A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges

A continuation method is applied to investigate the linear stability of the steady, axisymmetric thermocapillary flows in liquid bridges. The method is based upon an appropriate extended system of perturbation equations depending on the nature of transition of the basic flow. The dependence of the critical Reynolds number and corresponding azimuthal wavenumber on serval parameters is presented for both cylindrical and non-cylindrical liquid bridges.

Investigation on mechanism of critical cavitating flow in liquid jet pumps under operating limits

The critical cavitating flow in liquid jet pumps under operating limits is investigated in this paper. Measurements on the axial pressure distribution along the wall of jet pumps indicate that two-phase critical flow occurs in the throat pipe under operating limits. The entrained flow rate and the distribution of the wall pressure upstream lowest pressure section does not change when the outlet pressure is lower than a critical value. A liquid-vapor mixing shockwave is also observed under operating limits. The wave front moves back and forth in low frequency around the position of the lowest pressure. With the measured axial wall pressures, the Mach number of the two-phase cavitating flow is calculated. It's found that the maximum Mach number is very close to I under operating limits. Further analysis infers a cross-section where Mach number approaches to I near the wave front. Thus, the liquid-vapor mixture velocity should reach the local sound velocity and resulting in the occurrence of operating limits.

Influence of Rayleigh-Taylor Instability on Liquid Propellant Reorientation in a Low-Gravity Environment

A computational simulation is conducted to investigate the influence of Rayleigh-Taylor instability on liquid propellant reorientation flow dynamics for the tank of CZ-3A launch vehicle series fuel tanks in a low-gravity environment. The volume-of-fluid (VOF) method is used to simulate the free surface flow of gas-liquid. The process of the liquid propellant reorientation started from initially flat and curved interfaces are numerically studied. These two different initial conditions of the gas-liquid interface result in two modes of liquid flow. It is found that the Rayleigh-Taylor instability can be reduced evidently at the initial gas-liquid interface with a high curve during the process of liquid reorientation in a low-gravity environment.

Instabilities of a liquid film flowing down an inclined porous plane

The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy's law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d, the Darcy number delta, and the Beavers-Joseph coefficient alpha(BJ) on the instability of the system.

Effect of interfacial heat transfer on the onset of oscillatory convection in liquid bridge

In present study, effect of interfacial heat transfer with ambient gas on the onset of oscillatory convection in a liquid bridge of large Prandtl number on the ground is systematically investigated by the method of linear stability analyses. With both the constant and linear ambient air temperature distributions, the numerical results show that the interfacial heat transfer modifies the free-surface temperature distribution directly and then induces a steeper temperature gradient on the middle part of the free surface, which may destabilize the convection. On the other hand, the interfacial heat transfer restrains the temperature disturbances on the free surface, which may stabilize the convection. The two coupling effects result in a complex dependence of the stability property on the Biot number. Effects of melt free-surface deformation on the critical conditions of the oscillatory convection were also investigated. Moreover, to better understand the mechanism of the instabilities, rates of kinetic energy change and "thermal" energy change of the critical disturbances were investigated (C) 2009 Elsevier Ltd. All rights reserved.

The Convective Instabilities in a Liquid-Vapor System with a Non-equilibrium Evaporation Interface

Rayleigh-Marangoni-B,nard instability in a system consisting of a horizontal liquid layer and its own vapor has been investigated. The two layers are separated by a deformable evaporation interface. A linear stability analysis is carried out to study the convective instability during evaporation. In previous works, the interface is assumed to be under equilibrium state. In contrast with previous works, we give up the equilibrium assumption and use Hertz-Knudsen's relation to describe the phase change under non-equilibrium state. The influence of Marangoni effect, gravitational effect, degree of non-equilibrium and the dynamics of the vapor on the instability are discussed.

Experimental Study on the Combined Evaporation Effect and Thermocapillary Convection in a Thin Liquid Layer

The coupling mechanisms and flow characteristics of thermocapillary convection in a thin liquid layer with evaporating interface were studied. The planar liquid layer, with the upper surface open to air, was imposed externally horizontal temperature differences. The measured average evaporating rates and interfacial temperature profiles indicated the relative importance of evaporation effect and thermocapillary convection under different temperature gradients. A temperature jump was found at the interface, which was thought to be related to the influence of evaporation effect. All above mentioned results were repeated in a rarely evaporating liquid to compare the influence of evaporation effect.

NUMERICAL AND EXPERIMENTAL STUDY ON LIQUID-SOLID FLOW IN A HYDROCYCLONE

Hydrocyclones are widely used in industry, of which the geometrical design using CFD techniques is gaining more popularity in recent years. In this study, the Euler-Euler approach and the Reynolds stress model are applied to simulate the liquid-solid flowfield in a hydrocyclone. The methodology is validated by a good agreement between experimental data and numerical results. Within the research range, the simulation indicates that the liquid-solid separation mainly occurs in the conical segment, and increasing conical height or decreasing cylindrical height helps to improve the grade efficiencies of solid particles. Based on these results, two of the same hydrocyclones are designed and installed in series to establish a liquid-solid separation system. Many experiments are then conducted under different conditions, in which the effects of the water cut and the second hydrocyclone on the separation are investigated. The results also confirm that smaller solid particles are more susceptible to the inlet conditions, and the second hydrocyclone plays a more important role as the water cut reduces.

The hydro-kinetic theory of liquid helium II

In Part I the kinetic theory of excitations in flowing liquid He II is developed to a higher order than that carried out previously, by Landau and Khalatnikov, in order to demonstrate the existence of non-equilibrium terms of a new nature in the hydrodynamic equations. It is then shown that these terms can lead to spontaneous destabilization in counter currents when the relative velocity of the normal and super fluids exceeds a critical value that depends on the temperature, but not on geometry. There are no adjustable parameters in the theory. The critical velocities are estimated to be in the 14-20 m/sec range for T ≤ 2.0° K, but tend to zero as T → T_λ. The possibility that these critical velocities may be related to the experimentally observed "intrinsic" critical velocities is discussed.

Part II consists of a semi-classical investigation of rotonquantized vortex line interactions. An essentially classical model is used for the collision and the behavior of the roton in the vortex field is investigated in detail. From this model it is possible to derive the HVBK mutual friction terms that appear in the phenomenalogical equations of motion for rotating liquid He II. Estimates of the Hall and Vinen B and B' coefficients are in good agreement with experiments. The claim is made that the theory does not contain any arbitrary adjustable parameters.