Qiu-Sheng Liu

Viscous liquid films on a porous vertical cylinder: Dynamics and stability

In this paper, liquid films flowing down a porous vertical cylinder were investigated by an integral boundary layer model. Linear stability and nonlinear evolution were studied. Linear stability results of the integral boundary layer model were in good agreement with the linearized Navier-Stokes equations which indicated that the permeability of the porous medium enhanced the instability of the flow system. The growth rate and cut-off wave number increased with increasing the permeability and the Reynolds number. Linear stability analysis showed that the system was more unstable for a larger Reynolds number Re. Nonlinear studies showed that, for a very small Re, the film evolved with time while a saturated state was not observed. In addition, it was observed that the film ruptured when the permeability parameter beta > 0, and the rupture time decreased with increasing beta. However, for a moderate Reynolds number, a small finite harmonic disturbance evolved to a saturated traveling wave. Further investigation was conducted on the droplet-like wave solution. Results showed that the wave speed increased as the permeability parameter increased.

Non-modal stability in Hagen-Poiseuille flow of a Bingham fluid

Linear stability in Hagen-Poiseuille flow of a Bingham fluid is considered. Bingham fluid exhibits a yield stress in addition to a plastic viscosity. A Bingham number B, which describes the ratio of yield and viscous stresses, is used to characterize the behavior of Bingham-Hagen-Poiseuille flow. The effects of B on the stability are investigated using the energy method and the non-modal stability theory. The energy analysis shows that the non-axisymmetric disturbance has the lowest critical energy Reynolds number for all B. The global critical energy Reynolds number Re-g increases with B. At sufficient large B, Re-g has the order of B-1/2. For the non-modal stability, we focus on response to external excitations and initial conditions. The former is studied by examining the epsilon-pseudospectrum, and the latter is by examining the energy growth function G(t). For the problem of response to external excitations, the maximum response is achieved by non-axisymmetric and streamwise uniform disturbances at the frequency of omega = 0, with a possible choice of the azimuthal wavenumbers of n = 1, 2, or 3. For the problem of response to initial conditions, it is found that there can be a rather large transient growth even though the linear operator of the Bingham-Hagen-Poiseuille flow has no unstable eigenvalue. For small B, the optimal disturbance is in the form of streamwise uniform vortices and streaks. For large B, the optimal disturbance is in the form of oblique waves. The optimal energy growth decreases and the optimal azimuthal wavenumber increases with the increase of B

Influence of Forced Convection on Columnar Microstructure during Directional Solidification of Al - Ni Alloys

This paper presents a summary of cellular and dendritic morphologies resulting from the upward directional solidification of Al – Ni alloys in a cylindrical crucible. We analysed the coupling of solid-liquid interface morphology with natural and forced convection. The influence of natural convection was first analyzed as a function of growth parameters (solute concentration, growth rate and thermal gradient). In a second step, the influence of axial vibrations on solidification microstructure was investigated by varying vibration parameters (amplitude and frequency). Experimental results were compared to preliminary numerical simulations and a good agreement is found for natural convection. In this study, the critical role of the mushy zone in the interaction between fluid flow and solidification microstructure is pointed out.

Influence of high-frequency vibration on the Rayleigh–Marangoni instability in a two-layer system

The influences of high-frequency vibrations on the Rayleigh-Marangoni instability in a two-layer system are investigated theoretically in the framework of the averaging method. We focus on the effects of vertical and horizontal vibrations on the stability of different convection modes. The results show that vertical vibrations significantly stabilize the system, while horizontal vibrations significantly destabilize it. In the presence of vertical vibrations, instability only occurs in a system heated from below. However, in the presence of horizontal vibrations, instability can also occur in a system cooled from below. When Marangoni effect is dominant at the interface, it is found that there are four types of coupling modes. The oscillatory convection is the result of the competition between different modes. In the presence of Marangoni effect at the interface, the structure of the interfacial flow is complicated. In some cases, small counter-rolls may develop to preserve the nonslip condition of fluids in either the upper layer or the lower layer

Solutal Convection of Liquid Al-3.5 wt%Li during Its Upward Solidification

The onset of solutal convection during the directional solidification of Bridgman type of liquid Al-3.5 wt%Li is studied. Based on the analysis of a liquid-inhomogeneous-porous-double-layer system, a bimodal feature of neutral stability curve is found. The pulling rate is ascertained as the governing parameter for the mode transition, i.e., it determines whether the microstructure in the mushy layer is related to convection after the system destabilizes.

Linear spatio-temporal instability analysis of ice growth under a falling water film

A linear spatio-temporal stability analysis is conducted for the ice growth under a falling water film along an inclined ice plane. The full system of linear stability equations is solved by using the Chebyshev collocation method. By plotting the boundary curve between the linear absolute and convective instabilities (AI/CI) of the ice mode in the parameter plane of the Reynolds number and incline angle, it is found that the linear absolute instability exists and occurs above a minimum Reynolds number and below a maximum inclined angle. Furthermore, by plotting the critical Reynolds number curves with respect to the inclined angle for the downstream and upstream branches, the convectively unstable region is determined and divided into three parts, one of which has both downstream and upstream convectively unstable wavepackets and the other two have only downstream or upstream convectively unstable wavepacket. Finally, the effect of the Stefan number and the thickness of the ice layer on the AI/CI boundary curve is investigated.