On the competition of anti-lift-up mechanism and Reynolds stress mechanism in Spiral Poiseuille flow

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in Spiral Poiseuille flow (SPF). The Poiseuille number [Formula: see text], representing the dimensionless axial pressure gradient, is varied from 0 to 20,000. The results show that for the axisymmetric case, with the increase of axial shear, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the inner cylinder, and a second peak appears near the outer cylinder for both velocity components. Viewing the time evolution of azimuthal shear contribution [Formula: see text] and axial shear contribution [Formula: see text] to the kinetic energy growth of the optimal perturbation, while [Formula: see text] is large enough ([Formula: see text], 20,000), the Reynolds stress mechanism in the meridional plane [Formula: see text] is dominant for the transient growth behavior in SPF relative to anti-lift-up mechanism, which is dominant in the absence of axial flow for co-rotating Taylor–Couette flow with wide gap. For the oblique mode with azimuthal wave number [Formula: see text], which becomes the optimal azimuthal mode over a wide range of azimuthal wave number ([Formula: see text]–10) when [Formula: see text] is large enough, the peaks of the amplitudes of azimuthal and radial velocities are both shifted towards the outer cylinder, opposite to the axisymmetric case.

Experimental Study on Coherent Structures by Particles Suspended in Half-Zone Thermocapillary Liquid Bridges: Review

Coherent structures by the particles suspended in the half-zone thermocapillary liquid bridges via experimental approaches are introduced. General knowledge on the particle accumulation structures (PAS) is described, and then the spatial–temporal behaviours of the particles forming the PAS are illustrated with the results of the two- and three-dimensional particle tracking. Variations of the coherent structures as functions of the intensity of the thermocapillary effect and the particle size are introduced by focusing on the PAS of the azimuthal wave number m=3. Correlation between the particle behaviour and the ordered flow structures known as the Kolmogorov–Arnold—Moser tori is discussed. Recent works on the PAS of m=1 are briefly introduced.

Onset of Inertial Magnetoconvection in Rotating Fluid Spheres

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied in this paper. Thermo-inertial convection is a distinctive flow regime on the border between rotating thermal convection and wave propagation. It occurs in astrophysical and geophysical contexts where self-sustained or external magnetic fields are commonly present. To investigate the onset of motion, a perturbation method is used here with an inviscid balance in the leading order and a buoyancy force acting against weak viscous dissipation in the next order of approximation. Analytical evaluation of constituent integral quantities is enabled by applying a Green’s function method for the exact solution of the heat equation following our earlier non-magnetic analysis. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained. In both cases, explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. It is found that an imposed azimuthal magnetic field exerts a stabilizing influence on the onset of inertial convection and as a consequence magneto-inertial convection with azimuthal wave number of unity is generally preferred.

The Identification and Prediction of Helical Modes Induced by a Multi-Passage Swirl Stabilised Lean Burn Aero-Engine Fuel Injector Under Steady State and Acoustically Forced Conditions

Thermoacoustic instabilities in gas turbine combustion systems, caused by a feedback loop between acoustic fluctuations and the flame, can be a major factor in determining the durability of the combustor. Of interest here are helical modes caused by a Kelvin-Helmholtz instability emanating from a region of high shear close to the outlet of the fuel injector. A liquid fuelled lean burn fuel injector, containing three air flow passages is studied in the present work using non-reacting compressible unsteady RANS CFD simulations. An acoustic wave is injected at the downstream boundary with excitation frequencies of 300Hz and 450Hz to compare to an unforced case. Analysis of the flow response is carried out using linear stability analysis, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The linear stability analysis required interpolation of the solution from the unstructured CFD grid onto a uniform cylindrical polar mesh. The analysis found an absolute instability in the shear region between two passages. This m = −2 mode is unstable over frequencies from 400Hz to 1000Hz with wavelengths of 1.08 to 1.41 of the injector outer diameter. For the unforced case the POD identifies the first two modes with azimuthal wave number m = 1 and these are seen to spiral from the splitter plate inwards to disturb the pilot and outwards to the main. The dominant frequency is around 450Hz which is consistent with measurements and close to the linear stability analysis value. For the 300Hz forced case POD identifies the first four modes as being helical but has difficulty determining the dominant azimuthal wave number. There is shown to be a significant interaction between the acoustic and helical modes and double the total resolved kinetic energy as compared to the unforced case. The 450Hz forced case shows the asymmetric m = 1 mode to be damped and the m = 2 helical mode is relatively unchanged. The resolved kinetic energy was only marginally higher than the unforced case and significantly lower than the 300Hz forced case. The DMD analysis showed how, as the forcing increased the flow through the injector, the flow is simultaneously pushed radially inwards and accelerated azimuthally. It also identified the region downstream of the splitter plate with significant fluctuations and is likely to be the wavemaker region responsible for the generation of helical instabilities. This work improves understanding of how helical modes of different azimuthal wave numbers react to acoustic forcing. The ability to manipulate the strength of these modes through alteration of the fuel injector geometry gives designers an additional tool to control thermo-acoustic instabilities.

On Estimates for Growth Rates of Unstable Azimuthal Disturbances in the Stability Problem of Swirling Flows with Radius- Dependent Density

Estimates for the growth rate of unstable two-dimensional disturbances to swirling flows with variable density are obtained and as a consequence it is proved that the growth rate tends to zero as the azimuthal wave number tends to infinity for two classes of basic flows.

Latitudinal amplitude-phase structure of MHD waves: STARE radar and image magnetometer observations and modeling

We have developed a numerical model that yields a steady-state distribution of field components of MHD wave in an inhomogeneous plasma box simulating the realistic magnetosphere. The problem of adequate boundary condition at the ionosphere–magnetosphere interface for coupled MHD mode is considered. To justify the model’s assumptions, we have derived the explicit inequality showing when the ionospheric inductive Hall effect can be neglected upon the consideration of Alfven wave reflection from the ionospheric boundaries. The model predicts a feature of the ULF spatial amplitude/phase distribution that has not been noticed by the field line resonance theory: the existence of a region with opposite phase delays on the source side of the resonance. This theoretical prediction is supported by the amplitude-phase latitudinal structures of Pc5 waves observed by STARE radar and IMAGE magnetometers. A gradual decrease in azimuthal wave number m at smaller L-shells was observed at longitudinally separated radar beams.

Latitudinal amplitude-phase structure of MHD waves: STARE radar and image magnetometer observations and modeling

We have developed a numerical model that yields a steady-state distribution of field components of MHD wave in an inhomogeneous plasma box simulating the realistic magnetosphere. The problem of adequate boundary condition at the ionosphere–magnetosphere interface for coupled MHD mode is considered. To justify the model’s assumptions, we have derived the explicit inequality showing when the ionospheric inductive Hall effect can be neglected upon the consideration of Alfven wave reflection from the ionospheric boundaries. The model predicts a feature of the ULF spatial amplitude/phase distribution that has not been noticed by the field line resonance theory: the existence of a region with opposite phase delays on the source side of the resonance. This theoretical prediction is supported by the amplitude-phase latitudinal structures of Pc5 waves observed by STARE radar and IMAGE magnetometers. A gradual decrease in azimuthal wave number m at smaller L-shells was observed at longitudinally separated radar beams.