scholarly journals An integral boundary layer equation for film flow over inclined wavy bottoms

2009 ◽  
Vol 21 (9) ◽  
pp. 092105 ◽  
Author(s):  
T. Häcker ◽  
H. Uecker
Keyword(s):  
Boundary Layer ◽  
Film Flow ◽  
Boundary Layer Equation ◽  
Integral Boundary

scholarly journals Nonlinear waves in counter-current gas–liquid film flow

2011 ◽  
Vol 673 ◽  
pp. 19-59 ◽  
Author(s):  
D. TSELUIKO ◽  
S. KALLIADASIS
Keyword(s):  
Boundary Layer ◽  
Liquid Film ◽  
Film Flow ◽  
Additional Term ◽  
Current Case ◽  
Integral Boundary ◽  
Boundary Layer Approximation ◽  
Long Wave ◽  
Liquid Film Flow ◽  
Counter Current

We investigate the dynamics of a thin laminar liquid film flowing under gravity down the lower wall of an inclined channel when turbulent gas flows above the film. The solution of the full system of equations describing the gas–liquid flow faces serious technical difficulties. However, a number of assumptions allow isolating the gas problem and solving it independently by treating the interface as a solid wall. This permits finding the perturbations to pressure and tangential stresses at the interface imposed by the turbulent gas in closed form. We then analyse the liquid film flow under the influence of these perturbations and derive a hierarchy of model equations describing the dynamics of the interface, i.e. boundary-layer equations, a long-wave model and a weakly nonlinear model, which turns out to be the Kuramoto–Sivashinsky equation with an additional term due to the presence of the turbulent gas. This additional term is dispersive and destabilising (for the counter-current case; stabilizing in the co-current case). We also combine the long-wave approximation with a weighted-residual technique to obtain an integral-boundary-layer approximation that is valid for moderately large values of the Reynolds number. This model is then used for a systematic investigation of the flooding phenomenon observed in various experiments: as the gas flow rate is increased, the initially downward-falling film starts to travel upwards while just before the wave reversal the amplitude of the waves grows rapidly. We confirm the existence of large-amplitude stationary waves by computing periodic travelling waves for the integral-boundary-layer approximation and we corroborate our travelling-wave results by time-dependent computations.

Long-Wave and Integral Boundary Layer Analysis of Falling Film Flow on Walls With Three-Dimensional Periodic Structures

2009 ◽  
Author(s):  
Tatiana Gambaryan-Roisman ◽  
Hongyi Yu ◽  
Karsten Lo¨ffler ◽  
Peter Stephan
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Inclination Angle ◽  
Film Flow ◽  
Three Dimensional ◽  
Falling Film ◽  
Integral Boundary ◽  
Long Wave ◽  
Surface Patterns ◽  
Periodic Microstructures

Falling films exhibit very complex wavy patterns, which depend on the properties of the liquid, the Reynolds number, the wall inclination angle, and the distance from the film inlet. The film hydrodynamics and the surface patterns have a high impact on heat and mass transfer. Our aim is to control and enhance heat and mass transport by using walls with specific micro topographies that influence the falling film flow, stability and wavy pattern. In the present work long-wave theory and integral boundary layer (IBL) approximation are used for modelling the falling film flow on walls with three-dimensional periodic microstructures. The wall topography is periodic both in the main flow direction and in the transverse direction. Examples of such microstructures are longitudinal grooves with sinusoidal path (or meandering grooves) and herringbone structures. The effects of the Reynolds number, the wall inclination angle and the longitudinal and transverse periods of the structure on the shape of liquid-gas interface are investigated. It is shown that, as opposed to straight grooves in longitudinal direction, grooves with meandering path may lead to significant interface deformations.

Optimization Based on Boundary Layer Concept for Compressible Flows

1975 ◽  
Vol 97 (2) ◽  
pp. 195-204 ◽  
Author(s):  
Shuang Huo
Keyword(s):  
Boundary Layer ◽  
Compressible Flows ◽  
Boundary Layer Equation ◽  
Potential Method ◽  
Integral Boundary ◽  
Layer Method ◽  
Boundary Layer Development ◽  
Boundary Layer Method ◽  
Layer Development ◽  
Layer Concept

A dissipation integral boundary layer method is briefly presented which serves as the basis of the optimization. The principles of optimum deceleration are explained. Following these principles the optimum boundary layer development is specified and the velocity distribution follows from the boundary layer equation. The corresponding shape is obtained from a potential method. It is found that the straight channel and conical diffusers do have a boundary layer development close to the optimum one and it is not worth to improve their performances by wall shaping. Two conical diffusers at high inlet Mach number are anaylzed and the predictions agree satisfactorily with the experiment.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

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