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.

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.

scholarly journals Instabilities in a high-Reynolds-number boundary layer on a film-coated surface

1997 ◽  
Vol 353 ◽  
pp. 163-195 ◽  
Author(s):  
S. N. TIMOSHIN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Film Flow ◽  
Lower Branch ◽  
Interfacial Instabilities ◽  
Layer Potential ◽  
Tollmien Schlichting ◽  
High Reynolds ◽  
Film Viscosity

A high-Reynolds-number asymptotic theory is developed for linear instability waves in a two-dimensional incompressible boundary layer on a flat surface coated with a thin film of a different fluid. The focus in this study is on the influence of the film flow on the lower-branch Tollmien–Schlichting waves, and also on the effect of boundary-layer/potential flow interaction on interfacial instabilities. Accordingly, the film thickness is assumed to be comparable to the thickness of a viscous sublayer in a three-tier asymptotic structure of lower-branch Tollmien–Schlichting disturbances. A fully nonlinear viscous/inviscid interaction formulation is derived, and computational and analytical solutions for small disturbances are obtained for both Tollmien–Schlichting and interfacial instabilities for a range of density and viscosity ratios of the fluids, and for various values of the surface tension coefficient and the Froude number. It is shown that the interfacial instability contains the fastest growing modes and an upper-branch neutral point within the chosen flow regime if the film viscosity is greater than the viscosity of the ambient fluid. For a less viscous film the theory predicts a lower neutral branch of shorter-scale interfacial waves. The film flow is found to have a strong effect on the Tollmien–Schlichting instability, the most dramatic outcome being a powerful destabilization of the flow due to a linear resonance between growing Tollmien–Schlichting and decaying capillary modes. Increased film viscosity also destabilizes Tollmien–Schlichting disturbances, with the maximum growth rate shifted towards shorter waves. Qualitative and quantitative comparisons are made with experimental observations by Ludwieg & Hornung (1989).

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

Darryl E. Metzger Memorial Session Paper: Comparison of Calculated and Measured Heat Transfer Coefficients for Transonic and Supersonic Boundary-Layer Flows

1995 ◽  
Vol 117 (2) ◽  
pp. 248-254 ◽  
Author(s):  
C. Hu¨rst ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Supersonic Boundary Layer ◽  
Nozzle Wall ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Three Dimensional Finite Element

The present study compares measured and computed heat transfer coefficients for high-speed boundary layer nozzle flows under engine Reynolds number conditions (U∞=230 ÷ 880 m/s, Re* = 0.37 ÷ 1.07 × 106). Experimental data have been obtained by heat transfer measurements in a two-dimensional, nonsymmetric, convergent–divergent nozzle. The nozzle wall is convectively cooled using water passages. The coolant heat transfer data and nozzle surface temperatures are used as boundary conditions for a three-dimensional finite-element code, which is employed to calculate the temperature distribution inside the nozzle wall. Heat transfer coefficients along the hot gas nozzle wall are derived from the temperature gradients normal to the surface. The results are compared with numerical heat transfer predictions using the low-Reynolds-number k–ε turbulence model by Lam and Bremhorst. Influence of compressibility in the transport equations for the turbulence properties is taken into account by using the local averaged density. The results confirm that this simplification leads to good results for transonic and low supersonic flows.

Secondary instability and subcritical transition of the leading-edge boundary layer

2016 ◽  
Vol 792 ◽  
pp. 682-711 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Bypass Transition ◽  
Wall Suction ◽  
Transition Mechanism

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as$Re\approx 175$, i.e. far below the linear critical Reynolds number$Re_{crit}\approx 583$of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above$Re_{tr}\approx 250$. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number$Re_{tr}\approx 250$at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

The Three-Dimensional Turbulent Boundary Layer on an Infinite Yawed Wing

1971 ◽  
Vol 22 (4) ◽  
pp. 346-362 ◽  
Author(s):  
J. F. Nash ◽  
R. R. Tseng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Numerical Representation ◽  
Two Dimensional ◽  
Incompressible Turbulent Boundary Layer ◽  
Displacement Thickness ◽  
Attachment Line

SummaryThis paper presents the results of some calculations of the incompressible turbulent boundary layer on an infinite yawed wing. A discussion is made of the effects of increasing lift coefficient, and increasing Reynolds number, on the displacement thickness, and on the magnitude and direction of the skin friction. The effects of the state of the boundary layer (laminar or turbulent) along the attachment line are also considered.A study is made to determine whether the behaviour of the boundary layer can adequately be predicted by a two-dimensional calculation. It is concluded that there is no simple way to do this (as is provided, in the laminar case, by the principle of independence). However, with some modification, a two-dimensional calculation can be made to give an acceptable numerical representation of the chordwise components of the flow.

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