Horizontal Liquid Layer Research Articles

Stability analysis of Rayleigh–Bénard–Marangoni convection in fluids with cross-zero expansion coefficient

Cross-zero expansion coefficient Rayleigh–Bénard–Marangoni (CRBM) convection refers to the convective phenomenon where thermal convection with stratified positive and negative expansion coefficients in a liquid layer is coupled with the Marangoni convection. In the Bénard convection, fluids with a cross-zero expansion coefficient contain a neutral expansion layer where the expansion coefficient (α) is zero, and the local buoyancy-driven convection is coupled with the Marangoni convection, leading to unique flow instability phenomena. This paper uses linear stability theory to analyze the CRBM convection in a horizontal liquid layer under a vertical temperature gradient and performs numerical calculations for fluids under different Bond numbers (Bd) in both bottom-heated and bottom-cooled models, obtaining the critical destabilization conditions and modes. In the bottom-heated model, different combinations of buoyancy instability mechanism (BIM), tension instability mechanism, and coupled instability mechanism (CIM) appear depending on the dimensionless temperature for the neutral expansion layer (Tα0) and the Bd. In the bottom-cooled model, two mechanisms occur according to the variation of Tα0: BIM and CIM.

Effect of shape and thermal conductivity of microstructured capillary-porous coatings on heat transfer during evaporation and boiling in thin horizontal liquid layers

Investigation results on heat transfer during evaporation and boiling in thin horizontal liquid layers on 2D modulated capillary-porous coatings with a sinusoidal profile in a wide range of relative pressures and layer heights are presented in this paper. Coatings were made on a 3D laser printer using the technology of additive selective laser sintering (SLS). One coating was made of bronze with a modulation wavelength equal to the Laplace constant of the working fluid and two coatings were made of stainless steel and bronze with a doubled wavelength. The experimental data obtained on the coatings were compared with each other and with the values obtained by evaporation and boiling of n-dodecane on a smooth surface under the same conditions. It is shown that in the region of low relative pressures in liquid layers with a height less than the Laplace constant, heat transfer intensification achieved on a sample made of a material with low thermal conductivity (stainless steel) was five times higher as compared to a smooth surface. In the range of relative pressures, when nucleate boiling was observed in the layers, the temperature difference reached on the bronze coatings was approximately 3–4 times less than on a smooth surface. The temperature difference for the stainless steel coating changed little with an increase in the heat flux. In pre-crisis conditions, the temperature difference during boiling on the stainless steel coating was less than on the bronze coatings in the entire range of relative pressures and layer heights. The highest critical heat fluxes were obtained on a bronze coating with a modulation wavelength equal to the Laplace constant.

Thermo-magnetic convection and convective magneto-gravitational parametric resonance in a horizontal ferrofluid layer under time quasi-periodic vibrations: A balance harmonic analysis

Convective instability in a horizontal ferromagnetic liquid layer with rigid boundaries is investigated in the presence of both an uniform magnetic field and a vertical quasi-periodic forcing having two incommensurate frequencies ω1 and ω2. A linearized convective instability analysis predicting the onset of convection is performed and by means of a Galerkin projection truncated to the first order, the linear dynamic of the system is reduced to a damped quasi-periodic Mathieu oscillator. Using a balance harmonic analysis, it turns out that at sufficiently low vibration frequencies, we recover the critical instability parameters related to the unmodulated case where the convection is mainly due to the magnetic mechanism. This feature means that the buoyancy mechanism does not contribute into the convective cells formation and consequently heating from below or from above does not alter the onset of convection. However, at sufficiently high vibration frequencies, both the magnetic and buoyancy mechanisms are operative and here we are dealing with a magneto-gravitational parametric resonance convection. The transition between these convective modes is occurred via bicritical states giving rise to cusp points in the magnetic Rayleigh number besides discontinuities in its corresponding critical wave number. In addition, it is shown that a proper tuning of the irrational frequency ratio ω=ω2/ω1 provides a control of the convection onset as well as the nature of its mechanism. Moreover, special attention is devoted to highlight the effect of the Prandtl number on the dynamic of the system at different values of the frequency ratio ω.

