Relaminarization in highly accelerated turbulent boundary layers

1973 ◽  
Vol 61 (3) ◽  
pp. 417-447 ◽  
Author(s):  
R. Narasimha ◽  
K. R. Sreenivasan
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Pressure Gradient ◽  
Laminar Boundary Layer ◽  
Outer Layer ◽  
Transitional Region ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Turbulence Decay ◽  
The Mean

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

Response of turbulent boundary layers to multiple strain rates

2002 ◽  
Vol 458 ◽  
pp. 333-377 ◽  
Author(s):  
A. C. SCHWARZ ◽  
M. W. PLESNIAK ◽  
S. N. B. MURTHY
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Effective Strain ◽  
Production Cycle ◽  
Wall Region ◽  
Strain Rates ◽  
Mean Flow ◽  
Local Flow ◽  
Axial Pressure Gradient ◽  
The Mean

Many practical applications, such as in blade cascades and turbomachinery, involve inhomogeneous turbulent shear flows subjected simultaneously to multiple strains. In principle, the applied strain can be combined to yield an effective strain. However, no simple stress–strain relation is capable of establishing turbulent stress or energy balance in the mean or on an instantaneous basis. In the current investigation, a turbulent boundary layer is examined in the presence of convex curvatures of different strengths combined with streamwise (favourable and adverse) pressure gradients, with various values of pressure gradient ratio, (∂P/∂s)/(∂P/∂n). Measurements of the mean and turbulent parameters and flux Richardson number show appreciable changes, mainly in the outer portion of the boundary layer (y+ > 100). The turbulent burst frequency, particularly at the location of application of the additional strain rate, also changes relative to its value with wall curvature alone.Three primary observations from these experiments are as follows: (i) in all cases, the mean velocity profile and all of the measured Reynolds stresses collapse in the near-wall region using standard inner scaling; (ii) the applied strains combine nonlinearly, with one of the strains dominating the local flow during its development; (iii) the ratio of the radial to axial pressure gradient magnitude influences both classical turbulence correlations and mean flow, as well as the physical production cycle of turbulence; and (iv) application rate of newly introduced strain rates is at least as important as their magnitudes.

Measurement of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer

1982 ◽  
Vol 119 ◽  
pp. 121-153 ◽  
Author(s):  
Udo R. Müller
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Flow Field ◽  
Three Dimensional ◽  
Turbulent Shear ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Acceleration ◽  
The Mean

An experimental study of a steady, incompressible, three-dimensional turbulent boundary layer approaching separation is reported. The flow field external to the boundary layer was deflected laterally by turning vanes so that streamwise flow deceleration occurred simultaneous with cross-flow acceleration. At 21 stations profiles of the mean-velocity components and of the six Reynolds stresses were measured with single- and X-hot-wire probes, which were rotatable around their longitudinal axes. The calibration of the hot wires with respect to magnitude and direction of the velocity vector as well as the method of evaluating the Reynolds stresses from the measured data are described in a separate paper (Müller 1982, hereinafter referred to as II). At each measuring station the wall shear stress was inferred from a Preston-tube measurement as well as from a Clauser chart. With the measured profiles of the mean velocities and of the Reynolds stresses several assumptions used for turbulence modelling were checked for their validity in this flow. For example, eddy viscosities for both tangential directions and the corresponding mixing lengths as well as the ratio of resultant turbulent shear stress to turbulent kinetic energy were derived from the data.

scholarly journals Near-field flow structure of a confined wall jet on flat and concave rough walls

2008 ◽  
Vol 606 ◽  
pp. 27-49 ◽  
Author(s):  
I. ALBAYRAK ◽  
E. J. HOPFINGER ◽  
U. LEMMIN
Keyword(s):  
Shear Stress ◽  
Shear Layer ◽  
Outer Layer ◽  
Reynolds Shear Stress ◽  
Near Field ◽  
Wall Jet ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Free Jet ◽  
The Mean

Experimental results are presented of the mean flow and turbulence characteristics in the near field of a plane wall jet issuing from a nozzle onto flat and concave walls consisting of fixed sand beds. This is a flow configuration of interest for sediment erosion, also referred to as scouring. The measurements were made with an acoustic profiler that gives access to the three components of the instantaneous velocities. For the flat-wall flow, it is shown that the outer-layer spatial growth rate and the maxima of the Reynolds stresses approach the values accepted for the far field of a wall jet at a downstream distance x/b0 ≈ 8. These maxima are only about half the values of a plane free jet. This reduction in Reynolds stresses is also observed in the shear-layer region, x/b0 < 6, where the Reynolds shear stress is about half the value of a free shear layer. At distances x/b0 > 11, the maximum Reynolds shear stress approaches the value of a plane free jet. This change in Reynolds stresses is related to the mean vertical velocity that is negative for x/b0 < 8 and positive further downstream. The evolution of the inner region of the wall jet is found to be in good agreement with a previous model that explicitly includes the roughness length.On the concave wall, the mean flow and the Reynolds stresses are drastically changed by the adverse pressure gradient and especially by the development of Görtler vortices. On the downslope side of the scour hole, the flow is nearly separating with the wall shear stress tending to zero, whereas on the upslope side, the wall-friction coefficient is increased by a factor of about two by Görtler vortices. These vortices extend well into the outer layer and, just above the wall, cause a substantial increase in Reynolds shear stress.

