Turbulence intensity in wall-bounded and wall-free flows

2015 ◽  
Vol 770 ◽  
pp. 289-304 ◽  
Author(s):  
Ian P. Castro
Keyword(s):  
Turbulence Intensity ◽  
Shear Flows ◽  
Outer Region ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Number Range ◽  
Reference Velocity ◽  
Wall Flows ◽  
Diagnostic Plot ◽  
Suitable Reference

Turbulence intensity variations in the outer region of turbulent shear flows are considered, in the context of the diagnostic plot first introduced by Alfredsson et al. (Phys. Fluids, vol. 23, 2011, 041702) and for both (smooth and rough) wall-bounded flows and classical free shear flows. With $U$ defined as the mean velocity within the flow, $U_{e}$ as a suitable reference velocity and $u^{\prime }$ as the root mean square of the fluctuating velocity, it is demonstrated that, for wall flows, the attached eddy hypothesis yields a closely linear diagnostic plot ($u^{\prime }/U$ versus $U/U_{e}$) over a certain Reynolds number range, explaining why the relation seems to work well for both boundary layers and channels despite its lack of any physical basis (Castro et al., J. Fluid Mech., vol. 727, 2013, pp. 119–131). It is shown that mixing layers, jets and wakes also exhibit linear variations of $u^{\prime }/U$ versus $U/U_{e}$ over much of the flows (starting roughly from where the turbulence production is a maximum), with slopes of these variations determined by the total mean strain rate, characterised by Townsend’s flow constant $R_{s}$. The diagnostic plot thus has a wider range of applicability than might have been anticipated.

Weakly sheared turbulent flows generated by multiscale inhomogeneous grids

2018 ◽  
Vol 848 ◽  
pp. 788-820 ◽  
Author(s):  
Shaokai Zheng ◽  
P. J. K. Bruce ◽  
J. M. R. Graham ◽  
J. C. Vassilicos
Keyword(s):  
Velocity Profile ◽  
Turbulence Intensity ◽  
Shear Flows ◽  
Vertical Direction ◽  
Turbulent Shear ◽  
Incoming Flow ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean ◽  
Vertical Bars

A group of three multiscale inhomogeneous grids have been tested to generate different types of turbulent shear flows with different mean shear rate and turbulence intensity profiles. Cross hot-wire measurements were taken in a wind tunnel with Reynolds number$Re_{D}$of 6000–20 000, based on the width of the vertical bars of the grid and the incoming flow velocity. The effect of local drag coefficient$C_{D}$on the mean velocity profile is discussed first, and then by modifying the vertical bars to obtain a uniform aspect ratio the mean velocity profile is shown to be predictable using the local blockage ratio profile. It is also shown that, at a streamwise location$x=x_{m}$, the turbulence intensity profile along the vertical direction$u^{\prime }(y)$scales with the wake interaction length$x_{\ast ,n}^{peak}=0.21g_{n}^{2}/(\unicode[STIX]{x1D6FC}C_{D}w_{n})$($\unicode[STIX]{x1D6FC}$is a constant characterizing the incoming flow condition, and$g_{n}$,$w_{n}$are the gap and width of the vertical bars, respectively, at layer$n$) such that$(u^{\prime }/U_{n})^{2}\unicode[STIX]{x1D6FD}^{2}(C_{D}w_{n}/x_{\ast ,n}^{peak})^{-1}\sim (x_{m}/x_{\ast ,n}^{peak})^{b}$, where$\unicode[STIX]{x1D6FD}$is a constant determined by the free-stream turbulence level,$U_{n}$is the local mean velocity and$b$is a dimensionless power law constant. A general framework of grid design method based on these scalings is proposed and discussed. From the evolution of the shear stress coefficient$\unicode[STIX]{x1D70C}(x)$, integral length scale$L(x)$and the dissipation coefficient$C_{\unicode[STIX]{x1D716}}(x)$, a simple turbulent kinetic energy model is proposed that describes the evolution of our grid generated turbulence field using one centreline measurement and one vertical profile of$u^{\prime }(y)$at the beginning of the evolution. The results calculated from our model agree well with our measurements in the streamwise extent up to$x/H\approx 2.5$, where$H$is the height of the grid, suggesting that it might be possible to design some shear flows with desired mean velocity and turbulence intensity profiles by designing the geometry of a passive grid.

