We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the corresponding caustic contribution in $d$ spatial dimensions. The distribution of relative velocities Δv at small separations R acquires the universal form ρ(Δv,R) ~ R^{d-1}|Δv|^{D_2-2d} for large (but not too large) values of |Δv|. Here D_2 is the phase-space correlation dimension. Our conclusions are in excellent agreement with numerical simulations of particles suspended in a randomly mixing flow in two dimensions, and in quantitative agreement with published data on direct numerical simulations of particles in turbulent flows.
We perform direct numerical simulations of a bi-disperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and longitudinal relative velocities between particles of different sizes, and compare the results with recent theoretical predictions [Meibohm et al. Phys. Rev. E 96 (2017) 061102] for the shape of this distribution. We also compute the moments of relative velocities as a function of particle separation, and compare with the theoretical predictions. We observe good a…
The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterised by low vort…
We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols, via a new first-passage-time problem for Lagrangian tracers that are advected by a turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressible, Navier-Stokes equation, we obtain the time $t_R$ at which a tracer, initially at the origin of a sphere of radius $R$, crosses the surface of the sphere \textit{for the first time}. We obtain the probability distribution function $\mathcal{P}(R,t_R)$ and show that it displays two qualitatively different behaviors: (a) for $R \ll L_{\rm I}$, $\m…
We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analysing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, ${\rm St}$, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal ${\rm St}$. The power-law exponent is a non-analytic function of the mean Stokes number $\overline{\rm St}$, so that the exponent cannot be calculat…
We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme values of relative particle velocities for moderately inertial particles (St < 1). The probability distributions of relative velocities in the simulations were qualitatively similar to those in the experiments. The agreement improved with increasing Stokes number and decreasing relative velocity. Simulations underestimated the probability of extreme events, w…
Residence Time Distribution Analysis of Aerosol Transport and Associated Healthcare Worker Exposure in a Mock Hospital Isolation Room via Computational Fluid Dynamics
With the microdroplets of water serving as light scattering particles, the mist flow patterns of round micro-jets can be visualized using the Aerosol Jet(R) direct-write system. The visualization images show that the laminar mist jet appears to extend to more than 20 times the diameter of nozzle orifice, D, for jet Reynolds number Re < 600, especially with D = 0.3 mm and less. For smaller jets (e.g., with D = 0.15 mm), laminar collimated mist flow might be retained to 40xD for Re < 600 and for Re ~ 1500 within 20xD from the nozzle. The laminar part of mist flow associated with larger jets (e.g…
We analyze the effect of the Basset history force on the sedimentation of nearly neutrally buoyant particles, exemplified by marine snow, in a three-dimensional turbulent flow. Particles are characterized by Stokes numbers much smaller than unity, and still water settling velocities, measured in units of the Kolmogorov velocity, of order one. The presence of the history force in the Maxey-Riley equation leads to individual trajectories which differ strongly from the dynamics of both inertial particles without this force, and ideal settling tracers. When considering, however, a large ensemble o…
A key ingredient for single particle diffractive imaging experiments is the successful and efficient delivery of sample. Current sample-delivery methods are based on aerosol injectors in which the samples are driven by fluid-dynamic forces. These are typically simulated using Stokes' drag forces and for micrometer-size or smaller particles, the Cunningham correction factor is applied. This is not only unsatisfactory, but even using a temperature dependent formulation it fails at cryogenic temperatures. Here we propose the use of a direct computation of the force, based on Epstein's formulation…
The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures a timelike axis appears to emerge with which we can define vortex velocities in a useful way: with both numerical simulations and optical experiments, we show that the statistics of these velocities match those of turbulent quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. These statistics are shown to be independent of system scale. These results raise dee…
A model that predicts the outcome of collisions between droplets and particles in terms of the distribution of the droplet volume post-collision is lacking, in contrast to the case for droplet-droplet interactions. Taking existing models that successfully predict the outcomes (coalescence, stretching or reflexive separation) and post-separation characteristics (sizes, numbers and velocities of the resulting droplets) of droplet-droplet collisions and adapting them to take into account an inextensible, non-deformable particle with varying wettability characteristics, a new model is presented fo…
Wind-wave interaction involves wind forcing on wave surface and wave effects on the turbulent wind structures, which essentially influences the wind and wave loading on structures. Existing research on wind-wave interaction modeling ignores the inherent strong turbulences of wind. The present study aims to characterize the turbulent airflow over wave surfaces and wave dynamics under wind driving force. A high-fidelity two-phase model is developed to simulate highly turbulent wind-wave fields. Instead of using uniform wind, inherent wind turbulences are prescribed at the inlet boundary using th…
