An Exact Axisymmetric Solution in Anisotropic Plasticity

A hollow cylinder of incompressible material obeying Hill’s orthotropic quadratic yield criterion and its associated flow rule is contracted on a rigid cylinder inserted in its hole. Friction occurs at the contact surface between the hollow and solid cylinders. An axisymmetric boundary value problem for the flow of the material is formulated and solved, and the solution is in closed form. A numerical technique is only necessary for evaluating ordinary integrals. The solution may exhibit singular behavior in the vicinity of the friction surface. The exact asymptotic representation of the solution shows that some strain rate components and the plastic work rate approach infinity in the friction surface’s vicinity. The effect of plastic anisotropy on the solution’s behavior is discussed.

Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions

The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions.

Balanced Response of an Axisymmetric Tropical Cyclone to Periodic Diurnal Heating

A modified version of the Sawyer–Eliassen equation is applied to determine the impact of periodic diurnal heating on a balanced vortex. The TC diurnal cycle is a coherent signal that arises in the cirrus canopy. However, despite thorough documentation in the literature, the dynamical mechanism remains unknown. Recent work demonstrates that periodic radiative heating in the TC outflow layer is linked with an anomalous upper-level circulation; this heating is also associated with a cycle of latent heating in the lower troposphere that corresponds to a cycle in storm intensity. Using a method that is analogous to the Sawyer–Eliassen equation, but for solutions having the same time scale as time-periodic forcing, these distributions are analyzed to determine the effect of periodic diurnal heating on an axisymmetric vortex. Results for periodic heating in the lower troposphere show an overturning circulation that resembles the Sawyer–Eliassen solution. The model simulates positive perturbations in the azimuthal wind field of 2.5 m s−1 near the radius of maximum wind. Periodic heating near the top of the vortex produces a local overturning response in the region of heating and an inertia–buoyancy wave response in the storm environment. Comparison of the results from the modified Sawyer–Eliassen equation to those of an idealized axisymmetric solution for both heating distributions shows similarities in the structure of the perturbation wind fields, suggesting that the axisymmetric TC diurnal cycle is primarily a balanced response driven by periodic heating.

Control of Interface Shape by Non-Axisymmetric Solution Convection in Top-Seeded Solution Growth of SiC Crystal

We achieved the convex growth interface shape in top-seeded solution growth of SiC applying non-axisymmetric solution convection induced by non-axisymmetric temperature distribution. The detailed solution flow, temperature distribution and carbon concentration distribution were calculated by 3-dimensional numerical analysis. In the present case, the solution flow below the crystal was unidirectional and the supersaturation was increased along the solution flow direction. By the rotation of the crystal in the unidirectional flow and the temperature distribution, we successfully obtained the crystal with the convex growth interface shape.

Investigation of flow asymmetry around axi-symmetric spiked blunt bodies in hypersonic speeds

The assumption that a zero-incidence flow around bodies of revolution is axisymmetric has been broadly adopted by many researchers, even for cases where the flow around such bodies becomes unstable. In this study, the validity of this assumption is revisited using CFD simulation. As a case study, the simulations of both stable and unstable hypersonic flows around spiked blunt bodies in 2D axisymmetric and full 3D computational domains are compared. It is found that, for the stable flow cases, the main flow features are apparently axisymmetric and the assumption is generally acceptable. However, some degree of asymmetry can be observed inside the shear layer in the separated region, causing small variation in the drag coefficient. For the unstable flow cases, the asymmetry of the flow features is much more significant. More importantly, the assumption that the flow is axisymmetric is found to overestimate the level of flow unsteadiness. The amplitude of temporal drag variation as predicted by the axisymmetric solution is higher than that predicted by the full 3D solution.

The Variability and Predictability of Axisymmetric Hurricanes in Statistical Equilibrium

The variability and predictability of axisymmetric hurricanes are determined from a 500-day numerical simulation of a tropical cyclone in statistical equilibrium. By design, the solution is independent of the initial conditions and environmental variability, which isolates the “intrinsic” axisymmetric hurricane variability. Variability near the radius of maximum wind is dominated by two patterns: one associated primarily with radial shifts of the maximum wind, and one primarily with intensity change at the time-mean radius of maximum wind. These patterns are linked to convective bands that originate more than 100 km from the storm center and propagate inward. Bands approaching the storm produce eyewall replacement cycles, with an increase in storm intensity as the secondary eyewall contracts radially inward. A dominant time period of 4–8 days is found for the convective bands, which is hypothesized to be determined by the time scale over which subsidence from previous bands suppresses convection; a leading-order estimate based on the ratio of the Rossby radius to band speed fits the hypothesis. Predictability limits for the idealized axisymmetric solution are estimated from linear inverse modeling and analog forecasts, which yield consistent results showing a limit for the azimuthal wind of approximately 3 days. The optimal initial structure that excites the leading pattern of 24-h forecast-error variance has largest azimuthal wind in the midtroposphere outside the storm and a secondary maximum just outside the radius of maximum wind. Forecast errors grow by a factor of 24 near the radius of maximum wind.

Euler Inverse Axisymmetric Solution for Design of Axial Flow Multistage Turbomachinery

An axisymmetric model is used that replaces the blades with hub-to-tip streamsurfaces and their main effects on the flow with blade force terms. Euler equations are solved by means of an upwind finite-volume scheme for a specified swirl distribution in the meridional blade regions. This quantity drives the spanwise distribution of specific work for rotors and the swirl adding/removing property for stators. The time-marching procedure includes an evolutionary equation for the hub-to-tip geometry in each blade region. This equation involves use of a specified leading edge as a blade stacking line. Throughout the computation, the streamsurfaces take that shape providing the desired swirl distribution. The method is suitable to highly loaded blades i.e. turbine design. Compared to a traditional through-flow method, it predicts the overall turbine performances with about a 1% error. A satisfactory agreement is found concerning the spanwise distribution of the core flow quantities as well.