Numerical Simulations of Hydrodynamics and Heat Transfer in Wavy Falling Liquid Films on Vertical and Inclined Walls

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Hongyi Yu ◽  
Tatiana Gambaryan-Roisman ◽  
Peter Stephan
Keyword(s):  
Heat Transfer ◽  
Solitary Waves ◽  
Flow Instability ◽  
Liquid Films ◽  
Capillary Waves ◽  
Wave Dynamics ◽  
Disturbance Frequency ◽  
Wide Range ◽  
Falling Liquid Films ◽  
Low Amplitude

The flow of thin falling liquid films is unstable to long-wave disturbances. The flow instability leads to development of waves at the liquid–gas interface. The effect of the waves on heat and mass transfer in falling liquid films is a subject of ongoing scientific discussion. In this work, numerical investigation of the wave dynamics has been performed using a modified volume-of-fluid (VOF) method for tracking the free surface. The surface tension is described using the continuum surface force (CSF) model. With low disturbance frequency, solitary waves of large amplitude are developed, which are preceded by low-amplitude capillary waves. With high disturbance frequency, low amplitude sinusoidal waves are developed. The waveforms dependent on the Reynolds number and disturbance frequency are summarized in a form of a regime map. A correlation describing the separation curve between the sinusoidal waves regime and solitary waves regime is proposed. The wave parameters (peak height, length, and propagation speed) are computed from the simulation results and compared with available experimental correlations in a wide range of parameters. The effects of the disturbance frequency and the plane inclination angle on the wave dynamics have been studied. The interaction of waves initiated by simultaneous disturbances of two different frequencies has been investigated. The heat transfer in the wavy film has been simulated for the constant wall temperature boundary condition. The effects of Prandtl number and disturbance frequency on local and global heat transfer parameters have been investigated. It has been shown that the influence of waves on heat transfer is significant for large Prandtl numbers in a specific range of disturbance frequencies.

Numerical Simulations of Hydrodynamics and Heat Transfer in Wavy Falling Liquid Films on Vertical and Inclined Walls

2012 ◽  
Author(s):  
Hongyi Yu ◽  
Tatiana Gambaryan-Roisman ◽  
Peter Stephan
Keyword(s):  
Heat Transfer ◽  
Inclination Angle ◽  
Flow Instability ◽  
Liquid Films ◽  
Capillary Waves ◽  
Wave Dynamics ◽  
Disturbance Frequency ◽  
Wide Range ◽  
Falling Liquid Films ◽  
Low Amplitude

The flow of thin falling liquid films is unstable to long-wave disturbances. The flow instability leads to development of waves at the liquid-gas interface. The wave patterns depend on the properties of the liquid, the Reynolds number, the plate inclination angle, and the distance from the film inlet. The effect of the waves on heat and mass transfer in falling liquid films is a subject of ongoing scientific discussion. In this work numerical investigation of the wave dynamics has been performed using a modified Volume of Fluid (VOF) method for tracking the free surface. The surface tension is described using the Continuum Surface Force (CSF) model. At low disturbance frequency solitary waves of large amplitude are developed, which are preceded by low-amplitude capillary waves. At high disturbance frequency low amplitude sinusoidal waves are developed. The wave parameters (peak height, length, propagation speed) are computed from the simulation results and compared with available experimental correlations in a wide range of parameters. The effects of the disturbance frequency and the plane inclination angle on the wave dynamics have been studied. The interaction of waves initiated by simultaneous disturbances of two different frequencies has been investigated. The heat transfer in the wavy film has been simulated for constant wall temperature boundary condition. The effect of the Prandtl number and the disturbance frequency on the local and global heat transfer parameters has been investigated. It has been shown that the influence of waves on heat transfer is significant for large Prandtl numbers in a specific range of disturbance frequencies.