THE INFLUENCE OF THE MARANGONI EFFECT ON THE ONSET OF GRAVITACTIC BIOCONVECTION

Self-movement of such microorganisms as Tetrahymena against gravity leads to the accumulation of cells at the free surface and, as a consequence, to an unstable density distribution. The study considers the onset of gravitactic bioconvection in a horizontal layer of a nonisothermal liquid with a free nondeformable boundary, taking into account the dependence of surface tension on the concentration of microorganisms. The dependence of the critical concentration Rayleigh number characterizing the onset of instability on the Marangoni number is analytically obtained in the long-wave approximation. It is shown that the long-wave concentration Rayleigh number does not depend on the thermal Rayleigh number, as well as on the Schmidt and Lewis numbers. The parameter ranges (the Marangoni and thermal Rayleigh numbers) in which the long-wave instability exists are found. Critical wave numbers and critical concentration Rayleigh numbers are determined from the numerical solution of the linear stability problem.

Influence of liquid layer height on pressure pulsations during evaporation/boiling under reduced pressure conditions

The paper presents experimental data on the influence of the height of the horizontal liquid layer on the amplitude of pressure pulsations obtained during evaporation/boiling under reduced pressure conditions. Also presented are the spectra of pressure pulsation power versus frequency obtained using fast Fourier transform for different heights of the horizontal liquid layer under reduced pressure conditions. It is obtained that the use of a thin film of working fluid during evaporation/boiling under reduced pressure conditions reduces the amplitude of pressure pulsations compared to thicker fluid layers. Analysis of the pressure pulsation spectra for explosive boiling regimes allows us to determine the characteristic frequency corresponding to the periodicity of explosive boiling. Also, this approach allows a quantitative comparison of the power of pressure pulsations obtained in different heat exchange systems and apparatuses.

Symmetry of Structures under Two-Dimensional Instability in a Finite-Height Horizontal Layer of Boiling Liquid

The two-dimensional instability of a horizontal layer of boiling liquid with a finite height was experimentally studied. In this layer, “vapor columns” rose at the corners of a square rectangular grid, and the symmetry of “vapor column” location on the heating surface was considered. The model adopts an approach to the boiling crisis from the side of both developed nucleate boiling and transitional boiling (the Zuber problem). When dealing with developed nucleate boiling, the layer of boiling liquid is considered in calculations as an isotropic homogeneous system (foam). It is shown how the conditions on the heating surface (capillary-porous coating) affect the external hydrodynamics of the liquid layer and, ultimately, the value of the critical heat flux. The calculation ratio obtained by approaching the boiling crisis from the side of developed nucleate boiling takes into account the dependence of the critical heat flux on the void fraction of the boiling liquid layer. A new solution to the boiling crisis problem is proposed when approaching the crisis from the side of transitional boiling (the Zuber problem). This new solution eliminates some shortcomings of the classical problem (in particular, the void fraction of the layer corresponds to the experiments).

Heat Transfer during Evaporation/Boiling of Horizontal Layers of Liquid at Low Pressure

Heat Transfer during Evaporation/Boiling of Horizontal Layers of Liquid at Low Pressure

THERMAL EFFECT IN THE EVAPORATION PROCESS FROM THE INTERFACE OF THE HORIZONTAL LIQUID LAYER UNDER A SHEAR GAS FLOW

This manuscript presents the experimental study of interfacial motion and convection in a horizontal liquid layer (ethanol and HFE 7100) evaporating from a localized surface (10 × 10 mm<sup>2</sup>) into the gas flow (dry air). The novel IR-Schlieren system has been developed. The system can almost simultaneously maintain the gas-liquid interface in a flat position in a confined square area and perform thermal imaging of the volatile liquid surface by IR camera. We consider the thermal effect of gas and liquid temperature (20°C-50°C) for various gas velocities (0.0138-0.138 m/s) on interfacial liquid motion and their influence on the convective flow structure within the liquid layer. It is found that the influence of the gas flow action on the Marangoni convection at the interface is reduced with an increase in temperature. We explain this fact by the growth of the diffusion resistance for the gas flow under a strong evaporation from the interface.

