Secondary vortex street in the wake of two tandem circular cylinders at low Reynolds number.

The experiments on two tandem circular cylinders were conducted in a horizontal soap film tunnel for the Reynolds number Re=60 , 80, and 100 and the nondimensional center-to-center spacing Gamma ranging in 1 approximately 12. The flow patterns were recorded by a high-speed camera and the vortex shedding frequency was obtained by a spatiotemporal evolution method. The secondary vortex formation (SVF) mode characterized by the formation of a secondary vortex street in the wake of the downstream cylinder was found at large gamma. Moreover, some typical modes predicted by previous investigations, including the single bluff-body, shear layer reattachment, and synchronization of vortex shedding modes, were also revisited in our experiments. Further, numerical simulations were carried out using a space-time finite-element method and the results confirmed the existence of the SVF mode. The mechanism of SVF mode was analyzed in terms of the numerical results. The dependence of the Strouhal number Sr on Gamma was given and the flow characteristics relevant to the critical spacing values and the hysteretic mode transitions were investigated.

Instability of a leaky dielectric coaxial jet in both axial and radial electric fields.

The temporal linear instability of a coaxial jet with two immiscible Newtonian liquids in both the axial and radial electric fields is studied. The outer liquid is supposed to be a leaky dielectric and the inner liquid a perfect dielectric. The eigenvalue problem for both axisymmetric instability and helical instability is formulated and solved using the spectral method. Different from axisymmetric instability, for helical instability there is only one unstable mode, i.e., the helical mode, located in the long wave region. The axial electric field is found to have a strong stabilization effect on both the axisymmetric and helical modes, and the radial electric field has a great destabilization effect on them. The competition between the axisymmetric and helical instability under the action of the axial and radial electric fields is calculated. The boundary curve separating the stabilization and destabilization regions of the parasinuous mode, the neutral stability curve of the helical mode, and the boundary curve between the dominant regions of the axisymmetric and helical instability are plotted on the Q0-Eu plane and Pi-Eu plane, respectively (Q0 is the dimensionless surface charge density; Eu is the electrical Euler number representing the characteristic tangential electrostatic force; and Pi=Q0;2Eu is the dimensionless parameter representing the characteristic normal electrostatic force). In general, when surface charge density is small, the helical mode is stable, and the parasinuous mode is dominant; however, when surface charge density is sufficiently large, the helical mode is destabilized and becomes dominant in jet instability. Liquid viscosity influences the predominance of the helical mode significantly. Although liquid viscosity decreases the growth rates of both the axisymmetric and helical modes, it suppresses the axisymmetric instability much more than the helical instability, and therefore favors the realization of the helical instability in experiments.

Passive oscillations of two tandem flexible filaments in a flowing soap film.

The passive oscillations of flexible filaments in a flowing soap film were investigated to learn the serial interaction between them. When arranged in tandem, the downstream filament flaps at the same frequency as that of the upstream one, but with a larger amplitude, whereas the upstream one is almost unaffected compared to the single filament case. The data analysis shows the downstream filament indeed extracts energy from the vortex street and receives greater force than the upstream one or a single filament in a uniform flow.

Linear instability of a coflowing jet under an axial electric field.

A temporal linear stability analysis is carried out for a coflowing jet with two immiscible inviscid liquids under a uniform axial electric field. According to the electrical properties of the inner and outer liquids, four cases, i.e., IDOC (inner: dielectric; outer: conductor), ICOD (inner: conductor; outer: dielectric), ICOC (inner and outer: conductor), and IDOD (inner and outer: dielectric), are considered. The analytical dimensionless dispersion relation is derived for both axisymmetric and nonaxisymmetric perturbations and is solved for axisymmetric ones. Three unstable modes, i.e., the paravaricose, parasinuous and transitional modes, are identified in the Rayleigh regime. The influences of the axial electric field, liquid electrical properties, and Weber number are studied at length. The results show that the axial electric field has a generally stabilizing effect on the unstable modes. The effects of the liquid electrical properties are quite different but all great for each case. The change of dominant mode is detected with the variation of the electric field intensity, electrical properties or Weber number. It is found that the parasinuous instability is the easiest to realize in IDOC. And the comparison with the experiment validates that the parasinuous mode is predominant in coaxial electrospray.