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.

High-Fidelity Simulations of a High-Pressure Turbine Stage: Effects of Reynolds Number and Inlet Turbulence

2021 ◽  
Author(s):  
Yaomin Zhao ◽  
Richard D. Sandberg
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Suction Side ◽  
Rotor Blades ◽  
High Fidelity ◽  
Mean Flow ◽  
High Pressure Turbine ◽  
Flow Shear ◽  
Phase Lock ◽  
The Mean

Abstract We present the first wall-resolved high-fidelity simulations of high-pressure turbine (HPT) stages at engine-relevant conditions. A series of cases have been performed to investigate the effects of varying Reynolds numbers and inlet turbulence on the aerothermal behavior of the stage. While all of the cases have similar mean pressure distribution, the cases with higher Reynolds number show larger amplitude wall shear stress and enhanced heat fluxes around the vane and rotor blades. Moreover, higher-amplitude turbulence fluctuations at the inlet enhance heat transfer on the pressure-side and induce early transition on the suction-side of the vane, although the rotor blade boundary layers are not significantly affected. In addition to the time-averaged results, phase-lock averaged statistics are also collected to characterize the evolution of the stator wakes in the rotor passages. It is shown that the stretching and deformation of the stator wakes is dominated by the mean flow shear, and their interactions with the rotor blades can significantly intensify the heat transfer on the suction side. For the first time, the recently proposed entropy analysis has been applied to phase-lock averaged flow fields, which enables a quantitative characterization of the different mechanisms responsible for the unsteady losses of the stages. The results indicate that the losses related to the evolution of the stator wakes is mainly caused by the turbulence production, i.e. the direct interaction between the wake fluctuations and the mean flow shear through the rotor passages.

Kolmogoroff's theory of locally isotropic turbulence

1947 ◽  
Vol 43 (4) ◽  
pp. 533-559 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Isotropic Turbulence ◽  
Flow Characteristics ◽  
Turbulent Motion ◽  
Statistical Characteristics ◽  
Considerable Proportion ◽  
Arbitrary Field ◽  
Mean Flow ◽  
Local Mean

A new and fruitful theory of turbulent motion was published in 1941 by A. N. Kolmogoroff. It does not seem to be as widely known outside the U.S.S.R. as its importance warrants, and the present paper therefore describes the theory in some detail before presenting a number of extensions and making a comparison of experimental results with some of the theoretical predictions.Kolmogoroff's basic notion is that at high Reynolds number all kinds of turbulent motion, of arbitrary mean-flow characteristics, show a similar structure if attention is confined to the smallest eddies. The motion due to these eddies of limited size is conceived to be isotropic and statistically steady. Within this range of eddies we recognize two limiting processes. The influence of viscosity on the larger eddies of the range is negligible if the Reynolds number is large enough, so that their motion is determined entirely by the amount of energy which they are continually passing on to smaller eddies. This quantity of energy is the local mean energy dissipation due to turbulence. On the other hand, the smaller eddies of the range dissipate through the action of viscosity a considerable proportion of the energy which they receive, and the motion of the very smallest eddies is entirely laminar. The analytical expression of this physical picture is that the motion due to eddies less than a certain limiting size in an arbitrary field of turbulence is determined uniquely by two quantities, the viscosity and the local mean energy dissipation per unit mass of the fluid.The mathematical method of describing the motion due to eddies of a particular size is to construct correlations between the differences of parallel-velocity components at two points at an appropriate distance apart. Kinematical results analogous to those for turbulence which is isotropic in the ordinary sense are obtained, and then the scalar functions occurring in the expressions for the correlations are determined by dimensional analysis. The consequences of the theory in the case of turbulence which possesses ordinary isotropy are analysed and various predictions are made. One of these, namely that dimensionless ratios of moments of the probability distribution of the rate of extension of the fluid in any direction are universal constants, is confirmed by recent experiments, so far as the second and third moments are concerned. In several other cases it can be said that relations predicted by the theory have the correct form, but further experiments at Reynolds numbers higher than those hitherto used will be required before the theory can be regarded as fully confirmed. If valid, Kolmogoroff's theory of locally isotropic turbulence will provide a powerful tool for the analysis of problems of non-uniform turbulent flow, and for the determination of statistical characteristics of space and time derivatives of quantities influenced by the turbulence.

