Xie-Yuan Yin

Coupling modes between two flapping filaments

The flapping coupling between two filaments is studied theoretically and experimentally in this paper. A temporal linear instability analysis is carried out based on a simplified hydrodynamic model. The dispersion relationship between the eigen-frequency ω and wavenumber k is expressed by a quartic equation. Two special cases of flapping coupling, i.e. two identical filaments having the same length and two filaments having different lengths, are studied in detail. In the case of two identical filaments, the theoretical analysis predicts four coupling modes, i.e. the stretched-straight mode, the antisymmetrical in-phase mode, the symmetrical out-of-phase mode and the indefinite mode. The theory also predicts the existence of an eigenfrequency jump during transition between the in-phase and out-of-phase modes, which has been observed in previous experiments and numerical simulations. In the case of two filaments having different lengths, four modes similar to those in the former case are identified theoretically. The distribution of coupling modes for both the cases is shown in two planes. One is a dimensionless plane of S vs. U , where S is the density ratio of solid filament to fluid and U 2 is the ratio of fluid kinetic energy to solid elastic potential energy. The other is a dimensional plane of the half-distance ( h ) between two filaments vs. the filament length ( L ). Relevant experiments are carried out in a soap-film tunnel and the stable and unstable modes are observed. Theory and experiment are compared in detail. It should be noted that the model used in our analysis is a very simplified one that can provide intuitional analytical results of the coupling modes as well as their qualitative distributions. The factors neglected in our model, such as vortex shedding, viscous and nonlinear effects, do not allow the model to predict results precisely consistent with the experiments. Moreover, the Strouhal numbers of the flapping filaments are found to be generally around a fixed value in the experiments for both cases, implying that the filaments try to maintain a lower potential energy state.

Hopf bifurcation in wakes behind a rotating and translating circular cylinder

A low‐dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two‐dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time‐periodic solution is investigated. A curve indicating the transitional boundary is given in the two‐dimensional parameter plane of Reynolds number Re and rotating parameter α. Our results show that rotation may delay the onset of vortex street and decrease the vortex‐shedding frequency.

Modes in flow focusing and instability of coaxial liquid―gas jets

Six flow modes are distinguished in the flow-focusing experiments of a liquid jet forced by a high-speed air stream. The domains of the modes are identified on the parameter space of the liquid flow rate Q 1 and the gas pressure drop Δp g . The disturbance wavelength and breakup length L of the jet are also measured. A theoretical model considering axisymmetric disturbances is proposed, and a basic velocity profile of hyperbolic-tangent function is utilized. The linear temporal and spatio-temporal instability analyses are carried out using the Chebyshev collocation method. The effects of the flow parameters and the velocity profile on the flow instability are discussed. The temporal instability analysis demonstrates that the interfacial shear causes the instability of short waves and retards the instability of long waves. Moreover, the spatio-temporal instability analysis gives the transition boundary between the absolute and convective instability (AI/CI). The most unstable wavelength predicted by the temporal instability analysis and the AI/CI boundary predicted by the spatio-temporal instability analysis are in good agreement with the experimental results.

Absolute and convective instability character of slender viscous vortices

Motivated by the need for effective vortex control, the character of absolute and convective instabilities (AI/CI) of incompressible and high-Mach number slender vortices with axial-velocity deficit is studied. Attention is focused on the disturbance modes which lead to the maximum absolute growth rate, and their dependence on flow conditions such as axial-flow profile, Reynolds number, and Mach number. A significant difference between the AI/CI and temporal-instability characters of the vortices occurs as the axial velocity deficit reduces. These theoretical results are applied to the flow region where vortex breakdown happens. It is found that the breakdown region is absolutely unstable, where waves are dominated by the spiral disturbance with lowest azimuthal wave number, in reasonable agreement with measurement.

A vorticity dynamics theory of three-dimensional flow separation

A theory of three-dimensional incompressible flow separation is presented in terms of the on-wall signatures of the flow. Some long-standing controversial issues are revisited and answers given, such as the inconsistency of the separation criteria based on the topological theory and “open separation,” and whether a separation line is an asymptote or envelope of neighboring skin-friction lines. General criteria for identifying an “open” or “closed” flow separation zone and separation line (including the initial point of the latter), steady and unsteady, are obtained, which apply to a generic smooth curved wall at any Reynolds numbers. The criteria are found to be most clearly given in terms of on-wall signatures of vorticity dynamics. These are then specified to steady boundary layer separation at large Reynolds numbers. A scale analysis under mild assumptions leads to a three-dimensional triple-deck structure near a generic boundary layer separation line. Criteria are presented for “separation watch,” whi...

