Modification of Turbulence in Boundary Layers by Mean and Fluctuating Pressure Gradients

2012 ◽  
Author(s):  
Pranav Joshi ◽  
Xiaofeng Liu ◽  
Joseph Katz
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Wall Region ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Time Resolved ◽  
Freestream Velocity ◽  
Vortical Structures ◽  
Fluctuating Pressure ◽  
Near Wall

In this study we focus on the effect of mean and fluctuating pressure gradients on the structure of boundary layer turbulence. Two dimensional, time-resolved PIV measurements have been performed upstream of and inside an accelerating sink flow for inlet Reynolds number of Reθ = 3071, and acceleration parameter of K=1.1×10−6. The time-resolved data enables us to calculate the planer projection of pressure gradient by integrating the in-plane components of the material acceleration of the fluid (neglecting out-of-plane contribution). We use it to study the effect of boundary layer scale fluctuating pressure gradients ∂p′~/∂x, which are expected to be mostly two-dimensional, on the flow structure. Due to the imposed mean favorable pressure gradient (FPG) within the sink flow, the Reynolds stresses normalized by the local freestream velocity decrease over the entire boundary layer. However, when scaled by the inlet freestream velocity, the stresses increase close to the wall and decrease in the outer part of the boundary layer. This trend is caused by the confinement of the newly generated vortical structures in the near-wall region of the accelerating flow due to combined effects of downward mean flow, and stretching by velocity gradients. Within both the zero pressure gradient (ZPG) and FPG boundary layers, sweeping motions mostly occur during positive fluctuating pressure gradients ∂p′~/∂x>0 as the fluid moving towards the wall is decelerated by the presence of the wall. Vorticity is depleted in the near-wall region, as the wall absorbs −ω′ from the flow by viscous diffusion. On the other hand, ejections occur mostly during periods of favorable fluctuating pressure gradients ∂p′~/∂x<0. During these periods, there is more viscous flux of vorticity −ω′ into the flow, since ∂−ω′/∂y<0 at the wall. Large scale ejection motions associated with ∂p′~/∂x<0 are more likely to transport smaller scale turbulence to the outer region of the boundary layer, while turbulence remains largely confined close to the wall due to the sweeping motions accompanying ∂p′~/∂x>0. During periods of ∂p′~/∂x>0 in the ZPG boundary layer, sweeps tend to increase the momentum in the near-wall region, whereas the adverse pressure gradient decelerates the fluid. These competing effects result in an unstable ω′<0 shear layer which rolls up into coherent vortical structures and increases ω′ω′ near the wall as compared to periods of ∂p′~/∂x<0. Due to the strong mean acceleration of the flow and weaker sweeps in the FPG boundary layer, the formation of an unstable shear layer, and hence vortical structures, is suppressed, decreasing the enstrophy close to the wall as compared to periods of ∂p′~/∂x<0.

The Effects of Spatial Resolution in Turbulent Boundary Layers with Pressure Gradients

2012 ◽  
Vol 225 ◽  
pp. 109-117 ◽  
Author(s):  
Zambri Harun ◽  
Mohamad Dali Isa ◽  
Mohammad Rasidi Rasani ◽  
Shahrir Abdullah
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Spatial Resolution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Wall Region ◽  
Pressure Gradients ◽  
Layer Flow ◽  
Near Wall

