Turbulence in Accelerating Boundary Layers

HAL (Le Centre pour la Communication Scientifique Directe), 2017

Journal of Turbulence, 2012

Two-point correlations and quadrant two-point correlations (termed and introduced by authors) have been employed in order to study low-and high-speed large-scale structures in the outer region of a turbulent boundary layer subjected to a strong adverse pressure gradient. They are computed with particle image velocimetry (PIV) data comprising of large sets of streamwise-spanwise instantaneous velocity fields at three wall-normal positions (0.2δ, 0.5δ, 0.8δ; δ is the boundary layer thickness) at three different streamwise locations in the adverse-pressure-gradient zone, from downstream of the strong suction peak up to detachment. Two-point correlations of the streamwise velocity fluctuation confirm the existence of alternating zones of high-and low-speed fluid in the middle (0.5δ) and lower (0.2δ) parts of the outer region similar to those observed in the log and wake regions of zero-pressure-gradient turbulent boundary layers. However, the negative-positive-negative pattern of these two-point correlations disappears in the lower part (0.2δ) of the large-velocity-defect zone, i.e. near detachment. In the latter region, the results support the existence of large-scale u-structures, many of which are streamwise elongated, that meander more or are less streamwise aligned than the u-structures elsewhere. The ratio of streamwise to spanwise length scales associated with the twopoint correlations reveals that u-structures in the zero-pressure-gradient cases are more elongated in the streamwise direction than those in the adverse-pressure-gradient cases, especially in the lower part of the boundary layer. The quadrant two-point analysis allows us to discriminate events with respect to the sign of the streamwise velocity fluctuation at the reference and second points in the two-point correlation function. By using this technique, it is found that in the lower part of the outer region, i.e. 0.2δ (in the upper part of boundary layer, i.e. 0.8δ), large-scale high-speed events (low-speed events) are more intense than low-speed (high-speed) ones and also contribute more to the two-point correlations. In the middle of the boundary layer where the maximum turbulence activity occurs, large-scale low-and high-speed motions have comparable intensities and frequencies of occurrence. However, the low-speed events are slightly more intense and seem to be spatially more coherent.

Pranav Joshi (2013). Ph.D. Thesis, Johns Hopkins University.

The present study focuses on the effect of mean (favorable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional particle image velocimetry measurements, some of which are time-resolved, have been performed in multiple streamwise-wall-normal and wall-parallel planes upstream of and within a sink flow region, for two different inlet Reynolds numbers, Re θ (x 1)=3360 and 5285. The corresponding values of the acceleration parameter, K, are 1.3×10-6 and 0.6×10-6 , respectively. The time-resolved data at the lower Reynolds number enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the material acceleration of the fluid. v Finally, I thank my parents and my sister, who have supported me through thick and thin. Words would fail to express my gratitude towards them.

Journal of Fluid Mechanics, 2009

The effects of adverse pressure gradients on turbulent structures were investigated by carrying out direct numerical simulations of turbulent boundary layers subjected to adverse and zero pressure gradients. The equilibrium adverse pressure gradient flows were established by using a power law free-stream distribution U ∞ ∼ x m . Twopoint correlations of velocity fluctuations were used to show that the spanwise spacing between near-wall streaks is affected significantly by a strong adverse pressure gradient. Low-momentum regions are dominant in the middle of the boundary layer as well as in the log layer. Linear stochastic estimation was used to provide evidence for the presence of low-momentum regions and to determine their statistical properties. The mean width of such large-scale structures is closely associated with the size of the hairpin-like vortices in the outer layer. The conditionally averaged flow fields around events producing Reynolds stress show that hairpin-like vortices are the structures associated with the production of outer turbulence. The shapes of the vortices beyond the log layer were found to be similar when their length scales were normalized according to the boundary layer thickness. Estimates of the conditionally averaged velocity fields associated with the spanwise vortical motion were obtained by using linear stochastic estimation. These results confirm that the outer region of the adverse pressure gradient boundary layer is populated with streamwise-aligned vortex organizations, which are similar to those of the vortex packet model proposed by Adrian, Meinhart & Tomkins (J. Fluid Mech., vol. 422, 2000, pp. 1-54). The adverse pressure gradient augments the inclination angles of the packets and the mean streamwise spacing of the vortex heads in the packets.

