An investigation of falling liquid films on a vertical heated/cooled plate

The temperature field and flow patterns of a liquid film flowing over a vertical uniformly heated surface have been experimentally investigated. Our experiments show that this film flow is sensitive to the heating conditions. When the film is cooled by the substrate, its surface area increases, and when it is heated its surface area decreases. The analysis attributed the changing properties of the flow to lateral Marangoni effect, i.e. to surface tension gradient transverse to the flow. The influence of the viscosity variations on the non-isothermal liquid film flow was also considered and compared with that of the surface tension variations. It was shown that the contraction or extension of the films was mainly caused by the lateral surface tension gradient that might be determined by the viscosity variations.     

Simulation of three-dimensional incompressible flows in generalized curvilinear coordinates using a high-order compact finite-difference lattice Boltzmann method

In the present study, a high-order compact finite-difference lattice Boltzmann method is applied for accurately computing 3-D incompressible flows in the generalized curvilinear coordinates to handle practical and realistic geometries with curved boundaries and nonuniform grids. The incompressible form of the 3-D nineteen discrete velocity lattice Boltzmann method is transformed into the generalized curvilinear coordinates. Herein, a fourth-order compact finite-difference scheme and a fourth-order Runge-Kutta scheme are used for the discretization of the spatial derivatives and the temporal term, respectively, in the resulting 3-D nineteen discrete velocity lattice Boltzmann equation to provide an accurate 3-D incompressible flow solver. A high-order spectral-type low-pass compact filtering technique is applied to have a stable solution. All boundary conditions are implemented based on the solution of the governing equations in the 3-D generalized curvilinear coordinates. Numerical solutions of different 3-D benchmark and practical incompressible flow problems are performed to demonstrate the accuracy and performance of the solution methodology presented. Herein, the 2-D cylindrical Couette flow, the decay of a 3-D double shear wave, the cubic lid-driven cavity flow with nonuniform grids, the flow through a square duct with 90° bend and the flow past a sphere at different flow conditions are considered for validating the present computations. Numerical results obtained show the accuracy and robustness of the present solution methodology based on the implementation of the high-order compact finite-difference lattice Boltzman method in the generalized curvilinear coordinates for solving 3-D incompressible flows over practical and realistic geometries.     

Pressure Distribution in a Curvilinear Thrust Bearing with One Porous Wall Lubricated by a Bingham Fluid

The influence of wall porosity on the pressure distribution of a Bingham fluid flowing in the clearance of a curvilinear thrust bearing is considered. The formulae expressing the pressure distribution are obtained for two cases, namely: an externally pressurized bearing and a squeeze film bearing. The example of a squeeze film between parallel disks is discussed in detail.     

Thermal imaging study on the surface wave of heated falling liquid films

By using thermal imaging technique and film thickness metering system, the surface wave and film thickness of the heated falling liquid film were experimentally investigated. Temperature variations of the heated film induce surface tension gradient and so-caused Marangoni flow that attempts to avoid the temperature variations. There are three kinds of Marangoni flow appearing in the heated falling liquid film. It is found that the lateral Marangoni flow (MF I) and the streamwise Marangoni flow (MF II) make the heated film thick, while the Marangoni flow in the surface wave (MF III) reinforces the wave and makes the heated film thin. The intensity of Marangoni flow is determined by the flow rate and the heating conditions. MF I and MF II are both enhanced with the increasing liquid flow rate. Moreover, MF III is prominent under moderate flow rates and is gradually weakened at high flow rates. The distance over which MF III starts, increases with a rise in flow rate, but is independent of the heating condition.     

