Adverse Pressure Gradient Turbulent Boundary Research Articles

Spatial Averaging Effects in Adverse Pressure Gradient Turbulent Boundary Layers

Spatial Averaging Effects in Adverse Pressure Gradient Turbulent Boundary Layers

Hot-wire spatial resolution issues in adverse pressure gradient turbulent boundary layers

The effect of a finite length of hot-wire probe sensor length on the measured streamwise velocity fluctuations is well understood in canonical wall-bounded flow, where the small-scale energy has been found to be universal and invariant with Reynolds number. A straightforward application of that assumption to non-canonical flows such as strong adverse pressure gradient (APG) flows has, however, been hampered since the effect of Re and APG could not conclusively be studied separately due to the lack of data with a clear scale separation. The present experimental investigation at Reτ≈4000 in weak, moderate and strong APGs with different wire length shows that spatial averaging effects are not only limited to the inner layer. A note of caution is hence warranted for measurements that seemingly try to take the bias effect of spatial attenuation into account by performing measurements with albeit long but fixed viscous-scaled wire length.

Aeroacoustics of a ducted fan ingesting an adverse pressure gradient boundary layer

The aeroacoustics of a boundary layer ingesting (BLI) ducted fan is investigated experimentally. The study examines a ducted fan immersed in an adverse streamwise pressure gradient turbulent boundary layer developed over a curved wall. Aeroacoustics measurements indicate that the noise from the BLI ducted fan results from a complex interaction among the fan, duct and the incoming boundary layer. The fundamental mechanisms of noise generation are explained using a general source separation strategy. A detailed noise comparison is made at varying fan rotational speeds and across a wide range of axial inflow velocities. In a low thrust regime, the noise is found to be driven by the fan loading, coupled with duct acoustics and the haystacking phenomenon. In a high thrust regime, the contribution from duct acoustics diminishes, and the noise is predominantly driven by the fan loading coupled with the haystacking phenomenon.

Turbulent activity in the near-wall region of adverse pressure gradient turbulent boundary layers

Two direct numerical simulation (DNS) databases are investigated to understand the effect of the outer-layer turbulence on the inner layer’s structures and energy transfer mechanisms. The first DNS database is the non-equilibrium adverse-pressure-gradient (APG) turbulence boundary layer (TBL) of Gungor et al. [1]. Its Reynolds number and the inner-layer pressure gradient parameter reach above 8000 and 10, respectively. The shape factor spans between 1.4 and 3.3, which indicates the flow has various velocity defect situations. The second database is the same flow as the first one but the outer layer turbulence is artificially eliminated in this flow. Turbulence is removed above 0.15 local boundary layer thickness. For the analysis, we chose four streamwise positions with small, moderate, large, and very-large velocity defect. We compare the wall-normal distribution of Reynolds stresses, two-point correlations and spectral distributions of energy, production and pressure strain. The results show that the inner layer turbulence can sustain itself when the outer-layer turbulence does not exist regardless of the velocity defect or the pressure gradient. The two-point correlations of both cases show that outer large-scale structures affect the inner layer structures significantly. The streamwise extent of the correlation contours scales with pressure-viscous units. This shows the importance of the pressure gradient’s effect on the inner-layer structures. The spectral distributions demonstrate that the energy transfer mechanisms are probably the same in the inner layer regardless of the velocity defect, which suggests the near-wall cycle may exist even in very-large defect APG TBLs where the mean shear in the inner layer is considerably lower than small-defect APG TBLs.