We revisit the longstanding question of the onset of sediment transport driven by a turbulent fluid flow via laboratory measurements. We use particle tracking velocimetry to quantify the fluid flow as well as the motion of individual grains. As we increase the flow speed above the transition to sediment transport, we observe that an increasing fraction of grains are transported downstream, although the average downstream velocity of the transported grains remains roughly constant. However, we find that the fraction of mobilized grains does not vanish sharply at a critical flow rate. Additional…
As everyone knows who has opened a kitchen faucet, pipe flow is laminar at low flow velocities and turbulent at high flow velocities. At intermediate velocities there is a transition wherein plugs of laminar flow alternate along the pipe with "flashes" of a type of fluctuating, non-laminar flow which remains poorly known. We show experimentally that the fluid friction of flash flow is diagnostic of turbulence. We also show that the statistics of flash flow are in keeping with Kolmogorov's phenomenological theory of turbulence (so that, e.g., the energy spectra of both flash flow and turbulent …
A dry deposition model suitable for use in the moment method has been developed. Contributions from five main processes driving the deposition - Brownian diffusion, interception, impaction, turbulent impaction, and sedimentation - are included in the model. The deposition model was employed in the moment method solver implemented in the OpenFOAM framework. Applicability of the developed expression and the moment method solver was tested on two example problems of particle dispersion in the presence of a vegetation on small scales: a flow through a tree patch in 2D and a flow through a hedgerow…
Direct Numerical Simulations of turbulent convection in a large aspect-ratio box are carried out in the range of Rayleigh number $7 \times 10^4 \le Ra \le 2 \times 10^6$ at Prandtl number Pr=0.71. A strong correlation between the vertical velocity and temperature is observed in the turbulent regime at almost all the length scales. Frequency spectra of all the velocities and temperature show a $-5/3$ law for a wide band of frequencies. The variances of horizontal velocities at different points in the flow yield a single power-law. Probability density functions of velocities and temperature are …
From the simplest models to complex deep neural networks, modeling turbulence with machine learning techniques still offers multiple challenges. In this context, the present contribution proposes a robust strategy using patch-based training to learn turbulent viscosity from flow velocities, and demonstrates its efficient use on the Spallart-Allmaras turbulence model. Training datasets are generated for flow past two-dimensional (2D) obstacles at high Reynolds numbers and used to train an auto-encoder type convolutional neural network with local patch inputs. Compared to a standard training tec…
Turbulent boundary layers over flat walls in the presence of a hill are frequently found in nature and industry. Some examples are the air flows over hills and desert dunes, but also water flows over aquatic dunes inside closed conduits. The perturbation of a two-dimensional boundary layer by a hill introduces new scales in the problem, changing the way in which velocities and stresses are distributed along the flow. When in the presence of sediment transport, the stress distribution along the hill is strongly related to bed instabilities. This paper presents an experimental study on the pertu…
We study the typical collisional velocities in a polydisperse suspension of droplets in two and three-dimensional turbulent flow and obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. We show that the impact velocity saturates exponentially with the inverse of the particle-size ratios. Our results are important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining pre…
The transport of sediments by a fluid flow is commonly found in nature and in industry. In nature, it is found in rivers, oceans, deserts, and other environments. In industry, it is found in petroleum pipelines conveying grains, in sewer systems, and in dredging lines, for example. This study investigates experimentally the transport of the grains of a granular bed sheared by a turbulent liquid flow. In our experiments, fully developed turbulent water flows were imposed over a flat granular bed of known granulometry. Under the tested conditions, the grains were transported as bed load, i.e., t…
A theoretical analysis is presented for turbulent flows, applicable for canonical (channel, boundary-layer and free jet) geometries. Momentum and energy balance for a control volume moving at the local mean velocity decouples the fluctuation from the mean velocities, resulting in a symmetric set of transport equations for the Reynolds normal and shear stresses. In this formalism, gradients of the fluctuating velocities represent flux vectors, easily verifiable using the available DNS data. A derivative of this transport concept is the scaling for the Reynolds stresses in the dissipation space.…
Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision-coagulation, on particle clustering and particle relative motion. We perform direct numerical simulation (DNS) of coagulating particles in isotropic turbulent flow in the regime of small Stokes number ($St=0.001-0.54$) and find that, due to collision-coagulation, the radial distribution functions (RDFs) fall-off dramatically at scales $r \sim d\,\,$ (where $d$ is the particle diameter) to small but finite values, while the mean radial-component of particle …
