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.

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.

On the stretching of material lines and surfaces in isotropic turbulence with zero fourth cumulants

1955 ◽  
Vol 51 (2) ◽  
pp. 350-362 ◽  
Author(s):  
W. H. Reid
Keyword(s):  
Fourth Order ◽  
Isotropic Turbulence ◽  
Constant Width ◽  
Scalar Fields ◽  
Volume Element ◽  
Strain Rates ◽  
Arbitrary Vector ◽  
Material Volume ◽  
Fourth Order Cumulant ◽  
Molecular Conduction

ABSTRACTThe convective effects of isotropic turbulence on arbitrary vector and scalar fields satisfying certain conservation conditions are studied under the assumption that all fourth-order cumulant tensors are zero. In the absence of molecular conduction, the behaviours of such vector and scalar fields are related to those of material lines and surfaces respectively, and the diffusive action of the turbulence results in a stretching of these lines and surfaces. The present analysis leads to a definite prediction for the corresponding strain rates which suggests that an initially spherical material volume element is drawn out into a long thin ribbon of constant width.

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.

scholarly journals Investigating the Use of Natural and Artificial Records for Prediction of Seismic Response of Regular and Irregular RC Bridges Considering Displacement Directions

2021 ◽  
Vol 11 (3) ◽  
pp. 906
Author(s):  
Payam Tehrani ◽  
Denis Mitchell
Keyword(s):  
Seismic Response ◽  
Radial Displacement ◽  
Time History ◽  
Good Prediction ◽  
3D Analysis ◽  
Combination Rules ◽  
Principal Axes ◽  
Artificial Records ◽  
The Mean ◽  
Irregular Bridges

The seismic responses of continuous multi-span reinforced concrete (RC) bridges were predicted using inelastic time history analyses (ITHA) and incremental dynamic analysis (IDA). Some important issues in ITHA were studied in this research, including: the effects of using artificial and natural records on predictions of the mean seismic demands, effects of displacement directions on predictions of the mean seismic response, the use of 2D analysis with combination rules for prediction of the response obtained using 3D analysis, and prediction of the maximum radial displacement demands compared to the displacements obtained along the principal axes of the bridges. In addition, IDA was conducted and predictions were obtained at different damage states. These issues were investigated for the case of regular and irregular bridges using three different sets of natural and artificial records. The results indicated that the use of natural and artificial records typically resulted in similar predictions for the cases studied. The effect of displacement direction was important in predicting the mean seismic response. It was shown that 2D analyses with the combination rules resulted in good predictions of the radial displacement demands obtained from 3D analyses. The use of artificial records in IDA resulted in good prediction of the median collapse capacity.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

scholarly journals Turbulence kinetic energy exchanges in flows with highly variable fluid properties

2017 ◽  
Vol 834 ◽  
pp. 5-54 ◽  
Author(s):  
Dorian Dupuy ◽  
Adrien Toutant ◽  
Françoise Bataille
Keyword(s):  
Reynolds Number ◽  
Temperature Gradient ◽  
Velocity Fluctuation ◽  
Spectral Studies ◽  
Spectral Energy ◽  
Correlation Tensor ◽  
Variable Fluid Properties ◽  
Fluid Properties ◽  
Energy Exchanges ◽  
The Mean

This paper investigates the energy exchanges associated with the half-trace of the velocity fluctuation correlation tensor in a strongly anisothermal low Mach fully developed turbulent channel flow. The study is based on direct numerical simulations of the channel within the low Mach number hypothesis and without gravity. The overall flow behaviour is governed by the variable fluid properties. The temperature of the two channel walls are imposed at 293 K and 586 K to generate the temperature gradient. The mean friction Reynolds number of the simulation is 180. The analysis is carried out in the spatial and spectral domains. The spatial and spectral studies use the same decomposition of the terms of the evolution equation of the half-trace of the velocity fluctuation correlation tensor. The importance of each term of the decomposition in the energy exchanges is assessed. This lets us identify the terms associated with variations or fluctuations of the fluid properties that are not negligible. Then, the behaviour of the terms is investigated. The spectral energy exchanges are first discussed in the incompressible case since the analysis is not present in the literature with the decomposition used in this study. The modification of the energy exchanges by the temperature gradient is then investigated in the spatial and spectral domains. The temperature gradient generates an asymmetry between the two sides of the channel. The asymmetry can in a large part be explained by the combined effect of the mean local variations of the fluid properties, combined with a Reynolds number effect.

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

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