Thin Horizontal Layer Research Articles

Experimental investigation and numerical modeling of destruction dynamics of thin silicone oil layers under the local heating

The processes of heat and mass transfer in systems with liquid-gas interface are of interest to a wide range of problems. Destruction dynamics of thin horizontal layers of silicone oils were investigated using confocal sensor on a 3D-positioning system. The numerical solution of the problem was obtained in the lubrication approximation theory for two-dimensional axisymmetric thermocapillary flow. The model takes into account the surface tension, viscosity, gravity and heat transfer in the substrate. The numerical algorithm for the joint solution of the energy equation and the evolution equation for the liquid layer thickness has been developed. The establishment method was used to obtain the stationary solutions. Experimental measurements and numerical calculations were made for silicone oils of different viscosities, heating power and initial thickness. The significant effect of the surface tension coefficient and its temperature coefficient on thermocapillary deformation was detected. It was experimentally established that the deformation value depends on a heat flux value. A liquid bump is formed at the boundary of the heating region that is also observed in numerically calculated profiles.

Dissolution-driven convection in a heterogeneous porous medium

Motivated by subsurface carbon sequestration, an experimental investigation of dissolution-driven Rayleigh–Darcy convection using two miscible fluids in a Hele-Shaw cell is conducted. A thin horizontal layer of circular impermeable discs is inserted to create an environment with heterogeneous and anisotropic permeability. The Sherwood number that measures the convective mass transfer rate between two fluids at the interface is linked to different parameters of the disc layer, including the disc size, spacing, layer permeability and its relative height with respect to the fluid interface. It is surprising that the convective mass transfer rate in our configuration is dominated by the disc spacing, but almost independent of either the disc size or the mean permeability of the layer. To explain this dependence, the convective mass transfer rate is decomposed into the number, velocity and density contrast of fingers travelling through the disc layer. Both the number and density contrast of fingers show dependences on the disc layer permeability, even though the product of them, the mass transfer rate, does not. In addition, the density contrast also shows a non-monotonic dependence on the disc spacing. The transition point is at a spacing that is close to the finger width. Based on this observation, a simple model based on mixing and scale competition is proposed, and it shows an excellent agreement with the experimental results.

The influence of characteristic scales of convection on non-isothermal evaporation of a thin liquid layer

Here, the effect of convection in liquid on non-isothermal evaporation of a horizontal thin layer on a hot wall is investigated. It is considered that the evaporation rate of salts always decreases with the growth of salt concentration. Depending on the nature of evaporation rate, the aqueous salt solutions can be classified into two different types: (1) the equilibrium partial pressure of water vapor ps varies slightly with time; (2) with an increase in salt mass concentration, ps decreases many times, which leads to a sharp drop in evaporation rate j. The criteria for attributing the salt to characteristic types are proposed, and relation between j and thermodynamic properties of salt solutions is determined. Different approaches to modeling are proposed for each group. For the first time, a simple calculation method linking the Peclet and Marangoni criteria with convection in a liquid and non-stationary heat exchange is proposed. The analysis shows that it is impossible to simulate the heat transfer without knowing the local characteristics of the velocity field in the liquid phase and without clearly distinguishing the characteristic convective scales of the velocity and temperature fields. So far, it has been believed that the surface Marangoni flow can be neglected due to the negative impact of surfactants. However, the studies of this paper show that a noticeable increase in free convection relates to the thermal and solutal Marangoni flows. A strong influence of the Marangoni flow on liquid convection at high heat fluxes is extremely important for reliable simulation of layer evaporation in a wide range of modern technologies.

Regimes of Intensified Heat Transfer during Evaporation of Thin Horizontal Liquid Layers at Reduced Pressures

The influence of structures formed during the evaporation and boiling of a liquid (n-dodecane) in thin horizontal layers on heat transfer has been analyzed. Structures shaped with the shapes of funnels and craters are formed at low pressures in liquid layers with thicknesses above the capillary constant under the action of a vapor recoil force. Increasing pressure leads to the onset of bubble boiling. It is established that the formation of these structures in the regime of intense evaporation at low reduced pressures leads to an about 70% increase in the heat-transfer coefficient at analogous layer thicknesses in comparison to the case of bubble boiling.

