Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

2018 ◽  
Vol 860 ◽  
pp. 465-486 ◽  
Author(s):  
Nimish Pujara ◽  
Greg A. Voth ◽  
Evan A. Variano
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Inertial Range ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Scaling Exponents ◽  
Slender Body Theory ◽  
Velocity Statistics ◽  
Rigid Rods ◽  
Dissipation Range

We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.

scholarly journals Small-scale dynamics of settling, bidisperse particles in turbulence

2018 ◽  
Vol 839 ◽  
pp. 594-620 ◽  
Author(s):  
Rohit Dhariwal ◽  
Andrew D. Bragg
Keyword(s):  
Froude Number ◽  
Isotropic Turbulence ◽  
Spatial Clustering ◽  
Fluid Velocity ◽  
Vertical Motion ◽  
Collision Kernel ◽  
Small Scale ◽  
Inertial Particles ◽  
Plane Normal ◽  
The Difference

Mixing and collisions of inertial particles at the small scales of turbulence can be investigated by considering how pairs of particles move relative to each other. In real problems the two particles will have different sizes, i.e. they are bidisperse, and the effect of gravity on their motion is often important. However, how turbulence and gravity compete to control the motion of bidisperse inertial particles is poorly understood. Motivated by this, we use direct numerical simulations (DNS) to investigate the dynamics of settling, bidisperse particles in isotropic turbulence. In agreement with previous studies, we find that without gravity (i.e. $Fr=\infty$, where $Fr$ is the Froude number), bidispersity leads to an enhancement of the relative velocities, and a suppression of their spatial clustering. For $Fr<1$, the relative velocities in the direction of gravity are enhanced by the differential settling velocities of the bidisperse particles, as expected. However, we also find that gravity can strongly enhance the relative velocities in the ‘horizontal’ directions (i.e. in the plane normal to gravity). This non-trivial behaviour occurs because fast settling particles experience rapid fluctuations in the fluid velocity field along their trajectory, leading to enhanced particle accelerations and relative velocities. Indeed, the results show that even when $Fr\ll 1$, turbulence can still play an important role, not only on the horizontal motion, but also on the vertical motion of the particles. This is related to the fact that $Fr$ only characterizes the importance of gravity compared with some typical acceleration of the fluid, yet accelerations in turbulence are highly intermittent. As a consequence, there is a significant probability for particles to be in regions of the flow where the Froude number based on the local, instantaneous fluid acceleration is ${>}1$, even though the typically defined Froude number is $\ll 1$. This could imply, for example, that extreme events in the mixing of settling, bidisperse particles are only weakly affected by gravity even when $Fr\ll 1$. We also find that gravity drastically reduces the clustering of bidisperse particles. These results are strikingly different to the monodisperse case, for which recent results have shown that when $Fr<1$, gravity strongly suppresses the relative velocities in all directions, and can enhance clustering. Finally, we consider the implications of these results for the collision rates of settling, bidisperse particles in turbulence. We find that for $Fr=0.052$, the collision kernel is almost perfectly predicted by the collision kernel for bidisperse particles settling in quiescent flow, such that the effect of turbulence may be ignored. However, for $Fr=0.3$, turbulence plays an important role, and the collisions are only dominated by gravitational settling when the difference in the particle Stokes numbers is ${\geqslant}O(1)$.

Inertial particle relative velocity statistics in homogeneous isotropic turbulence

2012 ◽  
Vol 696 ◽  
pp. 45-66 ◽  
Author(s):  
Juan P. L. C. Salazar ◽  
Lance R. Collins
Keyword(s):  
Structure Function ◽  
Relative Velocity ◽  
Velocity Structure ◽  
Structure Functions ◽  
Inertial Subrange ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Scaling Exponents ◽  
Velocity Statistics ◽  
Dissipation Range

AbstractIn the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349–358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called ‘crossing trajectories’, the ‘sling effect’ or ‘caustics’, and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527–536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219–251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75–109), and highlights the interesting array of phenomena induced by inertia.

