Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer

2014 ◽  
Vol 763 ◽  
pp. 136-165 ◽  
Author(s):  
Nicola De Tullio ◽  
Neil D. Sandham
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
High Speed ◽  
Stokes Equations ◽  
Roughness Element ◽  
Transition To Turbulence ◽  
Local Boundary ◽  
Wake Modes

AbstractThe excitation of instability modes in the wake generated behind a discrete roughness element in a boundary layer at Mach 6 is analysed through numerical simulations of the compressible Navier–Stokes equations. Recent experimental observations show that transition to turbulence in high-speed boundary layers during re-entry flight is dominated by wall roughness effects. Therefore, understanding the roughness-induced transition to turbulence in this flow regime is of primary importance. Our results show that a discrete roughness element with a height of about half the local boundary-layer thickness generates an unstable wake able to sustain the growth of a number of modes. The most unstable of these modes are a sinuous mode (mode SL) and two varicose modes (modes VL and VC). The varicose modes grow approximately 17 % faster than the most unstable Mack mode and their growth persists over a longer streamwise distance, thereby leading to a notable acceleration of the laminar–turbulent transition process. Two main mechanisms are identified for the excitation of wake modes: the first is based on the interaction between the external disturbances and the reverse flow regions induced by the roughness element and the second is due to the interaction between the boundary-layer modes (first modes and Mack modes) and the non-parallel roughness wake. An important finding of the present study is that, while being less unstable, mode SL is the preferred instability for the first of the above excitation mechanisms, which drives the wake modes excitation in the absence of boundary-layer modes. Modes VL and VC are excited through the second mechanism and, hence, become important when first modes and Mack modes come into interaction with the roughness wake. The new mode VC presents similarities with the Mack mode instability, including the tuning between its most unstable wavelength and the local boundary-layer thickness, and it is believed to play a fundamental role in the roughness-induced transition of high-speed boundary layers. In contrast to the smooth-wall case, wall cooling is stabilising for all the roughness-wake modes.

scholarly journals Computational Characterization of a Rectangular Vortex Generator on a Flat Plate for Different Vane Heights and Angles

2019 ◽  
Vol 9 (5) ◽  
pp. 995 ◽  
Author(s):  
Iosu Ibarra-Udaeta ◽  
Iñigo Errasti ◽  
Unai Fernandez-Gamiz ◽  
Ekaitz Zulueta ◽  
Javier Sancho
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Vortex Generator ◽  
Vortex Generators ◽  
Local Boundary ◽  
Passive Flow Control ◽  
Vortex Size

Vortex generators (VG) are passive flow control devices used for avoiding or delaying the separation of the boundary layer by bringing momentum from the higher layers of the fluid towards the surface. The Vortex generator usually has the same height as the local boundary layer thickness, and these Vortex generators can produce overload drag in some cases. The aim of the present study was to analyze the characteristics and path of the primary vortex produced by a single rectangular vortex generator on a flat plate for the incident angles of β = 10 ∘ , 15 ∘ , 18 ∘ and 20 ∘ . A parametric study of the induced vortex was performed for six VG heights using Reynolds average Navier–Stokes equations at Reynodls number R e = 27,000 based on the local boundary layer thickness, using computational fluid dynamics techniques with OpenFOAM open-source code. In order to determine the vortex size, the so-called half-life radius was computed and compared with experimental data. The results showed a similar trend for all the studied vortex generator heights and incident angles with small variations for the vertical and the lateral paths. Additionally, 0.4H and 0.6H VG heights at incident angles of β = 18 ∘ and β = 20 ∘ showed the best performance in terms of vortex strength and generation of wall shear stress.