Experimental Thermal and Fluid Science, 2021

High-spatial-resolution (HSR) two-component, two-dimensional particle-image-velocimetry (2C-2D PIV) measurements of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) and an adverse-pressure-gradient (APG)-TBL were taken in the LMFL High Reynolds number Boundary Layer Wind Tunnel. The ZPG-TBL has a momentum-thickness based Reynolds number Re δ 2 = δ 2 U e /ν = 7, 750 (where δ 2 is the momentum thickness and U e is the edge velocity), while the APG-TBL has a Re δ 2 = 16, 240 and a Clauser's pressure gradient parameter β = δ 1 P x /τ w = 2.27 (where δ 1 is the displacement thickness, P x is the pressure gradient in streamwise direction and τ w is the wall shear stress). After analysing the singleexposed PIV image data using a multigrid/multipass digital PIV (Soria, 1996) with in-house software, proper orthogonal decomposition (POD) was performed on the data to separate flow-fields into large-and small-scale motions (LSMs and SSMs), with the LSMs further categorized into high-and low-momentum events. The LSMs are energized in the outer-layer and this phenomenon becomes stronger in the presence of an adverse-pressure-gradient. Profiles of the conditionally averaged Reynolds stresses show that the high-momentum events contribute more to the Reynolds stresses than the low-momentum between wall to the end of the log-layer and the opposite is the case in the wake region. The cross-over point of the profiles of the Reynolds stresses from the high-and low-momentum LSMs always has a higher value than the corresponding Reynolds stress from the original ensemble at the same wall-normal location. This difference is up to 80% in Reynolds streamwise and shear stresses and up to 15% in the Reynolds wall-normal stresses. Furthermore, the cross-over point in the APG-TBL moves further from the wall than in the ZPG-TBL. By removing the velocity fields with LSMs which contribute significantly to the most energetic POD mode, the estimate of the Reynolds streamwise stress and Reynolds shear stress from the remaining velocity fields is reduced by up to 42% in the ZPG-TBL. The reduction effect is observed to be even larger (up to 50%) in the APG-TBL. However, the removal of these LSMs has a minimal effect on the Reynolds wall-normal stress in both the ZPG and the APG cases.

Journal of Fluid Mechanics, 1987

The coupling between high-amplitude wall-pressure peaks and flow structures, especially in the near-wall region, was studied for a zero-pressure-gradient turbulentboundary-layer flow and for the flow in the interior of artificially generated turbulent spots. By use of an 'enhanced' conditional averaging technique it was shown that buffer region shear-layer structures are to a high degree responsible for the generation of large positive wall-pressure peaks. The relation was proved to be bi-directional in that strong shear layers were shown to accompany positive pressure peaks and correspondingly that large pressure peaks were associated with shear-layer structures detected in the buffer region. This also indicates a link between the wall-pressure peaks and turbulence-producing mechanisms. The pressure-peak amplitude was found to scale linearly with the velocity amplitude of the generating flow structure, indicating that a dominating role here is played by the so-called turbulence-mean shear interaction. The large negative wall-pressure peaks were found to be associated primarily with sweep-type motions. All essential features of the relation between wall-pressure peaks and flow structures in artificially generated spots in a laminar boundary layer were found to be identical to those in the equilibrium turbulent boundary layer.

Journal of Fluid Mechanics, 2011

Experiments have been conducted in a large oscillatory flow tunnel to investigate the effects of acceleration skewness on oscillatory boundary layer flow over fixed beds. As well as enabling experimental investigation of the effects of acceleration skewness, the new experiments add substantially to the relatively few existing detailed experimental datasets for oscillatory boundary layer flow conditions that correspond to full-scale sea wave conditions. Two types of bed roughness and a range of high-Reynolds-number, Re ∼ O(10 6 ), oscillatory flow conditions, varying from sinusoidal to highly acceleration-skewed, are considered. Results show the structure of the intrawave velocity profile, the time-averaged residual flow and boundary layer thickness for varying degrees of acceleration skewness, β. Turbulence intensity measurements from particle image velocimetry (PIV) and laser Doppler anemometry (LDA) show very good agreement. Turbulence intensity and Reynolds stress increase as the flow accelerates after flow reversal, are maximum at around maximum free-stream velocity and decay as the flow decelerates. The intra-wave turbulence depends strongly on β but period-averaged turbulent quantities are largely independent of β. There is generally good agreement between bed shear stress estimates obtained using the loglaw and using the momentum integral equation, and flow acceleration skewness leads to high bed shear stress asymmetry between flow half-cycles. Turbulent Reynolds stress is much less than the shear stress obtained from the momentum integral; analysis of the stress contributors shows that significant phase-averaged vertical velocities exist near the bed throughout the flow cycle, which lead to an additional shear stress, −ρũw; near the bed this stress is at least as large as the turbulent Reynolds stress.

