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.

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.

Modeling and Simulation of High Reynolds' Number Flows During Reaction Injection Mold Filling

1994 ◽  
Vol 9 (3) ◽  
pp. 279-285 ◽  
Author(s):  
Rahima K. Mohammed ◽  
Tim A. Osswald ◽  
Timothy J. Spiegelhoff ◽  
Esther M. Sun
Keyword(s):  
Reynolds Number ◽  
Modeling And Simulation ◽  
High Reynolds Number ◽  
Mold Filling ◽  
Injection Mold ◽  
High Reynolds ◽  
Reynolds Number Flows

Immersed Methods for High Reynolds Number Fluid-Structure Interactions

2017 ◽  
Vol 14 (06) ◽  
pp. 1750068 ◽  
Author(s):  
Lucy T. Zhang
Keyword(s):  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
High Reynolds Number ◽  
Fluid Structure Interactions ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
High Reynolds ◽  
Immersed Methods ◽  
Reynolds Number Flows

Immersed methods are considered as a class of nonboundary-fitted meshing technique for simulating fluid–structure interactions. However, the conventional approach of coupling the fluid and solid domains, as in the immersed boundary method and the immersed finite element method, often cannot handle high Reynolds number flows interacting with moving and deformable solids. As the solid dynamics is imposed by the fluid dynamics, it often leads to unrealistically large deformation of the solid in cases of high Reynolds number flows. The first attempt in resolving this issue was proposed in the modified immersed finite element method (mIFEM), however, some terms were determined heuristically. In this paper, we provide a full and rigorous derivation for the mIFEM with corrections to the previously proposed terms, which further extends the accuracy of the algorithm. In the “swapped” coupling logic, we solve for the dynamics of the solid, and then numerically impose it to the background fluid, which allows the solid to control its own dynamics and governing laws instead of following that of the fluid. A few examples including a biomedical engineering application are shown to demonstrate the capability in handling large Reynolds number flows using the derived mIFEM.

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