A Runback Criterion for Water Drops in a Turbulent Accelerated Boundary Layer

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Edward B. White ◽  
Jason A. Schmucker
Keyword(s):  
Leading Edge ◽  
Reynolds Numbers ◽  
Critical Parameters ◽  
Challenging Problem ◽  
Aircraft Icing ◽  
Liquid Drops ◽  
Air Interface ◽  
Displacement Thickness ◽  
Water Drops ◽  
Accelerated Flow

Predicting the runback threshold for liquid drops in aerodynamic boundary layers is a challenging problem with numerous applications including aircraft icing simulations. The critical parameters that govern drop runback are investigated in this experiment by using a wind tunnel that provides a turbulent accelerated flow similar to flows near an unswept wing’s leading edge. The experiments feature water drops on aluminum with a contact angle of 70±5deg. Results show that significant water∕air interface unsteadiness precedes drop runback. This is likely due to air-flow separation in the drop wakes. For displacement-thickness-scaled Reynolds numbers ranging from 348 to 429, a constant-Weber-number runback threshold We=3.45±0.09 is found to adequately correlate the runback results.

scholarly journals On surfactant-enhanced spreading and superspreading of liquid drops on solid surfaces

2011 ◽  
Vol 670 ◽  
pp. 5-37 ◽  
Author(s):  
GEORGE KARAPETSAS ◽  
RICHARD V. CRASTER ◽  
OMAR K. MATAR
Keyword(s):  
Contact Line ◽  
Surfactant Concentration ◽  
Evolution Equations ◽  
Leading Edge ◽  
Chemical Kinetic ◽  
Droplet Radius ◽  
Liquid Drops ◽  
Air Interface ◽  
Experimental Values ◽  
Spreading Rates

The mechanisms driving the surfactant-enhanced spreading of droplets on the surface of solid substrates, and particularly those underlying the superspreading behaviour sometimes observed, are investigated theoretically. Lubrication theory for the droplet motion, together with advection–diffusion equations and chemical kinetic fluxes for the surfactant transport, leads to coupled evolution equations for the drop thickness, interfacial concentrations of surfactant monomers and bulk concentrations of monomers and micellar, or other, aggregates. The surfactant can be adsorbed on the substrate either directly from the bulk monomer concentrations or from the liquid–air interface through the contact line. An important feature of the spreading model developed here is the surfactant behaviour at the contact line; this is modelled using a constitutive relation, which is dependent on the local surfactant concentration. The evolution equations are solved numerically, using the finite-element method, and we present a thorough parametric analysis for cases of both insoluble and soluble surfactants with concentrations that can, in the latter case, exceed the critical micelle, or aggregate, concentration. The results show that basal adsorption of the surfactant plays a crucial role in the spreading process; the continuous removal of the surfactant that lies upon the liquid–air interface, due to the adsorption at the solid surface, is capable of inducing high Marangoni stresses, close to the droplet edge, driving very fast spreading. The droplet radius grows at a rate proportional to ta with a = 1 or even higher, which is close to the reported experimental values for superspreading. The spreading rates follow a non-monotonic variation with the initial surfactant concentration also in accordance with experimental observations. An accompanying feature is the formation of a rim at the leading edge of the droplet. In some cases, the drop spreads to form a ‘pancake’ or creates a ‘secondary’ front separated from the main droplet.

Investigation on the effect of leading edge tubercles of sweptback wing at low reynolds number

2020 ◽  
Vol 21 (6) ◽  
pp. 621
Author(s):  
Veerapathiran Thangaraj Gopinathan ◽  
John Bruce Ralphin Rose ◽  
Mohanram Surya
Keyword(s):  
Leading Edge ◽  
Reynolds Numbers ◽  
Sweep Angle ◽  
Laminar Separation ◽  
Low Reynolds Numbers ◽  
Flow Energy ◽  
Airplane Wing ◽  
Low Reynolds ◽  
Naca 0015 ◽  
Wing Performance