Plane-Parallel Advective Flow in a Horizontal Layer of Incompressible Permeable Fluid

In this paper a new exact solution of the Navier – Stokes equations in the Boussinesq approximation describing advective flow in a horizontal liquid layer with free boundaries, where the vertical velocity component is a constant value, is obtained. The temperature is linear along the boundaries of the layer. Solutions of this kind are used to close three-dimensional equations averaged across the layer in the derivation of two-dimensional models of nonisothermal large-scale flows in a thin layer of liquid or incompressible gas. The properties of advective flow at different values of Reynolds number and Prandtl number are investigated.

Heat transfer during boiling in a thin horizontal layer of the dielectric liquid

Heat transfer during boiling in a thin horizontal layer of the dielectric liquid

Guided wave propagation along surface of vertical solid partially submerged in horizontal liquid layer

Guided waves can propagate along the surface of a solid structure at a large distance with little attenuation. Hidden defects within the structure can be detected based on the abnormal reflection or transmission of guided waves. The distance between the defect and the transducer can be calculated according to the arrival time of the wave package and wave speed. Therefore, the guided wave speed should be known prior. However, existing analytical models can only predict the guided wave speed along the surface of a horizontal solid covered by a liquid layer. These models are not suited for the characterization of ultrasonic nondestructive testing of ship hulls, sluice gates, water dams, bridge piers, etc. In this study, an analytical model is proposed for the guided wave propagation along a vertical solid partially inserted into a horizontal liquid layer. A secular equation is derived and solved to predict the guided wave speed at the vertical solid–liquid interface. Twenty finite element simulations and thirty-three physical experiments are conducted on different materials with different dimensions by using varying incident frequencies. The results demonstrate that the proposed model can provide accurate analytical wave speeds to guide the nondestructive testing and structural health monitoring of underwater structures.

Thermal convection instability of two miscible viscous fluids in a rotating annular Hele–Shaw cell

We investigate thermal convection instability in a system of two horizontal miscible liquid layers confined in an annular Hele–Shaw cell rotating uniformly about its axis and subjected to a radial temperature gradient. We first determine the Hele–Shaw averaged velocity field in each fluid layer by taking into account the Coriolis force. Thereafter, the linear stability analysis leads to an eigenvalue problem solved numerically by the spectral collocation method. Depending on the buoyancy number, the ratio of the stabilizing chemical density anomaly to the destabilizing thermal density anomaly, the centrifugal force gives rise to two convection regimes: the oscillating regime corresponding to single-cell convection over the entire width of the Hele–Shaw cell and the stratified regime with separate convection in each of the two layers. In the stratified regime, it turns out that the cells rotate in the same direction and, thus, only thermal coupling is dominant in the Hele–Shaw cell geometry, regardless of the value of the viscosity ratio. We show that increasing the curvature parameter of the cell has a stabilizing effect and decreases the critical Buoyancy number corresponding to the transition from the oscillatory to the stratified regime. At a low Ekman number, the Coriolis force is strongly stabilizing and has little effect on the critical buoyancy number. Moreover, the increase in the curvature parameter and the decrease in the Ekman number together cause the transition from the oscillating regime to a nearly stratified regime. The effects of fluid layer thicknesses and the ratio of kinematic viscosities on the active or passive character of a layer are also examined.

Buoyancy instabilities in a liquid layer subjected to an oblique temperature gradient

We investigate the temporal and spatio-temporal buoyancy instabilities in a horizontal liquid layer supported by a poorly conducting substrate and subjected to an oblique temperature gradient (OTG) with horizontal and vertical components, denoted as HTG and VTG, respectively. General linear stability analysis (GLSA) reveals a strong stabilizing effect of the HTG on the instabilities introduced by the VTG for Prandtl numbers $Pr>1$ via inducing an extra vertical temperature gradient opposing the VTG through energy convection. For $Pr<1$ , a new mode of instability arises as a result of a velocity jump in the liquid layer caused by cellular circulation. A long-wave weakly nonlinear evolution equation governing the spatio-temporal dynamics of the temperature perturbations is derived. Spatio-temporal stability analysis reveals the existence of a convectively unstable long-wave regime due to the HTG. Weakly nonlinear stability analysis reveals the supercritical type of bifurcation changing from pitchfork in the presence of a pure VTG to Hopf in the presence of the OTG. Numerical investigation of the spatio-temporal dynamics of the temperature disturbances in the layer in the weakly nonlinear regime reveals the emergence of travelling wave regimes propagating against the direction of the HTG and whose phase speed depends on $Pr$ . In the case of a small but non-zero Biot number, the wavelength of these travelling waves is larger than that of the fastest-growing mode obtained from GLSA.