Annulus Wall Boundary-Layer Measurements in a Four-Stage Compressor

1986 ◽  
Vol 108 (1) ◽  
pp. 2-6 ◽  
Author(s):  
N. A. Cumpsty
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Tip Clearance ◽  
The Other ◽  
Wall Boundary Layer ◽  
Multistage Compressors ◽  
Full Design

There are few available measurements of the boundary layers in multistage compressors when the repeating-stage condition is reached. These tests were performed in a small four-stage compressor; the flow was essentially incompressible and the Reynolds number based on blade chord was about 5 • 104. Two series of tests were performed; in one series the full design number of blades were installed, in the other series half the blades were removed to reduce the solidity and double the staggered spacing. Initially it was wished to examine the hypothesis proposed by Smith [1] that staggered spacing is a particularly important scaling parameter for boundary layer thickness; the results of these tests and those of Hunter and Cumpsty [2] tend to suggest that it is tip clearance which is most potent in determining boundary-layer integral thicknesses. The integral thicknesses agree quite well with those published by Smith.

scholarly journals Influence of localised smooth steps on the instability of a boundary layer

2017 ◽  
Vol 817 ◽  
pp. 138-170 ◽  
Author(s):  
Hui Xu ◽  
Jean-Eloi W. Lombard ◽  
Spencer J. Sherwin
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Gaussian White Noise ◽  
Random Phase ◽  
Linear Analysis ◽  
Base Flow ◽  
Neutral Stability ◽  
Local Boundary ◽  
Type Transition

We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %–30 % and four times the width of the local boundary layer thickness $\unicode[STIX]{x1D6FF}_{99}$. The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the two-dimensional Tollmien–Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency ${\mathcal{F}}\in [140,160]$ (${\mathcal{F}}=\unicode[STIX]{x1D714}\unicode[STIX]{x1D708}/U_{\infty }^{2}\times 10^{6}$, where $\unicode[STIX]{x1D714}$ and $U_{\infty }$ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and $\unicode[STIX]{x1D708}$ denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter ${\mathcal{F}}=150$ and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.

A Review of Cascade Data on Secondary Losses in Turbines

1970 ◽  
Vol 12 (1) ◽  
pp. 48-59 ◽  
Author(s):  
J. Dunham
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Blade Loading ◽  
Axial Turbine ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Turbine Cascades

Theories and experiments on secondary losses in axial turbine cascades without end clearance are reviewed. A formula is given which correlates the effect of blade loading on secondary losses more successfully than hitherto. However, it is also shown that secondary losses increase with upstream wall boundary layer thickness. Only a tentative expression for that effect can be suggested. In order to predict secondary losses reliably more must be known about these wall boundary layers.

Some Characteristics of the Vortical Motions in the Outer Region of Turbulent Boundary Layers (Data Bank Contribution)

1992 ◽  
Vol 114 (4) ◽  
pp. 530-536 ◽  
Author(s):  
J. C. Klewicki ◽  
R. E. Falco ◽  
J. F. Foss
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Outer Region ◽  
Signal Amplitude ◽  
Threshold Level ◽  
Data Bank ◽  
Turbulent Boundary Layers ◽  
Spanwise Vorticity

Time-resolved measurements of the spanwise vorticity component, ωz, are used to investigate the motions in the outer region of turbulent boundary layers. The measurements were taken in very thick zero pressure gradient boundary layers (Rθ = 1010, 2870, 4850) using a four wire probe. As a result of the large boundary layer thickness, at the outer region locations where the measurements were taken the wall-normal and spanwise dimensions of the probe ranged between 0.7 < Δy/η < 1.2 and 2.1 < Δz/η < 3.9, respectively, where η is the local Kolmogorov length. An analysis of vorticity based intermittency is presented near y/δ = 0.6 and 0.85 at each of the Reynolds numbers. The average intermittency is presented as a function of detector threshold level and position in the boundary layer. The spanwise vorticity signals were found to yield average intermittency values at least as large as previous intermittency studies using “surrogate” signals. The average intermittency results do not indicate a region of threshold independence. An analysis of ωz event durations conditioned on the signal amplitude was also performed. The results of this analysis indicate that for decreasing Rθ, regions of single-signed ωz increase in size relative to the boundary layer thickness, but decrease in size when normalized by inner variables.

