On the instability of flow in a streamwise corner

1993 ◽  
Vol 441 (1911) ◽  
pp. 201-210 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Outer Boundary ◽  
Cross Flow ◽  
Downstream Distance ◽  
Blasius Boundary Layer ◽  
Flow Approximation ◽  
Wave Angle ◽  
The Stability ◽  
Spanwise Location

The linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90° streamwise corner and a Blasius boundary layer well away from the corner is examined using a locally parallel flow approximation. It is shown that the magnitude of the cross flow in the boundary layer is too small to be a significant factor in the observed early transition in the blending layer. However, the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti-symmetric about the bisector plane are shown to have a profound effect on the stability of the flow. As a result, the square root of the critical streamwise Reynolds number R er , associated with a spanwise location is significantly reduced as the corner is approached, being R er = 54 approximately for spanwise distance of z * = 6 x * R -1 from the corner compared with R er = 322 approximately for z * = 20 x * R -1 , where x * measures downstream distance from the leading edges and R 2 is the streamwise Reynolds number. At R = 600, the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter; the corresponding wave angle at the two locations is respectively 44° and 5°, approximately.

Higher eigenstates in boundary-layer stability theory

1976 ◽  
Vol 77 (1) ◽  
pp. 81-104 ◽  
Author(s):  
D. Corner ◽  
D. J. R. Houston ◽  
M. A. S. Ross
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stability Theory ◽  
Free Stream ◽  
Angular Frequency ◽  
Boundary Layer Stability ◽  
Fundamental State ◽  
Blasius Boundary Layer ◽  
The Stability ◽  
Sommerfeld Equation

Using the Orr-Sommerfeld equation with the wavenumber as the eigenvalue, a search for higher eigenstates in the stability theory of the Blasius boundary layer has revealed the existence of a number of viscous states in addition to the long established fundamental state. The viscous states are discrete, belong to two series, and are all heavily damped in space. Within the limits of the investigation the number of viscous states existing in the layer increases as the Reynolds number and the angular frequency of the perturbation increase. It is suggested that the viscous eigenstates may be responsible for the excitation of some boundary-layer disturbances by disturbances in the free stream.

Effects of uniform suction on the stability of flow on a rotating disc

1992 ◽  
Vol 439 (1906) ◽  
pp. 431-440 ◽  
Keyword(s):  
Flow Instability ◽  
Linear Equations ◽  
Cross Flow ◽  
Neutral Curve ◽  
Critical Conditions ◽  
Rotating Disc ◽  
Suction Parameter ◽  
Flow Approximation ◽  
Wave Angle ◽  
The Stability

The effects of uniform distributed suction on the cross-flow instability of the boundary layer on a rotating disc are considered. A vorticity-velocity formulation is used to obtain exact linear equations governing the development of infinitesimal disturbances to the steady flow on a rotating disc. A parallel flow approximation is made as a first step in determining the effect of suction on the instability. It is shown that suction has a stabilizing effect on the flow, whereas blowing is destabilizing. Small values of the suction parameter are found to increase significantly the critical Reynolds number associated with stationary modes of disturbance. The wave angle of the spiral vortices that precede turbulent flow is estimated from critical conditions and is shown to decrease with increase in suction rate. This is shown to be consistent with prediction based on an in viscid analysis. The corresponding estimate of the expected number of vortices is shown to increase with suction. Suction appears to make the second minimum on the neutral curve more pronounced, suggesting a possible increase in the relative importance of the associated low wavenumber mode of disturbance.

Stability of Flat Plate Boundary Layer Over Compliant Coating with Increased Rigidity

2011 ◽  
Vol 6 (4) ◽  
pp. 25-41
Author(s):  
Andrey Boiko ◽  
Viktor Kulik ◽  
V. Filimonov
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Viscoelastic Properties ◽  
Loss Factor ◽  
Plate Boundary ◽  
Single Layer ◽  
Interface Conditions ◽  
Compliant Coating ◽  
Blasius Boundary Layer ◽  
Flat Plate Boundary Layer

In the paper the results of hydrodynamic stability computations for Blasius boundary layer over single-layer compliant coatings in the framework of complete (in respect to interface conditions) linear quasi-parallel approach are presented. Data on viscoelastic properties (elastic modulus and loss factor) of the coatings as functions of frequency obtained in a series of special experiments were used. A range of the coating parameters, which provide a compromise between their rigidity and intensity of interaction with the flow, was determined. Based on en -method, estimations of the transition Reynolds number were done

Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches

2001 ◽  
Vol 439 ◽  
pp. 403-412 ◽  
Author(s):  
RAMA GOVINDARAJAN ◽  
R. NARASIMHA
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Small Difference ◽  
Detailed Comparison ◽  
The Other ◽  
Boundary Layer Stability ◽  
Mean Flow ◽  
Amplitude Ratios ◽  
The Stability ◽  
Local Reynolds Number

We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the ‘full’ non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R−1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R−2/3) and O(R−1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.