Asymptotic model of slow three-dimensional liquid film flow in a space drop catcher

Slow steady-state film flows formed on the inner surface of a drop catcher funnel due to inertial deposition of drops of a dispersed working matter in the spacecraft cooling system are considered. A limiting asymptotic model of slow three-dimensional coolant film flow is constructed assuming that the deposited drops transfer all their mass, momentum, and energy to the film described by the equations of creeping viscous fluid flow in a thin layer of a priori unknown thickness. A first-order quasi-linear partial differential equation for the film thickness is derived. The shape of the film surface is investigated numerically as a function of parameters using the method of characteristics. The range of optimum parameters ensuring the steady-state film flow is found. The limits of existence of the solutions corresponding to the limiting model proposed are investigated.     

Stability of a laminar film flow

The problem of the wave motion of a liquid layer was first investigated by Kapitsa [1, 2], who gave an approximate analysis of the free flow and flow in contact with gas stream, and evaluated the influence of the heat transfer processes on the flow. The problem of the stability of such a flow was studied in detail by Benjamin [3] and Yih [4, 5], These authors proposed seeking the solution of the resulting Orr-Sommerfeld equation in the form of a series in a small parameter and developed a corresponding method of successive approximations. As the small parameter [3–5], they made use of the product of the disturbance wave number and the Reynolds number. In these studies, the tangential stress on the free surface was taken equal to zero, and the fluid film was always considered essentially plane. At the same time, there are certain types of problems of considerable interest in which neither of these assumptions is satisfied. A good example might be the problem on the stability of the annular regime of two-phase flow in pipes and capillaries, when the basic stream of one fluid is separated from the pipe walls by an annular layer of another fluid. In this case, the interface has a finite radius of curvature and the tangential stress on the interface may be significantly different from zero.In the present paper, the problem of the flow stability of a fluid layer with respect to small disturbances of the boundary surface is considered with account for both the finite radius of curvature of the boundary surface and the nonzero hydrodynamic friction at the boundary. The film is assumed to be quite thin. This enables us, firstly, to consider the Reynolds number small, to use the general method of [5], and, second ly, to consider the film thickness sufficiently small in comparison with the radius of curvature of the substrate on which the film lies. Furthermore, for evaluating the stability of the laminar flow of the curved film we can use the results obtained for a plane film with account for the terms which depend on the curvature of the substrate.As a rule, previous studies have considered only one-dimensional disturbances of the boundary surface. In the present paper, in the first approximation, the stability is examined in relation to two-dimensional disturbances of this surface, corresponding to three-dimensional flow disturbances.As an example, the results obtained are applied to the investigation of the stability of the free flow of a layer of fluid over an inclined plane under the sole influence of gravity.     

The role of external influences in the formation of waves on the surface of a flowing-down film of a viscous fluid

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave regimes of the film freely flowing down a vertical surface. The first case describes a ferromagnetic fluid film affected by the magnetic field, and the second case touches upon a dielectric fluid film affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces have a great impact on the flow.     

DYNAMIC STABILITY OF PNEUMATIC STRUCTURES IN WIND: THEORY AND EXPERIMENT

The present paper is concerned with the vibration of a three-dimensional pneumatic structures in wind flow. The aeroelastic dynamic stability of the structure is investigated. The flow is treated as a superposition of the mean flow and a potential flow associated with deformation of the structure. In the wake, the surface flow is considered to be negligible. It is observed that for a hemispherical pneumatic structure certain modes of vibration induce a negative aerodynamic damping, which increases with the increase of flow velocity. The velocity potential of the air-flow is expressed in integral form as a single-layer and double-layer potential. The problem is described by differential and integral equations and the FEM and BEM are used to solve these equations, respectively. To discretize the surface of the structure, triangular curvilinear 6-node elements are applied. The eigenvalues of the matrix equation representing the quadratic eigenvalue problem enable prediction of whether the motion of the structure is stable or unstable. Numerical examples are given. These analytical predictions are in agreement with observations of wind-tunnel experiments. The predicted and measured critical flow velocity is of the same order of magnitude.     

Local thickness of a washing film in the entrance section

A method of graphic analysis is considered for the calculation of the local thickness of a liquid film in the entrance section of the transformation of slot flow into film flow over a vertical plate. The proposed method can also be used in calculating the local thicknesses of a thin layer during liquid flow over curved surfaces.