Single normal hot-wire measurements of the streamwise component of velocity were taken in boundary layer flows subjected to pressure gradients at matched friction Reynolds numbers Reτ ≈ 3000. To evaluate spatial resolution effects, the sensor lengths are varied in both adverse pressure gradient (APG) and favorable pressure gradient (FPG). A control boundary layer flow in zero pressure gradient ZPG is also presented. It is shown here that, when the sensor length is maintained a constant value, in a contant Reynolds number, the near-wall peak increases with (adverse) pressure gradient. Both increased contributions of the small- and especially large-scale features are attributed to the increased broadband turbulence intensities. The two-mode increase, one centreing in the near-wall region and the other one in the outer region, makes spatial resolution studies in boundary layer flow more complicated. The increased large-scale features in the near-wall region of an APG flow is similar to large-scales increase due to Reynolds number in ZPG flow. Additionally, there is also an increase of the small-scales in the near-wall region when the boundary layer is exposed to adverse pressure gradient (while the Reynolds number is constant). In order to collapse the near-wall peaks for APG, ZPG and FPG flows, the APG flow has to use the longest sensor and conversely, the FPG has to use the shortest sensor. This study recommends that the empirical prediction by Huthins et. al. (2009) to be reevaluated if pressure gradient flows were to be considered such that the magnitude of the near-wall peak is also a function of the adverse pressure gradient parameter.

Effect of mean and fluctuating pressure gradients on boundary layer turbulence

2014 ◽  
Vol 748 ◽  
pp. 36-84 ◽  
Author(s):  
Pranav Joshi ◽  
Xiaofeng Liu ◽  
Joseph Katz
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Small Scale ◽  
Pressure Gradients ◽  
Time Resolved ◽  
Boundary Layer Turbulence ◽  
Scale Turbulence ◽  
Near Wall

AbstractThis study focuses on the effects of mean (favourable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) particle image velocimetry (PIV) measurements, some of which are time-resolved, have been performed upstream of and within a sink flow for two inlet Reynolds numbers, ${Re}_{\theta }(x_{1})=3360$ and 5285. The corresponding acceleration parameters, $K$, are ${1.3\times 10^{-6}}$ and ${0.6\times 10^{-6}}$. The time-resolved data at ${Re}_{\theta }(x_{1})=3360$ enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the fluid material acceleration. As expected, all the locally normalized Reynolds stresses in the favourable pressure gradient (FPG) boundary layer are lower than those in the zero pressure gradient (ZPG) domain. However, the un-scaled stresses in the FPG region increase close to the wall and decay in the outer layer, indicating slow diffusion of near-wall turbulence into the outer region. Indeed, newly generated vortical structures remain confined to the near-wall region. An approximate analysis shows that this trend is caused by higher values of the streamwise and wall-normal gradients of mean streamwise velocity, combined with a slightly weaker strength of vortices in the FPG region. In both boundary layers, adverse pressure gradient fluctuations are mostly associated with sweeps, as the fluid approaching the wall decelerates. Conversely, FPG fluctuations are more likely to accompany ejections. In the ZPG boundary layer, loss of momentum near the wall during periods of strong large-scale adverse pressure gradient fluctuations and sweeps causes a phenomenon resembling local 3D flow separation. It is followed by a growing region of ejection. The flow deceleration before separation causes elevated near-wall small-scale turbulence, while high wall-normal momentum transfer occurs in the ejection region underneath the sweeps. In the FPG boundary layer, the instantaneous near-wall large-scale pressure gradient rarely becomes positive, as the pressure gradient fluctuations are weaker than the mean FPG. As a result, the separation-like phenomenon is markedly less pronounced and the sweeps do not show elevated small-scale turbulence and momentum transfer underneath them. In both boundary layers, periods of acceleration accompanying large-scale ejections involve near-wall spanwise contraction, and a high wall-normal momentum flux at all elevations. In the ZPG boundary layer, although some of the ejections are preceded, and presumably initiated, by regions of adverse pressure gradients and sweeps upstream, others are not. Conversely, in the FPG boundary layer, there is no evidence of sweeps or adverse pressure gradients immediately upstream of ejections. Apparently, the mechanisms initiating these ejections are either different from those involving large-scale sweeps or occur far upstream of the peak in FPG fluctuations.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

Influence of large-scale motions on the frictional drag in a turbulent boundary layer