Axisymmetric and non-axisymmetric instability of an electrified viscous coaxial jet

A linear study is carried out for the axisymmetric and non-axisymmetric instability of a viscous coaxial jet in a radial electric field. The outer liquid is considered to be a leaky dielectric and the inner a perfect dielectric. The generalized eigenvalue problem is solved and the growth rate of disturbance is obtained by using Chebyshev spectral collocation method. The effects of the radial electric field, liquid viscosity, surface tension as well as other parameters on the instability of the jet are investigated. The radial electric field is found to have a strong destabilizing effect on non-axisymmetric modes, especially those having smaller azimuthal wavenumbers. The helical mode becomes prevalent over other modes when the electric field is sufficiently large. Non-axisymmetric modes with high azimuthal wavenumbers may be the most unstable at zero wavenumber. Liquid viscosity has a strong stabilizing effect on both the axisymmetric and non-axisymmetric instability. Relatively, the helical instability is less suppressed and therefore becomes predominant at high liquid viscosity. Surface tension promotes the instability of the para-sinuous mode and meanwhile suppresses the helical and the other non-axisymmetric modes in long wavelength region.

A numerical study of dynamics of a temporally evolving swirling jet

Direct numerical simulation (DNS) of a swirling jet near the outlet of a nozzle with axisymmetric and non-axisymmetric disturbances is performed to investigate the dynamic characteristics of the flow. The early (linear) stage of the jet evolution agrees well with the predictions of linear stability theory. In the nonlinear stage, the axisymmetric DNS shows that the interaction between the primary vortex ring and the streamwise columnar vortex creates a secondary vortex structure with opposite azimuthal vorticity near the columnar vortex. Then a vortex pair consisting of the primary and secondary vortices forms and travels radially away from the symmetry axis, causing a rapid increase of the thickness of mixing layer. The non-axisymmetric DNS shows that the streamwise vortex layer developed in the early stage of evolution due to azimuthal instability breakdowns into small eddies under the joint stretch of the axial and azimuthal shear. The results reveal several mechanisms of mixing enhancement by swirl, i...

Instability of a viscous coflowing jet in a radial electric field

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor-Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

Linear instability analysis of an electrified coaxial jet

A temporal linear instability analysis of an electrified coaxial jet inside a coaxial electrode is carried out in this paper. The analytic dispersion equation is derived. The characteristic of the temporal instability is investigated and effects of the parameters, including the dimensionless electrostatic force, the dimensionless velocity difference, the density ratio, the inner and the outer diameter ratios, and the Weber numbers, are discussed systematically. The axisymmetric and the helical modes are both considered. Two independent unstable modes, mode 1 and mode 2, are identified. Among all the parameters the dimensionless electrostatic force has remarkable influence on mode 1. It can change mode 1 from the Rayleigh regime to the wind induced regime, and to the atomization regime by increasing the electric-field intensity. Nevertheless, the dimensionless electrostatic force has no apparent effect on mode 2. The behaviors of mode 2 resemble those of a coaxial jet not having electric field. The surface...

Perturbation analysis on gas flow in a straight microchannel

In the present paper, a steady subsonic gas flow either in a circular micropipe or in a planar microchannel driven by pressure within the slip flow regime is studied theoretically by using a perturbation expansion method to solve compressible Navier-Stokes equations. The isothermal flow assumption used in previous theoretical studies is given up. High-order boundary conditions of velocity slip and temperature jump are adopted at the wall. The set of dimensionless governing equations with two small similarity parameters, namely, the ratio of height to length e, and the Knudsen number Kn, is approximated successively by using the perturbation expansions. The various cases such as e≪Kn2, e∼Kn2, and e∼Kn1.5 are studied in detail. Explicit analytical solutions for pressure, density, velocity, temperature, and mass flow rate are obtained up to order of O(Kn2). It is shown that the solution formulas for long channels (e≪Kn2) in lower order are in exact agreement with previous theoretical results. In particular, ...