On the disturbance evolution downstream of a cylindrical roughness element

2014 ◽  
Vol 758 ◽  
pp. 238-286 ◽  
Author(s):  
B. Plogmann ◽  
W. Würz ◽  
E. Krämer
Keyword(s):  
Boundary Layer ◽  
Roughness Element ◽  
Low Frequency ◽  
Initial Growth ◽  
Mean Flow ◽  
Flow Distortion ◽  
Near Wake ◽  
Local Boundary ◽  
Displacement Thickness ◽  
The Mean

AbstractRoughness-induced transition is one of the main parameters contributing to performance loss of airfoils. Within this paper, the disturbance evolution downstream of a single, cylindrical roughness element, which is placed in a laminar boundary layer in an airfoil leading edge region, is investigated. The experiments focus on medium height roughness elements with respect to the local boundary layer displacement thickness. Hence, transition is not directly tripped at the roughness element. The roughness diameter is comparable to the streamwise wavelength of the most amplified (linear) disturbance eigenmodes. The vortical structures observed downstream of the roughness are in agreement with previous findings in the literature. In the near roughness wake, a distinct growth of high-frequency (fundamental) modes, that is modes with a high $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$-factor at the roughness location, is observed. In the far roughness wake, these fundamental modes recover linear stability characteristics due to a possible relaxation of the mean flow. However, an interaction of particularly two-dimensional fundamental modes and by the roughness interference excited oblique fundamental modes results in an excitation of subharmonic type, low-frequency combination modes, which are associated with a phase-locked interaction mechanism. Depending on the initial growth of the fundamental modes in the near wake, the low-frequency modes can experience a nonlinear growth in the far roughness wake and, thereby, trip turbulence. The fundamental mode growth rate in the near wake in turn is a weak function of the disturbance frequency and of the pressure gradient, whereas it is decisively increasing with the roughness height, that is with the mean flow distortion caused by the roughness.

Fluctuating boundary layer on a magnetized plate

1967 ◽  
Vol 63 (2) ◽  
pp. 513-525 ◽  
Author(s):  
Sahib Singh Chawla
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Surface Current ◽  
Frequency Range ◽  
Mean Flow ◽  
Wave Type ◽  
High Frequencies ◽  
Phase Lead ◽  
The Mean ◽  
The Magnetic Field

The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.

scholarly journals Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011 ◽  
Vol 681 ◽  
pp. 116-153 ◽  
Author(s):  
NICHOLAS J. VAUGHAN ◽  
TAMER A. ZAKI
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Low Frequency ◽  
Finite Amplitude ◽  
Base Flow ◽  
Streamwise Vorticity ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Tollmien Schlichting

The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the Tollmien–Schlichting (T–S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

Local boundary-layer receptivity to a convected free-stream disturbance

1999 ◽  
Vol 378 ◽  
pp. 291-317 ◽  
Author(s):  
A. J. DIETZ
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Experimental Verification ◽  
Free Stream ◽  
Linear Stability Theory ◽  
Mean Flow ◽  
Flow Distortion ◽  
Instability Waves ◽  
Free Stream Turbulence ◽  
Local Boundary

An investigation of the local receptivity of a Blasius boundary layer to a harmonic vortical disturbance is presented as a step towards understanding boundary-layer receptivity to free-stream turbulence. Although there has been solid experimental verification of the linear theory describing acoustic receptivity of boundary layers, this was the first experimental verification of the mechanism behind local receptivity to a convected disturbance. The harmonic wake from a vibrating ribbon positioned upstream of a flat plate provided the free-stream disturbance. Two-dimensional roughness elements on the surface of the plate acted as a local receptivity site. Hot-wire measurements in the boundary layer downstream of the roughness confirmed the generation of Tollmien–Schlichting (TS) instability waves by an outer-layer interaction between the long-wavelength convected disturbance and the short-scale mean-flow distortion due to the roughness. The characteristics of the instability waves were carefully measured to ensure that their behaviour was correctly modelled by linear stability theory. This theory was then used to determine the immeasurably small initial wave amplitudes resulting from the receptivity process, from wave amplitudes measured downstream. Tests were performed to determine the range of validity of the linear assumptions made in current receptivity theories. Experimental data obtained in the linear regime were then compared to theoretical results of other authors by expressing the experimental data in the form of an efficiency function which is independent of the free-stream amplitude, roughness height and roughness geometry. Reasonable agreement between the experimental and theoretical efficiency functions was obtained over a range of frequencies and Reynolds numbers.