Consistent outer scaling and analysis of adverse pressure gradient turbulent boundary layers

Under adverse pressure gradient (APG) conditions, the outer regions of turbulent boundary layers (TBLs) are characterized by an increased velocity defect $U_{e}-U$ , an outwards shift of the peak value of the Reynolds shear stress $-\langle uv\rangle$ and an appearance of the outer peak value of the Reynolds normal stress $\langle uu\rangle$ . Here $U_{e}$ is the TBL edge velocity. Scaling APG TBLs is challenging due to the non-equilibrium effects caused by changes in the APG. To address this, the response distance of TBLs to non-equilibrium conditions is utilized to extend the Zagarola–Smits scaling $U_{zs} = U_{e}({\delta ^{*} }/{\delta })$ and ensure that the original properties of the Zagarola–Smits scaling are maintained as $Re \to \infty$ . Here $\delta ^{*}$ is the displacement thickness and $\delta$ is the boundary layer thickness. Based on the established correlation between $U_{e}-U$ and $-\langle uv\rangle$ , the scaling is extended to $-\langle uv\rangle$ . Furthermore, considering the coupling relationship between Reynolds stress components, the scaling is extended to encompass each Reynolds stress component. The proposed consistent scaling is verified using five non-equilibrium databases and five near-equilibrium databases, successfully collapsing the data of the TBL outer region. The pressure gradient parameter $\beta =({\delta ^{*} }/{\rho u_{\tau }^{2} }) ({\mathrm {d} P_{e} }/{\mathrm {d}\kern0.7pt x})$ of these databases spans two orders of magnitude. Here $P_{e}$ is the boundary layer edge pressure, $u_{\tau }$ is the friction velocity and $\rho$ is the density. Finally, the influence of the APG on the inner and outer regions of TBLs is analysed using the mean momentum balance equation. The analysis suggests that the shift of the $-\langle uv\rangle$ peak to the outer region under APG conditions is due to an insufficient inertia term near the inner region to balance the APG. It is observed that the APG promotes interaction between the inner and outer regions of TBLs, but the inner and outer regions still retain distinctive properties.

Direct numerical simulation of adverse pressure gradient turbulent boundary layer up to [formula omitted

A direct numerical simulation of a moderate adverse pressure gradient turbulent boundary layer flow on a flat plate was performed on a fairly long domain with a Reynolds number from Reθ≃2000 to Reθ≃8000. The mean streamwise velocity profile does not exhibit a clear log region even at the highest Reynolds number. The Reynolds stresses exhibit a well defined peak in the outer region which moves away from the wall before to stabilise at a wall distance y of 0.45 boundary layer thickness after evolving over 20 local boundary layer thicknesses. These outer peaks are the consequences of an excess of production over dissipation and they all scale with the shear stress velocity for wall distance 0.2δ<y<0.85δ. The different terms of the Reynolds stresses equations are analysed in the outer region and the analysis confirms that the leading terms are the same as for a zero pressure gradient turbulent boundary layer except that the production and dissipation are not negligible in the outer region. The most significant contribution of scales smaller than two Taylor scales is on the pressure strain term of the shear stress equation. The probability of the occurrence of small scale vortices conditioned by the presence of an ejection or a sweep shows that the shear stress contained in ejections is associated with the production and transport of near wall vortices away from the wall. The local mean shear generated by the sweeps increases the production of near wall vortices. Lastly, the large scale structures analysed by means of two point correlations of the streamwise fluctuating velocity are shown to be strongly modified by the adverse pressure gradient. The correlation reveals a decoupling between the near wall streaks and the large scale streamwise structures enhanced by the adverse pressure gradient.

A family of adverse pressure gradient turbulent boundary layers with upstream favourable pressure gradients

