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.

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.

Wall Suction Effects on the Structure of Fully Developed Turbulent Pipe Flow

1996 ◽  
Vol 118 (1) ◽  
pp. 33-39 ◽  
Author(s):  
D. Sofialidis ◽  
P. Prinos
Keyword(s):  
Shear Stress ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Turbulent Pipe Flow ◽  
Turbulent Shear ◽  
Experimental Measurements ◽  
Wall Region ◽  
Wall Suction ◽  
Law Of The Wall ◽  
Near Wall

The effects of wall suction on the structure of fully developed pipe flow are studied numerically by solving the Reynolds averaged Navier-Stokes equations. Linear and nonlinear k-ε or k-ω low-Re models of turbulence are used for “closing” the system of the governing equations. Computed results are compared satisfactorily against experimental measurements. Analytical results, based on boundary layer assumptions and the mixing length concept, provide a law of the wall for pipe flow under the influence of low suction rates. The analytical solution is found in satisfactory agreement with computed and experimental data for a suction rate of A = 0.46 percent. For the much higher rate of A = 2.53 percent the above assumptions are not valid and analytical velocities do not follow the computed and experimental profiles, especially in the near-wall region. Near-wall velocities, as well as the boundary shear stress, are increased with increasing suction rates. The excess wall shear stress, resulting from suction, is found to be 1.5 to 5.5 times the respective one with no suction. The turbulence levels are reduced with the presence of the wall suction. Computed results of the turbulent shear stress uv are in close agreement with experimental measurements. The distribution of the turbulent kinetic energy k is predicted better by the k-ω model of Wilcox (1993). Nonlinear models of the k-ε and k-ω type predict the reduction of the turbulence intensities u’, v’, w’, and the correct levels of v’ and w’ but they underpredict the level of u’.

scholarly journals Similarity Behavior in Transitional Boundary Layers Over a Range of Adverse Pressure Gradients and Turbulence Levels

1990 ◽  
Author(s):  
J. P. Gostelow ◽  
G. J. Walker
Keyword(s):  
Boundary Layer ◽  
Form Factor ◽  
Velocity Profile ◽  
Transition Region ◽  
Boundary Layers ◽  
Free Stream ◽  
Local Equilibrium ◽  
Pressure Gradients ◽  
Lag Effects ◽  
Free Stream Turbulence

Boundary layer transition has been investigated experimentally under low, moderate and high free-stream turbulence levels and varying adverse pressure gradients. Under high turbulence levels and adverse pressure gradients a pronounced subtransition was present. A strong degree of similarity in intermittency distributions was observed, for all conditions, when the Narasimha procedure for determination of transition inception was used. Effects of free-stream turbulence on the velocity profile are particularly strong for the laminar boundary layer upstream of the transition region. This could reflect the influence of the turbulence on the shear stress distribution throughout the layer and this matter needs further attention. The velocity profiles in wall coordinates undershoot the turbulent wall layer asymptote near the wall over most of the transition region. The rapidity with which transition occurs under adverse pressure gradients produces strong lag effects on the velocity profile; the starting turbulent boundary layer velocity profile may depart significantly from local equilibrium conditions. The practice of deriving integral properties and skin friction for transitional boundary layers by a linear combination of laminar and turbulent values for equilibrium layers is inconsistent with the observed lag effects. The velocity profile responds sufficiently slowly to the perturbation imposed by transition that much of the anticipated drop in form factor will not have occurred prior to the completion of transition. This calls into question both experimental techniques which rely on measured form factor to characterize transition and boundary layer calculations which rely on local equilibrium assumptions in the vicinity of transition.

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.

Turbulent shear flow over slowly moving waves

1993 ◽  
Vol 251 ◽  
pp. 109-148 ◽  
Author(s):  
S. E. Belcher ◽  
J. C. R. Hunt
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Shear Stress ◽  
Surface Layer ◽  
Reynolds Shear Stress ◽  
Surface Velocity ◽  
Wave Crest ◽  
Turbulent Shear ◽  
Effective Roughness ◽  
Inner Surface