Numerical Study of Nonlinear Structures of Locally Excited Marangoni Convection in the Long-Wave Approximation

We investigate stationary and non-stationary solutions of nonlinear equations of the long-wave approximation for the Marangoni convection caused by a localized source of heat or a surface active impurity (surfactant) in a thin horizontal layer of a viscous incompressible fluid with a free surface. The distribution of heat or concentration flux is determined by the uniform vertical gradient of temperature or impurity concentration, distorted by the imposition of a slightly inhomogeneous heating or of surfactant, localized in the horizontal plane. The lower boundary of the layer is considered thermally insulated or impermeable, whereas the upper boundary is free and deformable. The equations obtained in the long-wave approximation are formulated in terms of the amplitudes of the temperature distribution or impurity concentration, deformation of the surface, and vorticity. For a simplification of the problem, a sequence of nonlinear equations is obtained, which in the simplest form leads to a nonlinear Schrodinger equation with a localized potential. The basic state of the system, its dependence on the parameters and stability are investigated. For stationary solutions localized in the region of the surface tension inhomogeneity, domains of parameters corresponding to different spatial patterns are delineated.

Режимы с интенсификацией теплообмена при испарении в тонких горизонтальных слоях жидкости при пониженных давлениях

AbstractThe influence of structures formed during the evaporation and boiling of a liquid (n-dodecane) in thin horizontal layers on heat transfer has been analyzed. Structures shaped with the shapes of funnels and craters are formed at low pressures in liquid layers with thicknesses above the capillary constant under the action of a vapor recoil force. Increasing pressure leads to the onset of bubble boiling. It is established that the formation of these structures in the regime of intense evaporation at low reduced pressures leads to an about 70% increase in the heat-transfer coefficient at analogous layer thicknesses in comparison to the case of bubble boiling.

Experimental assessment of sound velocity and bulk modulus in high damping rubber bearings under compressive loading

The present paper deals with the non-destructive evaluation of stressed High Damping Rubber Bearings (HDRB) in civil engineering. Such bearings are commonly made with alternating thin horizontal layers of High Damping Rubber (HDR) bonded to steel laminates. The influence of uniaxial compressive loading on pressure waves' velocity and bulk modulus is investigated for two types of bearings (with and without laminates). In the presence of laminates, bulk modulus increases with the applied compressive loading (e.g. ΔK = 20% at a mean stress σ = 16 MPa). In the absence of laminates, slipping on walls is visually observed in spite of their roughness and is thus confirmed by limitation in the increase of sound velocity. The feasibility of stress measurements using ultrasonic methods in HDRB is proved.

Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

Heat transfer and critical phenomena during evaporation and boiling in a thin horizontal liquid layer at low pressures

The results of an experimental study of heat transfer and high-speed video recording of evaporation and boiling processes in horizontal liquid films of n-dodecane are presented for the wide ranges of layer height and pressure. Evaporation regimes at low reduced pressures were characterized by formation of dry spots and structures with the shape of “funnels” (depressions with a hemispherical bottom on the layer surface) and “craters” in the layers. In contrast to dry spots, the surface of “craters” is covered with a residual layer of liquid. The paper presents regime maps indicating the regions of dry spots, “funnels”, “craters”, and nucleate boiling observed for each layer height depending on the reduced pressure and heat flux density. It is shown that in the region of low reduced pressures, the Kutateladze formula describes change in hydrodynamics in the layers, whose height is equal to the Laplace constant or higher, by the regime where only “craters” remain in the layer. In the region of reduced pressures less than 7.4 · 10−5 (133 Pa) the critical heat fluxes (CHF) decrease with decreasing pressure. In the range of reduced pressures from 7.4 · 10−5 (133 Pa) to 5.5 · 10−3 (104 Pa), the CHF depends weakly on the pressure. With an increase in the layer height, CHFs increase sharply, and when achieving a constant value, are described by the Yagov dependence obtained for pool boiling of liquids. For the reduced pressure above 5.5 · 10−3 (104 Pa), in the layers with a height exceeding the Laplace constant, the CHF is the same as that calculated by the Kutateladze and Yagov formulas for nucleate boiling crisis. The slope of the curve of heat flux dependence on the temperature head depends on the layer height at both evaporation and nucleate boiling.

