Stall onset on aerofoils at low to moderately high Reynolds number flows

2013 ◽  
Vol 733 ◽  
pp. 439-472 ◽  
Author(s):  
Wallace J. Morris ◽  
Zvi Rusak
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Numerical Simulations ◽  
Separation Zone ◽  
Model Problem ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Inner Region ◽  
Reynolds Number Flows

AbstractThe inception of leading-edge stall on stationary, two-dimensional, smooth, thin aerofoils at low to moderately high chord Reynolds number flows is investigated by a reduced-order, multiscale model problem via numerical simulations. The asymptotic theory demonstrates that a subsonic flow about a thin aerofoil can be described in terms of an outer region, around most of the aerofoil’s chord, and an inner region, around the nose, that asymptotically match each other. The flow in the outer region is dominated by the classical thin aerofoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number $(R{e}_{M} )$ are used to correctly account for the nonlinear behaviour and extreme velocity changes in the inner region, where both the near-stagnation and high suction areas occur. It results in a model problem of a uniform, incompressible and viscous flow past a semi-infinite parabola with a far-field circulation governed by a parameter $\tilde {A} $ that is related to the aerofoil’s angle of attack, nose radius of curvature, thickness ratio, and camber. The model flow problem is solved for various values of $\tilde {A} $ through numerical simulations based on the unsteady Navier–Stokes equations. The value ${\tilde {A} }_{s} $ where a global separation zone first erupts in the nose flow, accompanied by loss of peak streamwise velocity ahead of it and change in shedding frequency behind it, is determined as a function of $R{e}_{M} $. These values indicate the stall onset on the aerofoil at various flow conditions. It is found that ${\tilde {A} }_{s} $ decreases with $R{e}_{M} $ until some limit $R{e}_{M} $ (${\sim }300$) and then increases with further increase of Reynolds number. At low values of $R{e}_{M} $ the flow is laminar and steady, even when stall occurs. The flow in this regime is dominated by the increasing effect of the adverse pressure gradient, which eventually overcomes the ability of the viscous stress to keep the boundary layer attached to the aerofoil. The change in the nature of stall at the limit $R{e}_{M} $ is attributed to the appearance of downstream travelling waves in the boundary layer that shed from the marginal separation zone and grow in size with either $\tilde {A} $ or $R{e}_{M} $. These unsteady, convective vortical structures relax the effect of the adverse pressure gradient on the viscous boundary layer to delay the onset of stall in the mean flow to higher values of ${\tilde {A} }_{s} $. Computed results show agreement with marginal separation theory at low $R{e}_{M} $ and with available experimental data at higher $R{e}_{M} $. This simplified approach provides a universal criterion to determine the stall angle of stationary thin aerofoils with a parabolic nose.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

2018 ◽  
Author(s):  
Yvan Maciel ◽  
Tie Wei ◽  
Ayse G. Gungor ◽  
Mark P. Simens
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Inertial Parameter ◽  
Velocity Scale ◽  
Gradient Parameter

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows — not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow — in a global sense — the streamwise evolution of the stream-wise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

Stall Onset on Airfoils at Moderately High Reynolds Number Flows

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Zvi Rusak ◽  
Wallace J. Morris
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
High Reynolds Number ◽  
Outer Region ◽  
Navier Stokes ◽  
Radius Of Curvature ◽  
Nose Radius ◽  
High Reynolds ◽  
Inner Region ◽  
Reynolds Number Flows

