scholarly journals Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows

1997 ◽  
Vol 336 ◽  
pp. 351-378 ◽  
Author(s):  
P. DIMITRAKOPOULOS ◽  
J. J. L. HIGDON
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Viscosity Ratio ◽  
Low Reynolds Number ◽  
Contact Angles ◽  
Solid Boundary ◽  
Critical Shear Rate ◽  
Wide Range ◽  
Low Reynolds ◽  
Yield Conditions

The yield conditions for the displacement of fluid droplets from solid boundaries are studied through a series of numerical computations. The study includes gravitational and interfacial forces, but is restricted to two-dimensional droplets and low-Reynolds-number flow. A comprehensive study is conducted, covering a wide range of viscosity ratio λ, Bond number Bd, capillary number Ca and contact angles θA and θR. The yield conditions for drop displacement are calculated and the critical shear rates are presented as functions Ca(λ, Bd, θA, Δθ) where Δθ=θA−θR is the contact angle hysteresis. The numerical solutions are based on the spectral boundary element method, incorporating a novel implementation of Newton's method for the determination of equilibrium free surface profiles. The numerical results are compared with asymptotic theories (Dussan 1987) based on the lubrication approximation. While excellent agreement is found in the joint asymptotic limits Δθ[Lt ]θA[Lt ]1, the useful range of the lubrication models proves to be extremely limited. The critical shear rate is found to be sensitive to viscosity ratio with qualitatively different results for viscous and inviscid droplets. Gravitational forces normal to the solid boundary have a significant effect on the displacement process, reducing the critical shear rate for viscous drops and increasing the rate for inviscid droplets. The low-viscosity limit λ→0 is shown to be a singular limit in the lubrication theory, and the proper scaling for Ca at small λ is identified.

On the displacement of three-dimensional fluid droplets from solid surfaces in low-Reynolds-number shear flows

1998 ◽  
Vol 377 ◽  
pp. 189-222 ◽  
Author(s):  
P. DIMITRAKOPOULOS ◽  
J. J. L. HIGDON
Keyword(s):  
Reynolds Number ◽  
Optimization Problem ◽  
Shear Flows ◽  
Viscosity Ratio ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Yield Condition ◽  
Contact Angles ◽  
Solid Surfaces ◽  
Low Reynolds

The yield conditions for the displacement of three-dimensional fluid droplets from solid boundaries are studied through a series of numerical computations. The study considers low-Reynolds-number shear flows over plane boundaries and includes interfacial forces with constant surface tension. A comprehensive study is conducted, covering a wide range of viscosity ratio γ, capillary number Ca and advancing and receding contact angles, θA and θR. This study seeks the optimal shape of the contact line which yields the maximum flow rate (or Ca) for which a droplet can adhere to the surface. The critical shear rates are presented as functions Ca(γ, θA, Δθ) where Δθ=θA−θR is the contact angle hysteresis. The solution of the optimization problem provides an upper bound for the yield condition for droplets on solid surfaces. Additional constraints based on experimental observations are considered, and their effect on the yield condition is determined. The numerical solutions are based on the spectral boundary element method, incorporating a novel implementation of Newton's method for the determination of equilibrium free surfaces and an optimization algorithm which is combined with the Newton iteration to solve the nonlinear optimization problem. The numerical results are compared with asymptotic theories (Dussan 1987) based on the lubrication approximation. While good agreement is found in the joint asymptotic limits Δθ[Lt ]θA[Lt ]1, the useful range of the lubrication models proves to be extremely limited. The critical shear rate is found to be sensitive to viscosity ratio with qualitatively different results for viscous and inviscid droplets.

scholarly journals An assessment of the laminar kinetic energy concept for the prediction of high-lift, low-Reynolds number cascade flows

2011 ◽  
Vol 225 (7) ◽  
pp. 995-1003 ◽  
Author(s):  
R Pacciani ◽  
M Marconcini ◽  
A Arnone ◽  
F Bertini
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
High Speed ◽  
Low Reynolds Number ◽  
Flow Region ◽  
Freestream Turbulence ◽  
High Lift ◽  
Numerical Predictions ◽  
Wide Range ◽  
Low Reynolds

The laminar kinetic energy (LKE) concept has been applied to the prediction of low-Reynolds number flows, characterized by separation-induced transition, in high-lift airfoil cascades for aeronautical low-pressure turbine applications. The LKE transport equation has been coupled with the low-Reynolds number formulation of the Wilcox's k − ω turbulence model. The proposed methodology has been assessed against two high-lift cascade configurations, characterized by different loading distributions and suction-side diffusion rates, and tested over a wide range of Reynolds numbers. The aft-loaded T106C cascade is studied in both high- and low-speed conditions for several expansion ratios and inlet freestream turbulence values. The front-loaded T108 cascade is analysed in high-speed, low-freestream turbulence conditions. Numerical predictions with steady inflow conditions are compared to measurements carried out by the von Kármán Institute and the University of Cambridge. Results obtained with the proposed model show its ability to predict the evolution of the separated flow region, including bubble-bursting phenomenon and the formation of open separations, in high-lift, low-Reynolds number cascade flows.