A flat-plate turbulent boundary layer (TBL) is experimentally subjected to a family of 22 favourable–adverse pressure gradients (FAPGs) using a ceiling panel of variable convex curvature. We define FAPGs as a sequence of streamwise pressure gradients in the order of favourable followed by adverse, similar in sequence to the pressure gradients over the suction side of an airfoil. For the strongest pressure gradient case, the acceleration parameter, $K$ , varied spatially from $6 \times 10^{-6}$ to $- 4.8 \times 10^{-6}$ . The adverse pressure gradient (APG) region of this configuration is studied using particle image velocimetry in the streamwise–wall-normal plane. The statistics of the APG TBL show that the upstream favourable pressure gradient (FPG) exerts a strong and lasting downstream influence, and that the rapid spatial changes in the pressure gradients imposed cause an internal boundary layer to grow within the TBL for 15 of the cases studied. The internal layer typically occupies 20 $\%$ of the boundary layer thickness and dominates the boundary layer response, containing the peak turbulent production, peak strength and population of vortices, and most of the spectral energy content of the flow. The outer layer, on the other hand, develops in the APG region without considerable changes to the state dictated by the upstream FPG. These trends are in contrast to APG TBLs that originate from a zero pressure gradient region, where the outer/wake region is known to dominate TBL response. The observed changes are quantified across the family of FAPGs imposed.

Turbulent superstructure statistics in a turbulent boundary layer with pressure gradients

In turbulent boundary layers, streamwise elongated regions of high- and low-momentum in the log-law layer that can extent up to several boundary layer thicknesses are often referred to as turbulent superstructures. These structures contain a relatively large portion of the layer’s turbulent kinetic energy and have been shown to interact with the near-wall flow structures. In the last few decades extensive research on zero-pressure gradient (ZPG) turbulent boundary layers has been done, however by comparison, the structural characteristics for adverse pressure gradient turbulent (APG) boundary layer flows are much less studied despite their strong significance aero-hydrodynamic vehicle design. Therefore, the three-dimensional dynamics of turbulent superstructures in a turbulent boundary layer flow are investigated in the Atmospheric Wind Tunnel Munich (AWM) using a multi-camera 3D time-resolved Lagrangian particle tracking approach. In this study, Lagrangian and Eulerian statistics will be used to characterize the dynamics and interaction of turbulent superstructures within a zero pressure gradient (ZPG) turbulent boundary layer at Reτ = 5000 or Reθ = 14 000 that then flows over a curved plate subjected to a favorable (FPG) and strong adverse (APG) pressure gradient, which eventually separates. An Eulerian analysis, using multi-point correlations of 3D velocity fields, found that the average superstructure topology is modulated by decelerating flow in the APG region when compared to the ZPG region, however the basic shape and spanwise pattern is preserved. Looking into the behavior of individual trajectories, it was found that the dispersion of single particles along trajectories in the log-law layer are capable of moving more than the average Eulerian superstructure spacing in the spanwise direction. Furthermore, the mean square of the single particle dispersion indicates that the maximum dispersion in the spanwise direction comes from particles released at the wall-normal location corresponding to the so-called “second-peak/plateau” region in the streamwise normal Reynolds stress.

Velocity spectra and scale decomposition of adverse pressure gradient turbulent boundary layers considering history effects

Experiments at relatively large Reynolds number were conducted to better understand the influence of an adverse pressure gradient on the turbulence in two-dimensional boundary layer flows. One focus is on documenting the scale contributions to the Reynolds normal and shear stress profiles under the influence of a positive streamwise pressure gradient. Toward these aims, velocity spectra at friction Reynolds numbers (7100≤Reτ≤8600) are presented, analyzed, and compared to a zero pressure gradient case from the same facility at nominally matching Reynolds number. Distance-from-the-wall scaling is central to numerous theoretical and modeling considerations of the canonical flat plate flow. Consistently, the present spectral measurements reveal clear evidence for its preservation on the inertial sublayer under modest adverse pressure gradients. Increases are seen in the viscous-scaled premultiplied spectra in the outer region as the pressure gradient increases — commensurate with the increases observed in the outer peaks of the streamwise and wall-normal velocity variances, as well as the Reynolds shear stress. Effects of varying Reτ on the streamwise and wall-normal velocity variances and the Reynolds shear stress are studied by comparing the present data at varying Clauser pressure gradient parameter, β, with previous experiments having similarly varying β at significantly lower Reτ (≈1900). This allows to study the effects of changing Reynolds number at matched β. Cases at similar β and Reynolds number, but with varying flow history are also examined, wherein the same β value is arrived either by starting from a smaller or larger initial β. The effects of β>0 on the large and small scale motions are investigated by segregating the signal contributions according to a cut-off wavelength established in previous zero pressure gradient flows. Under a normalization that uses a hybrid velocity scale this analysis reveals similarity between the outer regions of the spectrally-decomposed variances and Reynolds shear stress. These analyses also reveal a more dramatic reduction in the near-wall large scale contribution to the Reynolds shear stress gradient in the β>0 flow when compared to the β=0 flow.

