scholarly journals On the identification of well-behaved turbulent boundary layers

2017 ◽  
Vol 822 ◽  
pp. 109-138 ◽  
Author(s):  
C. Sanmiguel Vila ◽  
R. Vinuesa ◽  
S. Discetti ◽  
A. Ianiro ◽  
P. Schlatter ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Shape Factor ◽  
Outer Region ◽  
The Other ◽  
Diagnostic Plot ◽  
Other Hand

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

Effects of sandpaper roughness and stream turbulence on the turbulent boundary layer

1999 ◽  
Vol 213 (5) ◽  
pp. 507-515 ◽  
Author(s):  
J. C. Gibbings ◽  
S. M. Al-Shukri
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Pipe Flow ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Experimental Measurements ◽  
Two Dimensional

This paper reports experimental measurements of two-dimensional turbulent boundary layers over sandpaper surfaces under turbulent streams to complement the Nikuradse experiments on pipe flow. The study included the recovery region downstream of the end of transition. Correlations are given for the thickness, the shape factor, the skin friction and the parameters of the velocity profile of the layer. Six further basic differences from the pipe flow are described to add to the five previously reported.

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

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.

Annulus Wall Boundary-Layer Measurements in a Four-Stage Compressor

1986 ◽  
Vol 108 (1) ◽  
pp. 2-6 ◽  
Author(s):  
N. A. Cumpsty
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
Tip Clearance ◽  
The Other ◽  
Wall Boundary Layer ◽  
Multistage Compressors ◽  
Full Design

There are few available measurements of the boundary layers in multistage compressors when the repeating-stage condition is reached. These tests were performed in a small four-stage compressor; the flow was essentially incompressible and the Reynolds number based on blade chord was about 5 • 104. Two series of tests were performed; in one series the full design number of blades were installed, in the other series half the blades were removed to reduce the solidity and double the staggered spacing. Initially it was wished to examine the hypothesis proposed by Smith [1] that staggered spacing is a particularly important scaling parameter for boundary layer thickness; the results of these tests and those of Hunter and Cumpsty [2] tend to suggest that it is tip clearance which is most potent in determining boundary-layer integral thicknesses. The integral thicknesses agree quite well with those published by Smith.

Power Law Velocity Profile in the Turbulent Boundary Layer on Transitional Rough Surfaces

2007 ◽  
Vol 129 (8) ◽  
pp. 1083-1100 ◽  
Author(s):  
Noor Afzal
Keyword(s):  
Boundary Layer ◽  
Functional Equation ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Skin Friction ◽  
Power Law ◽  
Wall Roughness ◽  
Closure Model ◽  
Log Law

A new approach to scaling of transitional wall roughness in turbulent flow is introduced by a new nondimensional roughness scale ϕ. This scale gives rise to an inner viscous length scale ϕν∕uτ, inner wall transitional variable, roughness friction Reynolds number, and roughness Reynolds number. The velocity distribution, just above the roughness level, turns out to be a universal relationship for all kinds of roughness (transitional, fully smooth, and fully rough surfaces), but depends implicitly on roughness scale. The open turbulent boundary layer equations, without any closure model, have been analyzed in the inner wall and outer wake layers, and matching by the Izakson-Millikan-Kolmogorov hypothesis leads to an open functional equation. An alternate open functional equation is obtained from the ratio of two successive derivatives of the basic functional equation of Izakson and Millikan, which admits two functional solutions: the power law velocity profile and the log law velocity profile. The envelope of the skin friction power law gives the log law, as well as the power law index and prefactor as the functions of roughness friction Reynolds number or skin friction coefficient as appropriate. All the results for power law and log law velocity and skin friction distributions, as well as power law constants are explicitly independent of the transitional wall roughness. The universality of these relations is supported very well by extensive experimental data from transitional rough walls for various different types of roughnesses. On the other hand, there are no universal scalings in traditional variables, and different expressions are needed for various types of roughness, such as inflectional roughness, monotonic roughness, and others. To the lowest order, the outer layer flow is governed by the nonlinear turbulent wake equations that match with the power law theory as well as log law theory, in the overlap region. These outer equations are in equilibrium for constant value of m, the pressure gradient parameter, and under constant eddy viscosity closure model, the analytical and numerical solutions are presented.

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

2018 ◽  
Author(s):  
Yvan Maciel ◽  
Tie Wei ◽  
Ayse G. Gungor ◽  
Mark P. Simens
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Inertial Parameter ◽  
Velocity Scale ◽  
Gradient Parameter

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows — not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow — in a global sense — the streamwise evolution of the stream-wise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

scholarly journals On the decay of dispersive motions in the outer region of rough-wall boundary layers

2019 ◽  
Vol 862 ◽  
Author(s):  
Johan Meyers ◽  
Bharathram Ganapathisubramani ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Layer ◽  
Stokes Equations ◽  
Outer Region ◽  
Rough Wall ◽  
Rough Boundary ◽  
Mean Flow ◽  
Wall Boundary