There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, b, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer. Crown

Journal of Physics: Conference Series, 2018

Mean Reynolds stress profiles and instantaneous Reynolds stress structures are investigated in a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL) at the verge of separation using data from direct numerical simulations. The use of a self-similar APG-TBL provides a flow domain in which the flow gradually approaches a constant nondimensional pressure gradient, resulting in a flow in which the relative contribution of each term in the governing equations is independent of streamwise position over a domain larger than two boundary layer thickness. This allows the flow structures to undergo a development that is less dependent on the upstream flow history when compared to more rapidly decelerated boundary layers. This APG-TBL maintains an almost constant shape factor of H = 2.3 to 2.35 over a momentum thickness based Reynolds number range of Re δ 2 = 8420 to 12400. In the APG-TBL the production of turbulent kinetic energy is still mostly due to the correlation of streamwise and wall-normal fluctuations, uv , however the contribution form the other components of the Reynolds stress tensor are no longer negligible. Statistical properties associated with the scale and location of sweeps and ejections in this APG-TBL are compared with those of a zero pressure gradient turbulent boundary layer developing from the same inlet profile, resulting in momentum thickness based range of Re δ 2 = 3400 to 3770. In the APG-TBL the peak in both the mean Reynolds stress and the production of turbulent kinetic energy move from the near wall region out to a point consistent with the displacement thickness height. This is associated with a narrower distribution of the Reynolds stress and a 1.6 times higher relative number of wall-detached negative uv structures. These structures occupy 5 times less of the boundary layer volume and show a similar reduction in their streamwise extent with respect to the boundary layer thickness. A significantly lower percentage of wall-attached structures is observed in the present case when compared with a similar investigation of a rapidly decelerating APG-TBL, suggesting that these wall-attached features could be the remanent from the lower pressure gradient domain upstream.

Journal of Fluid Mechanics, 2005

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds number approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds number and have the same order of magnitude, there is additional theoretical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall. † A similar presentation of stress-gradient ratio data was earlier given by Cenedese, , but only explored in the context of viscous sublayer structure.

Physics of Fluids, 2001

Based upon high resolution LDA measurements over a range of momentum deficit thickness Reynolds numbers (Rθ=U∞θ/ν) from 1430 to 31 000, DeGraaff and Eaton [J. Fluid Mech. 422, 319 (2000)] propose a new mixed scaling for the near-wall region profile of the axial turbulent stress, u2¯. The present results support the validity of this scaling over an extended Reynolds number range 1000⩽Rθ⩽5×106.

Journal of Fluid Mechanics, 2013

The positive and negative high-amplitude pressure peaks (HAPP) are investigated in a turbulent boundary layer at $R{e}_{\theta } = $ 1900 in order to identify their turbulent structure. The three-dimensional velocity field is measured within the inner layer of the turbulent boundary layer using tomographic particle image velocimetry (tomo-PIV). The measurements are performed at an acquisition frequency of 10 000 Hz and over a volume of $418\times 149\times 621$ wall units in the streamwise, wall-normal and spanwise directions, respectively. The time-resolved velocity fields are applied to obtain the material derivative using the Lagrangian method followed by integration of the Poisson pressure equation to obtain the three-dimensional unsteady pressure field. The simultaneous volumetric velocity, acceleration, and pressure data are conditionally sampled based on local maxima and minima of wall pressure to analyse the three-dimensional turbulent structure of the HAPPs. Analysis has as...

2016

Adverse pressure gradient (APG) turbulent boundary layer (APG-TBL) flow are pervasive throughout engineering and geophysical flows, yet the least is known of the physics of these wall-bounded flows. This paper reports on certain aspects of an international collaborative experiment that was undertaken under the auspices of EuHIT to quantify the statistical and detailed structure of an APG-TBL that develops on an inclined wall from a high Reynolds number upstream zero-pressure gradient (ZPG) turbulent boundary layer (ZPG-TBL) flow as depicted in Fig. 1. Specifically in this paper the spatially resolved wall shear stress distribution and the temporally resolved wall-normal distribution of the streamwise and wall-normal velocity at Position 1 shown in Fig. 1 will be reported and analysed in this paper.