New modification of background-oriented schlieren (BOS) technique using periodic grayscale and color patterns and phase-shifting profilometry (PSP) image processing is proposed. Its accuracy, spatial resolution and robustness with respect to large displacement gradient are analyzed using synthetic images. Comparison with multi-pass direct cross-correlation, wavelet-based optical flow analysis and Fourier transform profilometry (FTP) is performed. Grayscale PSP BOS requires at least three phase-shifted images to be taken with the schlieren object remaining unchanged. Its accuracy improves with growing number of images. The required three grayscale images can also be coded as the channels of a single color image. Thus, single-frame color PSP BOS is realized, which can be used to measure the unsteady flows. The negative effects of the color channels cross-talk and imbalance are corrected. PSP BOS yields reliable results for displacement gradient far above 1 pix/pix, which is the limit for other image processing techniques. However, its accuracy is affected by the camera sensor noise. The ability of color PSP BOS to measure strongly refracting objects is confirmed by experimental measurements of the glycerol mass fraction in glycerol–water diffusion layer. Quantitative comparison between PSP, direct cross-correlation and FTP is also performed for the measurements of natural convection in water near a heated vertical plate.

Axisymmetric turbulent jet of hot air is completely reconstructed from the experimentally measured temperature field using physics-informed neural network (PINN), which takes into account both the experimental data and the governing equations. The proposed data assimilation technique allows determination of the velocity and turbulent viscosity fields without usage of specific turbulence model equations. The input experimental data are obtained using nonintrusive background oriented schlieren (BOS) measurements. The accuracy of the flow reconstruction is assessed for synthetic data and two different experimental setups. The data assimilation results are shown to be in good agreement with the conventional Reynolds-averaged Navier-Stokes (RANS) simulations using the Spalart-Allmaras (SA) and k-epsilon turbulence models. The following advantages of PINN data assimilation are demonstrated: it does not require regularization of the equations or smoothing of the experimental data and allows omission of the boundary condition for the inlet turbulence level.

The presence of the drift current complicates analysis of the dispersion relation for wind waves. In the general case, this relation is derived from analysis of the Rayleigh equation which has no analytical solution for an arbitrary velocity profile. In the limiting case, when the length of the gravity–capillary wave is significantly less than the typical flow depth, the simple Doppler approximation can be used. However, this approximation is not valid in the general case and it is necessary to take into account the vertical profile of the horizontal velocity up to the depth that corresponds to the considered wavelengths. The drift velocity profile is determined using Particle Image Velocimetry. The high-resolution spatiotemporal spectra of waves are obtained using the color schlieren technique. A small addition of sodium dodecyl sulfate allows one to estimate the effect of soluble impurities on the structure of the drift current and to modify the ratio between the drift current depth and length of the gravity–capillary wave. In the present work, an algorithm for numerical calculation of the dispersion relation for a given velocity profile is used. It is shown that the Rayleigh equation adequately describes the dispersion relation in a wind channel under conditions where the influence of the profile is strong and cannot be reduced to simple Doppler corrections. Thus, deviations of dispersion relations obtained in geophysics from simple approximations can correspond to different relationships between wavelengths and drift current depth.

New data assimilation technique for turbulent flows is proposed, which allows determination of the turbulent viscosity, velocity and pressure distributions from the experimentally measured temperature fields. Measurements are performed for a round jet of hot air using nonintrusive Background Oriented Schlieren technique. Thus, seedless velocity and pressure measurement is realized, as well as measurement of the turbulent viscosity field without usage of any particular turbulence model. Data assimilation results are shown to be in good agreement with the conventional RANS simulations using the Spalart–Allmaras and k-ɛ turbulence models, if adequate smoothing of the input temperature field is performed and sufficient regularization of the energy equation in regions with uniform temperature is provided.