Calculation of High-Lift Cascades in Low Pressure Turbine Conditions Using a Three-Equation Model

2010 ◽  
Vol 133 (3) ◽  
Author(s):  
Roberto Pacciani ◽  
Michele Marconcini ◽  
Atabak Fadai-Ghotbi ◽  
Sylvain Lardeau ◽  
Michael A. Leschziner
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Eddy Viscosity ◽  
Low Reynolds Number ◽  
Low Pressure ◽  
Equation Model ◽  
Bypass Transition ◽  
High Lift ◽  
Wide Range ◽  
Low Reynolds

A three-equation model has been applied to the prediction of separation-induced transition in high-lift low-Reynolds-number cascade flows. Classical turbulence models fail to predict accurately laminar separation and turbulent reattachment, and usually overpredict the separation length, the main reason for this being the slow rise of the turbulent kinetic energy in the early stage of the separation process. The proposed approach is based on solving an additional transport equation for the so-called laminar kinetic energy, which allows the increase in the nonturbulent fluctuations in the pretransitional and transitional region to be taken into account. The model is derived from that of Lardeau et al. (2004, “Modelling Bypass Transition With Low-Reynolds-Number Non-Linear Eddy-Viscosity Closure,” Flow, Turbul. Combust., 73, pp. 49–76), which was originally formulated to predict bypass transition for attached flows, subject to a wide range of freestream turbulence intensity. A new production term is proposed, based on the mean shear and a laminar eddy-viscosity concept. After a validation of the model for a flat-plate boundary layer, subjected to an adverse pressure gradient, the T106 and T2 cascades, recently tested at the von Kármán Institute, are selected as test cases to assess the ability of the model to predict the flow around high-lift cascades in conditions representative of those in low-pressure turbines. Good agreement with experimental data, in terms of blade-load distributions, separation onset, reattachment locations, and losses, is found over a wide range of Reynolds-number values.

Calculations of Wall Shear Stress in Harmonically Oscillated Turbulent Pipe Flow Using a Low-Reynolds-Number k-ε Model

1996 ◽  
Vol 118 (1) ◽  
pp. 189-194 ◽  
Author(s):  
J. O. Ismael ◽  
M. A. Cotton
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pipe Flow ◽  
Low Reynolds Number ◽  
Turbulent Pipe Flow ◽  
Frequency Model ◽  
Wide Range ◽  
Wall Shear ◽  
Low Reynolds

The low-Reynolds-number k-ε turbulence model of Launder and Sharma is applied to the calculation of wall shear stress in spatially fully-developed turbulent pipe flow oscillated at small amplitudes. It is believed that the present study represents the first systematic evaluation of the turbulence closure under consideration over a wide range of frequency. Model results are well correlated in terms of the parameter ω+ = ωv/Uτ2 at high frequencies, whereas at low frequencies there is an additional Reynolds number dependence. Comparison is made with the experimental data of Finnicum and Hanratty.

Computational Analysis of a High-Lift and Low Reynolds Number Airfoil at Turbulent Atmospheric Conditions

2009 ◽  
Author(s):  
Mazharul Islam ◽  
M. Ruhul Amin ◽  
Yasir M. Shariff
Keyword(s):  
Reynolds Number ◽  
Wind Turbines ◽  
Turbulence Intensity ◽  
Computational Analysis ◽  
Low Reynolds Number ◽  
Experimental Results ◽  
High Lift ◽  
Wide Range ◽  
Low Reynolds ◽  
Low Reynolds Number Airfoil

Selection of airfoil is crucial for better aerodynamic performance and design of aerodynamic applications such as wind turbine and aircrafts. In this paper, a high-lift and low-Reynolds number airfoil has been selected and investigated through computational analysis for applying it for small-sized wind turbines as blades. The S1223 airfoil, designed by the University of Illinois at Urbana-Champaign, was chosen for its high-lift characteristics at low Reynolds number typically encountered by the small wind turbines. CFD work is performed with S1223 airfoil profile over a wide range of conditions of interest to analyze the performance of the airfoil using the Spalart-Allmaras turbulence model. The results obtained from the simulation works have been compared with experimental data for validation purpose. It has been found that the Spalart-Allmaras model conforms well with the experimental results, though the values of lift coefficients (Cl) are slightly less than the experimental results. In the present analysis, velocity distributions are analyzed at different angle of attacks for different turbulence intensities. It has been observed that there is vortex shedding around the trailing edge of the airfoil for both turbulence levels. It has been observed in the present study that due to increase in turbulence intensity, both the maximum lift coefficient and the stall angle increases significantly. It has been found after investigating the effect of turbulence intensity over lift-to-drag coefficient ratio that it drastically decreases due to increase in turbulence intensity up to certain value (about 3.5%), then it starts decreasing in gradual manner.

