air film shape and predicts two asymptotic regimes for the film thickness ${h}_{0} $: for large drops ${h}_{0} \sim {\mathit{Ca}}^{2/ 3} { \kappa }_{b}^{- 1} $, as in the Bretherton problem, where $\mathit{Ca}$ is the capillary number based on the air viscosity and ${\kappa }_{b} $ is the curvature at the bottom of the drop; for small drops ${h}_{0} \sim {\mathit{Ca}}^{4/ 5} {(a{\kappa }_{b} )}^{4/ 5} { \kappa }_{b}^{- 1} $, where $a$ is the capillary length.

Heat Transfer Analysis of a Solid-Solid Heat Recuperation System for Solar-Driven Nonstoichiometric Redox Cycles

Heat transfer is predicted for a solid-solid heat recuperation system employed in a novel directly-irradiated solar thermochemical reactor realizing a metal oxide based nonstoichiometric redox cycle for production of synthesis gas from water and carbon dioxide. The system is designed for continuous operation with heat recuperation from a rotating hollow cylinder of a porous reactive material to a counter-rotating inert solid cylinder via radiative transfer. A transient heat transfer model coupling conduction, convection, and radiation heat transfer predicts temperatures, rates of heat transfer, and the effectiveness of heat recovery. Heat recovery effectiveness of over 50% is attained within a parametric study of geometric and material parameters corresponding to the design of a two-step solar thermochemical reactor.