The pre-transitional Klebanoff modes and other boundary-layer disturbances induced by small-wavelength free-stream vorticity

2009 ◽  
Vol 638 ◽  
pp. 267-303 ◽  
Author(s):  
PIERRE RICCO
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Matched Asymptotic Expansion ◽  
Two Dimensional ◽  
Mean Flow ◽  
Flow Distortion ◽  
The Mean

The response of the Blasius boundary layer to free-stream vortical disturbances of the convected gust type is studied. The vorticity signature of the boundary layer is computed through the boundary-region equations, which are the rigorous asymptotic limit of the Navier–Stokes equations for low-frequency disturbances. The method of matched asymptotic expansion is employed to obtain the initial and outer boundary conditions. For the case of forcing by a two-dimensional gust, the effect of a wall-normal wavelength comparable with the boundary-layer thickness is taken into account. The gust viscous dissipation and upward displacement due to the mean boundary layer produce significant changes on the fluctuations within the viscous region. The same analysis also proves useful for computing to second-order accuracy the boundary-layer response induced by a three-dimensional gust with spanwise wavelength comparable with the boundary-layer thickness. It also follows that the boundary-layer fluctuations of the streamwise velocity match the corresponding free-stream velocity component. The velocity profiles are compared with experimental data, and good agreement is attained.The generation of Tollmien–Schlichting waves by the nonlinear mixing between the two-dimensional unsteady vorticity fluctuations and the mean flow distortion induced by localized wall roughness and suction is also investigated. Gusts with small wall-normal wavelengths generate significantly different amplitudes of the instability waves for a selected range of forcing frequencies. This is primarily due to the disparity between the streamwise velocity fluctuations in the free stream and within the boundary layer.

Calculation of the Mean Flow Past Circular Cylinders by Viscous-Inviscid Interaction

1985 ◽  
Vol 107 (2) ◽  
pp. 218-223 ◽  
Author(s):  
I. Celik ◽  
V. C. Patel ◽  
L. Landweber
Keyword(s):  
Boundary Layer ◽  
Pressure Distribution ◽  
Flow Model ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Mean Flow ◽  
Irrotational Flow ◽  
Flow Past ◽  
Displacement Thickness ◽  
The Mean

A method for the calculation of the mean flow past smooth circular cylinders is presented and evaluated. It utilizes an iterative procedure that couples a boundary-layer calculation method, by which the location of separation and the displacement thickness are predicted, and a new two-parameter irrotational-flow model, which predicts the pressure distribution. The displacement effect of the boundary layer is explicitly taken into account in the irrotational-flow model. The location of separation, drag coefficient, and pressure-distribution parameters are predicted at Reynolds numbers as high as 108. The results are compared with experiments in the subcritical and the supercritical flow regimes and with empirically developed design criteria for cylindrical structures at high Reynolds numbers.

