CRITICAL AMPLITUDE OF THE TRAVELING PRESSURE WAVE CAUSING THE VORTEX SHEET FORMATION IN THE BOUNDARY LAYER

2010 ◽  
Vol 41 (6) ◽  
pp. 611-617
Author(s):  
V. Ya. Neiland
Keyword(s):  
Boundary Layer ◽  
Pressure Wave ◽  
Vortex Sheet ◽  
Critical Amplitude

Formation of Vortex Street in Laminar Boundary Layer

1980 ◽  
Vol 47 (2) ◽  
pp. 227-233 ◽  
Author(s):  
M. Kiya ◽  
M. Arie
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Laminar Boundary Layer ◽  
Solid Wall ◽  
Vortex Sheet ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Vortex Patterns

Main features of the formation of vortex street from free shear layers emanating from two-dimensional bluff bodies placed in uniform shear flow which is a model of a laminar boundary layer along a solid wall. This problem is concerned with the mechanism governing transition induced by small bluff bodies suspended in a laminar boundary layer. Calculations show that the background vorticity of shear flow promotes the rolling up of the vortex sheet of the same sign whereas it decelerates that of the vortex sheet of the opposite sign. The steady configuration of the conventional Karman vortex street is not possible in shear flow. Theoretical vortex patterns are experimentally examined by a flow-visualization technique.

Improved calculations of leading-edge separation from slender, thin, delta wings

1968 ◽  
Vol 306 (1484) ◽  
pp. 67-90 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Lower Surface ◽  
Lateral Position ◽  
Quantitative Agreement ◽  
Delta Wings ◽  
Real Flow ◽  
Edge Separation ◽  
Secondary Separation

In previous calculations (Mangler & Smith 1959) of the vortex-sheet model of leading-edge separation, only qualitative agreement was found with experimental observations. Because the numerical treatment of the model was then necessarily incomplete, it was uncertain how far the lack of quantitative agreement was to be attributed to the limitations of the model. The use of an automatic digital computer has now made it possible to reduce the uncertainties in the calculation to a negligible level. The features of interest in the real flow are more accurately predicted and the remaining discrepancies can be ascribed to the deficiencies in the model. The paper describes the method used to locate the vortex sheet and determine its strength in terms of the two boundary conditions on it; assesses the credibility of the results; and relates them to the observations. It is concluded that the model successfully predicts the observed height of the vortex above the wing, though the predicted lateral position is in error by up to 6% of the semi-span of the wing. This error falls as the incidence increases and is less when transition occurs in the boundary-layer upstream of secondary separation. Normal force is predicted accurately as is the distribution of pressure on the lower surface and the inboard part of the upper surface. The observed suction peak below the vortex changes its character when transition occurs in the boundary-layer upstream of secondary separation. The model predicts the suction peak in the turbulent case fairly well, but it is clear that detailed prediction of the suction peak is not possible by a model which is wholly inviscid.

scholarly journals Airfoil in a high amplitude oscillating stream

2016 ◽  
Vol 793 ◽  
pp. 79-108 ◽  
Author(s):  
C. Strangfeld ◽  
H. Müller-Vahl ◽  
C. N. Nayeri ◽  
C. O. Paschereit ◽  
D. Greenblatt
Keyword(s):  
Boundary Layer ◽  
High Frequency ◽  
Lift Coefficient ◽  
Closed Form Solution ◽  
Harmonic Oscillation ◽  
Vortex Sheet ◽  
High Amplitude ◽  
High Frequency Oscillation ◽  
Recirculation Bubble ◽  
Theoretical Approaches

