The intense vorticity structures near the turbulent/non-turbulent interface in a jet

2011 ◽  
Vol 685 ◽  
pp. 165-190 ◽  
Author(s):  
Carlos B. da Silva ◽  
Ricardo J. N. dos Reis ◽  
José C. F. Pereira
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Isotropic Turbulence ◽  
Tangential Velocity ◽  
Sharp Decrease ◽  
Good Representation ◽  
Micro Scale ◽  
Vortex Model ◽  
Burgers Vortex ◽  
The Mean

AbstractThe characteristics of the intense vorticity structures (IVSs) near the turbulent/non-turbulent (T/NT) interface separating the turbulent and the irrotational flow regions are analysed using a direct numerical simulation (DNS) of a turbulent plane jet. The T/NT interface is defined by the radius of the large vorticity structures (LVSs) bordering the jet edge, while the IVSs arise only at a depth of about $5\eta $ from the T/NT interface, where $\eta $ is the Kolmogorov micro-scale. Deep inside the jet shear layer the characteristics of the IVSs are similar to the IVSs found in many other flows: the mean radius, tangential velocity and circulation Reynolds number are $R/ \eta \approx 4. 6$, ${u}_{0} / {u}^{\ensuremath{\prime} } \approx 0. 8$, and ${\mathit{Re}}_{\Gamma } / { \mathit{Re}}_{\lambda }^{1/ 2} \approx 28$, where ${u}_{0} $, and ${\mathit{Re}}_{\lambda } $ are the root mean square of the velocity fluctuations and the Reynolds number based on the Taylor micro-scale, respectively. Moreover, as in forced isotropic turbulence the IVSs inside the jet are well described by the Burgers vortex model, where the vortex core radius is stable due to a balance between the competing effects of axial vorticity production and viscous diffusion. Statistics conditioned on the distance from the T/NT interface are used to analyse the effect of the T/NT interface on the geometry and dynamics of the IVSs and show that the mean radius $R$, tangential velocity ${u}_{0} $ and circulation $\Gamma $ of the IVSs increase as the T/NT interface is approached, while the vorticity norm $\vert \omega \vert $ stays approximately constant. Specifically $R$, ${u}_{0} $ and $\Gamma $ exhibit maxima at a distance of roughly one Taylor micro-scale from the T/NT interface, before decreasing as the T/NT is approached. Analysis of the dynamics of the IVS shows that this is caused by a sharp decrease in the axial stretching rate acting on the axis of the IVSs near the jet edge. Unlike the IVSs deep inside the shear layer, there is a small predominance of vortex diffusion over stretching for the IVSs near the T/NT interface implying that the core of these structures is not stable i.e. it will tend to grow in time. Nevertheless the Burgers vortex model can still be considered to be a good representation for the IVSs near the jet edge, although it is not as accurate as for the IVSs deep inside the jet shear layer, since the observed magnitude of this imbalance is relatively small.

Material-element deformation in isotropic turbulence

1990 ◽  
Vol 220 ◽  
pp. 427-458 ◽  
Author(s):  
S. S. Girimaji ◽  
S. B. Pope
Keyword(s):  
Reynolds Number ◽  
Growth Rates ◽  
Isotropic Turbulence ◽  
Volume Element ◽  
Stationary Distributions ◽  
Principal Axes ◽  
Material Element ◽  
Material Volume ◽  
The Mean ◽  
Material Line

The evolution of infinitesimal material line and surface elements in homogeneous isotropic turbulence is studied using velocity-gradient data generated by direct numerical simulations (DNS). The mean growth rates of length ratio (l) and area ratio (A) of material elements are much smaller than previously estimated by Batchelor (1952) owing to the effects of vorticity and of non-persistent straining. The probability density functions (p.d.f.'s) of l/〈l〉 and A/〈A〉 do not attain stationarity as hypothesized by Batchelor (1952). It is shown analytically that the random variable l/〈l〉 cannot be stationary if the variance and integral timescale of the strain rate along a material line are non-zero and DNS data confirm that this is indeed the case. The application of the central limit theorem to the material element evolution equations suggests that the standardized variables $\hat{l}(\equiv (\ln l - \langle \ln l\rangle)/({\rm var} l)^{\frac{1}{2}})$ and Â(≡(ln A − 〈ln A〉)/(var A)½) should attain stationary distributions that are Gaussian for all Reynolds numbers. The p.d.f.s of $\hat{l}$ and  calculated from DNS data appear to attain stationary shapes that are independent of Reynolds number. The stationary values of the flatness factor and super-skewness of both $\hat{l}$ and  are in close agreement with those of a Gaussian distribution. Moreover, the mean and variance of ln l (and ln A) grow linearly in time (normalized by the Kolmogorov timescale, τη), at rates that are nearly independent of Reynolds number. The statistics of material volume-element deformation are also studied and are found to be nearly independent of Reynolds number. An initially spherical infinitesimal volume of fluid deforms into an ellipsoid. It is found that the largest and the smallest of the principal axes grow and shrink respectively, exponentially in time at comparable rates. Consequently, to conserve volume, the intermediate principal axis remains approximately constant.The performance of the stochastic model of Girimaji & Pope (1990) for the velocity gradients is also studied. The model estimates of the growth rates of 〈ln l〉 and 〈ln A〉 are close to the DNS values. The growth rate of the variances are estimated by the model to within 17%. The stationary distributions of $\hat{l}$ and  obtained from the model agree very well with those calculated from DNS data. The model also performs well in calculating the statistics of material volume-element deformation.

