Large-scale motions in turbulent boundary layers subjected to adverse pressure gradients

2016 ◽  
Vol 810 ◽  
pp. 323-361 ◽  
Author(s):  
Jae Hwa Lee
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale ◽  
Pressure Gradients ◽  
Large Scale Structures ◽  
Scale Structures ◽  
Layer Flow

It is known that large-scale streamwise velocity-fluctuating structures ($u^{\prime }$) are frequently observed in the log region of a zero pressure gradient turbulent boundary layer, and that these motions significantly influence near-wall small-scale $u^{\prime }$-structures by modulating the amplitude (Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28; Mathis et al., J. Fluid Mech., vol. 628, 2009, pp. 311–337). In the present study, we provide evidence that the spatial organization of large-scale structures in the log region is significantly influenced by the strength of adverse pressure gradients in turbulent boundary layers based on a direct numerical simulation dataset. For a mild adverse pressure gradient boundary layer flow, groups of hairpin vortices are coherently aligned in the streamwise direction to form hairpin vortex packets, and streamwise merging events of the induced large-scale $u^{\prime }$-structures create a larger streamwise length scale of structures than that for a zero pressure gradient boundary layer flow. As the pressure gradient strength increases further, however, the formation of hairpin packets is continuously suppressed, and large-scale motions are consequently not concatenated to create a longer motion, resulting in a significant reduction of the streamwise coherence of large-scale structures in the log layer. Although energy spectrum maps for $u^{\prime }$-structures show that the large-scale energy is continuously intensified above the log layer with an increase in the pressure gradient, amplitude modulation of the near-wall small-scale motions is dominantly induced by log region large-scale structures for adverse pressure gradient flows. Conditional averaged flow fields with large-scale Q2 and Q4 events indicate that large-scale counter-rotating roll modes play an important role in organizing the flows under the pressure gradients, and the large-scale roll modes associated with Q4 events are more enhanced in the outer layer than those associated with Q2 events, reducing the streamwise coherence of the vortices in a packet.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

A supersonic turbulent boundary layer in an adverse pressure gradient

1990 ◽  
Vol 211 ◽  
pp. 285-307 ◽  
Author(s):  
Emerick M. Fernando ◽  
Alexander J. Smits
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Large Scale Structures ◽  
Streamline Curvature ◽  
The Mean ◽  
Scale Structures

This investigation describes the effects of an adverse pressure gradient on a flat plate supersonic turbulent boundary layer (Mf ≈ 2.9, βx ≈ 5.8, Reθ, ref ≈ 75600). Single normal hot wires and crossed wires were used to study the Reynolds stress behaviour, and the features of the large-scale structures in the boundary layer were investigated by measuring space–time correlations in the normal and spanwise directions. Both the mean flow and the turbulence were strongly affected by the pressure gradient. However, the turbulent stress ratios showed much less variation than the stresses, and the essential nature of the large-scale structures was unaffected by the pressure gradient. The wall pressure distribution in the current experiment was designed to match the pressure distribution on a previously studied curved-wall model where streamline curvature acted in combination with bulk compression. The addition of streamline curvature affects the turbulence strongly, although its influence on the mean velocity field is less pronounced and the modifications to the skin-friction distribution seem to follow the empirical correlations developed by Bradshaw (1974) reasonably well.

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.

Turbulent boundary layers in decreasing adverse pressure gradients

1966 ◽  
Vol 26 (3) ◽  
pp. 481-506 ◽  
Author(s):  
A. E. Perry
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Streamwise Direction ◽  
Mean Velocity ◽  
Boundary Layer Development ◽  
Regional Similarity ◽  
Layer Development

The results of a detailed mean velocity survey of a smooth-wall turbulent boundary layer in an adverse pressure gradient are described. Close to the wall, a variety of profiles shapes were observed. Progressing in the streamwise direction, logarithmic, ½-power, linear and$\frac{3}{2}$-power distributions seemed to form, and generally each predominated at a different stage of the boundary-layer development. It is believed that the phenomenon occurred because of the nature of the pressure gradient imposed (an initially high gradient which fell to low values as the boundary layer developed) and attempts are made to describe the flow by an extension of the regional similarity hypothesis proposed by Perry, Bell & Joubert (1966). Data from other sources is limited but comparisons with the author's results are encouraging.

Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients

1978 ◽  
Vol 89 (2) ◽  
pp. 305-342 ◽  
Author(s):  
B. A. Kader ◽  
A. M. Yaglom
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Local Equilibrium ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Experimental Information ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Pressure Gradients

Dimensional analysis is applied to the velocity profile U(y) of turbulent boundary layers subjected to adverse pressure gradients. It is assumed that the boundary layer is in moving or local equilibrium in the sense that the free-stream velocity U∞ and kinematic pressure gradient α = ρ−1dP/dx vary only slowly with the co-ordinate x. This assumption implies a rather complicated general equation for the velocity gradient dU/dy which may be considerably simplified for several specific regions of the flow. A general family of velocity profiles is derived from the simplified equations supplemented by some experimental information. This family agrees well with almost all existing data on velocity profiles in adverse-pressure-gradient turbulent boundary layers. It may be used for the derivation of a skin-friction law which predicts satisfactorily the values of the wall shear stress at any non-negative value of the pressure gradient. The variation of the boundary-layer thickness with x is also predicted by dimensional considerations.

Structures in turbulent boundary layers subjected to adverse pressure gradients

2009 ◽  
Vol 639 ◽  
pp. 101-131 ◽  
Author(s):  
JOUNG-HO LEE ◽  
HYUNG JIN SUNG
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stochastic Estimation ◽  
Pressure Gradients ◽  
Linear Stochastic Estimation ◽  
Mean Width ◽  
The Mean

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∞ ~ xm. Two-point 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.

Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow

1995 ◽  
Vol 286 ◽  
pp. 137-171 ◽  
Author(s):  
Stephen R. Snarski ◽  
Richard M. Lueptow
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Wall Pressure ◽  
Small Scale ◽  
Fluctuating Pressure ◽  
Large Scale Structures ◽  
Transverse Curvature ◽  
Scale Structures

Measurements of wall pressure and streamwise velocity fluctuations in a turbulent boundary layer on a cylinder in an axial air flow (δ/a = 5.04, Reθ = 2870) have been used to investigate the turbulent flow structures in the cylindrical boundary layer that contribute to the fluctuating pressure at the wall in an effort to deduce the effect of transverse curvature on the structure of boundary layer turbulence. Wall pressure was measured at a single location with a subminiature electret condenser microphone, and the velocity was measured throughout a large volume of the boundary layer with a hotwire probe. Auto- and cross-spectral densities, cross-correlations, and conditional sampling of the pressure and streamwise velocity indicate that two primary groups of flow disturbances contribute to the fluctuating pressure at the wall: (i) low-frequency large-scale structures with dynamical significance across the entire boundary layer that are consistent with a pair of large-scale spanwise-oriented counter-rotating vortices and (ii) higher frequency small-scale disturbances concentrated close to the wall that are associated with the burst-sweep cycle and are responsible for the short-duration large-amplitude wall pressure fluctuations. A bidirectional relationship was found to exist between both positive and negative pressure peaks and the temporal derivative of u near the wall. Because the frequency of the large-scale disturbance observed across the boundary layer is consistent with the bursting frequency deduced from the average time between bursts, the burst-sweep cycle appears to be linked to the outer motion. A stretching of the large-scale structures very near the wall, as suggested by space-time correlation convection velocity results, may provide the coupling mechanism. Since the high-frequency disturbance observed near the wall is consistent with the characteristic frequency deduced from the average duration of bursting events, the bursting process provides the two characteristic time scales responsible for the bimodal distribution of energy near the wall. Because many of the observed structural features of the cylindrical boundary layer are similar to those observed in flat-plate turbulent boundary layers, transverse curvature appears to have little effect on the fundamental turbulent structure of the boundary layer for the moderate transverse curvature ratio used in this investigation. From differences that exist between the turbulence intensity, skewness, and spectra of the streamwise velocity, however, it appears that transverse curvature may enhance (i.e. energize) the large-scale motion owing to the reduced constraint imposed on the flow by the smaller cylindrical wall.

Predicting Turbulent Boundary Layer Wall Pressure Fluctuations in Adverse Pressure Gradients

2005 ◽  
Author(s):  
Frank J. Aldrich
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Prediction Tool ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
The Difference

A physics-based approach is employed and a new prediction tool is developed to predict the wavevector-frequency spectrum of the turbulent boundary layer wall pressure fluctuations for subsonic airfoils under the influence of adverse pressure gradients. The prediction tool uses an explicit relationship developed by D. M. Chase, which is based on a fit to zero pressure gradient data. The tool takes into account the boundary layer edge velocity distribution and geometry of the airfoil, including the blade chord and thickness. Comparison to experimental adverse pressure gradient data shows a need for an update to the modeling constants of the Chase model. To optimize the correlation between the predicted turbulent boundary layer wall pressure spectrum and the experimental data, an optimization code (iSIGHT) is employed. This optimization module is used to minimize the absolute value of the difference (in dB) between the predicted values and those measured across the analysis frequency range. An optimized set of modeling constants is derived that provides reasonable agreement with the measurements.

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