Simulation of nonlinear waves on the surface of a thin fluid film moving under the action of turbulent gas flow

This paper derives a new system of equations for the simulation of the long-wave perturbation dynamics on the surface of a thin horizontal layer of heavy viscous fluid moving under the action of turbulent gas flow. In the case of small Reynolds numbers of the fluid, this system of equations is used to derive an evolution equation for the value of deviation of the film thickness from the unperturbed level. Some solutions of this equation are given.

The bearing capacity of footings on sand with a weak layer

Minor details of the ground, such as thin weak layers, shear bands and slickensided surfaces, can substantially affect the behaviour of soil–footing and other geotechnical systems, despite their seeming insignificance. In this paper, the influence of the presence of a thin horizontal weak layer on the ultimate bearing capacity of a strip footing on dense sand is investigated by single-gravity tests on small-scale physical models of the soil–footing system. The test results show that the weak layer strongly influences both the failure mechanism and the ultimate bearing capacity if its depth is lower than about four times the footing width. It is found that the presence of a thin weak layer can cause decreases of the ultimate bearing capacity of up to 80%. Numerical simulations, by finite-element analysis, of the behaviour of the reduced-scale models are able to capture the failure mechanism and the ultimate bearing capacity correctly, only if the mean equivalent constant value of the secant angle of shearing resistance used in calculations is selected, taking into account the curvature of the shear strength envelope of the sand within the very low normal stress range existing in the tested models.

Centrifuge tests on strip footings on sand with a weak layer

Tests on small-scale physical models of a strip footing resting on a dense sand bed containing a thin horizontal weak soil layer were carried out at normal gravity (1 g ). The results, reported in a companion paper, point out that the weak layer plays an important role in the failure mechanism and the ultimate bearing capacity of the footing if it falls within the ground volume relevant to the behaviour of the sand–footing system. The same problem was also investigated by means of centrifuge tests on reduced-scale models at 25 g and 40 g . The results of these tests, reported and discussed in this paper, confirm that failure mechanisms are governed substantially by the presence of the weak layer if its depth does not exceed a critical value and highlight marked scale effects involving the ultimate bearing capacity related essentially to the mean equivalent stress level in the soil beneath and around the footing. Equivalent bearing capacity factors, [Formula: see text], for footings on a dense sand bed containing a thin weak layer are derived from experimental results and are proposed in the paper.

Fast-forward modeling of compressional arrival slowness logs in high-angle and horizontal wells

Compressional (P) and shear (S) sonic propagation modes are routinely measured with modern borehole acoustic logging instruments. Slownesses (inverse of velocity) of P- and S-modes provide information on compressional and shear slownesses of rock formations surrounding the wellbore, respectively. When a high-angle well penetrates horizontal thin layers, the layers function as waveguides for the propagation of sonic waves. Layer-trapped and borehole-guided waves interfere with each other, giving rise to abnormal amplitude variations and phase discontinuity in the time waveforms acquired at receivers. Consequently, waveforms measured across the receiver array often exhibit low semblance, which renders conventional waveform semblance-based processing techniques inadequate for reliable estimation of formation slowness. Instead of calculating waveform semblance, we invoke compressional first-arrival times to describe the propagation properties of the P-mode in high-angle and horizontal (HA/HZ) wells, and we derive P-arrival slownesses from the first-arrival times of the measured waveforms. Because the first-arrival time at a particular receiver is associated with the fastest P-wave, the P-arrival slowness log is much less affected by mode interference than the conventional log obtained using semblance-based processing techniques. Furthermore, numerical tests with high-angle wells indicate that compressional first arrivals are mainly associated with converted P-waves through deviated layers. Accordingly, we introduce a 1D layered simulation method to model P-mode first-arrival times in HA/HZ wells across thinly bedded formations. Synthetic examples confirm that P-arrival slowness logs obtained with our simulation method in HA/HZ wells agree to within 5% with logs obtained using 3D finite-difference simulations. In addition, because the new method simplifies the geometric complexity of the models from 3D to 1D, it saves 99% of CPU time compared with rigorous numerical simulations.