scholarly journals The scaling of straining motions in homogeneous isotropic turbulence

2017 ◽  
Vol 829 ◽  
pp. 31-64 ◽  
Author(s):  
G. E. Elsinga ◽  
T. Ishihara ◽  
M. V. Goudar ◽  
C. B. da Silva ◽  
J. C. R. Hunt
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Local Strain ◽  
Scale Structure ◽  
Small Scale ◽  
Length Scale ◽  
Local Flow ◽  
Small Scale Structure

The scaling of turbulent motions is investigated by considering the flow in the eigenframe of the local strain-rate tensor. The flow patterns in this frame of reference are evaluated using existing direct numerical simulations of homogeneous isotropic turbulence over a Reynolds number range from $Re_{\unicode[STIX]{x1D706}}=34.6$ up to 1131, and also with reference to data for inhomogeneous, anisotropic wall turbulence. The average flow in the eigenframe reveals a shear layer structure containing tube-like vortices and a dissipation sheet, whose dimensions scale with the Kolmogorov length scale, $\unicode[STIX]{x1D702}$. The vorticity stretching motions scale with the Taylor length scale, $\unicode[STIX]{x1D706}_{T}$, while the flow outside the shear layer scales with the integral length scale, $L$. Furthermore, the spatial organization of the vortices and the dissipation sheet defines a characteristic small-scale structure. The overall size of this characteristic small-scale structure is $120\unicode[STIX]{x1D702}$ in all directions based on the coherence length of the vorticity. This is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Comparing the overall size of the characteristic small-scale structure with the largest flow scales and the vorticity stretching motions on the scale of $4\unicode[STIX]{x1D706}_{T}$ shows that transitions in flow structure occur where $Re_{\unicode[STIX]{x1D706}}\approx 45$ and 250. Below these respective transitional Reynolds numbers, the small-scale motions and the vorticity stretching motions are progressively less well developed. Scale interactions are examined by decomposing the average shear layer into a local flow, which is induced by the shear layer vorticity, and a non-local flow, which represents the environment of the characteristic small-scale structure. The non-local strain is $4\unicode[STIX]{x1D706}_{T}$ in width and height, which is consistent with observations in high Reynolds number flow of a $4\unicode[STIX]{x1D706}_{T}$ wide instantaneous shear layer with many $\unicode[STIX]{x1D702}$-scale vortical structures inside (Ishihara et al., Flow Turbul. Combust., vol. 91, 2013, pp. 895–929). In the average shear layer, vorticity aligns with the intermediate principal strain at small scales, while it aligns with the most stretching principal strain at larger scales, consistent with instantaneous turbulence. The length scale at which the alignment changes depends on the Reynolds number. When conditioning the flow in the eigenframe on extreme dissipation, the velocity is strongly affected over large distances. Moreover, the associated peak velocity remains Reynolds number dependent when normalized by the Kolmogorov velocity scale. It signifies that extreme dissipation is not simply a small-scale property, but is associated with large scales at the same time.