Asymptotic theory of turbulent shear flows

1970 ◽  
Vol 42 (2) ◽  
pp. 411-427 ◽  
Author(s):  
Kirit S. Yajnik
Keyword(s):  
Shear Flows ◽  
Functional Relationship ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Underdetermined System ◽  
Different Types ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
The Law

A theory is proposed in this paper to describe the behaviour of a class of turbulent shear flows as the Reynolds number approaches infinity. A detailed analysis is given for simple representative members of this class, such as fully developed channel and pipe flows and two-dimensional turbulent boundary layers. The theory considers an underdetermined system of equations and depends critically on the idea that these flows consist of two rather different types of regions. The method of matched asymptotic expansions is employed together with asymptotic hypotheses describing the order of various terms in the equations of mean motion and turbulent kinetic energy. As these hypotheses are not closure hypotheses, they do not impose any functional relationship between quantities determined by the mean velocity field and those determined by the Reynolds stress field. The theory leads to asymptotic laws corresponding to the law of the wall, the logarithmic law, the velocity defect law, and the law of the wake.

Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers

2016 ◽  
Vol 795 ◽  
pp. 210-240 ◽  
Author(s):  
D. T. Squire ◽  
C. Morrill-Winter ◽  
N. Hutchins ◽  
M. P. Schultz ◽  
J. C. Klewicki ◽  
...  
Keyword(s):  
Outer Region ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Smooth Wall ◽  
Mean Velocity ◽  
Wide Range ◽  
Velocity Variance ◽  
The Mean

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, ${\it\delta}_{99}^{+}$, and equivalent sand grain roughness Reynolds numbers, $k_{s}^{+}$ (smooth wall: $2020\leqslant {\it\delta}_{99}^{+}\leqslant 21\,430$, rough wall: $2890\leqslant {\it\delta}_{99}^{+}\leqslant 29\,900$; $22\leqslant k_{s}^{+}\leqslant 155$; and $28\leqslant {\it\delta}_{99}^{+}/k_{s}^{+}\leqslant 199$). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth- and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend’s (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with ${\it\delta}_{99}^{+}\gtrsim 14\,000$. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low ${\it\delta}_{99}^{+}$, the outer region of the inner-normalised streamwise velocity variance indicates a dependence on $k_{s}^{+}$ for the present rough surface.

scholarly journals Blind test comparison of the performance and wake flow between two in-line wind turbines exposed to different turbulent inflow conditions

2017 ◽  
Vol 2 (1) ◽  
pp. 55-76 ◽  
Author(s):  
Jan Bartl ◽  
Lars Sætran
Keyword(s):  
Wind Tunnel ◽  
Wind Turbines ◽  
Turbulence Intensity ◽  
Wake Flow ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Blind Test ◽  
Turbulent Inflow ◽  
The Mean ◽  
Inflow Conditions

Abstract. This is a summary of the results of the fourth blind test workshop that was held in Trondheim in October 2015. Herein, computational predictions on the performance of two in-line model wind turbines as well as the mean and turbulent wake flow are compared to experimental data measured at the wind tunnel of the Norwegian University of Science and Technology (NTNU). A detailed description of the model geometry, the wind tunnel boundary conditions and the test case specifications was published before the workshop. Expert groups within computational fluid dynamics (CFD) were invited to submit predictions on wind turbine performance and wake flow without knowing the experimental results at the outset. The focus of this blind test comparison is to examine the model turbines' performance and wake development with nine rotor diameters downstream at three different turbulent inflow conditions. Aside from a spatially uniform inflow field of very low-turbulence intensity (TI = 0.23 %) and high-turbulence intensity (TI = 10.0 %), the turbines are exposed to a grid-generated highly turbulent shear flow (TI = 10.1 %).Five different research groups contributed their predictions using a variety of simulation models, ranging from fully resolved Reynolds-averaged Navier–Stokes (RANS) models to large eddy simulations (LESs). For the three inlet conditions, the power and the thrust force of the upstream turbine is predicted fairly well by most models, while the predictions of the downstream turbine's performance show a significantly higher scatter. Comparing the mean velocity profiles in the wake, most models approximate the mean velocity deficit level sufficiently well. However, larger variations between the models for higher downstream positions are observed. Prediction of the turbulence kinetic energy in the wake is observed to be very challenging. Both the LES model and the IDDES (improved delayed detached eddy simulation) model, however, consistently manage to provide fairly accurate predictions of the wake turbulence.

