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.

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.

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.

Generation Mechanism of Streaky Structure in Natural Transition

2003 ◽  
Author(s):  
Ayumu Inasawa ◽  
Fredrik Lundell ◽  
Masaharu Matsubara ◽  
P. H. Alfredsson ◽  
Yasuaki Kohama
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Streamwise Velocity ◽  
Mean Flow ◽  
Integral Scale ◽  
Free Stream Turbulence ◽  
Local Boundary ◽  
Streaky Structure ◽  
Streaky Structures

In a transitional boundary layer subjected to free-stream turbulence, streaky structures develop and eventually break down to turbulence after wavy motions. The purpose of the present study is to reveal the dominant scales of the streaky structures using a novel stereo PTV system measuring the streamwise and wall-normal velocities. The correlation of the streamwise velocity exhibit a negative peak at a certain spanwise separation. If normalized with the local boundary layer thickness, the spanwise separation minimizing the correlation decreases downstream and reaches the boundary layer thickness at the most downstream position. The streamwise correlation coefficient is asymptotically decreasing to zero and the streamwise integral scales are increasing downstream, indicating the large streamwise elongation of the streaky structure. The normalized spanwise scale of the wall-normal disturbance velocity also decreases downstream and it is always narrower than the width of the disturbances of the streamwise velocity. In contrast to the elongating streamwise velocity disturbance, the integral scale in the streamwise direction of the wall-normal disturbance is constant with downstream position. The length scales of the wall-normal disturbance are more less constant with the streamwise position and this result concludes that the wall-normal disturbance is simply convected by the mean flow after the receptivity process.

Definition Of The Parameters Of Surface Undulations For Small Scale Aircraft Wing

2015 ◽  
Vol 10 (3) ◽  
pp. 5-18
Author(s):  
Ilya Zverkov ◽  
Alexey Kryukov ◽  
Genrich Grek ◽  
I. Konovalov ◽  
Georgiy Evtushok
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Flow Instability ◽  
Small Scale ◽  
Local Boundary ◽  
Flow Parameters ◽  
Turbulent Transition ◽  
Definition Of

This work is devoted to investigation of flow parameters on classic and wavy wing with Z-15-25 profile in area of Reynolds number from 0,35 to 2 ´ 105 with α = 0ᶛ. The oil-film visualization are demonstrate the transformation of separation area on low Reynolds wing surfaces. Influence of distribution of a pressure gradient on a profile upon the sizes of separation area is shown and limits of applicability of a wavy surface of a wing are defined. The thermoanemometric data provided to determine boundary layer thickness and pulsation characteristics. As shown that at Reynolds number area 0,6–2 ´ 105 the mechanisms of flow instability and laminar-turbulent transition are invariable and depend from local boundary layer parameters at preseparation area. As well as for a classical wing, in the area of a groove of a wavy wing, the central frequency of a package of waves of instability of a shift layer can be well foretold both by means of the linear theory of stability, and by means of a hypothesis that the wavelength of the running indignations is proportional to the doubled boundary layer thickness. At result the technique of a finding of parameters of a undulations of a wing for any profile in the range of numbers of Reynolds from 104 до 105 is offered.

EFFECTS OF BOUNDARY-LAYER THICKNESS ON UNSTEADY FLOW CHARACTERISTICS INSIDE OPEN CAVITIES AT SUBSONIC AND TRANSONIC SPEEDS

2012 ◽  
Vol 19 ◽  
pp. 206-213
Author(s):  
DANG-GUO YANG ◽  
JIAN-QIANG LI ◽  
ZHAO-LIN FAN ◽  
XIN-FU LUO
Keyword(s):  
Boundary Layer ◽  
Unsteady Flow ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Sound Pressure ◽  
Flow Characteristics ◽  
Open Cavity ◽  
Aerodynamic Noise ◽  
Sustained Oscillation ◽  
Cavity Depth

An experimental study was conducted in a 0.6m by 0.6m wind-tunnel to analyze effects of boundary-layer thickness on unsteady flow characteristics inside a rectangular open cavity at subsonic and transonic speeds. The sound pressure level (SPL) distributions at the centerline of the cavity floor and Sound pressure frequency spectrum (SPFS) characteristics on some measurement positions presented herein was obtained with cavity length-to-depth ratio (L/D) of 8 over Mach numbers (Ma) of 0.6 and 1.2 at a Reynolds numbers (Re) of 1.23 × 107 and 2.02 × 107 per meter under different boundary-layer thickness to cavity-depth ratios (δ/D). The experimental angle of attack, yawing and rolling angles were 0°. The results indicate that decrease in δ/D leads to severe flow separation and unsteady pressure fluctuation, which induces increase in SPL at same measurement points inside the cavity at Ma of 0.6. At Ma of 1.2, decrease in δ/D results in enhancing compressible waves. Generally, decrease in δ/D induces more flow self-sustained oscillation frequencies. It also makes severer aerodynamic noise inside the open cavity.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Magnetohydrodynamics Williamson Fluid Comprising Gyrotactic Microorganisms Flows Through a Permeable Stretching Layer with Variable Fluid Properties

2020 ◽  
Vol 9 (4) ◽  
pp. 375-387
Author(s):  
Amit Parmar ◽  
Rakesh Choudhary ◽  
Krishna Agarwal
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Schmidt Number ◽  
Gyrotactic Microorganisms ◽  
Williamson Fluid ◽  
Non Linear ◽  
Fluid Properties ◽  
Variable Prandtl Number

The present study shows the impacts of Williamson fluid with magnetohydrodynamics flow containing gyrotactic microorganisms under the variable fluid property past permeable stretching sheet. Variable Prandtl number, mass Schmidt number, and gyrotactic microorganisms Schmidt number were all considered. The momentum, energy, mass, and microorganism equations’ governing PDEs are converted into nonlinear coupled ODEs and numerically solved with the bvp4c solver using suitable transformations. The main outcome of this study is that Williamson fluid parameter constantly decreases in velocity profile, however reverse effects can be shown in temperature profile. Also, M parameter and Kp parameter enhance the heat transfer rate, concentration rate and microorganisms boundary layer thickness but declines in momentum boundary layer thickness and velocity profile. The aim of this research is to see how velocity slide, temperature jump, concentration slip, and microorganism slip affect MHD Williamson fluid flow with gyrotactic microorganisms over a leaky surface embedded in spongy medium, with non-linear radiation and non-linear chemical reaction.

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