Direct numerical simulation of high-speed transition due to an isolated roughness element

2014 ◽  
Vol 748 ◽  
pp. 848-878 ◽  
Author(s):  
Pramod K. Subbareddy ◽  
Matthew D. Bartkowicz ◽  
Graham V. Candler
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Large Scale ◽  
Stokes Equations ◽  
Roughness Element ◽  
Dynamic Mode Decomposition ◽  
Large Reynolds Number ◽  
Dynamic Mode ◽  
Low Dissipation

AbstractWe study the transition of a Mach 6 laminar boundary layer due to an isolated cylindrical roughness element using large-scale direct numerical simulations (DNS). Three flow conditions, corresponding to experiments conducted at the Purdue Mach 6 quiet wind tunnel are simulated. Solutions are obtained using a high-order, low-dissipation scheme for the convection terms in the Navier–Stokes equations. The lowest Reynolds number ($Re$) case is steady, whereas the two higher $Re$ cases break down to a quasi-turbulent state. Statistics from the highest $Re$ case show the presence of a wedge of fully developed turbulent flow towards the end of the domain. The simulations do not employ forcing of any kind, apart from the roughness element itself, and the results suggest a self-sustaining mechanism that causes the flow to transition at a sufficiently large Reynolds number. Statistics, including spectra, are compared with available experimental data. Visualizations of the flow explore the dominant and dynamically significant flow structures: the upstream shock system, the horseshoe vortices formed in the upstream separated boundary layer and the shear layer that separates from the top and sides of the cylindrical roughness element. Streamwise and spanwise planes of data were used to perform a dynamic mode decomposition (DMD) (Rowley et al., J. Fluid Mech., vol. 641, 2009, pp. 115–127; Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28).

Wind-Tunnel Screens: Flow Instability and its Effect on Aerofoil Boundary Layers

1964 ◽  
Vol 68 (639) ◽  
pp. 198-198 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Flow Instability ◽  
Flow Direction ◽  
Flat Plates ◽  
Mixing Processes ◽  
Flow Through

Morgan has described a spatial instability in the flow through screens or grids of small open-area ratio. Head and Rechenberg and others have observed large span-wise variations in the thickness and shear stress of nominally two-dimensional boundary layers on flat plates and aerofoils in wind tunnels. It now appears that these spanwise variations are caused by the instability of flow through the screens. The jets of air issuing from the pores of the screen attempt to entrain more air by the usual mixing processes, but can only entrain it from each other, so that groups of jets coalesce in rather random (steady) patterns determined by small irregularities in the weave. The resulting variations in axial velocity are virtually eliminated by the wind tunnel contraction, but variations in flow direction are not so greatly reduced: a theoretical analysis shows that the observed variations of boundary-layer thickness, which often reach ± 10 per cent of the mean, can be produced by directional variations in the working section of the order of ± 1/20 deg, with a spanwise wavelength of the same order as the boundary-layer thickness.

Fluid-Acoustics Interaction in Self-Sustained Oscillations Over a Cavity in a Turbulent Boundary Layer

2008 ◽  
Author(s):  
H. Yokoyama ◽  
C. Kato
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Layer Thickness ◽  
Turbulent Flows ◽  
Acoustic Waves ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Practical Applications ◽  
Sustained Oscillations ◽  
Mach Numbers

Self-sustained oscillations with fluid-acoustics interaction over a cavity can radiate intense tonal sound and fatigue nearby components of industrial products. The prediction and the suppression of these oscillations are very important for many practical applications. However, the fluid-acoustics interaction has not been thoroughly clarified in particular for the oscillations in turbulent flows. We investigate the mechanism of the oscillations over a rectangular cavity with a length-to-depth ratio of 2:1 by directly solving the compressible Navier-Stokes equations. The boundary layer over the cavity is turbulent and the freestream Mach numbers are M = 0.4 and 0.7. The results clarify that the self-sustained oscillations occur in the shear layer of the cavity and the oscillations are reinforced by the streamwise acoustic mode in the cavity for both Mach numbers. The shear layer of the cavity undulates. This undulation causes the deformation of fine vortices in the shear layer and radiates acoustic waves from the downstream edge of the cavity. Also, we clarify by the conditional identification of longitudinal vortices that the acoustic waves cause the undulation of the shear layer and a feedback loop is formed. Moreover, the comparison of the flow field over the cavity with that over a simple backstep shows that the shear layer in the cavity becomes two-dimensional by the acoustic feedback. Finally, we show that the oscillations become weaker particularly at M = 0.4 and the frequencies of the oscillations become lower as the boundary layer thickness at the upstream edge of the cavity increases. Considering this effect of the boundary layer thickness, the peak frequencies predicted by our computations are in good agreement with those measured in a past experiment.