Synthetic tests of the accuracy, spatial resolution and robustness with respect to large gradient of the apparent displacement are performed for Background Oriented Schlieren (BOS) measurements using various background patterns and image processing techniques, including multi-pass cross-correlation, iterative Horn–Schunck and Lucas–Kanade optical flow algorithms and Fourier Transform Profilometry (FTP). It is shown that FTP with periodic sinusoidal or binary fringe pattern outperforms all the other methods. With optimal pattern period λpattern=6−15pix it is able to resolve perturbations with wavelength down to λpattern2 and to obtain reliable results for images with displacement gradient up to 0.9 pix/pix. Better performance of FTP, compared to multi-pass cross-correlation, is confirmed for real experimental measurements of water temperature in natural convection near a heated vertical plate. FTP advantages and limitations, including possible nonlocal error, associated with phase unwrapping, are discussed.

Processes of the formation of wind waves remain poorly understood, despite numerous studies. One of the main reasons, in our opinion, is that simplified theoretical analysis does not take into account the weak film of natural contaminants. In the present work, wave generation in two channels is experimentally studied and compared for ethanol, water, and water with the addition of a soluble surfactant (sodium dodecyl sulphate (SDS)) in various concentrations. These concentrations hardly affect the surface tension coefficient, but they lead to a significant modification of the subsurface flow structure. In ethanol, the surface film is not formed, so it can be considered a reference case. In water and water with the surfactant, the film is broken and the surface becomes pure at certain critical wind speed, which grows for increasing surfactant concentration. For the surface to remain pure, the contaminant adsorption to the surface must be compensated by its removal by the tangential stress. Three experimental techniques are used to study the influence of cool skin on the formation of the wind waves. The surface relief is measured with modified color schlieren technique and the liquid velocity fields are determined with particle image velocimetry (PIV). The surface temperature fields, which allow the identification of the regions of the rupture of cool skin, are obtained with IR thermography. IR thermography is also used to study the surface velocity field (IR PIV). The film is shown to have significant influence on both the wave amplitude and the structure of subsurface flow.

New experimental technique, based on IR thermography, is proposed to measure the surface pressure for dilute monomolecular films of surfactants on a liquid surface. The surfactant molecules are distributed unevenly along the surface, which leads to the formation of surface regions of two kinds. Part of the surface is covered with surfactant film, which suppresses the surface renewal and inhibits the heat transfer between the surface and the bulk liquid. Thus, these regions possess lower temperature compared to the rest of the surface, free of surfactant and exhibiting both buoyant and thermocapillary convection. High sensitivity of the modern IR cameras allows the measurement of the temperature difference between the surface regions, from which the surface pressure can be derived. Experiments with myristic acid are performed for different values of the surface temperature and mean concentration of the surfactant. The results demonstrate that it is possible to measure the surface pressure for liquid-expanded films with area per molecule up to 500\char1972. The derived parameters of 2D van der Waals gas are in agreement with published data . The proposed technique can also be used to compare the contamination level in dilute films of insoluble and soluble surfactants.

New variant of Background Oriented Schlieren (BOS) technique is proposed for the measurements of strongly refracting objects. The employed pattern presents a rectangular grid of color dots. Special color encoding makes every dot unique provided its nearest neighbors can be identified. This allows robust matching of the dot images for schlieren objects with arbitrary large apparent displacements. Also, possible formation of multiple images of the same dot due to strongly nonlinear variations of the refractive index can be used to improve the accuracy of the refractive index field measurement. Multi-frame approach is employed to improve the spatial resolution. Potential of the proposed technique is demonstrated by measurements of the diffusion layers in aqueous solutions of sodium chloride and ethanol.

Development of the convective flow from a line heat source located at the liquid surface is studied for the case when thermocapillary convection is inhibited by the surface film. Surface film is formed by small amounts of surfactants present in non-deionized (distilled or natural) water. It imposes a no-slip boundary condition for velocity at the surface and determines the fluid dynamics of the surface layer. For the heat source located at the surface, the vertical stratification is stable and the flow is driven by a horizontal pressure gradient, formed by non-uniform heating of the liquid along the surface. Experimental studies include measurements of velocity fields using particle image velocimetry, surface relief measurements using moon-glade background oriented Schlieren and surface temperature measurements using infrared thermography. Also, numerical simulations of the flow development are performed and a new similarity solution for the steady state in a laterally unbounded domain is constructed, which takes into account the pressure gradient. The results are shown to be in good agreement with experimental data. The obtained dependencies of the maximal velocity, boundary layer thickness, local and total Nusselt numbers on the Rayleigh number are consistent with literature data obtained for the non-uniformly heated bottom case, which demonstrates universal properties of horizontal convection.