Energy transfer mechanisms in adverse pressure gradient turbulent boundary layers: production and inter-component redistribution

Production and inter-component redistribution of turbulence in adverse pressure gradient (APG) turbulent boundary layers (TBLs) with small and large velocity defects are investigated, along with the structures playing a role in these energy transfer mechanisms. We examine the wall-normal and spectral distributions of energy, production and pressure-strain in APG TBLs, and compare these distributions with those in canonical flows. It is found that the spectral distributions of production and pressure-strain are not affected profoundly by an increase of the velocity defect, although the energy spectra change drastically in the inner layer of the large-defect APG TBL. In the latter, the signature of the inner-layer streaks is absent from the energy spectra. In the outer layer, energetic, production and pressure-strain structures appear to change from wall-attached to wall-detached structures with increasing velocity defect. Despite this, the two-dimensional spectral distributions have similar shapes and wavelength aspect ratios of the peaks in all these flows. Therefore, the conclusion is that the mechanisms responsible for turbulence production and inter-component energy transfer may remain the same within each layer in all these flows. It is the intensity of these mechanisms within one layer that changes with velocity defect, because of the local mean shear variation.

Intense large-scale motions in zero and adverse pressure gradient turbulent boundary layers

Proper orthogonal decomposition (POD) is used to study coherent structures in wall-bounded turbulent flows. The present study uses POD in turbulent boundary layers to determine the contributions of the intense large-scale motions (LSMs) to the Reynolds stresses. This study uses the 2C-2D PIV measurements of zero pressure gradient turbulent boundary layers (ZPG-TBL) at Re_{δ2} = 7750, and adverse pressure gradient turbulent boundary layer (APG-TBL) at β = 2.27 and Re_{δ2}= 16240, where Re_{δ2} is the momentum thickness based Reynolds number and β is the Clauser’s pressure gradient parameter. The measurements were obtained in the Laboratoire de Mécanique des Fluides de Lille (LMFL) High-Reynolds-Number (HRN) Boundary Layer Wind Tunnel, Lille, France. The snapshots of the flow field are segregated into those dominated by the intense and mild LSMs based on the intensity of the temporal coefficients of the first POD mode. The intense LSMs are further decomposed into high-momentum (HM) and low-momentum (LM) motions. The relative contributions of the HM motions to the Reynolds stresses are larger near the wall as compared to the LM motions. At the wall-normal distance of the displacement thickness (δ1), HM and LM motions have similar contributions. Beyond δ1, the LM motions have larger contributions with their peaks located closer to the displacement thickness height. This shows that in the presence of an APG, the turbulence activity is shifted closer to the displacement thickness height.

Stress equation based scaling framework for adverse pressure gradient turbulent boundary layers

This paper provides a framework for estimating appropriate turbulent velocity scales in adverse pressure gradient turbulent boundary layers (APG TBLs) via a study of the mean stress balance. We examine the velocity scales of APG TBLs using the relationship between the Reynolds shear stress and pressure stress. It is reasoned that as distance from the wall increases the velocity scaling transitions from one dominated by the wall-shear-stress velocity scale, uτ, to a scaling dominated by the pressure stress. A velocity scale, uhyb, is proposed that varies with distance from the wall and combines the wall-shear-stress velocity with a pressure-stress-based velocity. This investigation uses new high Reynolds number (7000≲Reτ≲7800) experimental measurements, existing lower Reynolds number experimental (600≲Reτ≲2000) and computational (Reτ<700) data sets. The proposed velocity scale realizes similarity in the turbulent stress profiles to a degree that is superior to that achievable via any wall-distance-independent velocity scale when considering the full extent of the flow domain.

