Lateral straining of turbulent boundary layers. Part 2. Streamline convergence

1997 ◽  
Vol 349 ◽  
pp. 1-30 ◽  
Author(s):  
N. R. PANCHAPAKESAN ◽  
T. B. NICKELS ◽  
P. N. JOUBERT ◽  
A. J. SMITS
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Transport ◽  
Turbulent Boundary Layers ◽  
Local Effect ◽  
Wall Region ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Dimensional Parameter ◽  
Outer Flow

Experimental measurements are presented showing the effects of streamline convergence on developing turbulent boundary layers. The longitudinal pressure-gradient in these experiments is nominally zero so the only extra rate-of-strain is the lateral convergence. Measurements have been made of mean flow and turbulence quantities at two different Reynolds numbers. The results show that convergence leads to a significant reduction in the skin-friction and an increase in the boundary layer thickness. There are also large changes in the Reynolds stresses with reductions occurring in the inner region and some increase in the outer flow. This is in contrast to the results of Saddoughi & Joubert (1991) for a diverging flow of the same included angle and zero pressure-gradient which show much smaller changes in the stresses and an approach to equilibrium. A new non-dimensional parameter, βD, is proposed to characterize the local effect of the convergence and it is shown how this parameter is related to Clauser's pressure-gradient parameter, βx. It is suggested that this is an equilibrium parameter for turbulent boundary layers with lateral straining. In the present flow case βD increases rapidly with streamwise distance leading to a significant departure from equilibrium. Measurement of terms in the transport equations suggest that streamline convergence leads to a reduction in production and generation and large increases in mean advection. The recovery of the flow after the removal of convergence has been shown to be characterized by a significant increase in the turbulent transport of shear-stress and turbulent kinetic energy from the very near-wall region to the flow further out where the stresses have been depleted by convergence.

Transpired Turbulent Boundary Layers Subject to Forced Convection and External Pressure Gradients

2005 ◽  
Vol 127 (2) ◽  
pp. 194-198 ◽  
Author(s):  
Rau´l Bayoa´n Cal, ◽  
Xia Wang, ◽  
Luciano Castillo
Keyword(s):  
Pressure Gradient ◽  
Forced Convection ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
External Pressure ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
Outer Flow ◽  
The Mean ◽  
Blowing Parameter

The problem of forced convection transpired turbulent boundary layers with external pressure gradient has been studied by using different scalings proposed by various researchers. Three major results were obtained: First, for adverse pressure gradient boundary layers with suction, the mean deficit profiles collapse with the free stream velocity, U∞, but into different curves depending on the strength of the blowing parameter and the upstream conditions. Second, the dependencies on the blowing parameter, the Reynolds number, and the strength of pressure gradient are removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits [Zagarola, M. V., and Smits, A. J., 1998, “Mean-Flow Scaling of Turbulent Pipe Flow,” J. Fluid Mech., 373, 33–79] scaling, U∞δ*/δ. Third, the temperature profiles collapse into a single curve using the new inner and outer scalings proposed by Wang and Castillo [Wang, X., and Castillo, L., 2003, “Asymptotic Solutions in Forced Convection Turbulent Boundary Layers,” J. Turbulence, 4(006)], which produce the true asymptotic profiles even at finite Pe´clet number.

scholarly journals Low-Reynolds-number turbulent boundary layers

1991 ◽  
Vol 230 ◽  
pp. 1-44 ◽  
Author(s):  
Lincoln P. Erm ◽  
Peter N. Joubert
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Low Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Wall Region ◽  
Mean Flow ◽  
Low Reynolds ◽  
High Reynolds ◽  
Turbulent Wall

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

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.

Comparison of mean flow similarity laws in zero pressure gradient turbulent boundary layers

2008 ◽  
Vol 20 (10) ◽  
pp. 105102 ◽  
Author(s):  
Peter A. Monkewitz ◽  
Kapil A. Chauhan ◽  
Hassan M. Nagib
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Mean Flow ◽  
Flow Similarity ◽  
Similarity Laws

scholarly journals Evolution and structure of sink-flow turbulent boundary layers

2001 ◽  
Vol 428 ◽  
pp. 1-27 ◽  
Author(s):  
M. B. JONES ◽  
IVAN MARUSIC ◽  
A. E. PERRY
Keyword(s):  
Boundary Layers ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Law Of The Wall ◽  
The Mean ◽  
Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

Developing turbulent boundary layers with system rotation

1985 ◽  
Vol 157 ◽  
pp. 405-448 ◽  
Author(s):  
J. H. Watmuff ◽  
H. T. Witt ◽  
P. N. Joubert
Keyword(s):  
Skin Friction ◽  
Boundary Layers ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Secondary Circulations ◽  
Spatially Periodic