New hybrid simulation technique is proposed for natural convection flows, which combines experimental measurements of the instantaneous temperature fields with numerical integration of the fluid dynamics equations. Experimental temperature distributions are used to determine the buoyancy term, which enables one to obtain the velocity and pressure fields without extra measurements. Solution of the energy equation is replaced with experimental data, hence the technique can be used even if the energy equation contains unknown source terms or if the boundary conditions for temperature are unknown. The approach is demonstrated for Background Oriented Schlieren (BOS) measurements of three natural convection flows: natural convection near a heated vertical plate, convective plume from a heated horizontal wire and horizontal convection driven by nonuniform radiative heating of liquid surface. The velocity fields, obtained by reconstruction in steady and unsteady flows, exhibit good agreement with numerical simulations if the input temperature data are accurate. Moreover, the hybrid simulation takes into account the flow asymmetries in a particular experimental run. However, spatially limited measurement region or underestimation of the peak temperature, typical for BOS measurements of the thin thermal layers in liquids, lead to underprediction of the velocity and pressure disturbances in hybrid simulation.

The onset of convection in an initially homogeneous liquid layer cooled from above is investigated by means of a non-normal approach. This method is based on the analysis of the temporal evolution of small perturbations. The most amplified perturbation and the moment, when convection can be observed, are determined. Experimental measurements are performed for a layer of distilled water cooled by evaporation. Instantaneous surface temperature fields are obtained using infrared thermography. The effect of the surface mobility on the size and onset time of convective cells is examined. The comparison of experimental results with numerical simulations for different boundary conditions reveals the presence of a film of adsorbed contaminants on the surface of distilled water, which corresponds to the no-slip condition. In the presence of the film, boundary conditions for cooling from above and heating from below become the same, and the obtained results agree with the experimental data available for a liquid layer with a heated bottom. As the layer depth increases, the onset time and the average horizontal wavenumber of convective cells become independent from the layer depth. The condition for the transition to a deep water approximation is determined by the surface heat flux and thermophysical parameters of the liquid.

Measurements of liquid surface topography are performed using new modification of Background Oriented Schlieren technique, which is based on the apparent distortion of a background pattern image reflected by the deformed surface. The optical setup comprises a camera and a backlit background, both installed above the liquid surface. The camera images the background pattern reflection. The apparent displacement of the pattern features with respect to the reference image, taken for the unperturbed liquid surface, is proportional to the local slope of the surface. This enables one to obtain instantaneous surface relief map by solving Poisson equation. Compared to the popular free-surface synthetic Schlieren technique, our approach allows measurements of the surface topography over deep liquid layers and for opaque liquids or multiphase flows. It is also more sensitive, which enables reliable measurements of perturbations as small as 1 pm. Experiments are performed for propagation of the circular surface waves, for convection driven by heating of a horizontal wire installed below the liquid surface and for Rayleigh-Benard-Marangoni convection in liquid heated from below. Attenuation coefficient of the gravity-capillary waves is determined for wave frequencies about 10 Hz. Comparison of the results, obtained in glycerol, distilled water and silicone oil, shows the remarkable difference between the surface deformation patterns, observed in liquids, which exhibit Marangoni convection, and liquids, where it is suppressed by the surface film. In distilled water and glycerol elevated surface is always observed in hot regions, whereas in silicone oil the effect of convection on surface relief depends on the competition between the buoyancy-driven and surface-tension-driven flows.

The application of high-resolution IR thermography for qualitative and quantitative determination of impurity concentrations in aqueous solutions is considered. Especially efficient turned out to be comparative analysis and analysis of contaminations: a film arises on the water surface in the presence of impurities, which can be seen well on an IR imager because of the difference in the surface temperatures and structures of convective vortices. It should be especially noted that the method makes it possible to determine low concentrations of impurities of neutral molecules, a case where no changes in the solution conductivity can be recorded using standard conductometric measurements. The problems related to the film simulation and influence of low-concentration impurities on the surface and volume properties of solution are considered.