Effects of wavelength and amplitude of a wavy cylinder in cross-flow at low Reynolds numbers

2009 ◽  
Vol 620 ◽  
pp. 195-220 ◽  
Author(s):  
K. LAM ◽  
Y. F. LIN
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Shear Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Free Shear Layer ◽  
The Mean

Three-dimensional numerical simulations of laminar flow around a circular cylinder with sinusoidal variation of cross-section along the spanwise direction, named ‘wavy cylinder’, are performed. A series of wavy cylinders with different combinations of dimensionless wavelength (λ/Dm) and wave amplitude (a/Dm) are studied in detail at a Reynolds number of Re = U∞Dm/ν = 100, where U∞ is the free-stream velocity and Dm is the mean diameter of a wavy cylinder. The results of variation of mean drag coefficient and root mean square (r.m.s.) lift coefficient with dimensionless wavelength show that significant reduction of mean and fluctuating force coefficients occurs at optimal dimensionless wavelengths λ/Dm of around 2.5 and 6 respectively for the different amplitudes studied. Based on the variation of flow structures and force characteristics, the dimensionless wavelength from λ/Dm = 1 to λ/Dm = 10 is classified into three wavelength regimes corresponding to three types of wake structures. The wake structures at the near wake of different wavy cylinders are captured. For all wavy cylinders, the flow separation line varies along the spanwise direction. This leads to the development of a three-dimensional free shear layer with periodic repetition along the spanwise direction. The three-dimensional free shear layer of the wavy cylinder is larger and more stable than that of the circular cylinder, and in some cases the free shear layer even does not roll up into a mature vortex street behind the cylinder. As a result, the mean drag coefficients of some of the typical wavy cylinders are less than that of a corresponding circular cylinder with a maximum drag coefficient reduction up to 18%. The r.m.s. lift coefficients are greatly reduced to practically zero at optimal wavelengths. In the laminar flow regime (60 ≤ Re ≤ 150), the values of optimal wavelength are Reynolds number dependent.

A Closer Investigation of the Mean Aerodynamic Forces for Two Staggered Circular Cylinders in Cross-Flow

2002 ◽  
Author(s):  
D. Sumner ◽  
M. D. Richards
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Incidence Angle ◽  
Cross Flow ◽  
Local Maximum ◽  
Circular Cylinders ◽  
Aerodynamic Forces ◽  
Gap Flow ◽  
The Mean ◽  
Small Increments

Two circular cylinders of equal diameter in a staggered configuration, with centre-to-centre pitch ratios of P/D = 1.125 – 4.0, were tested in the subcritical Reynolds number regime, at Re = 3.0×104 – 8.0×104. The incidence angle of the cylinder configuration was varied in small increments from α = 0° – 90° and the mean aerodynamic forces were measured on both the upstream and downstream cylinders. Based on the force measurements, the behaviour of the cylinders was broadly grouped into three categories, depending on P/D. For closely spaced staggered configurations, P/D = 1.125 – 1.25, the aerodynamic forces on both the upstream and downstream cylinders varied significantly with α. Several critical incidence angles were identified for each cylinder that corresponded to local maximum, minimum, or discontinuous behaviour in the forces, which were related to shear layer reattachment and the influence of the gap flow. For moderately spaced staggered configurations, P/D = 1.5 – 2.5, shear layer reattachment and the subsequent transition to gap flow at small α were responsible for the inner lift peak, a corresponding minimum drag, and a loss of lift with increasing α, which becomes more abrupt as P/D is increased. For widely spaced staggered configurations, P/D = 3.0 – 4.0, the two cylinders undergo Ka´rma´n vortex shedding for the entire range of α. At small α, the forces on the downstream cylinder are affected by vortex impingement, and the outer lift peak replaces the inner lift peak. This outer lift peak exhibits some sensitivity to the Reynolds number.

Assessment of Predictive Capabilities of Detached Eddy Simulation to Simulate Flow and Mass Transport Past Open Cavities

2007 ◽  
Vol 129 (11) ◽  
pp. 1372-1383 ◽  
Author(s):  
Kyoungsik Chang ◽  
George Constantinescu ◽  
Seung-O Park
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Transport Model ◽  
Detached Eddy Simulation ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Fine Mesh ◽  
The Mean

The three-dimensional (3D) incompressible flow past an open cavity in a channel is predicted using the Spalart–Almaras (SA) and the shear-stress-transport model (SST) based versions of detached eddy simulation (DES). The flow upstream of the cavity is fully turbulent. In the baseline case the length to depth (L∕D) ratio of the cavity is 2 and the Reynolds number ReD=3360. Unsteady RANS (URANS) is performed to better estimate the performance of DES using the same code and meshes employed in DES. The capabilities of DES and URANS to predict the mean flow, velocity spectra, Reynolds stresses, and the temporal decay of the mass of a passive contaminant introduced instantaneously inside the cavity are assessed based on comparisons with results from a well resolved large eddy simulation (LES) simulation of the same flow conducted on a very fine mesh and with experimental data. It is found that the SA-DES simulation with turbulent fluctuations at the inlet gives the best overall predictions for the flow statistics and mass exchange coefficient characterizing the decay of scalar mass inside the cavity. The presence of inflow fluctuations in DES is found to break the large coherence of the vortices shed in the separated shear layer that are present in the simulations with steady inflow conditions and to generate a wider range of 3D eddies inside the cavity, similar to LES. The predictions of the mean velocity field from URANS and DES are similar. However, URANS predictions show poorer agreement with LES and experiment compared to DES for the turbulence quantities. Additionally, simulations with a higher Reynolds number (ReD=33,600) and with a larger length to depth ratio (L∕D=4) are conducted to study the changes in the flow and shear-layer characteristics, and their influence on the ejection of the passive contaminant from the cavity.