The inception of leading-edge stall on two-dimensional smooth thin airfoils at moderately high Reynolds number flows [in the range O(104) to O(106)] is investigated by an asymptotic approach and numerical simulations. The asymptotic theory is based on the work of Rusak (1994) and demonstrates that a subsonic flow about a thin airfoil can be described in terms of an outer region, around most of the airfoil chord, and an inner region, around the nose, that asymptotically match each other. The flow in the outer region is dominated by the classical thin airfoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number are used to correctly account for the nonlinear behavior and extreme velocity changes in the inner region, where both the near stagnation and high suction areas occur. It results in a model (simplified) problem of a uniform flow past a semi-infinite parabola with a far-field circulation governed by a parameter à that is related to the airfoil’s angle of attack, nose radius of curvature, and camber and to the flow Mach number. The model parabola problem consists of a compressible and viscous flow described by the steady Navier-Stokes equations. This problem is solved numerically for various values of à using a Reynolds-averaged Navier-Stokes flow solver, and utilizing the Spalart-Allmaras viscous turbulent model to account for near-wall turbulence. The value Ãs where a large separation zone first appears in the nose flow concurrent with a sudden increase in the minimum pressure coefficient is determined. The change of Ãs with the modified Reynolds number is determined. These values indicate the stall onset on the airfoil at various flow conditions. The predictions according to this approach show good agreement with results from both numerical simulations and available experimental data of the stall of thin airfoils. This simplified approach provides a criterion to determine the stall angle of airfoils with a parabolic nose and the effect of airfoil’s thickness ratio, nose radius of curvature, camber and flaps, and flow compressibility on the onset of stall. This approach also presents an analysis method that can be used to predict the stall of airfoils with alternative nose geometry.

Prediction of Leading-Edge Sheet Cavitation Inception on Hydrofoils at Low to Moderate Reynolds Number Flows

2007 ◽  
Vol 129 (12) ◽  
pp. 1540-1546 ◽  
Author(s):  
Zvi Rusak ◽  
Wallace J. Morris ◽  
Yoav Peles
Keyword(s):  
Reynolds Number ◽  
Outer Region ◽  
Leading Edge ◽  
Radius Of Curvature ◽  
Nose Radius ◽  
Sheet Cavitation ◽  
Flow Reynolds Number ◽  
Moderate Reynolds Number ◽  
Inner Region ◽  
Reynolds Number Flows

The inception of leading-edge sheet cavitation on two-dimensional smooth thin hydrofoils at low to moderately high Reynolds number flows is investigated by an asymptotic approach and numerical simulations. The asymptotic theory is based on the work of Rusak (1994, “Subsonic Flow Around Leading Edge of a Thin Aerofoil With a Parabolic Nose,” Eur. J. Appl. Mech., 5, pp. 283–311) and demonstrates that the flow about a thin hydrofoil can be described in terms of an outer region, around most of the hydrofoil chord, and an inner region, around the nose, which asymptotically match each other. The flow in the outer region is dominated by the classical thin hydrofoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number (ReM) are used to correctly account for the nonlinear behavior and extreme velocity changes in the inner region, where both the near-stagnation and high suction areas occur. It results in a model (simplified) problem of a uniform flow past a semi-infinite smooth parabola with a far-field circulation governed by a parameter à that is related to the hydrofoil’s angle of attack, nose radius of curvature, and camber. The model parabola problem consists of a viscous flow that is solved numerically for various values of à and ReM to determine the minimum pressure coefficient and the cavitation number for the inception of leading-edge cavitation as function of the hydrofoil’s geometry, flow Reynolds number, and fluid thermodynamic properties. The predictions according to this approach show good agreement with results from available experimental data. This simplified approach provides a universal criterion to determine the onset of leading-edge (sheet) cavitation on hydrofoils with a parabolic nose in terms of the similarity parameters à and ReM and the effect of hydrofoil’s thickness ratio, nose radius of curvature, camber, and flow Reynolds number on the onset.

Pressure Gradient Effects on Smooth- and Rough-Surface Turbulent Boundary Layers—Part II: Adverse Pressure Gradient

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Ju Hyun Shin ◽  
Seung Jin Song
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Roughness Effects ◽  
Mean Velocity ◽  
Velocity Defect

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.