This paper employs an input-output based approach to analyze convective velocities and the transport of fluctuations in turbulent channel flows. The convective velocity for a fluctuating quantity associated with streamwise-spanwise wavelength pairs at each wall-normal location is obtained through the maximization of the power spectral density associated with the linearized Navier-Stokes equations with a turbulent mean profile and delta-correlated Gaussian forcing. We first demonstrate that the mean convective velocities computed in this manner agree well with those reported previously in the l…
It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We discuss the effect of a small viscosity on the self-similar solution of the Euler equations for inviscid fluids. Then we show that single point records of velocity fluctuations in the Modane wind tunnel display correlations between large velocities and large accelerations in full agreement with scaling laws derived from Leray's equations (1934) for self-similar…
Finding a quantitative description of the rate of collisions between small particles suspended in mixing flows is a long-standing problem. Here we investigate the validity of a parameterisation of the collision rate for identical particles subject to Stokes force, based on results for relative velocities of heavy particles that were recently obtained within a statistical model for the dynamics of turbulent aerosols. This model represents the turbulent velocity fluctuations by Gaussian random functions. We find that the parameterisation gives quantitatively good results in the limit where the \…
This paper presents an experimental study on the transition from smooth to rough walls, and back to the smooth one, in turbulent closed-conduit flows. These transitions cause a shift on flow velocity profiles that changes their parameters when compared to the flow over a smooth wall. Different water flow rates were imposed in a closed conduit of rectangular cross section, where rough elements consisting of cavities of d- and k-type were positioned covering a part of the bottom wall of the test section. Reynolds numbers based on the channel half-height were moderate, varying between 7800 and 96…
Direct numerical simulations of turbulent open channel flow with friction Reynolds numbers of $Re_τ=200,400,600$ are performed. Their results are compared with closed channel data in order to investigate the influence of the free surface on turbulent channel flows. The free surface affects fully developed turbulence statistics in so far that velocities and vorticities become highly anisotropic as they approach it. While the vorticity anisotropy layer scales in wall units, the velocity one is found to scale ith outer flow units and exhibits much larger extension. Furthermore the influence of th…
We study experimentally turbulent thermal diffusion of small particles in inhomogeneous and anisotropic stably stratified turbulence produced by one oscillating grid in the air flow. The velocity fields have been measured using a Particle Image Velocimetry (PIV). We have determined various turbulence characteristics: the mean and turbulent velocities, two-point correlation functions of the velocity field and an integral scale of turbulence from the measured velocity fields. The temperature field have been measured with a temperature probe equipped with 12 E thermocouples. Spatial distributions…
We extend the procedure outlined in [Basse, "Scaling of global properties of fluctuating and mean streamwise velocities in pipe flow: Characterization of a high Reynolds number transition region," Phys. Fluids Vol. 33, 065127 (2021)] to study global, i.e. radially averaged, scaling of streamwise velocity fluctuations. A viscous term is added to the log-law scaling which leads to the existence of a mathematical abstraction which we call the "global peak". The position and amplitude of this global peak are characterized and compared to the inner and outer peaks. A transition at a friction Reynol…
We study the self-similarity and dissipation scalings of a turbulent planar jet and the theoretically implied mean flow scalings. Unlike turbulent wakes where such studies have already been carried out (Dairay et al. 2015; Obligado et al. 2016), this is a boundary- free turbulent shear flow where the local Reynolds number increases with distance from inlet. The Townsend-George theory revised by Dairay et al. (2015) is applied to turbulent planar jets. Only a few profiles need to be self-similar in this theory. The self- similarity of mean flow, turbulence dissipation, turbulent kinetic energy …
We investigate the existence of multiple turbulent states in highly turbulent Taylor-Couette flow in the range of $\mathrm{Ta}=10^{11}$ to $9\cdot10^{12}$, by measuring the global torques and the local velocities while probing the phase space spanned by the rotation rates of the inner and outer cylinder. The multiple states are found to be very robust and are expected to persist beyond $\mathrm{Ta}=10^{13}$. The rotation ratio is the parameter that most strongly controls the transitions between the flow states; the transitional values only weakly depend on the Taylor number. However, complex p…
Dual-tip phase-detection probes can be used to measure flow properties in gas-liquid flows. Traditionally, time-averaged interfacial velocities have been obtained through cross-correlation analysis of long time-series of phase fraction signals. Using small groups of detected particles, a recently developed adaptive window cross-correlation (AWCC) technique enables the computation of pseudo-instantaneous interfacial velocities and turbulence quantities in highly aerated flows, albeit subject to some smoothing which is due to the use of a finite window duration. This manuscript provides guidance…