A turbulent equilibrium boundary layer near separation

1994 ◽  
Vol 272 ◽  
pp. 319-348 ◽  
Author(s):  
Per Egil Skåre ◽  
Per-åge Krogstad
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Diffusion Mechanism ◽  
Gradient Flow ◽  
Adverse Pressure Gradient ◽  
Turbulent Energy ◽  
Skin Friction Coefficient ◽  
Wall Region ◽  
Mean Flow ◽  
The Mean

The experimental results for an equilibrium boundary layer in a strong adverse pressure gradient flow are reported. The measurements show that similarity in the mean flow and the turbulent stresses has been achieved over a substantial streamwise distance where the skin friction coefficient is kept at a low, constant level. Although the Reynolds stress distribution across the layer is entirely different from the flow at zero pressure gradient, the ratios between the different turbulent stress components were found to be similar, showing that the mechanism for distributing the turbulent energy between the different components remains unaffected by the mean flow pressure gradient. Close to the surface the gradient of the mixing length was found to increase from Kl ≈ 0.41 to Kl ≈ 0.78, almost twice as high as for the zero pressure gradient case. Similarity in the triple correlations was also found to be good. The correlations show that there is a considerable diffusion of turbulent energy from the central part of the boundary layer towards the wall. The diffusion mechanism is caused by a second peak in the turbulence production, located at y/δ ≈ 0.45. This production was for the present case almost as strong as the production found near the wall. The energy budget for the turbulent kinetic energy also shows that strong dissipation is not restricted to the wall region, but is significant for most of the layer.

PIV Study of Separated and Reattached Open Channel Flow Over Surface Mounted Blocks

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Martin Agelinchaab ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
High Background ◽  
The Mean

A particle image velocimetry is used to study the mean and turbulent fields of separated and redeveloping flow over square, rectangular, and semicircular blocks fixed to the bottom wall of an open channel. The open channel flow is characterized by high background turbulence level, and the ratio of the upstream boundary layer thickness to block height is considerably higher than in prior experiments. The variation of the Reynolds stresses along the dividing streamlines is discussed within the context of vortex stretching, longitudinal strain rate, and wall damping. It appears that wall damping is a more dominant mechanism in the vicinity of reattachment. In the recirculation and reattachment regions, profiles of the mean velocity, turbulent quantities, and transport terms are used to document the salient features of block geometry on the flow. The flow characteristics in these regions strongly depend on block geometry. Downstream of reattachment, a new shear layer is formed, and the redevelopment of the shear layer toward the upstream open channel boundary layer is studied using the boundary layer parameters and Reynolds stresses. The results show that the mean flow rapidly redeveloped so that the Clauser parameter recovered to its upstream value at 90 step heights downstream of reattachment. However, the rate of development close to reattachment strongly depends on block geometry.

LDA Measurements on Rough Turbulent Boundary Layers Subject to Strong Favorable Pressure Gradients

2006 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Brian Brzek ◽  
Gunnar Johansson ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Rough Surface ◽  
Reynolds Stress ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Velocity Deficit ◽  
The Mean ◽  
Stress Profiles

Laser-Doppler anemometry (LDA) measurements of the mean velocity and Reynolds stresses are carried out on a rough surface favorable pressure gradient (FPG) turbulent boundary layer. These data is compared with smooth FPG turbulent boundary layer data possessing with the same strength of pressure gradient and also with rough zero pressure gradient (ZPG) data. The scales for the mean velocity deficit and Reynolds stresses are obtained through means of equilibrium similarity analysis of the RANS equations [1]. The mean velocity deficit profiles collapse, but to different curves when normalized using the free-stream velocity. The effects of the pressure gradient and roughness are clearly distinguished and separated. However, these effects are removed from the outer flow when the profiles are normalized using the Zagarola and Smits [2] scaling. It is also found that there is a clear effect of the roughness and pressure gradient on the Reynolds stresses. The Reynolds stress profiles augment due to the rough surface. Furthermore, the strength of the pressure gradient imposed of the flow changes the shape of the Reynolds stress profiles especially on the < v2 > and < uv > components. The rough surface influence is mostly noticed on the < u2 > component of the Reynolds stress, where the shape of the profiles change entirely. The boundary layer parameter δ*/δ shows the effects of the roughness and a dependence on the Reynolds number for the smooth FPG case. The pressure parameter, A, describes a development of the turbulent boundary layer and no influence of the roughness is linked with the parameter, k+. The boundary layers grow differently and depict the influence of the studied effects in their development. These measurements are the first of their nature due to the extensive number in downstream locations (12) and the combination of the studied external conditions (i.e., the strength of the pressure gradient and the surface roughness).

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