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 high-resolution infrared spectrum of thiophene between 600 and 1200 cm: A spectroscopic and theoretical study of the fundamental bands ν6, ν7, ν13, and the c-Coriolis interacting dyad ν5, ν19

The Fourier transform infrared spectrum of gaseous thiophene, C₄H₄S, has been recorded in the 600-1200 cm⁻¹ spectral region with a resolution of ca. 0.0030 cm⁻¹. Five fundamental bands ν₁₃ (B₁, 712.1 cm⁻¹), ν₇ (A₁; 840.0 cm⁻¹), ν₆ (A₁; 1036.4 cm⁻¹), ν₅ (A₁; 1081.5 cm⁻¹) and ν₁₉ (B₂; 1084.0 cm⁻¹) have been analysed by the standard Watson model (A-reduction). Ground state rotational and quartic centrifugal distortion constants have been obtained from a simultaneous fit of ground state combination differences from four of these bands and previous microwave transitions. Upper state spectroscopic constants have been obtained for all five bands from single band fits using the Watson model. A strong c-Coriolis resonance perturbs the close lying ν₅ and ν₁₉ bands. We have analysed this dyad system by a model including first and second order Coriolis resonance using the theoretically predicted Coriolis coupling constant . From this analysis we locate the previously unobserved ν₁₉ band at 1083.969 cm⁻¹. The rotational constants, ground state quartic centrifugal distortion constants, anharmonic frequencies, and vibration-rotational constants (α-constants) predicted by quantum chemical calculations using a cc-pVTZ basis with B3LYP methodology, are compared with the present experimental data, where there is generally good agreement. A complete set of anharmonic frequencies and α-constants for all fundamental levels of the molecule is given.     

High-resolution infrared spectroscopy of CH281BrF near 8 μm: rovibrational analysis of the ν3 and ν8 fundamentals and resonances with the dark states 2ν5 and ν6 + ν9

The infrared spectrum of isotopically enriched CH₂⁸¹BrF was investigated in the ν₃ and ν₈ region between 1150 and 1370 cm^?1 at a resolution of 0.003 cm^?1. The ν₃ vibration of symmetry species A^′ gives rise to an a-/b-hybrid band with a-type predominance, while the ν₈ mode of A^″ symmetry produces c-type absorption. Due to the proximity of the band origins to those of closely lying overtones and combination bands, the v₃ = 1 and v₈ = 1 levels were found perturbed through Coriolis resonance by the v₅ = 2 (A^′) and v₆ = v₉ = 1 (A^″) states, respectively. The spectral analysis resulted in the identification of 3132 transitions (J^″ ≤ 98 and K_a^″ ≤ 14) for the ν₃ and 2958 transitions (J^″ ≤ 68 and K_a^″ ≤ 19) for the ν₈ bands. The assigned data were fitted using the Watson's A-reduction Hamiltonian in the I^r representation and the perturbation operators. Although no transitions belonging to the perturbers were observed, the band origins and excited state parameters for fundamentals and ‘dark states’ together with coupling terms for the ν₃/2ν₅ and ν₈/ν₆ + ν₉ dyads were determined.     

Drift of spheres in a rotating fluid

The drift of spheres in a rotating fluid is investigated. The problem is studied experimentally and numerically using the Galerkin method. It is shown that for small angular velocities of the fluid Ω the drift velocity of the spheres is almost independent of Ω, but once a certain threshold value Ω_* is attained the drift velocity rapidly decreases. The experimental dependence of the translational velocity of the sphere on the fluid angular velocity is explained on the basis of a theoretical analysis.     

Experimental investigation of natural convective flows in slowly rotating wide spherical shells

Experimental results are presented on natural convection in a spherical shell of inner and outer radii r ₁ = 14 mm and r ₂ = 35 mm, with the inner sphere cooled and the outer sphere heated. The fluids filling the shell are two different silicon oils having Prandtl numbers 39 and 233. Both spheres are fixed together and can be rotated. In the studied regime, both Coriolis and centrifugal forces become significant. For sufficiently small Rayleigh numbers the resulting flow pattern is axisymmetric and steady, consisting of a plume descending from the south pole of the inner sphere, and returning in the equatorial regions. For greater Rayleigh numbers the flow becomes non-axisymmetric, with azimuthal modes m = 2 to 4 arising. We map out the critical Rayleigh number for the onset of these different modes, and consider how they vary with increasingly rapid overall rotation. Detailed flow measurements are done by converting a standard 2D particle image velocimetry system into a scanning quasi-3D PIV system.