     

Two-phase flow over a surface with the formation of a liquid film by particle deposition

A consistent asymptotic theory of wall flow with film formation is constructed with reference to subsonic two-phase flow over a blunt body. The external flow problem and the film equations are solved simultaneously. This formulation of the problem supplements the investigation carried out in [4] in which particles deposited on the surface were assumed to disappear from the flow. It is shown that depending on the values of the governing parameters the flow in the film should be described either by the boundary layer equations or by the equations of creeping flow in a layer of unknown thickness. At the outer edge of the film the mass, momentum and energy fluxes found from the numerical solution of the flow problem are given. The case of isothermal film flow on the front of a sphere is investigated. The thickness of the film and the friction and heat transfer coefficients near the axis of symmetry are found for nonisothermal flows. The conditions under which the presence of a film significantly reduces the heat flow to the wall are determined. A similar formulation of the problem (but with another type of mass, momentum and energy sources at the outer edge) is encountered in problems of film condensation on a cold surface [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 85–92, July–August, 1989.     

Numerical simulation of flow over an airfoil in heavy rain via a two-way coupled Eulerian–Lagrangian approach

Airfoil performance degradation in heavy rain has attracted many aeronautical researchers’ eyes. In this work, a two-way momentum coupled Eulerian–Lagrangian approach is developed to study the aerodynamic performance of a NACA 0012 airfoil in heavy rain environment. Scaling laws are implemented for raindrop particles. A random walk dispersion approach is adopted to simulate raindrop dispersion due to turbulence in the airflow. Raindrop impacts, splashback and formed water film are modeled with the use of a thin liquid film model. The steady-state incompressible air flow field and the raindrop trajectory are calculated alternately through a curvilinear body-fitted grid surrounding the airfoil by incorporating an interphase momentum coupling term. Our simulation results of aerodynamic force coefficients agree well with the experimental results and show significant aerodynamic penalties at low angles of attack for the airfoil in heavy rain. An about 3° rain-induced increase in stall angle of attack is predicted. The loss of boundary momentum by raindrop splashback and the effective roughening of the airfoil surface due to an uneven water film are testified to account for the degradation of airfoil aerodynamic efficiency in heavy rain environment.     

Model of a wavy flow in a falling film of a viscous liquid

A new model is developed for describing long-wave perturbations in a falling film of a viscous liquid. The model is based on an integral approach and an expansion of the velocity profile into a series in linearly independent basis functions of a boundary-value problem. A linear analysis of film flow stability is performed, and dispersion dependences are obtained. Results predicted by the new model are demonstrated to be in good agreement with available experimental data on the film flow over a gently sloping surface.     

Development of a PLIC-VOF method for the dynamic simulation of entry region flow in a laminar falling film

The present work describes a numerical procedure to simulate the development of hydrodynamic entry region in a gravity-driven laminar liquid film flow over an inclined plane. It provides a better insight into the physics of developing film in entry region. A novel numerical approach is proposed which has the potential to provide solutions for the complex physics of liquid film spreading on solid walls. The method employs an incompressible flow algorithm to solve the governing equations, a PLIC-VOF method to capture the free surface evolution and a continuum surface force (CSF) model to include the effect of surface tension. To account for the moving contact line on the solid substrate, a precursor film model based wall treatment is implemented. Liquid film flow has been simulated for the Reynolds number range of 5 ≤ Re ≤ 37.5, and the predicted results are found to agree well with the available analytical and experimental data.     