Field measurement of near-surface typhoon characteristics using a smart monitoring system on a long-span arch bridge site

2019 ◽  
Vol 22 (8) ◽  
pp. 1977-1987
Author(s):  
Xu Wang ◽  
Huaqiang Li ◽  
Zengshun Chen ◽  
Yuanhao Qian ◽  
Yanru Wang ◽  
...  
Keyword(s):  
Monitoring System ◽  
Wind Velocity ◽  
Turbulence Intensity ◽  
Eastern China ◽  
Mean Flow ◽  
Time Duration ◽  
Lateral Direction ◽  
Near Surface ◽  
Gust Factor ◽  
The Mean

During landfall of Typhoon Haikui in Eastern China in 2012, ground level wind data were recorded using a smart monitoring system installed on JiuBao Bridge in Hangzhou, China. This article documents the mean flow and turbulence characteristics from data recorded during the storm. The results show that both turbulence intensity and gust factor decrease with the increase in the mean wind velocity. However, as the mean wind velocity increases, this trend gradually attenuates. The peak factor distribution with gust averaging time duration derived with the Typhoon Haikui data agrees well with the Durst curve. However, the longitudinal gust factor derived from the typhoon wind-speed record in this study is higher compared with the curves proposed by Durst and Krayer-Marshall. Analyses of the gust factor distribution with the turbulence intensity during the passage of the storm reveal a similarity to the empirical curves of Ishizaki and Choi. Results show that the relationship between lateral turbulence and gust factors can be well represented by a quadratic polynomial. Turbulence scale increased with mean wind velocity. The values of autocorrelation coefficients in longitudinal direction are larger than those in lateral direction. There has no obvious dependency of cross-correlation coefficients with mean wind velocity. In general, the wind characteristics in this study are shown to be very similar to those of winds under normal circumstance.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

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.

Experimental Study of Vortex Shedding From a Solid Sphere in Turbulent Freestream

2005 ◽  
Author(s):  
Himanshu Tyagi ◽  
Rui Liu ◽  
David S.-K. Ting ◽  
Clifton R. Johnston
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Flow Velocity ◽  
Vortex Shedding ◽  
Isotropic Turbulence ◽  
Vortex Formation ◽  
Perforated Plate ◽  
Solid Sphere ◽  
Mean Flow ◽  
Static Pressure Distribution

The study of vortex shedding from a sphere assumes an important role because of its relevance to numerous aerodynamic and hydrodynamic applications. Parameters such as coefficient of drag and static pressure distribution are largely influenced by vortex shedding, and it is found by past studies that the freestream turbulence can interact and alter the vortex formation and shedding drastically. Most of these studies, however, were conducted in the low Reynolds number regime and the vortex shedding results had been described only qualitatively. To better understand the aerodynamics of a sphere in turbulent flow, an experimental study was initiated in a low speed wind tunnel to quantify the vortex shedding characteristics. The Reynolds number of the flow, based on the diameter of the sphere (d), was set at 3.3 × 104, 5 × 104 and 6.6 × 104 by varying the mean flow velocity. The sphere was placed at 20D (= 7.5d) downstream from a perforated plate, where D = 37.5 mm is the size of the holes in the perforated plate, uniquely designed for generating near-isotropic turbulence. Hot-wire measurements were taken at 10D (= 3.75d), 20D (= 7.5d) and 30D (= 11.25d) downstream of the sphere in absence and presence of the perforated plate. The vortex shedding frequency was deduced from the instantaneous flow velocity data.

Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

Reynolds number dependence of the mean flow in a circular pipe

1997 ◽  
Author(s):  
M. Zagarola ◽  
A. Smits ◽  
M. Zagarola ◽  
A. Smits
Keyword(s):  
Reynolds Number ◽  
Circular Pipe ◽  
Mean Flow ◽  
The Mean ◽  
Reynolds Number Dependence

Two-Dimensional Miter-Bend Flow

1971 ◽  
Vol 93 (3) ◽  
pp. 433-443 ◽  
Author(s):  
G. Heskestad
Keyword(s):  
Reynolds Number ◽  
Constant Width ◽  
Outer Wall ◽  
Two Dimensional ◽  
Mean Flow ◽  
Internal Flows ◽  
Concave Corner ◽  
Reynolds Number Effects ◽  
Bend Flow ◽  
The Mean

Measurements have been made of the mean flow in a two-dimensional, constant-width, ninety-degree miter bend and compared with predictions of available free-streamline theories. Agreement is quite favorable, especially with a model incorporating separation ahead of the concave corner. Reynolds number effects observed in real flows are argued to be associated with changes in the location of the outer-wall separation point. Requirements for relevancy of free-streamline models of internal flows separating at a salient edge are suggested and confirmed for cases examined.

Air-assisted atomization of liquid jets in varying levels of turbulence

2014 ◽  
Vol 764 ◽  
pp. 95-132 ◽  
Author(s):  
A. Kourmatzis ◽  
A. R. Masri
Keyword(s):  
Turbulence Intensity ◽  
Weber Number ◽  
Intensity Level ◽  
Flow Conditions ◽  
Mean Flow ◽  
Potential Core ◽  
Droplet Sizes ◽  
The Mean ◽  
Break Up ◽  
Primary Break

AbstractAir-assisted primary atomization is investigated in a configuration where liquid is injected in a turbulent gaseous jet flow both within as well as outside of the potential core. Cases are studied where the injection point is moved within the flow to maintain a range of constant gaseous mean velocities but changing local fluctuating velocity root-mean-square (r.m.s.) levels. Over a range of mean conditions, this allows for a systematic understanding of both the effects of gas-phase turbulence and mean shear on primary break-up independently. Extensive data is obtained and analysed from laser Doppler anemometry/phase Doppler anemometry, high-speed microscopic backlit imaging and advanced image processing. It is found that the ratio of the turbulent Weber number $\mathit{We}^{\prime }$ to the mean Weber number $\mathit{We}$ is a relevant parameter as is the turbulence intensity. The primary break-up length is found to be heavily influenced not only by the mean velocity, but also by the turbulence level and the mass fuel to air ratio. Above a particular threshold intensity level the break-up time changes in proportion to the change in the integral time scale of the flow. In addition, it is found that regardless of diameter and turbulent flow conditions at the liquid jet, the final size of ligaments converges to a value which is of the order of the measured primary instability wavelength (${\it\lambda}_{1}$). In contrast, cases of different turbulence intensity show the mean of droplet sizes diverging as the spray is advected downstream and this is because droplets are generated from ligaments, the latter of which are subjected both to Rayleigh–Taylor instabilities and turbulent fluctuations. This contribution, for the first time, examines the theoretical applicability of the Rayleigh–Taylor instability in flows where the turbulence is substantial with respect to the mean flow. It is shown that for high turbulence intensities a full theoretical reconstruction of the measured final droplet size distribution is possible from a probability density function of model Rayleigh–Taylor wavelengths (${\it\lambda}_{RT}$). In agreement with the literature (Varga et al. J. Fluid Mech., vol. 497, 2003, pp. 405–434), mean droplet sizes are found to be equal to a mean theoretical Rayleigh–Taylor wavelength normalized by a particular constant value. This, however, is only true for local turbulence intensities less than ${\sim}25\,\%$, or for ratios of the turbulent Weber number to mean Weber number ($\mathit{We}^{\prime }/\mathit{We}$) of less than ${\sim}6\,\%$. Above this, the normalization value is no longer constant, but increases with $\mathit{We}^{\prime }/\mathit{We}$. Finally, the instability wavelengths can be used as part of an approximation that estimates the total number of objects formed after break-up, where the object number is found to be dictated by a balance of both mean flow conditions and local turbulence.

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