Evolution of the deformation profile of a horizontal thin ethanol layer when heated locally

Thermocapillary breakdown of thin horizontal layer of ethanol when heated from a localized heat source was studied experimentally. The influence of layer depth on the breakdown process was investigated. Evolution of the layer thickness in the heating point and deformation profile were being monitored and the critical thickness of the layer was evaluated using confocal technique. Pulsations of layer thickness over the heating area before the breakdown have been found.

Natural convection in a differentially heated cubical cavity under the effects of wall and molecular gas radiation at Rayleigh numbers up to 3 × 109

Numerical simulations are carried out to analyze the effects of wall and molecular gas radiation on weakly turbulent natural convection in a differentially heated cubical cavity in the Rayleigh number range 3 × 107 – 3 × 109. Two opposite vertical walls are maintained at different temperatures and the four other walls are adiabatic. A direct numerical simulation (pseudo-spectral Chebyshev collocation) method for flow and temperature fields has been combined with direct ray-tracing method for radiation field, and, at the highest Rayleigh number, a spectral subgrid scale radiation model has been implemented to account for the smallest, though non-optically thin, turbulent scales. The effects of radiation on mean temperature and flow fields are to substantially decrease the thermal stratification in the core of the cavity (through different mechanisms in wall and gas radiation cases), to promote the organization of the flow near the top and bottom walls in the form of relatively thin horizontal boundary layers, and to lead to significant intensification of the mean circulation in the cavity. Both wall and gas radiation are shown to increase mechanical and thermal turbulence levels and to strongly modify the spatial distribution of the most turbulent regions. In the case of wall radiation, significant turbulence production is found upstream the vertical boundary layers due to Rayleigh-Bénard instabilities in unstably stratified regions along the horizontal walls. Gas radiation is shown to act as an additional dissipation mechanism for both the mean temperature variance and the variance of temperature fluctuations. However, radiative damping of temperature fluctuations decreases as the Rayleigh number increases.

Centrifuge modelling of the seismic performance of soft buried barriers

The paper presents the results of an experimental work carried out in a geotechnical centrifuge at the Schofield Centre of Cambridge University. Two reduced scale models of soft barriers in a sand layer underwent a series of ground shaking. In the first model a thin horizontal layer made of latex balloons filled with a cross-linked gel was created at about mid-height of the sand layer. In the second, the same balloons were deployed to form a V-shaped barrier aimed at isolating a relatively shallow volume of sand. The aim of the study was to get experimental evidence of the capability of such soft barriers to isolate a volume of soil thus reducing amplification of ground motion during severe seismic events. The experimental results were compared with FE numerical analyses of the same models, carried out also in free field to have a benchmark condition. By validating the FE modelling via the comparison with the experimental results, a robust model has been built, aimed at being used for carrying out a wider parametric numerical testing. The experimental results confirm the effectiveness of such soft barriers to reduce amplification in the isolated volumes during seismic events.