Turbulent Shear Flows Over a Step Change in Surface Roughness

1981 ◽  
Vol 103 (2) ◽  
pp. 344-351 ◽  
Author(s):  
W. H. Schofield
Keyword(s):  
Surface Roughness ◽  
Shear Flows ◽  
Large Body ◽  
Velocity Profiles ◽  
Step Change ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Wall Condition ◽  
Turbulent Shear Flows ◽  
Usual Equilibrium

A large body of data now exists on the response of turbulent shear flows to sudden or step changes in surface roughness. Authors have used a variety of methods to reduce and present the data; thus a consistent description of these flows has not yet been presented. This paper presents all available data reduced in a uniform way. As there are extremely few Reynolds stress measurements within this large body of data, the analyses presented here are necessarily based on mean velocity profiles. It is shown that the growth rate of the new internal layer for all types of flow both with and without pressure gradient can be described in terms of a single length scale associated with the new wall condition. It is also shown that all mean velocity profiles after a step change in roughness display semi-logarithmic distributions. However, in the region immediately downstream of a step the constant of proportionality (the von Karman constant) has values different from the usual equilibrium value of 0.41. The differences appear to be large with values for the constant ranging between about 0.2 to 0.8.

Estimation of turbulent convection velocities and corrections to Taylor's approximation

2009 ◽  
Vol 640 ◽  
pp. 5-26 ◽  
Author(s):  
JUAN C. DEL ÁLAMO ◽  
JAVIER JIMÉNEZ
Keyword(s):  
Reynolds Number ◽  
Convection Velocity ◽  
New Method ◽  
Spectral Information ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Spatial Direction ◽  
Number Range ◽  
Logarithmic Layer ◽  
Semi Empirical

A new method is introduced for estimating the convection velocity of individual modes in turbulent shear flows that, in contrast to most previous ones, only requires spectral information in the temporal or spatial direction over which a modal decomposition is desired, while only using local derivatives in other directions. If no spectral information is desired, the method provides a natural definition for the average convection velocity, as well as a way to estimate the accuracy of the frozen-turbulence approximation. Existing data from numerical turbulent channels at friction Reynolds numbers Reτ ≤ 1900 are used to validate the new method against classical ones, and to characterize the dependence of the convection velocity on the eddy wavelength and wall distance. The results indicate that the small scales in turbulent channels travel at the local mean velocity, while large ‘global’ modes travel at a more uniform speed proportional to the bulk velocity. To estimate the systematic deviations introduced in experimental spectra by the use of Taylor's approximation with a wavelength-independent convection velocity, a semi-empirical fit to the computed convection velocities is provided. It represents well the data throughout the Reynolds number range of the simulations. It is shown that Taylor's approximation not only displaces the large scales near the wall to shorter apparent wavelengths but also modifies the shape of the spectrum, giving rise to spurious peaks similar to those observed in some experiments. To a lesser extent the opposite is true above the logarithmic layer. The effect increases with the Reynolds number, suggesting that some of the recent challenges to the kx−1 energy spectrum may have to be reconsidered.

scholarly journals LiSBOA: LiDAR Statistical Barnes Objective Analysis for optimal design of LiDAR scans and retrieval of wind statistics. Part II: Applications to synthetic and real LiDAR data of wind turbine wakes

2020 ◽  
Author(s):  
Stefano Letizia ◽  
Lu Zhan ◽  
Giacomo Valerio Iungo
Keyword(s):  
Optimal Design ◽  
Velocity Field ◽  
Turbulence Intensity ◽  
High Speed ◽  
Cartesian Grid ◽  
Objective Analysis ◽  
Turbulent Shear ◽  
Lidar Data ◽  
Mean Velocity ◽  
First Case