Investigation of Large Scale Motions in Zero and Adverse Pressure Gradient Turbulent Boundary Layers Using High-Spatial-Resolution PIV

Particle image velocimetry (PIV) has been used to capture the high-spatial-resolution (HSR) two-component, two-dimensional (2C-2D) velocity fields of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) and of an adverse-pressure-gradient (APG) TBL. Proper Orthogonal Decomposition (POD) is performed on the measured velocity fields to characterize the velocity fields as large or small scale motions (LSMs or SSMs), with further characterisation of the LSMs into high and low momentum events. This paper reports the findings of the PIV experiment and the subsequent analysis of the high Reynolds number ZPG and APG TBLs

Investigation of large scale motions in zero and adverse pressure gradient turbulent boundary layers using high-spatial-resolution particle image velocimetry

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 Laboratoire de Mécanique des Fluides de Lille (LMFL) High Reynolds number Boundary Layer Wind Tunnel. The ZPG-TBL has a momentum-thickness based Reynolds number Reδ2=δ2Ue∕ν=7,750 (where δ2 is the momentum thickness and Ue is the edge velocity), while the APG-TBL has a Reδ2=16,240 and a Clauser’s pressure gradient parameter β=δ1Px∕τw=2.27 (where δ1 is the displacement thickness, Px is the pressure gradient in streamwise direction and τw is the wall shear stress). The 2C fluctuating flow field of each TBL was decomposed using proper orthogonal decomposition (POD) to investigate the large-scale motions (LSMs). The LSMs are found to be energized in the outer-layer, becoming stronger in the presence of the adverse-pressure-gradient. Profiles of the conditionally averaged Reynolds stresses show that high-momentum LSMs contribute more to the Reynolds stresses than low-momentum LSMs from the wall to the end of the log-layer while the opposite is found in the wake region. The cross-over point between the profiles of the conditionally averaged Reynolds stresses from the high- and low-momentum LSMs always has a higher value than the corresponding Reynolds stress from the unconditional ensemble average at the same wall-normal location. This difference is up to 80% in the Reynolds streamwise and shear stresses and up to 15% in the Reynolds wall-normal stresses. Furthermore, the cross-over point in the APG-TBL is found to be further from the wall than in the ZPG-TBL. The conditional Reynolds streamwise and shear stresses without the LSMs are reduced by up to 42% in the ZPG-TBL and by up to 50% in the APG-TBL, while having a minimal effect on the conditional Reynolds wall-normal stress without the LSMs in both the ZPG- and APG-TBL.

The effects of minute vortex generator jet in a turbulent boundary layer with adverse pressure gradient.

Experimental and numerical analysis of active and passive flow control is an important topic of practical value in the study of turbulent flows. This paper numerically analyzed the effects of an air microjet on an adverse pressure gradient turbulent boundary layer over a flat plane. Experimental data were employed to verify the numerical modeling. Vortex formation and development were then studied by changing the microjet to inflow velocity ratio (VR) and microjet angles. According to the results, the best values of the angles and for various velocities were found to be 30° and from 60° to 90°, respectively. Moreover, at VRs = 1, 2, and 4, the values (the distance at which the complete vortex persisted in the flow) were 0.058, 0.078, and 0.18, respectively. Compared to VR = 1, the vortex strength for VRs = 2 and 4 grew by 3.5 and 6.8 times, respectively. When the microjet was added to the flow, the highest variation in the Reynolds stress along the x-direction from VR = 1-4 was 10%. The corresponding values along the y and z- directions were 15% and 2.7 times, respectively.