A combined theoretical and experimental investigation was carried out with the objective of evaluating theoretical predictions relating to a two-dimensional airfoil subjected to high amplitude harmonic oscillation of the free stream at constant angle of attack. Current theoretical approaches were reviewed and extended for the purposes of quantifying the bound, unsteady vortex sheet strength along the airfoil chord. This resulted in a closed form solution that is valid for arbitrary reduced frequencies and amplitudes. In the experiments, the bound, unsteady vortex strength of a symmetric 18 % thick airfoil at low angles of attack was measured in a dedicated unsteady wind tunnel at maximum reduced frequencies of 0.1 and at velocity oscillations less than or equal to 50 %. With the boundary layer tripped near the leading edge and mid-chord, the phase and amplitude variations of the lift coefficient corresponded reasonably well with the theory. Near the maximum lift coefficient overshoot, the data exhibited an additional high-frequency oscillation. Comparisons of the measured and predicted vortex sheet indicated the existence of a recirculation bubble upstream of the trailing edge which sheds into the wake and modifies the Kutta condition. Without boundary layer tripping, a mid-chord bubble is present that strengthens during flow deceleration and its shedding produces a dramatically different effect. Instead of a lift coefficient overshoot, as per the theory, the data exhibit a significant undershoot. This undershoot is also accompanied by high-frequency oscillations that are characterized by the bubble shedding. In summary, the location of bubble and its subsequent shedding play decisive roles in the resulting temporal aerodynamic loads.

504 Characteristic of Unsteady Boundary Layer Induced by Propagating Pressure Wave in Long Tube

2014 ◽  
Vol 2014.67 (0) ◽  
pp. _504-1_-_504-2_
Author(s):  
Toshiyuki AOKI ◽  
Nobuaki KONDOH ◽  
Hiromu YAMASAKI ◽  
Takuya OGAWA ◽  
Masaki OGISHIMA
Keyword(s):  
Boundary Layer ◽  
Pressure Wave ◽  
Unsteady Boundary Layer

On the breakdown of boundary layer streaks

2001 ◽  
Vol 428 ◽  
pp. 29-60 ◽  
Author(s):  
PAUL ANDERSSON ◽  
LUCA BRANDT ◽  
ALESSANDRO BOTTARO ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Travelling Waves ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Mean Flow ◽  
Critical Amplitude ◽  
Flow Modification ◽  
Streamwise Streaks ◽  
Optimal Disturbances

A scenario of transition to turbulence likely to occur during the development of natural disturbances in a flat-plate boundary layer is studied. The perturbations at the leading edge of the flat plate that show the highest potential for transient energy amplification consist of streamwise aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, inviscid instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to properly identify neutral modes belonging to the discrete spectrum. The streak critical amplitude, beyond which streamwise travelling waves are excited, is about 26% of the free-stream velocity. The sinuous instability mode (either the fundamental or the subharmonic, depending on the streak amplitude) represents the most dangerous disturbance. Varicose waves are more stable, and are characterized by a critical amplitude of about 37%. Stability calculations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here using the nonlinearly modified mean fields; the need to consider a base flow which includes mean flow modification and harmonics of the fundamental streak is clearly demonstrated.

Unsteady laminar flow of gas near an infinite flat plate

1950 ◽  
Vol 46 (4) ◽  
pp. 603-613 ◽  
Author(s):  
C. R. Illingworth
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Flat Plate ◽  
Constant Temperature ◽  
Vortex Sheet ◽  
Absolute Temperature ◽  
Convection Current ◽  
Uniform Motion ◽  
Boundary Layer Equations ◽  
Set Up

AbstractBoundary-layer equations for the unsteady flow near an effectively infinite flat plate set into motion in its own plane are subjected to von Mises's transformation. Solutions are obtained for the flows in which gravity is neglected, the Prandtl number σ is arbitrary, and the plate has a constant temperature and a velocity that is either uniform or, with dissipation neglected, non-uniform. Explicit solutions are obtained for the case in which the viscosity μr varies directly as the absolute temperature Tr. Solutions are also obtained for the diffusion of a plane vortex sheet in a gas, and for the boundary layer near a uniformly accelerated plate of constant temperature when gravity is not neglected. For the non-uniform motion of a heat-insulated plate, dissipation not being negligible, a solution is obtained when σ is 1 and μr ∝ Tr. The relative importance of free convection due to gravity and forced convection due to viscosity is discussed, and a solution is obtained, with μr ∝ Tr, for the free convection current set up near a plate that is at rest in a gas at a temperature different from that of the plate, dissipation being neglected.

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