Numerical study of the axially symmetric motion of an incompressible viscous fluid in an annulus between two concentric rotating spheres

The research reported herein involved the study of the transient motion of a system consisting of an incompressible Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research was to study the use of a numerical method for analysing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly by the action of prescribed torques. The problems considered in this research included cases where: (a) one or both spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive t?orque. In this research the coupled solid and fluid equations were solved numerically by employing the finite difference technique. With the approach adopted in this research, only the derivatives with respect to spatial variables were approximated with the use of the finite difference formulae. The steady state problem was also solved as a separate problem (for verification purposes), and the results were compared with those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations which resulted from the steady state problem, and the Adams fourth-order predictor–corrector method was employed to solve the ordinary differential equations for the transient problem. Results were obtained for the streamfunction, circumferential function, angular velocity of the spheres and viscous torques acting on the spheres as a function of time for various values of the system dimensionless parameters.     

A finite element approximation of steady flow through a rotating non-aligned straight tube

A finite element solution is developed for a penalty function formulation of the equations which govern the steady motion of a Newtonian fluid through a pipe that rotates about an axis not parallel to its own. The motion in this system is driven by the Coriolis acceleration, which has components in the axial direction as well as in the transverse plane of the pipe. The relative magnitudes of these components significantly affect the qualitative and quantitative nature of the primary and secondary flow field. The present results compare favourably with those of previously reported experimental and theoretical studies over a wide range of flow regimes.     

The ideal relativistic spinning gas: Polarization and spectra

We study the physics of the ideal relativistic rotating gas at thermodynamical equilibrium and provide analytical expressions of the momentum spectra and polarization vector for the case of massive particles with spin 1/2 and 1. We show that the finite angular momentum J entails an anisotropy in momentum spectra, with particles emitted orthogonally to J having, on average, a larger momentum than along its direction. Unlike in the non-relativistic case, the proper polarization vector turns out not to be aligned with the total angular momentum with a non-trivial momentum dependence.     

Compression features of high density electron plasma in a long harmonic trap using a rotating wall technique

We studied radial compression features of electron plasmas in a Penning trap (an assembly of multi-ring electrodes (MRE) housed in a uniform magnetic field) using the rotating wall technique. The magnetic field was 5 T, and the MRE provide a long harmonic potential along the magnetic field axis. The compression features of the plasma were studied by varying the applied rotating electric field frequency, rotating electric field amplitude, compression time, as well as, the magnetic field strength in the Penning trap. The highest density achieved was $～5\times {10}^{10}$ cm^?3 and the compressed plasma shows slow expansion after the compression, with an expansion rate of $7\times {10}^{?4}$ s^?1.     

Brouwer?s problem on a heavy particle in a rotating vessel: Wave propagation, ion traps, and rotor dynamics

In 1918 Brouwer considered stability of a heavy particle in a rotating vessel. This was the first demonstration of a rotating saddle trap which is a mechanical analogue for quadrupole particle traps of Penning and Paul. We revisit this pioneering work in order to uncover its intriguing connections with classical rotor dynamics and fluid dynamics, stability theory of Hamiltonian and non-conservative systems as well as with the modern works on crystal optics and atomic physics. In particular, we find that the boundary of the stability domain of the undamped Brouwer?s problem possesses the Swallowtail singularity corresponding to the quadruple zero eigenvalue. In the presence of dissipative and non-conservative positional forces there is a couple of Whitney umbrellas on the boundary of the asymptotic stability domain. The handles of the umbrellas form a set where all eigenvalues of the system are pure imaginary despite the presence of dissipative and non-conservative positional forces.     

Study of propagation of linear and non-linear Alfvén-gravity waves in rotating medium

Travelling waves in an incompressible, infinitely conducting, inviscid fluid of variable density are investigated under the influence of a horizontal magnetic field and Coriolis force. Periodic solutions are found in the limit of infinite vertical wave length. Phase diagrams are drawn to show the solution.     

Selective and sensitive detection of nitrite based on NO sensing on a polymer-coated rotating disc electrode

A new effective way of nitrite detection in complex samples is presented. It is based on chemical conversion of nitrite to nitric monoxide (NO) in acidic aqueous solution containing hexacyanoferrate(II) as a reductor. NO is then detected on a poly-eugenol coated platinum electrode. When the electrode is rotating and the reduction medium is continuously purged with nitrogen, the addition of a nitrite-containing sample produces narrowed current spikes. The peak current is proportional to nitrite content in the sample over the range of 5.0–100 μM and detection limit is 0.6 μM. The method is simple and highly reproducible. Relative standard deviation of 10 repetitions is less than 4%. Practical utility of the proposed approach is demonstrated by nitrite determination in human saliva.     

Contact separation and failure analysis of a rotating thermo-elastoplastic shrink-fit assembly

Gas turbine propulsion and aircraft engines involve a great number of rotating shrink-fit assemblies. In presence of high-speed rotations and thermal effects, the reliability of such components with respect to contact separation and failure occurrences needs to be analyzed in the very early design of those structures. In particular, engineers and designers are to prescribe an adequate shrink interference to ensure a structural safe life for a given range of operating conditions. This paper is devoted to the determination of those critical contact and plastic states. To that end, a thermo-elastic–plastic analytical model of a rotating shrink-fit assembly is studied. The stress distributions and contact/plasticity/failure conditions are then derived analytically. In the last part, the determination of the safe operating domain and optimum shrink interference is illustrated through a numerical example.     

The Eckert number phenomenon: Experimental investigations on the heat transfer from a moving wall in the case of a rotating cylinder

The Eckert number phenomenon was investigated theoretically by Geropp in 1969 and describes a reversal in heat transfer from a moving wall at an Eckert number Ec ≈ 1. In this report the Eckert number phenomenon is confirmed experimentally for the first time. For that purpose the heat transfer from a heated, vertically rotating cylinder in a crossflow was investigated. In order to perform the experiments in a range where the predicted phenomenon occurs, extreme rotational speeds were necessary. A heating concept had to be developed which allowed an input of heating power independent of the speed and which therefore had to be contact-free. The results show, among other things, that the temperature difference between the wall and the surrounding fluid has a significant effect on the predicted reversal of heat transfer at the wall. Moreover, maximum heat transfer occurs at an Eckert number Ec ≈ 0.3, which is of great importance for the cooling of hot surfaces in a gas-flow.