Superstructures in turbulent boundary layers with pressure gradients

AbstractLarge‐scale coherent structures have been observed in various wall‐bounded turbulent flows. In turbulent boundary layers, streamwise elongated regions of high‐ and low‐momentum in the log‐law layer that can extent up to several boundary layer thicknesses are often referred to as superstructures. These structures contain a relatively large portion of the layer's turbulent kinetic energy and have been shown to interact with the near‐wall features. In the last few decades extensive research on zero‐pressure gradient turbulent boundary layers has been done, however by comparison, the structural characteristics for adverse pressure gradient turbulent boundary layer flows are much less studied. Therefore, the three‐dimensional dynamics of turbulent superstructures in a turbulent boundary layer flow is investigated in the Atmospheric Wind Tunnel Munich (AWM) measurement using a novel multi‐camera 3D time‐resolved Lagrangian particle tracking approach. In this study, the structural properties and dynamics of turbulent superstructures within a zero pressure gradient (ZPG) turbulent boundary layer at Reτ = 5000 or Reθ = 14000 that then flows over a curved plate subjected to a favorable (FGP) and strong adverse (APG) pressure gradient, which eventually separates, is considered. It was found that while the average superstructure topology is modulated by decelerating flow in the APG when compared to the ZPG region the basic shape and pattern is preserved.

The turbulent/non-turbulent interface in an adverse pressure gradient turbulent boundary layer

The turbulent/non-turbulent interface (TNTI) in an adverse pressure gradient (APG, β = 1.45) turbulent boundary layer (TBL) is explored here by using direct numerical simulation (DNS) data; β is the Clauser pressure gradient parameter. For comparison, the DNS data for a zero pressure gradient (ZPG) TBL is included. The interface is extracted with an approach based on enstrophy criteria. Depending on the enstrophy, the outer boundary layer flow can be classified into the free stream, boundary layer wake, and intermittent flow regimes. The fractal dimension of the interface is obtained by using the box-counting algorithm, and was found to be constant over a long range of box sizes. The TNTI shows a monofractal behavior. The geometric complexity of a TNTI can be determined in terms of the genus, which is defined as the number of handles in a geometric object. We examine the volume and projection area of the genus of the TNTI to analyze the entrainment process. The geometric complexity of the APG TBL interface and the local entrainment are greater than those of the ZPG TBL, as is evident in the increases in the genus near the interface. The local entrainment velocity is dominantly affected by the viscous diffusion at the interface.

Analysis of the spanwise extent and time persistence of uniform momentum zones in zero pressure gradient and adverse pressure gradient turbulent boundary layers

Time-resolved velocity fields from direct numerical simulations (DNS) are used to investigate the spanwise extent and the time persistence of uniform momentum zones (UMZs) in a zero pressure gradient turbulent boundary layer (ZPG-TBL) and a self-similar adverse pressure gradient turbulent boundary layer (APG-TBL) at the verge of separation. The instantaneous detection methodology introduced by Adrian et al. [1] is used to detect the UMZs and is extended to take into account the spanwise domain length and the temporal evolution of the UMZs. The Reynolds number based on friction velocity (Reτ) ranges from 1176 to 1277 for the ZPG-TBL and from 1652 to 1745 for the self-similar APG-TBL within the domain of interest. For both the TBL cases, probability density functions (PDFs) of the number of UMZs are computed as a function of the streamwise extent, spanwise extent and time extent. For the ZPG-TBL, when the streamwise length of the domain is greater than or equal to 3 boundary layer thickness, the probability of finding 4 UMZs becomes almost negligible. For the APG-TBL, even when the streamwise domain length is taken as large as 1.3 boundary layer thickness, the probability of finding 4 UMZs is still significant. The spanwise extent of the UMZs is found to be shorter than their streamwise extent regardless of the pressure gradient in the flow. In the ZPG-TBL flow, the majority of the UMZs have a spanwise extent of the order of one-tenth of a boundary layer thickness while for the APG-TBL, it is found to be on the order of one-hundredth of a boundary layer thickness. In the ZPG-TBL, the probability of finding 2 UMZs that persist over a time period of 2 integral time scale is around 50%. Similarly, for the APG-TBL, the probability of finding 2 UMZs with a time persistence of 0.4 integral time scale is over 50%. In the case of the ZPG-TBL, it is observed that some of the UMZs with higher persistence in time have higher streamwise momentum and are found to be closer to the free-stream in general. This result is consistent with the previous observations by Laskari et al. [2]. In contrast, for the APG-TBL, UMZs with longer time persistence are found closer to the wall with lower streamwise momentum.