We investigate the changes to a fully developed turbulent boundary layer caused by the presence of a two-dimensional moving wave of wavelength L = 2π/k and amplitude a. Attention is focused on small slopes, ak, and small wave speeds, c, so that the linear perturbations are calculated as asymptotic sequences in the limit (u* + c)/UB(L) → 0 (u* is the unperturbed friction velocity and UB(L) is the approach-flow mean velocity at height L). The perturbations can then be described by an extension of the four-layer asymptotic structure developed by Hunt, Leibovich & Richards (1988) to calculate the changes to a boundary layer passing over a low hill.When (u* + c)/UB(L) is small, the matched height, zm (the height where UB equals c), lies within an inner surface layer, where the perturbation Reynolds shear stress varies only slowly. Solutions across the matched height are then constructed by considering an equation for the shear stress. The importance of the shear-stress perturbation at the matched height implies that the inviscid theory of Miles (1957) is inappropriate in this parameter range. The perturbations above the inner surface layer are not directly influenced by the matched height and the region of reversed flow below zm: they are similar to the perturbations due to a static undulation, but the ‘effective roughness length’ that determines the shape of the unperturbed velocity profile is modified to zm = z0 exp (kc/u*).The solutions for the perturbations to the boundary layer are used to calculate the growth rate of waves, which is determined at leading order by the asymmetric pressure perturbation induced by the thickening of the perturbed boundary layer on the leeside of the wave crest. At first order in (u* + c)/UB(L), however, there are three new effects which, numerically, contribute significantly to the growth rate, namely: the asymmetries in both the normal and shear Reynolds stresses associated with the leeside thickening of the boundary layer, and asymmetric perturbations induced by the varying surface velocity associated with the fluid motion in the wave; further asymmetries induced by the variation in the surface roughness along the wave may also be important.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

scholarly journals A Bypass Transition Model for Boundary Layers

1993 ◽  
Author(s):  
Mark W. Johnson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Transition Model ◽  
Wall Region ◽  
Bypass Transition ◽  
Pressure Gradients ◽  
Turbulence Level ◽  
Velocity Fluctuations ◽  
Laminar Boundary Layers

Experimental data for laminar boundary layers developing below a turbulent free stream shows that the fluctuation velocities within the boundary layer increase in amplitude until some critical level is reached which initiates transition. In the near wall region, a simple model, containing a single empirical parameter which depends only on the turbulence level and length scale, is derived to predict the development of the velocity fluctuations in laminar boundary layers with favourable, zero or adverse pressure gradients. A simple bypass transition model which considers the streamline distortion in the near wall region brought about by the velocity fluctuations suggests that transition will commence when the local turbulence level reaches approximately 23%. This value is consistent with experimental findings. This critical local turbulence level is used to derive a bypass transition prediction formula which compares reasonably with start of transition experimental data for a range of pressure gradients (λθ = −0.01 to 0.01) and turbulence levels (Tu = 0.2% to 5%). Further improvement to the model is proposed through prediction of the boundary layer distortion, which occurs due to Reynolds stresses generated within the boundary layer at high free stream turbulence levels and also through inclusion of the effect of turbulent length scale as well as turbulence level.

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 wall cooling on boundary-layer-induced pressure fluctuations at Mach 6

2017 ◽  
Vol 822 ◽  
pp. 5-30 ◽  
Author(s):  
Chao Zhang ◽  
Lian Duan ◽  
Meelan M. Choudhari
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Pressure Fluctuation ◽  
Free Stream ◽  
Pressure Fluctuations ◽  
Turbulent Boundary Layers ◽  
Wall Pressure ◽  
Wall Region ◽  
Near Wall

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.

Similarity Behavior in Transitional Boundary Layers Over a Range of Adverse Pressure Gradients and Turbulence Levels

1991 ◽  
Vol 113 (4) ◽  
pp. 617-624 ◽  
Author(s):  
J. P. Gostelow ◽  
G. J. Walker
Keyword(s):  
Boundary Layer ◽  
Form Factor ◽  
Velocity Profile ◽  
Transition Region ◽  
Boundary Layers ◽  
Free Stream ◽  
Local Equilibrium ◽  
Pressure Gradients ◽  
Lag Effects ◽  
Free Stream Turbulence

Boundary layer transition has been investigated experimentally under low, moderate, and high free-stream turbulence levels and varying adverse pressure gradients. Under high turbulence levels and adverse pressure gradients a pronounced subtransition was present. A strong degree of similarity in intermittency distributions was observed, for all conditions, when the Narasimha procedure for determination of transition inception was used. Effects of free-stream turbulence on the velocity profile are particularly strong for the laminar boundary layer upstream of the transition region. This could reflect the influence of the turbulence on the shear stress distribution throughout the layer and this matter needs further attention. The velocity profiles in wall coordinates undershoot the turbulent wall layer asymptote near the wall over most of the transition region. The rapidity with which transition occurs under adverse pressure gradients produces strong lag effects on the velocity profile; the starting turbulent boundary layer velocity profile may depart significantly from local equilibrium conditions. The practice of deriving integral properties and skin friction for transitional boundary layers by a linear combination of laminar and turbulent values for equilibrium layers is inconsistent with the observed lag effects. The velocity profile responds sufficiently slowly to the perturbation imposed by transition that much of the anticipated drop in form factor will not have occurred prior to the completion of transition. This calls into question both experimental techniques, which rely on measured form factor to characterize transition, and boundary layer calculations, which rely on local equilibrium assumptions in the vicinity of transition.

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