Aerodynamic efficiency of an airplane wing can be improved either by increasing its lift generation tendency or by reducing the drag. Recently, Bio-inspired designs have been received greater attention for the geometric modifications of airplane wings. One of the bio-inspired designs contains sinusoidal Humpback Whale (HW) tubercles, i.e., protuberances exist at the wing leading edge (LE). The tubercles have excellent flow control characteristics at low Reynolds numbers. The present work describes about the effect of tubercles on swept back wing performance at various Angle of Attack (AoA). NACA 0015 and NACA 4415 airfoils are used for swept back wing design with sweep angle about 30°. The modified wings (HUMP 0015 A, HUMP 0015 B, HUMP 4415 A, HUMP 4415 B) are designed with two amplitude to wavelength ratios (η) of 0.1 & 0.24 for the performance analysis. It is a novel effort to analyze the tubercle vortices along the span that induce additional flow energy especially, behind the tubercles peak and trough region. Subsequently, Co-efficient of Lift (CL), Co-efficient of Drag (CD) and boundary layer pressure gradients also predicted for modified and baseline (smooth LE) models in the pre & post-stall regimes. It was observed that the tubercles increase the performance of swept back wings by the enhanced CL/CD ratio in the pre-stall AoA region. Interestingly, the flow separation region behind the centerline of tubercles and formation of Laminar Separation Bubbles (LSB) were asymmetric because of the sweep.

Experimental investigations of flow over NACA airfoils 0021 and 4412 of wind turbine blades with and without Tubercles

2021 ◽  
pp. 0309524X2110071
Author(s):  
Usman Butt ◽  
Shafqat Hussain ◽  
Stephan Schacht ◽  
Uwe Ritschel
Keyword(s):  
Wind Tunnel ◽  
Drag Coefficient ◽  
Wind Turbine ◽  
Critical Region ◽  
Lift Coefficient ◽  
Turbine Blades ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Experimental Investigations ◽  
Wind Turbine Blades

Experimental investigations of wind turbine blades having NACA airfoils 0021 and 4412 with and without tubercles on the leading edge have been performed in a wind tunnel. It was found that the lift coefficient of the airfoil 0021 with tubercles was higher at Re = 1.2×105 and 1.69×105 in post critical region (at higher angle of attach) than airfoils without tubercles but this difference relatively diminished at higher Reynolds numbers and beyond indicating that there is no effect on the lift coefficients of airfoils with tubercles at higher Reynolds numbers whereas drag coefficient remains unchanged. It is noted that at Re = 1.69×105, the lift coefficient of airfoil without tubercles drops from 0.96 to 0.42 as the angle of attack increases from 15° to 20° which is about 56% and the corresponding values of lift coefficient for airfoil with tubercles are 0.86 and 0.7 at respective angles with18% drop.

scholarly journals Analysis of the unstable Tollmien–Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

2009 ◽  
Vol 623 ◽  
pp. 167-185
Author(s):  
M. R. TURNER ◽  
P. W. HAMMERTON
Keyword(s):  
Asymptotic Theory ◽  
Free Stream ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
S Wave ◽  
Stability Equation ◽  
Stability Point ◽  
Tollmien Schlichting

The interaction between free-stream disturbances and the boundary layer on a body with a rounded leading edge is considered in this paper. A method which incorporates calculations using the parabolized stability equation in the Orr–Sommerfeld region, along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalized to bodies with an inviscid slip velocity which tends to a constant far downstream. We present results for the position of the lower branch neutral stability point and the magnitude of the unstable Tollmien–Schlichting (T-S) mode at this point for both a parabolic body and the Rankine body. For the Rankine body, which has an adverse pressure gradient along its surface far from the nose, we find a double maximum in the T-S wave amplitude for sufficiently large Reynolds numbers.

scholarly journals Flow past a square-section cylinder with a wavy stagnation face