Hybrid Technology Used in Foundry

The paper presents the ways to eliminate shrinkage defects of nature. These techniques are, primarily, technological overlaps, risers and refrigerators. The paper shows that these methods are based on the known principle of feeding, according to which the upper layers of the is the risers for the underlying layers. This provides directional solidification of casting. The paper describes the additive technologies that solve problems, which are unobtainable for conventional technologies. It shows that the thin horizontal layers form a configuration sequentially. Here is realized another principle of feeding that is formulated as follows: each layer feeds itself. There is no difficulty to eliminate shrinkage defects in thin horizontal layers. However, high cost of raw materials and equipment and low productivity disallow wide introduction of additive technologies to manufacture castings. One solution to this problem, which is offered to-date is to create hybrid-manufacturing processes that combine both additive and traditional manufacturing techniques of casting. Traditional manufacturing techniques of castings are macro-level technologies while the additive technology is a micro level. Hybrid technologies, which are in intermediate position, can be attributed to a meso-level of the review of processes occurring in the liquid melt and mold. The paper has shown that the techniques that provide layer-by-layer filling of liquid melt in the mold and (or) layer-by-layer solidification of liquid melt in the mold can serve as one of the examples of hybrid technology in foundry. The paper analyses some of the patents related to the group of casting ingots of two or more different melts, i.e. multilayer » (B22D7 / 02). It conducts an analysis of the patent developed in BMSTU. The main conclusions are as follows: 1. At present, there is a base created for a successful development of hybrid technology in the foundry industry. 2. Hybrid technology allows the production for a period of transition (the period of changing traditional technology) to provide a new quality of castings.

Numerical modelling of thermocapillary deformation in a locally heated thin horizontal volatile liquid layer

The thermocapillary flow in a thin horizontal layer of viscous incompressible liquid with free surface is considered. The deformable liquid layer is locally heated. The problem of thermocapillary deformation of the locally heated horizontal liquid layer has been solved numerically for two-dimensional unsteady case. The lubrication approximation theory is used. Capillary pressure, viscosity and gravity are taken into account. Evaporating rate is supposed to be proportional to the temperature difference between the liquid surface and ambient. Heat transfer in the substrate is also simulated. The deformation of the free surface has been calculated for different values of the heating power and thickness of the liquid layer. Initially the liquid layer has flat surface and uniform temperature. The model predicts the thermocapillary deformation of the liquid surface and the formation of the thin residual layer of the liquid.

Numerical Modeling of Thermocapillary Deformation and Film Breakdown in a Locally Heated Thin Horizontal Volatile Liquid Layer

The problem of thermocapillary deformation and film breakdown in a thin horizontal layer of viscous incompressible liquid with a free surface is considered. The deformable liquid layer is locally heated. The problem of thermocapillary deformation of the locally heated horizontal liquid layer has been solved numerically for two-dimensional unsteady case. The lubrication approximation theory is used. Capillary pressure, viscosity and gravity are taken into account. Evaporating rate is supposed to be proportional to the temperature difference between the liquid and ambient. Heat transfer in the substrate is also simulated. The numerical algorithm for the joint solution of the energy equation and the evolution equation for the thickness of liquid layer has been developed. The model predicts the thermocapillary deformation of the liquid surface and the formation of dry spots. The dynamics of liquid surface, the dry spots formation and the velocity of the contact line have been calculated. The deformation of the free surface has been calculated for different values of the heating power and thickness of the liquid layer. The effect of surface tension coefficient and wetting contact angle on the velocity of the contact line motion has been analyzed. It has been obtained that the velocity of the contact line increases with the increase of the wetting contact angle value and of the surface tension coefficient.

Thermocapillary breakdown of a horizontal spot-heated liquid layer

Thermocapillary breakdown of thin (0.3–0.7 mm) horizontal layers of liquid (ethanol) when heated from a localized hot spot was investigated experimentally. The effects of layer thickness and the surface properties of the substrates on the breakdown dynamics were studied. Visualization and control of the liquid layer were carried out using schlieren and shadowgraphy techniques. Main steps of the breakdown process were determined and average velocity of the dry spot formation was measured. Significant influence of the substrate properties on breakdown dynamics has been found. It was shown that one of the main factors affecting the dynamics of layer breakdown and the formation of dry spots in the heating area besides the thermocapillary effect is evaporation.