Turbulent Wake of a Stack and the Influence of Velocity Ratio

2006 ◽  
Author(s):  
M. S. Adaramola ◽  
D. Sumner ◽  
D. J. Bergstrom
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Reynolds Shear Stress ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Turbulent Wake ◽  
Mean Velocity ◽  
Distinct Structure ◽  
Flow Reynolds Number ◽  
Cross Flow Velocity

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake of a cylindrical stack of AR = 9 was investigated with two-component thermal anemometry. The cross-flow Reynolds number was ReD = 2.3×104, the jet Reynolds number ranged from Red = 7×103 to 4.6×104, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-height ratio of δ/H = 0.5 at the location of the stack. The flow around the stack was broadly classified into three flow regimes depending on the value of R, which were the downwash (R < 0.5), cross-wind dominated (0.5 < R < 1.5), and jet-dominated (R > 1.5) regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields.

On the stability of a Blasius boundary layer subject to localised suction

2019 ◽  
Vol 871 ◽  
pp. 717-741 ◽  
Author(s):  
Mattias Brynjell-Rahkola ◽  
Ardeshir Hanifi ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Flow Instability ◽  
Linear Instability ◽  
Boundary Layer Transition ◽  
Transition To Turbulence ◽  
Layer Transition ◽  
Structural Sensitivity ◽  
Blasius Boundary Layer ◽  
Structural Sensitivity Analysis ◽  
The Stability

In this study the origins of premature transition due to oversuction in boundary layers are studied. An infinite row of circular suction pipes that are mounted at right angles to a flat plate subject to a Blasius boundary layer is considered. The interaction between the flow originating from neighbouring holes is weak and for the parameters investigated, the pipe is always found to be unsteady regardless of the state of the flow in the boundary layer. A stability analysis reveals that the appearance of boundary layer transition can be associated with a linear instability in the form of two unstable eigenmodes inside the pipe that have weak tails, which extend into the boundary layer. Through an energy budget and a structural sensitivity analysis, the origin of this flow instability is traced to the structures developing inside the pipe near the pipe junction. Although the amplitudes of the modes in the boundary layer are orders of magnitude smaller than the corresponding amplitudes inside the pipe, a Koopman analysis of the data gathered from a nonlinear direct numerical simulation confirms that it is precisely these disturbances that are responsible for transition to turbulence in the boundary layer due to oversuction.

Flow-induced degradation of drag-reducing polymer solutions within a high-Reynolds-number turbulent boundary layer

2011 ◽  
Vol 670 ◽  
pp. 337-364 ◽  
Author(s):  
BRIAN R. ELBING ◽  
MICHAEL J. SOLOMON ◽  
MARC PERLIN ◽  
DAVID R. DOWLING ◽  
STEVEN L. CECCIO
Keyword(s):  
Boundary Layer ◽  
Molecular Weight ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
High Reynolds Number ◽  
Polymer Degradation ◽  
Rheological Analysis ◽  
Downstream Distance ◽  
High Reynolds

Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20ms−1. Measurements were acquired up to 10.7m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20ms−1) no drag reduction was discernible at the first measurement location (0.56m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (~10−3s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (~0.1s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.

scholarly journals On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

Development of a Tip-Leakage Flow—Part 1: The Flow Over a Range of Reynolds Numbers

2006 ◽  
Vol 128 (4) ◽  
pp. 751-764 ◽  
Author(s):  
Ghanem F. Oweis ◽  
David Fry ◽  
Chris J. Chesnakas ◽  
Stuart D. Jessup ◽  
Steven L. Ceccio
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Leakage Flow ◽  
Core Size ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Downstream Distance ◽  
Secondary Vortices

An extensive experimental investigation was carried out to examine the tip-leakage flow on ducted propulsors. The flow field around three-bladed, ducted rotors operating in uniform inflow was measured in detail with three-dimensional laser Doppler velocimetry and planar particle imaging velocimetry. Two geometrically similar, ducted rotors were tested over a Reynolds number range from 0.7×106 to 9.2×106 in order to determine how the tip-leakage flow varied with Reynolds number. An identification procedure was used to discern and quantify regions of concentrated vorticity in instantaneous flow fields. Multiple vortices were identified in the wake of the blade tip, with the largest vortex being associated with the tip-leakage flow, and the secondary vortices being associated with the trailing edge vortex and other blade-wake vortices. The evolution of identified vortex quantities with downstream distance is examined. It was found that the strength and core size of the vortices are weakly dependent on Reynolds number, but there are indications that they are affected by variations in the inflowing wall boundary layer on the duct. The core size of the tip-leakage vortex does not vary strongly with varying boundary layer thickness on the blades. Instead, its dimension is on the order of the tip clearance. There is significant flow variability for all Reynolds numbers and rotor configurations. Scaled velocity fluctuations near the axis of the primary vortex increase significantly with downstream distance, suggesting the presence of spatially uncorrelated fine scale secondary vortices and the possible existence of three-dimensional vortex-vortex interactions.

The stability of laminar boundary layers at separation

1965 ◽  
Vol 23 (4) ◽  
pp. 737-747 ◽  
Author(s):  
T. H. Hughes ◽  
W. H. Reid
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Adverse Pressure Gradient ◽  
Neutral Curve ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Laminar Boundary Layers ◽  
The Stability ◽  
Limiting Case

The effect of an adverse pressure gradient on the stability of a laminar boundary layer is considered in the limiting case when the skin friction at the wall vanishes, i.e. when U′(0) = 0. Such flows are not absolutely unstable as might have been expected but have a minimum critical Reynolds number of the order of 25. General results are given for the asymptotic behaviour of both the upper and lower branches of the neutral curve and a complete neutral curve is obtained for Pohlhausen's simple fourth-degree polynomial profile at separation.

Sign in / Sign up

Export Citation Format

Share Document