Thermal Boundary Layer Response to Periodic Fluctuations

2018 ◽  
Author(s):  
J. Saavedra ◽  
G. Paniagua ◽  
O. Chazot
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Low Frequency ◽  
Periodic Flow ◽  
Mean Flow ◽  
Flow Topology ◽  
Flow Acceleration ◽  
The Mean ◽  
Periodic Fluctuations ◽  
Wall Shear

Unsteady effects impact the aerothermal performance of the turbine blade rows, originating noise, mechanical and thermal fatigue. Blade row interactions are due to the relative motion between nearby rows of airfoils, the periodic occurrence of flow distortions generated by the airfoil rows or combustors. The detailed characterization of the thermal boundary layer under periodic fluctuations is vital to improve the performance of cooled turbine airfoils. In the present contribution, we performed series of Unsteady Reynolds Averaged Navier-Stokes simulations to investigate the wall heat flux response to periodic flow velocity fluctuations, on a flat plate of 0.5 m. We investigated the boundary layer response to sudden flow acceleration and periodic flow perturbations, caused by inlet total pressure variations. Because of the flow acceleration the boundary layer is first stretched, resulting in an increase of the wall shear stress. Later on, due to the viscous diffusion, the low momentum flow adjusts to the new free stream conditions. The behavior of the boundary layer at low frequency is similar to the response to an individual deceleration followed by one acceleration. However, at higher frequencies the mean flow topology is completely altered. One would expect that higher acceleration rates would cause a further stretching of the boundary layer that should cause even greater wall shear stresses and heat fluxes. However, we observed the opposite; instead, the amplitude of the skin friction coefficient is abated, while the peak level is one order of magnitude smaller than at low frequency. Two counteracting effects influence the response of both the momentum and the thermal boundary layer. In one hand, the stagnant flow quantities propagate at characteristic velocities guiding the establishment of the mean flow conditions. On the other hand, the diffusion across the boundary layer leads the final response of the near wall region. However, the dynamic pressure gradients imposed in the mean flow modulate the viscous properties of the boundary layer through local flow acceleration, transforming the expected pattern.

scholarly journals Rough-wall boundary layers: mean flow universality

2007 ◽  
Vol 585 ◽  
pp. 469-485 ◽  
Author(s):  
IAN P. CASTRO
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Roughness Element ◽  
Momentum Thickness ◽  
Mean Flow ◽  
Layer Depth ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean ◽  
Two Parameter

Mean flow profiles, skin friction, and integral parameters for boundary layers developing naturally over a wide variety of fully aerodynamically rough surfaces are presented and discussed. The momentum thickness Reynolds number Reθ extends to values in excess of 47000 and, unlike previous work, a very wide range of the ratio of roughness element height to boundary-layer depth is covered (0.03 < h/δ > 0.5). Comparisons are made with some classical formulations based on the assumption of a universal two-parameter form for the mean velocity profile, and also with other recent measurements. It is shown that appropriately re-written versions of the former can be used to collapse all the data, irrespective of the nature of the roughness, unless the surface is very rough, meaning that the typical roughness element height exceeds some 50% of the boundary-layer momentum thickness, corresponding to about $h/\delta\,{\widetilde{>}}\,0.2$.

Data Analysis Methods for Stereo PIV of a High Aspect Ratio Flexible Cylinder

2007 ◽  
Author(s):  
D. Furey ◽  
P. Atsavapranee ◽  
K. Cipolla
Keyword(s):  
Boundary Layer ◽  
Data Analysis ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Particle Image Velocimetry Data ◽  
Flow Fields ◽  
Mean Flow ◽  
Boundary Flow ◽  
The Mean ◽  
Cylinder Flow