2001 ◽  
Vol 426 ◽  
pp. 263-295 ◽  
Author(s):  
RUPAD M. DAREKAR ◽  
SPENCER J. SHERWIN
Keyword(s):  
Reynolds Number ◽  
Cross Flow ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Physical Structure ◽  
Near Wake ◽  
Hairpin Vortices ◽  
Independent State ◽  
Flow Past ◽  
Edge Surface

Numerical investigations have been performed for the flow past square-section cylinders with a spanwise geometric deformation leading to a stagnation face with a sinusoidal waviness. The computations were performed using a spectral/hp element solver over a range of Reynolds numbers from 10 to 150.Starting from fully developed shedding past a straight cylinder at a Reynolds number of 100, a sufficiently high waviness is impulsively introduced resulting in the stabilization of the near wake to a time-independent state. It is shown that the spanwise waviness sets up a cross-flow within the growing boundary layer on the leading-edge surface thereby generating streamwise and vertical components of vorticity. These additional components of vorticity appear in regions close to the inflection points of the wavy stagnation face where the spanwise vorticity is weakened. This redistribution of vorticity leads to the breakdown of the unsteady and staggered Kármán vortex wake into a steady and symmetric near-wake structure. The steady nature of the near wake is associated with a reduction in total drag of about 16% at a Reynolds number of 100 compared with the straight, non-wavy cylinder.Further increases in the amplitude of the waviness lead to the emergence of hairpin vortices from the near-wake region. This wake topology has similarities to the wake of a sphere at low Reynolds numbers. The physical structure of the wake due to the variation of the amplitude of the waviness is identified with five distinct regimes. Furthermore, the introduction of a waviness at a wavelength close to the mode A wavelength and the primary wavelength of the straight square-section cylinder leads to the suppression of the Kármán street at a minimal waviness amplitude.

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

Electrohydrodynamic rotation of drops at large electric Reynolds numbers

2016 ◽  
Vol 788 ◽  
Author(s):  
Ehud Yariv ◽  
Itzchak Frankel
Keyword(s):  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Mirror Image ◽  
Liquid Drops ◽  
Weakly Conducting ◽  
Strong Electric Fields ◽  
Quincke Rotation ◽  
Asymmetric Solution

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$, within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$. The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

A Numerical Model for Simulating Liquid Particles Deposition on Surface

2018 ◽  
Author(s):  
Zhenxia Liu ◽  
Fei Zhang ◽  
Zhengang Liu
Keyword(s):  
Particle Size ◽  
Numerical Model ◽  
Particle Deposition ◽  
Surface Profile ◽  
Leading Edge ◽  
Solid Particles ◽  
Liquid Particle ◽  
Aircraft Icing ◽  
Turbine Vane ◽  
Deposition Thickness

The deposition of liquid particles, which may be converted from solid particles due to high temperature gas heating, makes much more harm on turbine vane blades compared to solid particles, since it may block film-cooling holes, worsen the cooling efficiency and aerodynamic performance of the turbine vane blades. Due to the similarity between the deposition of liquid particles on a surface and the icing on a surface, a numerical model for simulating particles deposition was developed based on the Myers icing model, an extension of the Messinger model, which has been applied in predicting aircraft icing or aero-engine icing. Compared to the conventional liquid particle deposition model, the numerical model in this paper considers the heat transfer and the flow of liquid particles during the particles phase transition from liquid state to solid state. In this model, the change of the surface profile due to the particles deposition was also considered, which was implemented with dynamic mesh technique. To test this model, deposition distribution and thickness obtained from the numerical simulations were compared to the experimental results. Additionally, a numerical simulation was conducted for liquid particle deposition on a flat plate. The result showed that the deposition thickness at the leading edge was much larger than that on the upper surface where the deposition appeared mainly at the middle and rear of the plate. The deposition mass and thickness increased with the increasing in the particle size. The effect of the particle size on the deposition thickness was more notable on the upper surface compared to that at the leading edge.

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