2017 ◽  
Vol 829 ◽  
pp. 751-779 ◽  
Author(s):  
Jinyul Hwang ◽  
Hyung Jin Sung
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Large Scale ◽  
Wall Region ◽  
Local Skin ◽  
Velocity Fluctuations ◽  
Vortical Structures ◽  
Change Of Scale ◽  
Local Skin Friction ◽  
Near Wall

Direct numerical simulation data of a turbulent boundary layer ($Re_{\unicode[STIX]{x1D70F}}=1000$) were used to investigate the large-scale influences on the vortical structures that contribute to the local skin friction. The amplitudes of the streamwise and wall-normal swirling strengths ($\unicode[STIX]{x1D706}_{x}$and$\unicode[STIX]{x1D706}_{y}$) were conditionally sampled by measuring the large-scale streamwise velocity fluctuations ($u_{l}$). In the near-wall region, the amplitudes of$\unicode[STIX]{x1D706}_{x}$and$\unicode[STIX]{x1D706}_{y}$decreased under negative$u_{l}$rather than under positive$u_{l}$. This behaviour arose from the spanwise motions within the footprints of the large-scale low-speed ($u_{l}<0$) and high-speed structures ($u_{l}>0$). The intense spanwise motions under the footprint of positive$u_{l}$noticeably strengthened the small-scale spanwise velocity fluctuations ($w_{s}$) below the centre of the near-wall vortical structures as compared to$w_{s}$within the footprint of negative$u_{l}$. The streamwise and wall-normal components were attenuated or amplified around the modulated vortical motions, which in turn led to the dependence of the swirling strength on the$u_{l}$event. We quantified the contribution of the modulated vortical motions$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$, which were related to a change-of-scale effect due to the vortex-stretching force, to the local skin friction. In the near-wall region, intense values of$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$were observed for positive$u_{l}$. By contrast, these values were low for negative$u_{l}$, in connection with the amplification of$w_{s}$and$\unicode[STIX]{x1D706}_{y}$by the strong spanwise motions of the positive$u_{l}$. The resultant skin friction induced by the amplified vortical motions within$u_{l}^{+}>2$was responsible for 15 % of the total skin friction generated by the change-of-scale effect. Finally, we applied this analysis to a drag-reduced flow and found that the amplified vortical motions within the footprint of positive$u_{l}$were markedly diminished, which ultimately contributed to the total drag reduction.

Experimental observation of hairpin auto-generation events in a turbulent boundary layer

2016 ◽  
Vol 795 ◽  
pp. 611-633 ◽  
Author(s):  
Y. Jodai ◽  
G. E. Elsinga
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Shear Layer ◽  
Transition Process ◽  
Wall Region ◽  
Generation Model ◽  
Streamwise Vortices ◽  
Hairpin Vortices ◽  
Time Resolved ◽  
Near Wall

Time-resolved tomographic particle image velocimetry experiments show that new hairpin vortices are generated within a fully developed and unperturbed turbulent boundary layer. The measurements are taken at a Reynolds number based on the momentum thickness of 2038, and cover the near-wall region below $y^{+}=140$, where $y^{+}$ is the wall-normal distance in wall units. Instantaneous visualizations of the flow reveal near-wall low-speed streaks with associated quasi-streamwise vortices, retrograde inverted arch vortices, hairpin vortices and hairpin packets. The hairpin heads are observed as close to the wall as $y^{+}=30$. Examples of hairpin packet evolution reveal the development of new hairpin vortices, which are created upstream and close to the wall in a manner consistent with the auto-generation model (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). The development of the new hairpin appears to be initiated by an approaching sweep event, which perturbs the shear layer associated with the initial packet. The shear layer rolls up, thereby forming the new hairpin head. The head subsequently connects to existing streamwise vortices and develops into a hairpin. The time scale associated with the hairpin auto-generation is 20–30 wall units of time. This demonstrates that hairpins can be created over short distances within a developed turbulent boundary layer, implying that they are not simply remnants of the laminar-to-turbulent transition process far upstream.

Interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers

2019 ◽  
Vol 873 ◽  
pp. 287-321 ◽  
Author(s):  
Matthew Bross ◽  
Thomas Fuchs ◽  
Christian J. Kähler
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Flow Structures ◽  
Wall Region ◽  
Strong Impact ◽  
Wall Flow ◽  
Log Law ◽  
Near Wall

With the aim to characterize the near-wall flow structures and their interaction with large-scale motions in the log-law region, time-resolved planar and volumetric flow field measurements were performed in the near-wall and log-law region of an adverse pressure gradient turbulent boundary layer following a zero pressure gradient turbulent boundary layer at a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}=5000$. Due to the high spatial and temporal resolution of the measurements, it was possible to resolve and identify uniform-momentum zones in the region $z/\unicode[STIX]{x1D6FF}<0.15$ or $z^{+}<350$ and to relate them with well known coherent flow motions near the wall. The space–time results confirm that the turbulent superstructures have a strong impact even on the very near-wall flow motion and also their alternating appearance in time and intensity could be quantified over long time sequences. Using the time record of the velocity field, rare localized separation events appearing in the viscous sublayer were also analysed. By means of volumetric particle tracking velocimetry their three-dimensional topology and dynamics could be resolved. Based on the results, a conceptual model was deduced that explains their rare occurrence, topology and dynamics by means of a complex interaction process between low-momentum turbulent superstructures, near-wall low-speed streaks and tilted longitudinal and spanwise vortices located in the near-wall region.

The Influence of Pressure Gradient on Desinent Cavitation From Isolated Surface Protrusions

1986 ◽  
Vol 108 (2) ◽  
pp. 254-260 ◽  
Author(s):  
J. William Holl ◽  
Michael L. Billet ◽  
Masaru Tada ◽  
David R. Stinebring
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shape Factor ◽  
Cavitation Number ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Relative Height ◽  
Velocity Range ◽  
Circular Arc ◽  
Air Content

An experimental investigation was conducted to study the desinent cavitation characteristics of various sizes of two-dimensional triangular and circular arc protrusions in a turbulent boundary layer for favorable, zero, and unfavorable pressure gradients. The roughness height (h) varied from 0.025 cm (0.01 in.) to 0.762 cm (0.30 in.) and the relative height (h/δ) varied from 0.026 to 2.53. Desinent cavitation numbers (σd) were obtained visually over a velocity range of 9.1 mps (30 fps) to 18.3 mps (60 fps) at an average total air content of 3.8 ppm (mole basis). The data for zero pressure gradient were in fair agreement with data obtained for the same protrusion shapes by Holl (1958). The cavitation number (σd) was correlated with relative height (h/δ), Reynolds number (Uδ/ν) and Clauser’s (1954) equilibrium boundary layer shape factor (G) which includes the effect of pressure gradient. The data show that σd increases with pressure gradient. This result was not expected since it appears to contradict the trends implied by the so-called characteristic velocity theory developed by Holl (1958).

scholarly journals The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2 — Fluctuation Quantities

1995 ◽  
Author(s):  
Scott P. Mislevy ◽  
Ting Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6%. Boundary layer measurements were conducted for two constant K cases, K1=−0.51 × 10−6 and K2=−1.05 × 10−6. The fluctuation quantities, u′, v′, t′, the Reynolds shear stress (uv¯), and the Reynolds heat fluxes (vt¯ and ut¯) were measured. In general, u′/U∞, v′/U∞, and vt¯ have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K=0). The development of v′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+=7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+=70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+=70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y,+<20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/non-turbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non-turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt are also presented.

Turbulent boundary layers subjected to multiple curvatures and pressure gradients

1993 ◽  
Vol 246 ◽  
pp. 503-527 ◽  
Author(s):  
Promode R. Bandyopadhyay ◽  
Anwar Ahmed
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
The Other ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Internal Layers ◽  
Vortex Systems ◽  
Corner Vortex

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompanying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Górtler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

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