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

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.

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A Quasi-Three-Dimensional Blade Surface Boundary Layer Analysis for Rotating Blade Rows

Journal of Engineering for Power ◽

10.1115/1.3227299 ◽

1982 ◽

Vol 104 (2) ◽

pp. 439-449 ◽

Cited By ~ 2

Author(s):

W. T. Thompkins ◽

W. J. Usab

Keyword(s):

Boundary Layer ◽

Three Dimensional ◽

Normal Vector ◽

Surface Boundary ◽

Nasa Lewis Research ◽

Surface Boundary Layer ◽

Boundary Layer Analysis ◽

Rotating Blade ◽

Layer Analysis ◽

Coordinate Lines

A quasi-three-dimensional, finite difference boundary layer analysis for rotating blade rows has been developed which uses pressure distribution and streamline position data from a three-dimensional Euler equation solver. This analysis uses as coordinate lines the blade normal vector, the local inviscid streamline direction and a crossflow coordinate tine perpendicular to both normal and streamline coordinate lines. The equations solved may be determined either by assuming the crossflow velocity to be small or that its variation in the crossflow direction is small. Thus the analysis would not apply to a region where the boundary layer character changes rapidly such as a corner but could be expected to provide good results away from hub or tip casing boundary layers. Modified versions of Keller’s box scheme are used to solve the streamwise and crossflow momentum equations as well as the energy equation. Results are presented for a high-tip speed, low aspect ratio rotor designed by NASA Lewis Research Center which show that the three-dimensional boundary layer separates significantly sooner and has a much larger influence on rotor performance than would be expected from a two-dimensional analysis.

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Islands in three-dimensional steady flows

Journal of Fluid Mechanics ◽

10.1017/s002211209100023x ◽

1991 ◽

Vol 227 ◽

pp. 527-542 ◽

Cited By ~ 4

Author(s):

C. C. Hegna ◽

A. Bhattacharjee

Keyword(s):

Boundary Layer ◽

Classical Theory ◽

Three Dimensional ◽

Rational Surface ◽

Steady Flows ◽

Rational Surfaces ◽

Boundary Layer Analysis ◽

Layer Analysis ◽

Euler Flows ◽

Critical Layers

We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

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Coupled Euler/Integral Boundary Layer analysis in transonic flow

10.2514/6.1983-1806 ◽

1983 ◽

Cited By ~ 1

Author(s):

S. SAMANT ◽

L. WIGTON

Keyword(s):

Boundary Layer ◽

Transonic Flow ◽

Integral Boundary ◽

Euler Integral ◽

Boundary Layer Analysis ◽

Layer Analysis

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Nonlinear waves in counter-current gas–liquid film flow

Journal of Fluid Mechanics ◽

10.1017/s002211201000618x ◽

2011 ◽

Vol 673 ◽

pp. 19-59 ◽

Cited By ~ 43

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.

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Solution of the surface Euler equations for accurate three-dimensional boundary-layer analysis of aerodynamic configurations

10.2514/6.1987-1154 ◽

1987 ◽

Cited By ~ 3

Author(s):

V. IYER ◽

J. HARRIS

Keyword(s):

Boundary Layer ◽

Euler Equations ◽

Three Dimensional ◽

Boundary Layer Analysis ◽

Layer Analysis ◽

Dimensional Boundary

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Calculation of Three-Dimensional Boundary Layers on Rotating Turbine Blades

Journal of Fluids Engineering ◽

10.1115/1.3242613 ◽

1987 ◽

Vol 109 (1) ◽

pp. 41-49 ◽

Cited By ~ 4

Author(s):

O. L. Anderson

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Turbine Blades ◽

Three Dimensional ◽

Pressure Surface ◽

Boundary Layer Analysis ◽

Layer Analysis ◽

Edge Conditions ◽

Dimensional Boundary ◽

Pressure Suction

An assessment has been made of the applicability of a three-dimensional boundary-layer analysis to the calculation of heat transfer and streamline flow patterns on the surfaces of both stationary and rotating turbine passages. In support of this effort, an analysis has been developed to calculate a general nonorthogonal surface coordinate system for arbitrary three-dimensional surfaces and also to calculate the boundary-layer edge conditions for compressible flow using the surface Euler equations and experimental pressure distributions. Using available experimental data to calibrate the method, calculations are presented for the endwall, and suction surfaces of a stationary cascade and for the pressure surface of a rotating turbine blade. The results strongly indicate that the three-dimensional boundary-layer analysis can give good predictions of the flow field and heat transfer on the pressure, suction, and endwall surfaces in a gas turbine passage.

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