Natural convection driven by evaporation of heavier-than-air fluids from the surface of the heated horizontal and vertical flat plates is studied both experimentally and numerically. The combined buoyancy effects of temperature and vapor density are shown to result in either downward or upward flow depending on the plate temperature and evaporating substance volatility and molar mass. For some substances (e.g., butanol) flow reversals are observed: solutal buoyancy is dominant for low and high temperatures of the heated plate leading to downward flow, whereas at moderate temperatures thermal buoyancy prevails resulting in upward convection. Refractive index fields are measured using Background Oriented Schlieren (BOS). Similarity between the temperature and vapor density fields associated with heat and mass transfer analogy is used to obtain temperature and vapor density fields from experimental data. The validity of this approach is analyzed. Good agreement between experimental temperature and vapor density distributions and numerical simulations is obtained for ethanol vapor, which has Lewis number about 1.8. For butanol vapor, which has Lewis number about 2.5, similarity is violated and temperature and vapor density contributions to refractive index cannot be separated. This is also true for validity of simplified modeling using total expansion coefficient. Similarity is also shown to be violated for hot liquid evaporation from a tank with conductive walls. In this case boundary conditions are dissimilar and upward convective flow of warm clean air near the outer surface of the tank walls is observed, which entrains the heavy vapor.

Horizontal convection development in liquids with free surface nonuniformly heated by infrared radiation is investigated. Experimental measurements of velocity and temperature fields are performed by Particle Image Velocimetry (PIV) and Background Oriented Schlieren (BOS). Absence of Marangoni convection in distilled water due to presence of surface film leads to significant difference between the results obtained in distilled water and in ethanol. Strong Marangoni flow in ethanol results in quick dispersion of heat over the surface layer and acceleration of convective flow. In distilled water heat propagation along the surface is inhibited, because only weak secondary flow associated with 3D effects is observed at the surface. Experimental results are compared to numerical simulations with different boundary conditions for horizontal velocity at the free surface: no-slip condition for distilled water, representing stagnant surface film, and tangential-stress condition, taking into account Marangoni effect, for ethanol. Good agreement is obtained, demonstrating of prescribing appropriate boundary condition, which corresponds to surface behavior of the considered liquid. (C) 2018 Elsevier Ltd. All rights reserved.

Dynamics of the surface layer in different liquids is examined by means of infrared thermography of the surface and simultaneous velocity fields measurements using surface and infrared Particle Image Velocimetry. This technique allows measurements and comparison of two velocity fields—at the surface and at small depth about 50–200 μm. In distilled water the velocity fields at the surface and at small depth exhibit significant dissimilarity. The flow field below the surface is essentially 3D, whereas the surface flow is characterized by vanishing 2D divergence of velocity, indicating predominantly planar motion. In contrast, in ethanol–butanol mixture two velocity fields are well correlated, both corresponding to 3D flow with continuous surface renewal. Thermal patterns, observed at the surface, and the flow field structure in different liquids are associated with different boundary conditions for velocity at the surface. Water surface is seldom renewed, which inhibits heat and mass exchange between the liquid and atmosphere. However, absence of vertical advection also enables organisms to live within the surface layer, to stand and walk on the free surface. This is illustrated by the difficulties a water strider faces on the surface of ultrapure water, which exhibits Marangoni convection.

It is shown that convective structures that form upon heating a planar liquid layer from below are determined not only by standard similarity parameters, such as the Prandtl, Rayleigh, and Marangoni numbers, but also by the presence or absence of an elastic film on the surface of the liquid, which occurs because of impurities and stabilizes the surface. The level of impurities contained in distilled water is enough to prevent Marangoni convection, and only additional purification (deionization) of water allows one to induce the thermocapillary effect. Using the method of infrared surface thermography, the mean size of thermal structures that emerge on the surface in different liquids at different temperatures and layer thicknesses is determined. A convection theory that takes the impurities in the linear and nonlinear approximations into account is examined and good compliance of the theoretical calculations with the experimental data obtained in the present work is demonstrated.