Stereo Particle Image velocimetry data was collected over high aspect ratio flexible cylinders (L/a = 1.5 to 3 × 105) to evaluate the axial development of the turbulent boundary layer where the boundary layer thickness becomes significantly larger than the cylinder diameter (δ/a&gt;&gt;1). The flexible cylinders are approximately neutrally buoyant and have an initial length of 152 m and radii of 0.45 mm and 1.25 mm. The cylinders were towed at speeds ranging from 3.8 to 15.4 m/sec in the David Taylor Model Basin. The analysis of the SPIV data required a several step procedure to evaluate the cylinder boundary flow. First, the characterization of the flow field from the towing strut is required. This evaluation provides the residual mean velocities and turbulence levels caused by the towing hardware at each speed and axial location. These values, called tare values, are necessary for comparing to the cylinder flow results. Second, the cylinder flow fields are averaged together and the averaged tare fields are subtracted out to remove strut-induced ambient flow effects. Prior to averaging, the cylinder flow fields are shifted to collocate the cylinder within the field. Since the boundary layer develops slowly, all planes of data occurring within each 10 meter increment of the cylinder length are averaged together to produce the mean boundary layer flow. Corresponding fields from multiple runs executed using the same experimental parameters are also averaged. This flow is analyzed to evaluate the level of axisymmetry in the data and determine if small changes in cylinder angle affect the mean flow development. With axisymmetry verified, the boundary flow is further averaged azimuthally around the cylinder to produce mean boundary layer profiles. Finally, the fluctuating velocity levels are evaluated for the flow with the cylinder and compared to the fluctuating velocity levels in the tare data. This paper will first discuss the data analysis techniques for the tare data and the averaging methods implemented. Second, the data analysis considerations will be presented for the cylinder data and the averaging and cylinder tracking techniques. These results are used to extract relevant boundary layer parameters including δ, δ* and θ. Combining these results with wall shear and momentum thickness values extracted from averaged cylinder drag data, the boundary layer can be well characterized.

Effect of non-parallel mean flow on the Green’s function for predicting the low-frequency sound from turbulent air jets

2012 ◽  
Vol 695 ◽  
pp. 199-234 ◽  
Author(s):  
M. E. Goldstein ◽  
Adrian Sescu ◽  
M. Z. Afsar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Low Frequency ◽  
Source Location ◽  
Parallel Flow ◽  
Numerical Calculations ◽  
Mean Flow ◽  
Frequency Sound ◽  
The Mean ◽  
Radiated Sound

AbstractIt is now well-known that there is an exact formula relating the far-field jet noise spectrum to the convolution product of a propagator (that accounts for the mean flow interactions) and a generalized Reynolds stress autocovariance tensor (that accounts for the turbulence fluctuations). The propagator depends only on the mean flow and an adjoint vector Green’s function for a particular form of the linearized Euler equations. Recent numerical calculations of Karabasov, Bogey & Hynes (AIAA Paper 2011-2929) for a Mach 0.9 jet show use of the true non-parallel flow Green’s function rather than the more conventional locally parallel flow result leads to a significant increase in the predicted low-frequency sound radiation at observation angles close to the downstream jet axis. But the non-parallel flow appears to have little effect on the sound radiated at $9{0}^{\ensuremath{\circ} } $ to the downstream axis. The present paper is concerned with the effects of non-parallel mean flows on the adjoint vector Green’s function. We obtain a low-frequency asymptotic solution for that function by solving a very simple second-order hyperbolic equation for a composite dependent variable (which is directly proportional to a pressure-like component of this Green’s function and roughly corresponds to the strength of a monopole source within the jet). Our numerical calculations show that this quantity remains fairly close to the corresponding parallel flow result at low Mach numbers and that, as expected, it converges to that result when an appropriately scaled frequency parameter is increased. But the convergence occurs at progressively higher frequencies as the Mach number increases and the supersonic solution never actually converges to the parallel flow result in the vicinity of a critical- layer singularity that occurs in that solution. The dominant contribution to the propagator comes from the radial derivative of a certain component of the adjoint vector Green’s function. The non-parallel flow has a large effect on this quantity, causing it (and, therefore, the radiated sound) to increase at subsonic speeds and decrease at supersonic speeds. The effects of acoustic source location can be visualized by plotting the magnitude of this quantity, as function of position. These ‘altitude plots’ (which represent the intensity of the radiated sound as a function of source location) show that while the parallel flow solutions exhibit a single peak at subsonic speeds (when the source point is centred on the initial shear layer), the non-parallel solutions exhibit a double peak structure, with the second peak occurring about two potential core lengths downstream of the nozzle. These results are qualitatively consistent with the numerical calculations reported in Karabasov et al. (2011).

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.

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