Interfacial Wave Propagation Along Surface of Vertical Solid Partially Submerged in Horizontal Liquid Layer

Interfacial Wave Propagation Along Surface of Vertical Solid Partially Submerged in Horizontal Liquid Layer

Experimental study of heat transfer during boiling in a thin layer of liquid on surfaces with structured porous coatings

The paper presents the results of the study of evaporation and boiling in a thin horizontal layer of liquid on microstructured surfaces in a wide range of changes in pressure. It is found that the thermal conductivity of materials of microstructured surfaces significantly affects the mechanism of steam removal from the pores and circulation of liquid along the heat transfer surface. It is determined that the pressure change leads to three regimes of heat transfer: evaporation, transition regime, and bubble boiling. The lowest values of the heat transfer coefficients and CHF were obtained in the transition regime; the highest ones were obtained in the bubble regime on both surfaces. Due to the higher thermal conductivity, the higher heat transfer coefficients and CHF were obtained on the bronze coating than on stainless steel over the entire pressure range.

Laminar-turbulent transitions during thermal gravitational-capillary convection in horizontal liquid layers heated from below

The evolution of the spatial form of the flow versus the Rayleigh number in layers with two rigid horizontal boundaries and layers with a free surface is experimentally investigated depending on the Rayleigh and Marangoni numbers. The experiments were carried out with layers of ethyl alcohol and water. A thermal imager was used to measure temperature fields on free surfaces of liquids.

A map of regimes of evaporation and boiling in the horizontal liquid layer on the modified surface

The paper presents the results of the study of the evaporation and boiling regimes in thin horizontal layers of liquid on a modified surface in a wide range of changes in the pressure and height of the liquid layer. Depending on the heat flux, pressure, and height of the liquid layer, the formation of various structures was observed. In this paper, maps of the evaporation and boiling regimes are obtained, which show the heat fluxes from the natural convection regime up to the boiling crisis, depending on the height of the liquid layer. The results are compared with the calculation dependencies.

On numerical modeling of natural convection based on the OpenFOAM solver

This work considers numerical modelling of natural incompressible convection problems in the gravity field in the Boussinesq approximation using OpenFOAM. A mathematical model of natural convection in the gravity field, using Boussinesq approximation, was considered. The built-in solver was identified and modified. The exact solution, theoretical data and experiment were used to verify the solver. A numerical study of natural convection in a horizontal liquid layer was performed. Natural convection in a fluid layer between coaxial cylinders was considered.

Maps of hydrodynamic regimes of evaporation and boiling in the thin horizontal liquid layer on the modified surface

The paper reports the results of the study of evaporation and boiling regimes of a thin horizontal liquid layer on a modified surface. The formation of various structures was observed at the different heat fluxes, pressures, and heights of the liquid layer. The paper presents maps of the hydrodynamic regimes of evaporation and boiling of thin liquid layers on a modified surface. The regions of existence of various structures observed in the layer are indicated depending on the pressure and heat flux. The results are compared with the calculation dependencies.

Linear stability analysis of bubble-induced convection in a horizontal liquid layer.

We investigate with a linear analysis the stability of a horizontal liquid layer subjected to injection of gas bubbles through a bottom wall. The injection is assumed uniform in space and constant in time. Injected bubbles ascend in the liquid layer due to the Archimedean buoyancy force and are ejected from the top free surface of the liquid layer. Modeling this two-phase flow system as two interpenetrating liquid and gas continua, we show that homogeneous upward gas flows become unstable at large gas fluxes. We determine the critical conditions of this homogeneous-heterogeneous regime transition and show that the critical modes are made of stationary convection rolls, either multi- or whole-layered depending on liquid viscosity, the radius of bubbles, and the thickness of liquid layer. By examining the energy transfer from base to perturbation flows, we indicate that liquid convective motion is driven by the buoyancy on heterogeneously distributed bubbles. We also reveal that the lift forces on bubbles have significant stabilizing effects by homogenizing bubble distribution close to the bottom wall.