scholarly journals Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

2017 ◽  
Vol 825 ◽  
pp. 515-549 ◽  
Author(s):  
L. Sciacovelli ◽  
P. Cinnella ◽  
F. Grasso
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Equations Of State ◽  
Vapour Phase ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Dense Gas ◽  
Homogeneous Isotropic Turbulence ◽  
Third Invariant ◽  
Strong Expansion

The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics $\unicode[STIX]{x1D6E4}$ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

scholarly journals Fabrication of freestanding Pt nanowires for use as thermal anemometry probes in turbulence measurements

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Hai Le-The ◽  
Christian Küchler ◽  
Albert van den Berg ◽  
Eberhard Bodenschatz ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Room Temperature ◽  
Fluid Velocity ◽  
Current Mode ◽  
Constant Current ◽  
Small Scale ◽  
Turbulence Measurements ◽  
High Dynamic ◽  
Scale Turbulence ◽  
Constant Current Mode ◽  
Pt Nanowires

AbstractWe report a robust fabrication method for patterning freestanding Pt nanowires for use as thermal anemometry probes for small-scale turbulence measurements. Using e-beam lithography, high aspect ratio Pt nanowires (~300 nm width, ~70 µm length, ~100 nm thickness) were patterned on the surface of oxidized silicon (Si) wafers. Combining wet etching processes with dry etching processes, these Pt nanowires were successfully released, rendering them freestanding between two silicon dioxide (SiO2) beams supported on Si cantilevers. Moreover, the unique design of the bridge holding the device allowed gentle release of the device without damaging the Pt nanowires. The total fabrication time was minimized by restricting the use of e-beam lithography to the patterning of the Pt nanowires, while standard photolithography was employed for other parts of the devices. We demonstrate that the fabricated sensors are suitable for turbulence measurements when operated in constant-current mode. A robust calibration between the output voltage and the fluid velocity was established over the velocity range from 0.5 to 5 m s−1 in a SF6 atmosphere at a pressure of 2 bar and a temperature of 21 °C. The sensing signal from the nanowires showed negligible drift over a period of several hours. Moreover, we confirmed that the nanowires can withstand high dynamic pressures by testing them in air at room temperature for velocities up to 55 m s−1.

scholarly journals Flow topologies in bubble-induced turbulence: a direct numerical simulation analysis

2018 ◽  
Vol 857 ◽  
pp. 270-290 ◽  
Author(s):  
Josef Hasslberger ◽  
Markus Klein ◽  
Nilanjan Chakraborty
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Small Scale ◽  
Flow Topology ◽  
Two Phase ◽  
Local Flow ◽  
Interface Curvature

This paper presents a detailed investigation of flow topologies in bubble-induced two-phase turbulence. Two freely moving and deforming air bubbles that have been suspended in liquid water under counterflow conditions have been considered for this analysis. The direct numerical simulation data considered here are based on the one-fluid formulation of the two-phase flow governing equations. To study the development of coherent structures, a local flow topology analysis is performed. Using the invariants of the velocity gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible turbulent flows. The volume fraction of focal topologies in the gaseous phase is consistently higher than in the surrounding liquid phase. This observation has been argued to be linked to a strong vorticity production at the regions of simultaneous high fluid velocity and high interface curvature. Depending on the regime (steady/laminar or unsteady/turbulent), additional effects related to the density and viscosity jump at the interface influence the behaviour. The analysis also points to a specific term of the vorticity transport equation as being responsible for the induction of vortical motion at the interface. Besides the known mechanisms, this term, related to surface tension and gradients of interface curvature, represents another potential source of turbulence production that lends itself to further investigation.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian superdroplet simulations

2020 ◽  
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. Increase of the spectral width of initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase of the spectral width. We apply a large computational domain, 643 m3, one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with explicit small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence time scale is much larger than the droplet phase relaxation time scale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 μm is only sufficient for the lowest droplet concentration, 26 cm−3. For the highest droplet concentration, 650 cm−3, even an order of magnitude smaller bin size is not sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain, and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and relatively small number of Lagrangian particles that are used in the particle-based microphysics.

