Nonlinear waves in a liquid film entrained by a turbulent gas stream

In the long-wavelength approximation and on the basis of a simplified system of equations analogous to the one considered by Shkadov and Nabil' [1, 2], an investigation is made into waves of finite amplitude in thin films of a viscous liquid on the walls of a channel in the presence of a turbulent gas stream. A bibliography on the linear stability of such plane-parallel flows can be found in [3–5]. The nonlinear stability is considered in [6]. A stationary periodic solution is sought in the form of a Fourier expansion whose coefficients are found near the upper curve of neutral stability by Newton's method and near the lower branch of the stability curve by the method of Petviashvili and Tsvelodub [7, 8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 2, pp. 37–42, March–April, 1981.I thank V. Ya. Shkadov for supervising the work and all the participants of G. I. Petrov's seminar for a helpful discussion.     

Primary instabilities of liquid film flow sheared by turbulent gas stream

Evolution of excited waves on a viscous liquid film has been investigated experimentally for the annular gas–liquid flow in a vertical tube. For the first time the dispersion relations are obtained experimentally for linear waves on liquid film surface in the presence of turbulent gas flow. Both cocurrent and countercurrent flow regimes are investigated. As an example of comparison with theory, the experimental data are compared to the results of calculations based on the Benjamin quasi-laminar model for turbulent gas flow. The calculation results are found to be in good agreement with experiments for moderate values of film Reynolds number.     

Dynamics of a liquid film sheared by a co-flowing turbulent gas

Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model.     

Interaction of light with a turbulent liquid

A paper [1] recently published in a scientific journal summed up a recently conducted set of studies [2, 4] on the optics of heterogeneous media. A number of fundamental statements of these studies require examination.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 1, pp. 160–163, January–February, 1976.     

Interaction of light with a turbulent liquid flow

The relation between the rms fluctuation of a light current and the density fluctuation in a turbulent liquid flow is considered. Criteria are established for the effect of medium turbulence on the refractive index and on light attenuation. Experimental apparatus and new experimental data are described.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 115–123, July–August, 1973.     

Wavy flow of a liquid film in the presence of a cocurrent turbulent gas flow

Wavy downflow of viscous liquid films in the presence of a cocurrent turbulent gas flow is analyzed theoretically. The parameters of two-dimensional steady-state traveling waves are calculated for wide ranges of liquid Reynolds number and gas flow velocity. The hydrodynamic characteristics of the liquid flow are computed using the full Navier-Stokes equations. The wavy interface is regarded as a small perturbation, and the equations for the gas are linearized in the vicinity of the main turbulent flow. Various optimal film flow regimes are obtained for the calculated nonlinear waves branching from the plane-parallel flow. It is shown that for high velocities of the cocurrent gas flow, the calculated wave characteristics correspond to those of ripple waves observed in experiments.     

Investigation of droplet deposition from a turbulent gas stream

Turbulent deposition of particles from two-phase flow onto the smooth wall of a tube has been studied theoretically and experimentally. A model is proposed for the deposition motion of large particles based on turbulent diffusion in the core followed by a free flight towards the wall. The theory shows that within the Stokes regime, the dimensionless deposition velocity $\text{k-}{}_{\mathrm{<mtext>d</mtext>}}\text{/}\text{u}$* depends on Re and $\text{τ}{}^{\mathrm{+}}$ only, where u* is the friction velocity, Re is the tube Reynolds number and $\text{τ}{}^{\mathrm{+}}$ is the dimensionless particle relaxation time. Deposition data are obtained for air-water droplet flow through a 12.7-mm i.d. acrylic tubing at $\text{Re}\text{= 52,500}$ and 94,600. The proposed theory satisfactorily describes the existing deposition data as well as present measurements, covering a wide range of Re and $\text{τ}{}^{\mathrm{+}}$.     

Characteristics of solitary waves on a falling liquid film sheared by a turbulent counter-current gas flow