Analysis of the factors contributing to the skin friction coefficient in adverse pressure gradient turbulent boundary layers and their variation with the pressure gradient

This paper reports on a study of the various factors contributing to the skin friction in incompressible adverse pressure gradient turbulent boundary layer (APG-TBL) flows. Specifically, it deals with the contributions to the skin friction coefficient from the Reynolds stresses and the viscous effects and the role of the pressure gradient. The skin friction coefficient is calculated based on the theoretical decomposition for mean skin friction generation introduced by Renard and Deck (2016). This decomposition is compatible with spatially developing flows as it is applicable to every local streamwise position. The turbulent flows are generated through the direct numerical simulation of a TBL on a smooth flat plate with the desired farfield pressure gradient. It is observed that the Reynolds shear stress provides the dominant positive contribution to the skin friction coefficient for all the pressure gradient cases. However, with increasing adverse pressure gradient, the skin friction coefficient continues to decrease and approaches zero as the positive contribution from the Reynolds shear stress is diminished by the negative contribution of the pressure gradient. When the flow reaches the verge of separation, the predominant Reynolds shear stress contribution to the skin friction coefficient is from a spatially localized outer peak at an approximate height of the displacement thickness (y=δ1) which coincides with the inflection point of the mean streamwise velocity. Even though, the decompositions in Renard and Deck (2016) and Fukagata et al. (2002) give a different distribution for the skin friction coefficient in the zero pressure gradient (ZPG) and the mild APG cases, both of the identities capture the dominant outer peak of the Reynolds shear stress contribution when the flow reaches the verge of separation. This emphasizes the growing importance of the outer layer dynamics with increasing pressure gradient as it pertains to skin friction generation.

Characterisation of uniform momentum zones in adverse pressure gradient turbulent boundary layers

Uniform momentum zones (UMZs) for an adverse pressure gradient turbulent boundary layer (APG-TBL) are characterised in this paper.The database described by Cuvier et al.(2017), which was obtained using 2-component 2-dimensional (2C-2D) particle image velocimetry (PIV) at two free-stream velocities of 5 m/s and 9 m/s, is used for this study.The methodology described by Adrian et al.(2000) is used to identify and hence, statistically characterise the UMZs and UMZ interfaces in the APG-TBL. This study shows that the number of detected UMZs increases in the streamwise direction for both free-stream velocities.This increase is primarily thought to be due to the adverse pressure gradient (APG) since a comparison of the results between the two free-stream velocity APG-TBLs did not show any statistically significant difference with Reθ for the range of Reynolds number examined in this study.The thickness of the UMZs, δw and the jump in streamwise velocity across the UMZ interface were found to increase in the wall-normal direction, whereas the width of the UMZ interface, Δu, was found to decrease.The number of UMZs, Numz, identified appeared to influence the modal velocities/uniform velocities, geometrical properties of the UMZs and statistics of the flow.With increasing Numz, the modal velocities of the UMZs moved to higher values to accommodate new UMZs that developed closer to the wall and the thickness of each UMZ andΔu across the UMZ interface decreased, whereas δw increased. A slight difference in the magnitude of streamwise Reynolds stress and Reynolds shear stress was observed in the inner and outer regions, and a slight difference in the magnitude of turbulence production was also observed in the inner region between the velocity fields having a low or high number of UMZs indicating that the flow statistics are influenced by the number of UMZs present in the APG-TBL.