scholarly journals Concentration and velocity statistics of inertial particles in upward and downward pipe flow

2017 ◽  
Vol 822 ◽  
pp. 640-663 ◽  
Author(s):  
J. L. G. Oliveira ◽  
C. W. M. van der Geld ◽  
J. G. M. Kuerten
Keyword(s):  
Liquid Velocity ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Point Particle ◽  
Inertial Particles ◽  
Carrier Fluid ◽  
Velocity Statistics ◽  
The Difference

Three-dimensional particle tracking velocimetry is applied to particle-laden turbulent pipe flows at a Reynolds number of 10 300, based on the bulk velocity and the pipe diameter, for developed fluid flow and not fully developed flow of inertial particles, which favours assessment of the radial migration of the inertial particles. Inertial particles with Stokes number ranging from 0.35 to 1.11, based on the particle relaxation time and the radial-dependent Kolmogorov time scale, and a ratio of the root-mean-square fluid velocity to the terminal velocity of order 1 have been used. Core peaking of the concentration of inertial particles in up-flow and wall peaking in down-flow have been found. The difference in mean particle and Eulerian mean liquid velocity is found to decrease to approximately zero near the wall in both flow directions. Although the carrier fluid has all of the characteristics of the corresponding turbulent single-phase flow, the Reynolds stress of the inertial particles is different near the wall in up-flow. These findings are explained from the preferential location of the inertial particles with the aid of direct numerical simulations with the point-particle approach.

Kinematics of Small Scale Motions in Homogeneous Isotropic Turbulence

1991 ◽  
pp. 422-434 ◽  
Author(s):  
J. C. R. Hunt ◽  
J. C. H. Fung ◽  
N. A. Malik ◽  
R. J. Perkins ◽  
J. C. Vassilicos ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

A Nonlinear Method for Predicting Unsteady Sheet Cavitation on Marine Propellers

1983 ◽  
Vol 27 (01) ◽  
pp. 56-74
Author(s):  
Frederick Stern ◽  
William S. Vorus
Keyword(s):  
Complete Solution ◽  
Near Field ◽  
Fluid Velocity ◽  
Far Field ◽  
Static Potential ◽  
Nonlinear Method ◽  
Slender Body Theory ◽  
Marine Propellers ◽  
Sheet Cavitation ◽  
Dynamic Potential

A method is presented which provides a basis for predicting the nonlinear dynamic behavior of unsteady propeller sheet cavitation. The method separates the fluid velocity potential boundary-value problem into two parts, static and dynamic, which are solved sequentially in a forward time stepping procedure. The static potential problem is for the cavity fixed instantaneously relative to the propeller and the propeller translating through the nonuniform wake field. This problem can be solved by standard methods. The dynamic potential represents the instantaneous reaction of the cavity to the static potential field and thus predicts the cavity's deformation and motion relative to the blade. A solution is obtained for the dynamic potential by using the concepts of slender-body theory to define near-and far-field potentials which are matched to form the complete solution. In the far field, the cavity is represented by a three-dimensional spanwise line distribution of sources. In the near field, the cavity is approximated at each cross section as a semi-ellipse with unknown axes a(t), b(t), and position l(t) along the chord of the foil section. Conditions are derived that determine (a, b, l) by minimizing the square error in satisfying the dynamic boundary condition. These conditions yield the equations of motion of the cavity in the form of three coupled nonlinear second-order ordinary differential equations with time as the independent variable. The theory is presented for the general foil and not specifically for propellers. However, the method incorporates features in its formulation which facilitate its application to marine propellers. The method is demonstrated by using the steady noncavitating potential for the two-dimensional half-body as an approximation to the static potential. Both fixed and unsteady cavities are calculated. The unsteady cavities are calculated by varying the hydrostatic pressure in the half-body pressure field sinusoidally.

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