scholarly journals Viscoplastic boundary layers

2017 ◽  
Vol 813 ◽  
pp. 929-954 ◽  
Author(s):  
N. J. Balmforth ◽  
R. V. Craster ◽  
D. R. Hewitt ◽  
S. Hormozi ◽  
A. Maleki
Keyword(s):  
Boundary Layer ◽  
Yield Stress ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Boundary Layer Theory ◽  
Classical Solutions ◽  
Bingham Number ◽  
Boundary Layer Equations ◽  
Two Dimensional Flow

In the limit of a large yield stress, or equivalently at the initiation of motion, viscoplastic flows can develop narrow boundary layers that provide either surfaces of failure between rigid plugs, the lubrication between a plugged flow and a wall or buffers for regions of predominantly plastic deformation. Oldroyd (Proc. Camb. Phil. Soc., vol. 43, 1947, pp. 383–395) presented the first theoretical discussion of these viscoplastic boundary layers, offering an asymptotic reduction of the governing equations and a discussion of some model flow problems. However, the complicated nonlinear form of Oldroyd’s boundary-layer equations has evidently precluded further discussion of them. In the current paper, we revisit Oldroyd’s viscoplastic boundary-layer analysis and his canonical examples of a jet-like intrusion and flow past a thin plate. We also consider flow down channels with either sudden expansions or wavy walls. In all these examples, we verify that viscoplastic boundary layers form as envisioned by Oldroyd. For each example, we extract the dependence of the boundary-layer thickness and flow profiles on the dimensionless yield-stress parameter (Bingham number). We find that, while Oldroyd’s boundary-layer theory applies to free viscoplastic shear layers, it does not apply when the boundary layer is adjacent to a wall, as has been observed previously for two-dimensional flow around circular obstructions. Instead, the boundary-layer thickness scales in a different fashion with the Bingham number, as suggested by classical solutions for plane-parallel flows, lubrication theory and, for flow around a plate, by Piau (J. Non-Newtonian Fluid Mech., vol. 102, 2002, pp. 193–218); we rationalize this second scaling and provide an alternative boundary-layer theory.

Effect of transition on the aerodynamic characteristics of a spinning cone

2017 ◽  
Vol 232 (11) ◽  
pp. 2048-2058
Author(s):  
Qiao Zhang ◽  
Xiaosheng Wu ◽  
Jintao Yin ◽  
Ran Yao
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Transition Model ◽  
Magnus Force ◽  
The Right

In order to study the effect of transition on the aerodynamic characteristics of a pointed cone at small angles of attack in supersonic flows, the [Formula: see text] transition model, γ transition model, and a trip wire applied with [Formula: see text] transition model coupled with the Reynolds-averaged Navier–Stokes equations were used to simulate the flow over the spinning cone. The γ transition model, including the effects of crossflow instability, is better than other models in the transition and Magnus force prediction. The numerical calculations are in certain agreement with the experimental data. The results indicate that the positions of the maximum boundary layer thickness remain unchanged using different turbulence models, while the results obtained by the transition model shift towards spin direction, intensifying the difference of the boundary layer thickness between the right and the left side bodies; the contribution of the skin friction on the Magnus force increases due to the shift in the transition position; the contribution of pressure on the Magnus force also changes with the distortion of the boundary layer.

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