We report an experimental investigation of a falling water film sheared by a turbulent counter-current air flow in an inclined rectangular channel. Film thickness and wave velocity measurements associated with visual observation are conducted to study the influence of the air flow on controlled traveling waves consisting of a large wave hump preceded by capillary ripples. First, we focus on the variation of the shape, amplitude and velocity of the waves as the gas velocity is gradually increased. We demonstrate that the amplitude of the main hump grows substantially even for moderate gas velocities, whereas modification of the wave celerity becomes significant above a specific gas velocity around 4 m/s, associated with an alteration of the capillary region. The influence of the gas flow on 3D secondary instabilities of the solitary waves detected in a previous study Kofman et al. (2014), namely rugged or scallop waves, is also investigated. We show that the capillary mode is damped while the inertial mode is enhanced by the interfacial shear. Next, the gas velocity is increased until the onset of upstream-moving patterns referred to as flooding in our experiments. At moderate inclination angles (typically < 7 ^○), flooding occurs for a gas velocity around 8 m/s and is initiated at the scallop wave crests by a backward wave-breaking phenomenon preceded by the onset of ripples on the flat residual film separating two waves. At high inclination angle, a rapid development of solitons is observed as the air velocity is increased preventing the waves to turn back. Finally, at high liquid Reynolds number, sudden and intermittent events are triggered consisting of very large amplitude waves that go back upwards very fast. These “slugs” either extend over the whole width of the channel or are very localized and can thus potentially evolve towards atomization.     

Wavy motion of liquid films flowing concurrently with a gas stream

An experimental study was made of the wavy motion of a water film flowing concurrently with a turbulent flow of air. The measurements of the parameters of the film were made by an optical method for the absorption of light in a colored film. The sources of monochromatic radiation were heliumneon lasers. Near the curve of neutral stability, the data of the experiment were compared with the results of a calculation in accordance with the linear theory. A plane-parallel flow of a film loses its stability somewhat earlier than is predicted by the linear theory; the divergence decreases with an increase in the thickness of the film. Far from the curve of neutral stability, the simultaneous existence of two groups of waves was observed.     

Interaction of a gas-droplet turbulent jet with a cocurrent high-velocity high-temperature gas flow

A mathematical model and a method for calculating a gas-droplet turbulent jet with allowance for velocity nonequilibrium and virtual mass of the condensed phase during turbulent fluctuations and also heat and mass transfer within the three-temperature scheme are developed. Methodical calculations are performed. The results of these calculations are in reasonable agreement with available experimental data. The structure of the gas-droplet jet in a cocurrent high-velocity high-temperature gas flow is studied by numerical methods. The ratio of intensities of heat and mass transfer between the phases and turbulent diffusion transfers of substances is found to be different at the initial, transitional, and basic segments of the jet. This difference is responsible for the nonmonotonic axial distribution of vapor density and the lines of the halved mass flow of the condensed phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 85–94, May–June, 2008.     

Wave flow of a liquid film together with a flow of gas

The wave flow of a thin layer of viscous liquid in conjunction with a flow of gas was considered in a linear formulation earlier [1, 2]. In this paper the problem of the wave flow of a liquid film together with a gas flow is solved in a nonlinear setting. On this basis relationships are derived for calculating the parameters of the film and the hydrodynamic quantities.Ivanovo. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–18, January–February, 1972.     

Interaction of a two-dimensional nonstationary gas stream with a free cylindrical body in a channel

The stability of a circular cylinder in an unsteady gas stream is investigated in the case when shock waves are formed and interact in the flow region. The problem is of interest for simulating processes in light-gas mortars [2, 3] in which free bodies are launched by a gas stream [4] and the launching tube will be destroyed if the launched object strikes it at a high velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 180–184, March–April, 1981.     

Deceleration and deformation of a liquid drop in a gas stream

An analytic method is developed for calculating the nonstationary motion and spreading of two-dimensional and axisymmetric liquid drops in a gas stream. The method is based on an expansion of the Navier-Stokes equations in a small parameter.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–69, March–April, 1981.     

Combined heat and mass transfer in laminar gas stream flowing over an evaporating liquid film

A numerical analysis was carried out to study the detailed heat and mass transfer characteristics in laminar gas stream flowing over a falling liquid water film by solving the respective governing equations for the liquid film and gas stream together. It was observed that the cooling of the liquid film is mainly caused by the latent heat transfer connected with the vaporization of the liquid film. Significant liquid cooling results for the system with a high inlet liquid temperature, high gas stream velocity or a low liquid flowrate. Additionally, the predicted Nusselt and Sherwood numbers were correlated.     

Interfacial instability in turbulent flow over a liquid film in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no fitting parameters and that uses a base-state profile that has been validated against experiments is, as yet, unavailable. Furthermore, the significance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specification of a flow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the effect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, ‘interfacial’ and ‘internal’, with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between ‘slow’ and ‘fast’ waves, the latter being the case for ‘critical-layer’-induced instabilities; we demonstrate that for the parameter ranges studied, the large majority of the waves are ‘slow’. Finally, comparisons of our linear stability predictions are made with experimental data in terms of critical parameters for onset of wave-formation, wave speeds and wavelengths; these yield agreement within the bounds of experimental error.     

Efficiency of a protective gas film with high injection ratios in a highly turbulent main flow

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 48–52, January–February, 1994.