In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier–Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of $\exp (-kz)$ and $\exp (-Kz)$, with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $\boldsymbol{k}$, and where $K(\boldsymbol{k},Re)$ is a function of $\boldsymbol{k}$ and the Reynolds number $Re$. Moreover, for $k\rightarrow \infty$ or $k_{1}\rightarrow 0$ (with $k_{1}$ the stream-wise wavenumber), $K\rightarrow k$ is found, in which case solutions consist of a linear combination of $\exp (-kz)$ and $z\exp (-kz)$, and are independent of the Reynolds number. These analytical relations are compared in the limit of $k_{1}=0$ to the rough boundary layer experiments by Vanderwel & Ganapathisubramani (J. Fluid Mech., vol. 774, 2015, R2) and are in reasonable agreement for $\ell _{k}/\unicode[STIX]{x1D6FF}\leqslant 0.5$, with $\unicode[STIX]{x1D6FF}$ the boundary-layer thickness and $\ell _{k}=2\unicode[STIX]{x03C0}/k$.

The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer

1998 ◽  
Vol 359 ◽  
pp. 329-356 ◽  
Author(s):  
H. H. FERNHOLZ ◽  
D. WARNACK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Reynolds Stresses ◽  
The Mean

The effects of a favourable pressure gradient (K[les ]4×10−6) and of the Reynolds number (862[les ]Reδ2[les ]5800) on the mean and fluctuating quantities of four turbulent boundary layers were studied experimentally and are presented in this paper and a companion paper (Part 2). The measurements consist of extensive hot-wire and skin-friction data. The former comprise mean and fluctuating velocities, their correlations and spectra, the latter wall-shear stress measurements obtained by four different techniques which allow testing of calibrations in both laminar-like and turbulent flows for the first time. The measurements provide complete data sets, obtained in an axisymmetric test section, which can serve as test cases as specified by the 1981 Stanford conference.Two different types of accelerated boundary layers were investigated and are described: in this paper (Part 1) the fully turbulent, accelerated boundary layer (sometimes denoted laminarescent) with approximately local equilibrium between the production and dissipation of the turbulent energy and with relaxation to a zero pressure gradient flow (cases 1 and 3); and in Part 2 the strongly accelerated boundary layer with ‘inactive’ turbulence, laminar-like mean flow behaviour (relaminarized), and reversion to the turbulent state (cases 2 and 4). In all four cases the standard logarithmic law fails but there is no single parametric criterion which denotes the beginning or the end of this breakdown. However, it can be demonstrated that the departure of the mean-velocity profile is accompanied by characteristic changes of turbulent quantities, such as the maxima of the Reynolds stresses or the fluctuating value of the skin friction.The boundary layers described here are maintained in the laminarescent state just up to the beginning of relaminarization and then relaxed to the turbulent state in a zero pressure gradient. The relaxation of the turbulence structure occurs much faster than in an adverse pressure gradient. In the accelerating boundary layer absolute values of the Reynolds stresses remain more or less constant in the outer region of the boundary layer in accordance with the results of Blackwelder & Kovasznay (1972), and rise both in the vincinity of the wall in conjunction with the rising wall shear stress and in the centre region of the boundary layer with the increase of production.

Influence of the Wake Component on Turbulent Skin Friction at Subsonic and Supersonic Speeds

1979 ◽  
Vol 30 (4) ◽  
pp. 590-606 ◽  
Author(s):  
D.G. Mabey
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Significant Influence ◽  
Turbulent Boundary Layers ◽  
Number Range ◽  
Reynolds Number Range ◽  
Friction Measurements

SummarySome velocity profile and skin friction measurements for turbulent boundary layers at subsonic and supersonic speeds are reviewed to derive the magnitude of the wake component and the effects of its variation with Reynolds number on predictions of skin friction. As Reynolds number increases the wake component increases rapidly, reaches a maximum and then decreases. The measurements considered suggest that this maximum may be higher at supersonic speeds than at subsonic speeds. This wake component variation has a significant influence on predictions of skin friction in the Reynolds number range of interest on wind tunnel models.

Modeling mass transfer and substrate utilization in the boundary layer of biofilm systems

1998 ◽  
Vol 37 (4-5) ◽  
pp. 139-147 ◽  
Author(s):  
Harald Horn ◽  
Dietmar C. Hempel
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Film Theory ◽  
Substrate Utilization ◽  
The Other ◽  
Concentration Profiles ◽  
Hydrodynamic Conditions ◽  
Time Axis ◽  
Transfer Coefficients

The use of microelectrodes in biofilm research allows a better understanding of intrinsic biofilm processes. Little is known about mass transfer and substrate utilization in the boundary layer of biofilm systems. One possible description of mass transfer can be obtained by mass transfer coefficients, both on the basis of the stagnant film theory or with the Sherwood number. This approach is rather formal and not quite correct when the heterogeneity of the biofilm surface structure is taken into account. It could be shown that substrate loading is a major factor in the description of the development of the density. On the other hand, the time axis is an important factor which has to be considered when concentration profiles in biofilm systems are discussed. Finally, hydrodynamic conditions become important for the development of the biofilm surface when the Reynolds number increases above the range of 3000-4000.

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