scholarly journals Are mean vertical velocities from PMSE a good representation of mean vertical winds?

2018 ◽  
Author(s):  
Nikoloz Gudadze ◽  
Gunter Stober ◽  
Jorge L. Chau
Keyword(s):  
Vertical Velocity ◽  
Middle Atmosphere ◽  
Weighted Average ◽  
Sharp Decrease ◽  
Good Representation ◽  
Velocity Measurements ◽  
Particle Sedimentation ◽  
Lower Upper ◽  
The Mean ◽  
Vertical Winds

Abstract. Mean vertical velocity measurements obtained from Radars at polar latitudes using Polar Mesosphere Summer Echoes (PMSE) as an inert tracer have been considered as non-representative of the mean vertical winds over the last couple of decades. PMSEs observed with the Middle Atmosphere Alomar Radar System (MAARSY) over Andøya, Norway (69.30° N, 16.04° E) during summers of 2016 and 2017 are used to derive mean vertical winds in the upper mesosphere. The 3D vector wind components (zonal, meridional and vertical) are based on a Doppler beam swinging experiment using 5-beam directions (one vertical and four obliques). The 3D wind components are computed using a recently developed wind retrieval technique. The method includes full non-linear error-propagation, spatial and temporal regularization as well as beam pointing corrections and angular pointing uncertainties. Measurement uncertainties are used as weights to obtain seasonal weighted averages and characterize seasonal mean vertical velocity. Weighted average values of vertical velocities reveal a weak upward behaviour at altitudes 84–87 km after eliminating the influence of ice falling speed. At the same time, a sharp decrease/increase in the mean vertical velocities at the lower/upper edges of the summer mean altitude profile prevails, which are attributed to the sampling issues of PMSE due to disappearing of the target corresponding to the certain regions of motions and temperatures. Thus the mean vertical velocities can be biased with decrease up-/down-ward velocity measurements at lower/upper edges, while at the main central region the obtained mean vertical velocities are consistent with expected values of mean vertical winds after considering ice particle sedimentation.

Mean Rise-Rate of Droplets in Isotropic Turbulence

2002 ◽  
Author(s):  
P. D. Friedman ◽  
J. Katz
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
Isotropic Turbulence ◽  
Stokes Number ◽  
Mean Flow ◽  
Rise Rate ◽  
High Turbulence ◽  
The Mean ◽  
Surrounding Fluid ◽  
Quiescent Fluid

This paper investigates the rise-rate of droplets that are slightly lighter than the surrounding fluid. We experimentally investigate the effect of three parameters: Stokes number, turbulence intensity and droplet Reynolds number. Droplets were injected into a chamber with nearly isotropic turbulence and little mean flow. The results show that at high turbulence intensity, the mean droplet rise-rate is 25% of the rms velocity regardless of the Stokes number, while at low turbulence intensity, the droplets rise at a rate equal to the rise-rate in a quiescent fluid. At intermediate turbulence intensity, the rise-rate is strongly dependent on the Stokes number.

Triple velocity correlations in isotropic turbulence

1951 ◽  
Vol 47 (1) ◽  
pp. 146-157 ◽  
Author(s):  
R. W. Stewart
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Mean Wind Speed ◽  
The Mean ◽  
Mesh Grid ◽  
Working Section

AbstractThe triple velocity correlation, in turbulence produced by inserting a square-mesh grid near the beginning of the working section of a wind tunnel, has been measured for mesh Reynolds numbers of RM = 5300, 21,200 and 42,400 (RM = UM/ν, where U is the mean wind speed in the working section of the tunnel and M is the centre to centre spacing of the rods making up the grid; ν is the kinematic viscosity of air). At the lowest Reynolds number the correlation has been measured at distances downstream of the grid varying from 20 to 120M. This range covers practically all of the initial period of the decay of turbulence, where the turbulent intensity varies as t−1.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

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