Carbon Nanocones with Curvature Effects Close to the Vertex

The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature, and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly, curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles. Here, we construct carbon nanocones which, in the assembled cone, are assumed to comprise bond lengths and bond angles that are, as far as possible, equal throughout the structure at the same distance from the conical apex. The predicted bond angles and bond lengths are shown to agree well with those obtained by relaxing the conventional rolled-up model using Lammps software (version: 11 September 2008). The major objective here is not simply to model physically realisable carbon nanocones for which numerical procedures are far superior, but rather, to produce an improved model that takes curvature effects close to the vertex into account, and from which we may determine an analytical formula which represents an improvement on the conventional rolled-up model.

Carbon Nanocones with Curvature Effects Close to Vertex

The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles. Here we construct carbon nanocones which in the assembled cone are assumed to comprise bond lengths and bond angles which are, as far as possible, equal throughout the structure at the same distance from the conical apex. Predicted bond angles and bond lengths are shown to agree well with those obtained by relaxing the conventional rolled-up model using the LAMMPS software. The major objective here is not simply to model physically realisable carbon nanocones for which numerical procedures are far superior, but rather to produce an improved model that takes into account curvature effects close to the vertex, and from which we may determine an analytical formula which represents an improvement on that for the conventional rolled-up model.

Computational Investigation of Torque on Coaxial Rotating Cones

This article looks at a modification of Taylor–Couette flow, presenting a numerical investigation of the flow around a shrouded rotating cone, with and without throughflow, using the commercial computational fluid dynamics code FLUENT 6.2 and FLUENT 6.3. The effects of varying the cone vertex angle and the gap width on the torque seen by the rotating cone are considered, as well as the effect of a forced throughflow. The performance of various turbulence models are considered, as well as the ability of common wall treatments/functions to capture the near-wall behavior. Close agreement is found between the numerical predictions and previous experimental work, carried out by Yamada and Ito (1979, “Frictional Resistance of Enclosed Rotating Cones With Superposed Throughflow,” ASME J. Fluids Eng., 101, pp. 259–264; 1975, “On the Frictional Resistance of Enclosed Rotating Cones (1st Report, Frictional Moment and Observation of Flow With a Smooth Surface),” Bull. JSME, 18, pp. 1026–1034; 1976, “On the Frictional Resistance of Enclosed Rotating Cones (2nd Report, Effects of Surface Roughness),” Bull. JSME, 19, pp. 943–950). Limitations in the models are considered, and comparisons between two-dimensional axisymmetric models and three-dimensional models are made, with the three-dimensional models showing greater accuracy. The work leads to a methodology for modeling similar flow conditions to Taylor–Couette.

Frictional Resistance of Enclosed Rotating Cones With Superposed Throughflow

The research summarized in this paper is an experimental study of the frictional moment on a cone rotating in a conical casing with an outward throughflow. The cone vertex angles tested in the present experiment are θ = 30, 60 and 90 deg. In the region where the frictional moment on the rotating cone with no throughflow is increased by the effect of Taylor-type vortices, an increase of the throughflow rate results in a decrease of the frictional moment, if the throughflow rate is not so large. In the region where the Taylor-type vortices have no appreciable effect on the frictional moment, on the other hand, the rate of increase in CM with increasing Cq. sin (θ/2) is almost independent of θ, where CM and Cq denote the moment coefficient and the dimensionless throughflow rate, respectively.

Simple Formulae for Supersonic Flow past a Cone

SummaryThe problem of the supersonic flow with attached shock wave past a circular cone at zero angles of attack is treated, using the thin-shock-layer expansion. The solution is calculated to the fourth approximation. A simple formula is then derived for the surface pressure coefficient by the application of the parameter-straining technique and it is shown to be very accurate for the whole Mach number range for which the shock remains attached to the cone vertex.