Capillary Flow Separation in 2- and 3-Dimensional Laminar Falling Liquid Films

2010 ◽  
Author(s):  
Georg F. Dietze ◽  
Reinhold Kneer
Keyword(s):  
Heat Transfer ◽  
Flow Separation ◽  
Capillary Flow ◽  
Capillary Wave ◽  
Liquid Films ◽  
Transport Processes ◽  
Gravitational Acceleration ◽  
3 Dimensional ◽  
Wave Region ◽  
Falling Liquid Films

Due to the selective use of liquid films in specialized technical equipment (e.g. new generation nuclear reactors), a fundamental understanding of underlying momentum and heat transport processes inside these thin liquid layers (with a thickness of approximately 0.5 mm) is required. In particular, the influence of surface waves (which develop due to the film’s natural instability) on these transport processes is of interest. For a number of years, experimental and numerical observations in wavy falling liquid films have suggested that momentum and heat transfer in the capillary wave region, preceding large wave humps, undergo drastic modulations. Indeed, some results have indicated that upward flow, i.e. counter to the gravitational acceleration, takes place in this region. Further, evidence of a substantial increase in wall-side and interfacial transfer coefficients has also been noted. Recently, Dietze et al. [1,2] have established that flow separation takes place in the capillary wave region of 2-dimensional laminar falling liquid films, partially explaining the above mentioned observations. Thereby, it was shown that the strong third order deformation (i.e. change in curvature) of the liquid-gas interface in the capillary wave region causes an adverse pressure gradient sufficiently large to induce flow detachment from the wall. In the present paper, a detailed experimental and numerical account of the capillary flow separation’s kinematics and governing dynamics as well as its effect on heat transfer for two different 2-dimensional flow conditions is presented. Experimentally, velocity measurements (using Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV)) and film thickness measurements (using a Confocal Chromatic Imaging technique) were performed in a specifically designed optical test setup. On the numerical side, simulations of the full Navier-Stokes equations as well as the energy equation using the Volume of Fluid (VOF) method were performed. In addition to the 2-dimensional investigations, the characteristics of capillary flow separation under 3-dimensional wave dynamics were studied based on the 3-dimensional numerical simulation of a water film, which was previously investigated experimentally by Park and Nosoko [3]. Results show that flow separation persists over a wide area of the 3-dimensional capillary wave region, with multiple capillary separation eddies occurring in the shape of vortex tubes. In addition, strong spanwise flow induced by the same governing mechanism is shown to occur in this region, which could explain the drastic intensification of transfer to 3-dimensional liquid films.

Heat Transfer Analysis of Local Evaporative Turbulent Falling Liquid Films

1992 ◽  
Vol 114 (3) ◽  
pp. 688-694 ◽  
Author(s):  
N. M. Al-Najem ◽  
K. Y. Ezuddin ◽  
M. A. Darwish
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Homogeneous Problem ◽  
Interfacial Shear Stress ◽  
Liquid Films ◽  
Heat Transfer Analysis ◽  
Tube Length ◽  
Prandtl Numbers ◽  
Falling Liquid Films

A theoretical study has been conducted for evaporative heating of turbulent free-falling liquid films inside long vertical tubes. The methodology of the present work is based on splitting the energy equation into homogeneous and nonhomogeneous problems. Solving these simple problems yields a rapidly converging solution, which is convenient for computational purposes. The eigenvalues associated with the homogeneous problem can be computed efficiently, without missing any one of them, by the sign-count algorithm. A new correlation for the local evaporative heat transfer coefficient along the tube length is developed over wide ranges of Reynolds and Prandtl numbers. Furthermore, the average heat transfer coefficient is correlated as a function of Reynolds and Prandtl numbers as well as the interfacial shear stress. A correlation for the heat transfer coefficient in the fully developed region is also presented in terms of Reynolds and Prandtl numbers. Typical numerical results showed excellent agreement of the present approach with the available data in the literature. Moreover, a parametric study is made to illustrate the general effects of various variables on the velocity and temperature profiles.

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