Abstract. The LiDAR Statistical Barnes Objective Analysis (LiSBOA), presented in Letizia et al., is a procedure for the optimal design of LiDAR scans and calculation over a Cartesian grid of the statistical moments of the velocity field. The LiSBOA is applied to LiDAR data collected in the wake of wind turbines to reconstruct mean and turbulence intensity of the wind velocity field. The proposed procedure is firstly tested for a numerical dataset obtained by means of the virtual LiDAR technique applied to the data obtained from a large eddy simulation (LES). The optimal sampling parameters for a scanning Doppler pulsed wind LiDAR are retrieved from the LiSBOA, then the estimated statistics are calculated showing a maximum error of about 4 % for both the normalized mean velocity and the turbulence intensity. Subsequently, LiDAR data collected during a field campaign conducted at a wind farm in complex terrain are analyzed through the LiSBOA for two different configurations. In the first case, the wake velocity fields of four utility-scale turbines are reconstructed on a 3D grid, showing the capability of the LiSBOA to capture complex flow features, such as high-speed jet around the nacelle and the wake turbulent shear layers. For the second case, the statistics of the wakes generated by four interacting turbines are calculated over a 2D Cartesian grid and compared to the measurements provided by the nacelle-mounted anemometers. Maximum discrepancies as low as 3 % for the normalized mean velocity and turbulence intensity endorse the application of the LiSBOA for LiDAR-based wind resource assessment and diagnostic surveys for wind farms.

A unified approach for symmetries in plane parallel turbulent shear flows

2001 ◽  
Vol 427 ◽  
pp. 299-328 ◽  
Author(s):  
MARTIN OBERLACK
Keyword(s):  
Shear Flows ◽  
Stokes Equations ◽  
Turbulent Shear ◽  
Large Set ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Law Of The Wall ◽  
Turbulent Shear Flows ◽  
The Mean ◽  
Logarithmic Law

A new theoretical approach for turbulent flows based on Lie-group analysis is presented. It unifies a large set of ‘solutions’ for the mean velocity of stationary parallel turbulent shear flows. These results are not solutions in the classical sense but instead are defined by the maximum number of possible symmetries, only restricted by the flow geometry and other external constraints. The approach is derived from the Reynolds-averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile not previously reported that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near-wall regions in both experimental and DNS data of turbulent channel flows. In the case of the logarithmic law of the wall, the scaling with the distance from the wall arises as a result of the analysis and has not been assumed in the derivation. All solutions are consistent with the similarity of the velocity product equations to arbitrary order. A method to derive the mean velocity profiles directly from the two-point correlation equations is shown.

Some observations of the effects of micro-organisms growing on the bed of an open channel on the turbulence properties

2002 ◽  
Vol 450 ◽  
pp. 317-341 ◽  
Author(s):  
V. I. NIKORA ◽  
D. G. GORING ◽  
B. J. F. BIGGS
Keyword(s):  
Large Scale ◽  
Outer Region ◽  
Biologically Active ◽  
Turbulent Shear ◽  
Spectral Energy ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Flow Interactions ◽  
The Mean ◽  
Micro Organisms

In this paper we report the results of an experimental study of periphyton–flow interactions conducted in a specially designed outdoor hydraulic flume. ‘Periphyton’ is a collective term for the micro-organisms which grow on stream beds, and includes algae, bacteria, and fungi, with algae usually the dominant and most conspicuous component. The main goals of the study are to identify potential effects of periphyton–flow interactions as well as the potential mechanisms of mass transfer in the near-bed region, which could influence periphyton growth and losses. The main results of the study may be summarized as follows.A linear velocity distribution in the interfacial sublayer (i.e. below the roughness tops), and a logarithmic distribution above the roughness tops appeared to be reasonable approximations for both flow types, with and without periphyton on the bed. However, the appearance of periphyton on a rough bed shifts the origin of the bed upwards, increases the roughness length zo by 16–21%, and reduces the ratio of the mean velocity at the level of roughness tops to the shear velocity by ≈30%. In general, below the roughness tops the periphyton suppresses the mean velocities, the turbulent stresses, turbulence intensities, and vertical turbulent fluxes of the turbulent energy and turbulent shear stresses.It was found that in flows without periphyton large-scale eddies successfully penetrate the interfacial sublayer. However, tufts of periphyton on the tops of the roughness elements significantly weaken the penetration processes leading to spatial de-correlation in the velocity field within the interfacial sublayer. The appearance of periphyton on the bed does not change appreciably the velocity spectra above the roughness tops but reduces the total spectral energy and generates a wide spectral peak in the interfacial sublayer. Most probably, this peak is formed by penetration of sweep events into the interfacial sublayer, ‘filtered’ by the periphyton tufts. Thus, sweep events may be the main mechanism responsible for the delivery of nutrients from the outer region to the biologically active interfacial sublayer. The potential effects of flow properties on the periphyton community are also discussed.

Sign in / Sign up

Export Citation Format

Share Document