Droplet production from disintegrating bubbles at water surfaces. Single vs. multiple bubbles

We experimentally determine the droplet production rate at a water surface where either single or multiple bubbles (bubbly flow) with similar mean diameters disintegrate and produce film and jet droplets. A detailed assessment of film drop production from bubbly flow is important, since most presently used correlations are based on single-bubble measurements. Moreover, jet drops––even though they contain a much larger fluid volume––are de-entrained into the water surface in most technical and geophysical applications. Detailed phase Doppler anemometry (PDA) measurements are performed in the vicinity of the water surface with long sampling times. For a considered mean diameter of approximately 3 mm, the size distribution of the non spherical bubbles is determined from photographic images. From single-bubble measurements we find, consistent with literature data, a narrow size distribution of the jet drops with a mean diameter of 477 μm. For bubbly flow, the maximum is shifted to somewhat smaller jet drop diameters (425 μm) and the production of film droplets increases significantly. We relate this increase to the coalescence of bubbles prior to their disintegration at the surface. Our results therefore show that for a fixed bubble size and gas flow rate the number of film drops entrained from a bubbly flow is underestimated, if the estimate is based on single-bubble data.     

Coupled ghost fluid/two‐phase level set method for curvilinear body‐fitted grids

A coupled ghost fluid/two‐phase level set method to simulate air/water turbulent flow for complex geometries using curvilinear body‐fitted grids is presented. The proposed method is intended to treat ship hydrodynamics problems. The original level set method for moving interface flows was based on Heaviside functions to smooth all fluid properties across the interface. We call this the Heaviside function method (HFM). The HFM requires fine grids across the interface. The ghost fluid method (GFM) has been designed to explicitly enforce the interfacial jump conditions, but the implementation of the jump conditions in curvilinear grids is intricate. To overcome these difficulties a coupled GFM/HFM method was developed in which approximate jump conditions are derived for piezometric pressure and velocity and pressure gradients based on exact continuous velocity and stress and jump in momentum conditions with the jump in density maintained but continuity of the molecular and turbulent viscosities imposed. The implementation of the ghost points is such that no duplication of memory storage is necessary. The level set method is adopted to locate the air/water interface, and a fast marching method was implemented in curvilinear grids to reinitialize the level set function. Validations are performed for three tests: super‐ and sub‐critical flow without wave breaking and an impulsive plunging wave breaking over 2D submerged bumps, and the flow around surface combatant model DTMB 5512. Comparisons are made against experimental data, HFM and single‐phase level set computations. The proposed method performed very well and shows great potential to treat complicated turbulent flows related to ship flows. Copyright © 2007 John Wiley & Sons, Ltd.     

Effect of bottom topography on the flow of a non-Newtonian liquid film down an inclined plane

The problem of flow of a nonlinear viscous liquid film down an inclined surface with local microtopography is considered. Numerical and approximate analytic solutions are obtained for steady flows of power-law liquid films down inclined surfaces with topography. Steps, hills, and periodic structures are considered as local topography. Basic properties of flows are found.     

Controlling the Free‐Surface Profile of Film Flow over Complex Topography

A twodimensional model describing nonisothermal viscous thin film flow over complex topography is considered. The model is based on the Navier–Stokes equations in the Oberbeck–Boussinesq approximation. A numerical analysis of the effect of thermal loading on the location of the film free surface is performed. It is shown that changing the substrate temperature function, it is possible to control the freesurface profile on separate topographical features. The results of solution of model problems are presented).     

Surface tension driven flows in micro-gravity conditions

The importance of convective flows generated by surface tension gradients, in comparison with the ones generated by other driving forces, has been investigated in connection with space technological applications involving fluid processes. A theoretical model of the boundary conditions at the interface, considered free and diffusive, has been derived in general tensor form to allow for the use of non orthogonal curvilinear co-ordinates. For the study of flow fields contained in enclosures, these co-ordinates are more suitable to fit all teh boundaries, in particular near the contact angle between the interface and the solid walls, thus giving more accurate numerical solutions. A computational procedure to solve the complete set of bulk and surface equations is proposed and applied to a simplified two dimensional flow in a rectangular enclosure with a temperature gradient between the lateral walls. The numerical results show the importance of considering the interface to be deformable and diffusive for an accurate evaluation of the convective flow in the fluid bulk.