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

Scaling of adverse-pressure-gradient turbulent boundary layers

1992 ◽  
Vol 238 ◽  
pp. 699-722 ◽  
Author(s):  
P. A. Durbin ◽  
S. E. Belcher
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Wall Layer ◽  
Small Range ◽  
Surface Shear Stress ◽  
Pressure Gradients ◽  
Mean Flow ◽  
The Mean

An asymptotic analysis is developed for turbulent boundary layers in strong adverse pressure gradients. It is found that the boundary layer divides into three distinguishable regions: these are the wall layer, the wake layer and a transition layer. This structure has two key differences from the zero-pressure-gradient boundary layer: the wall layer is not exponentially thinner than the wake; and the wake has a large velocity deficit, and cannot be linearized. The mean velocity profile has a y½ behaviour in the overlap layer between the wall and transition regions.The analysis is done in the context of eddy viscosity closure modelling. It is found that k-ε-type models are suitable to the wall region, and have a power-law solution in the y½ layer. The outer-region scaling precludes the usual ε-equation. The Clauser, constant-viscosity model is used in that region. An asymptotic expansion of the mean flow and matching between the three regions is carried out in order to determine the relation between skin friction and pressure gradient. Numerical calculations are done for self-similar flow. It is found that the surface shear stress is a double-valued function of the pressure gradient in a small range of pressure gradients.

Reynolds Number Dependence of Zero Pressure Gradient Turbulent Boundary Layers Including Third-Order Moments and Spatial Correlations

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Ralph J. Volino
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Field Measurements ◽  
Turbulent Boundary Layers ◽  
Quadrant Analysis ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Spatial Correlations ◽  
Mean Velocity

Abstract Measurements were made in zero pressure gradient turbulent boundary layers on a smooth wall, at momentum thickness Reynolds numbers, ranging from 800 to 6340. The experiments were conducted in a recirculating water tunnel. Two-component velocity profiles were acquired using laser Doppler velocimetry at five streamwise stations and three different freestream velocities. Velocity field measurements were acquired using particle image velocimetry in streamwise-wall normal and streamwise–spanwise planes. Profiles of mean velocity and turbulence statistics including the Reynolds normal and shear stresses, and triple products of the velocity fluctuations are presented in both inner and outer coordinates. Variations in the profiles at representative distances from the wall are presented and quantified as functions of Reynolds number. The triple products are explained in terms of transport of Reynolds stresses though motions associated with quadrant analysis, and variation with Reynolds number is consistent with that of Reynolds stresses. The structure of turbulence was considered through two-point correlations of the fluctuations in velocity fields. In general, the shape and inclination angles of the structures did not change with Reynolds number, but some streamwise and spanwise growth was observed as Reynolds number increased.

Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers

2008 ◽  
Vol 615 ◽  
pp. 445-475 ◽  
Author(s):  
SHIVSAI AJIT DIXIT ◽  
O. N. RAMESH
Keyword(s):  
Differential Equations ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Mean Velocity ◽  
Wide Range ◽  
Gradient Parameter ◽  
The Mean

Experiments were done on sink flow turbulent boundary layers over a wide range of streamwise pressure gradients in order to investigate the effects on the mean velocity profiles. Measurements revealed the existence of non-universal logarithmic laws, in both inner and defect coordinates, even when the mean velocity descriptions departed strongly from the universal logarithmic law (with universal values of the Kármán constant and the inner law intercept). Systematic dependences of slope and intercepts for inner and outer logarithmic laws on the strength of the pressure gradient were observed. A theory based on the method of matched asymptotic expansions was developed in order to explain the experimentally observed variations of log-law constants with the non-dimensional pressure gradient parameter (Δp=(ν/ρU3τ)dp/dx). Towards this end, the system of partial differential equations governing the mean flow was reduced to inner and outer ordinary differential equations in self-preserving form, valid for sink flow conditions. Asymptotic matching of the inner and outer mean velocity expansions, extended to higher orders, clearly revealed the dependence of slope and intercepts on pressure gradient in the logarithmic laws.

scholarly journals Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer

2019 ◽  
Vol 880 ◽  
pp. 284-325 ◽  
Author(s):  
Tobias Gibis ◽  
Christoph Wenzel ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis ◽  
Mean Flow ◽  
Self Similarity ◽  
Displacement Thickness ◽  
Characteristic Scales

A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzel et al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter $\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption, $\unicode[STIX]{x1D6EC}_{c}$ values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form $\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$ with the kinematic (incompressible) displacement thickness $\unicode[STIX]{x1D6FF}_{K}^{\ast }$ is shown to be a valid parameter of the form $\unicode[STIX]{x1D6EC}_{c}$ and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale, $\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the $\bar{\unicode[STIX]{x1D70C}}\widetilde{u^{\prime \prime }v^{\prime \prime }}$ stress and thus also the wall shear stress $\bar{\unicode[STIX]{x1D70F}}_{w}$, the inclusion of $\text{d}L_{0}/\text{d}x$ leads to palpable improvements.

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