Aerodynamic and Heat Flux Measurements in a Single-Stage Fully Cooled Turbine—Part I: Experimental Approach

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
C. W. Haldeman ◽  
R. M. Mathison ◽  
M. G. Dunn ◽  
S. A. Southworth ◽  
J. W. Harral ◽  
...  
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Experimental Approach ◽  
Low Reynolds Number ◽  
Surface Heat ◽  
Pressure Data ◽  
Turbine Stage ◽  
Wide Range ◽  
Temperature And Pressure ◽  
Low Reynolds

This paper describes the experimental approach utilized to perform experiments using a fully cooled rotating turbine stage to obtain film effectiveness measurements. Significant changes to the previous experimental apparatus were implemented to meet the experimental objectives. The modifications include the development of a synchronized blowdown facility to provide cooling gas to the turbine stage, installation of a heat exchanger capable of generating a uniform or patterned inlet temperature profile, novel utilization of temperature and pressure instrumentation, and development of robust double-sided heat flux gauges. With these modifications, time-averaged and time-accurate measurements of temperature, pressure, surface heat flux, and film effectiveness can be made over a wide range of operational parameters, duplicating the nondimensional parameters necessary to simulate engine conditions. Data from low Reynolds number experiments are presented to demonstrate that all appropriate scaling parameters can be satisfied and that the new components have operated correctly. Along with airfoil surface heat transfer and pressure data, temperature and pressure data from inside the coolant plenums of the vane and rotating blade airfoils are presented. Pressure measurements obtained inside the vane and blade plenum chambers illustrate passing of the wakes and shocks as a result of vane/blade interaction. Part II of this paper (Haldeman, C. W., Mathison, R. M., Dunn, M. G., Southworth, S. A., Harral, J. W., and Heltland, G., 2008, ASME J. Turbomach., 130(2), p. 021016) presents data from the low Reynolds number cooling experiments and compares these measurements to CFD predictions generated using the Numeca FINE/Turbo package at multiple spans on the vanes and blades.

Analysis of transitional flow and heat transfer over turbine blades: Algebraic versus low-Reynolds-number turbulence model

2001 ◽  
Vol 215 (9) ◽  
pp. 1003-1018 ◽  
Author(s):  
S Sarkar
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Turbine Blades ◽  
Transitional Flow ◽  
Flow And Heat Transfer ◽  
Turbulent Transition ◽  
Wide Range ◽  
Low Reynolds ◽  
Laminar Turbulent Transition

The numerical simulation of flow and heat transfer over turbine blades involving laminar-turbulent transition is presented. The predicted results are compared with the experimental surface heat transfer and pressure distributions for two transonic turbine blades over a wide range of flow conditions. The time-dependent, mass-averaged Navier-Stokes equations are solved by an explicit four-stage Runge-Kutta scheme in the finite volume formulation. Local time stepping, variable-coefficient implicit residual smoothing and a full multigrid method have been implemented to accelerate the steady state calculation. The turbulence is simulated by the algebraic Baldwin-Lomax model together with an explicitly imposed model for transition. For comparison, the low-Reynolds-number version of the two-equation ( k-∊) model of Chien is also used. The modified Baldwin-Lomax model performs well in predicting the onset of laminar-turbulent transition, whereas the Chien model shows a tendency to mimic the transition early and over a shorter distance.

Low-Reynolds-Number k-e Modeling of Nonstationary Solid Boundary Flows

AIAA Journal ◽  
2003 ◽  
Vol 41 (2) ◽  
pp. 168-175 ◽  
Author(s):  
C. B. Hwang ◽  
C. A. Lin
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Solid Boundary ◽  
Low Reynolds

Numerical investigation of Gurney flap influences on aerodynamic performance of a pitching airfoil in low Reynolds number flow

2018 ◽  
Vol 233 (10) ◽  
pp. 3819-3832
Author(s):  
Alireza Naderi ◽  
Alireza Beiki ◽  
Bahram Tarvirdizadeh
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Aerodynamic Performance ◽  
Solid Boundary ◽  
Aerodynamic Efficiency ◽  
Drag Coefficients ◽  
Gurney Flap ◽  
Unified Algorithm ◽  
Low Reynolds ◽  
Lift And Drag

The main purpose of present work is to investigate the aerodynamic performance of a pitching NACA 0012 airfoil equipped with a Gurney flap in flow with low Reynolds number. The aerodynamic influences of flap location, mounting angle, and height are numerically studied. In this regard, a Lagrangian–Eulerian pressure-based numerical algorithm is developed on hybrid grids attached to a pitching solid boundary. A finite volume-based finite element method is used to discretize the governing equations. As reported in previously related studies, this unified algorithm could be used to solve the unsteady incompressible flow in domains with moving mesh and/or moving boundary with sufficient robustness and accuracy. The other advantage of this algorithm is that it does not need any type of dissipation term and/or damping function. Using this unified algorithm, the numerical experiments indicate that the Gurney flap increases the lift and drag coefficients and enhances the aerodynamic efficiency. The best aerodynamic performance is predicted for the case in which the flap is located at trailing edge with the mounting angle of 90°. The flap height is predicted to have different and most impacts on aerodynamic efficiency during upstroke and downstroke. The numerical results show that the airfoils equipped by flaps with height between 6% and 12% of the airfoil chord are the most aerodynamically efficient airfoils. Changing of lift and drag coefficients are due to increase of effective camber and thickness in all cases.

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