The Effects of Spatial Resolution in Turbulent Boundary Layers with Pressure Gradients

2012 ◽  
Vol 225 ◽  
pp. 109-117 ◽  
Author(s):  
Zambri Harun ◽  
Mohamad Dali Isa ◽  
Mohammad Rasidi Rasani ◽  
Shahrir Abdullah
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Spatial Resolution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Wall Region ◽  
Pressure Gradients ◽  
Layer Flow ◽  
Near Wall

Single normal hot-wire measurements of the streamwise component of velocity were taken in boundary layer flows subjected to pressure gradients at matched friction Reynolds numbers Reτ ≈ 3000. To evaluate spatial resolution effects, the sensor lengths are varied in both adverse pressure gradient (APG) and favorable pressure gradient (FPG). A control boundary layer flow in zero pressure gradient ZPG is also presented. It is shown here that, when the sensor length is maintained a constant value, in a contant Reynolds number, the near-wall peak increases with (adverse) pressure gradient. Both increased contributions of the small- and especially large-scale features are attributed to the increased broadband turbulence intensities. The two-mode increase, one centreing in the near-wall region and the other one in the outer region, makes spatial resolution studies in boundary layer flow more complicated. The increased large-scale features in the near-wall region of an APG flow is similar to large-scales increase due to Reynolds number in ZPG flow. Additionally, there is also an increase of the small-scales in the near-wall region when the boundary layer is exposed to adverse pressure gradient (while the Reynolds number is constant). In order to collapse the near-wall peaks for APG, ZPG and FPG flows, the APG flow has to use the longest sensor and conversely, the FPG has to use the shortest sensor. This study recommends that the empirical prediction by Huthins et. al. (2009) to be reevaluated if pressure gradient flows were to be considered such that the magnitude of the near-wall peak is also a function of the adverse pressure gradient parameter.

History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers

2017 ◽  
Vol 820 ◽  
pp. 667-692 ◽  
Author(s):  
A. Bobke ◽  
R. Vinuesa ◽  
R. Örlü ◽  
P. Schlatter
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
History Effects ◽  
Displacement Thickness ◽  
Gradient Parameter

Turbulent boundary layers under adverse pressure gradients are studied using well-resolved large-eddy simulations (LES) with the goal of assessing the influence of the streamwise pressure-gradient development. Near-equilibrium boundary layers were characterized through the Clauser pressure-gradient parameter $\unicode[STIX]{x1D6FD}$. In order to fulfil the near-equilibrium conditions, the free stream velocity was prescribed such that it followed a power-law distribution. The turbulence statistics pertaining to cases with a constant value of $\unicode[STIX]{x1D6FD}$ (extending up to approximately 40 boundary-layer thicknesses) were compared with cases with non-constant $\unicode[STIX]{x1D6FD}$ distributions at matched values of $\unicode[STIX]{x1D6FD}$ and friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. An additional case at matched Reynolds number based on displacement thickness $Re_{\unicode[STIX]{x1D6FF}^{\ast }}$ was also considered. It was noticed that non-constant $\unicode[STIX]{x1D6FD}$ cases appear to approach the conditions of equivalent constant $\unicode[STIX]{x1D6FD}$ cases after long streamwise distances (approximately 7 boundary-layer thicknesses). The relevance of the constant $\unicode[STIX]{x1D6FD}$ cases lies in the fact that they define a ‘canonical’ state of the boundary layer, uniquely characterized by $\unicode[STIX]{x1D6FD}$ and $Re$. The investigations on the flat plate were extended to the flow around a wing section overlapping in terms of $\unicode[STIX]{x1D6FD}$ and $Re$. Comparisons with the flat-plate cases at matched values of $\unicode[STIX]{x1D6FD}$ and $Re$ revealed that the different development history of the turbulent boundary layer on the wing section leads to a less pronounced wake in the mean velocity as well as a weaker second peak in the Reynolds stresses. This is due to the weaker accumulated effect of the $\unicode[STIX]{x1D6FD}$ history. Furthermore, a scaling law suggested by Kitsios et al. (Intl J. Heat Fluid Flow, vol. 61, 2016, pp. 129–136), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adverse-pressure-gradient turbulent boundary layers and highlights the fact that the values of the Clauser pressure-gradient parameter and the Reynolds number are not sufficient to characterize the state of the boundary layer.

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