Lagrangian statistics of pressure fluctuation events in homogeneous isotropic turbulence

Abstract

Homogeneous and isotropic turbulent fields obtained from two Direct Numerical Simulation databases (with Re λ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories. Motivated by cavitation inception modeling, the statistics of events in which such particles undergo low-pressure fluctuations were computed, parameterized by the amplitude of the fluctuations and by their duration. The main results are the average frequencies of these events and the probabilistic distribution of their duration, which are of predictive value. A connection is also established between these average frequencies and the pressure probability density function, thus justifying experimental methods proposed in the literature. Further analyses of the data show that the occurrence of very-low-pressure events is highly intermittent and is associated with worm-like vortical structures of length comparable to the integral scale of the flow.

On the pressure field, nuclei dynamics and their relation to cavitation inception in a turbulent shear layer

“…In contrast, for isotropic turbulence, the PDFs are non-symmetric with longer negative tails, which increase with Reynolds number (Bappy et al. 2019). The pressures are lower inside the QSVs, with similar shifts for both velocities, generally scaling with U 2 .…”

“…Hence, numerical simulations have been the primary source of information on the pressure in the core of eddies, although limited in Reynolds numbers. Recent studies aimed at understanding inception using Lagrangian pressure statistics following fluid elements or micro-bubbles have been performed for isotropic turbulence based on DNS data (Bappy, Carrica & Buscaglia 2019; Bappy et al. 2020).…”

A Short Review on the Preferential Concentration of Particles in Fluid Flow

“…Numerical investigations of the particle concentration in turbulence solve the Navier-Stokes equation and use the Eulerian velocity field u(x, t) to evolve the trajectories of tracers x(t), integrating the transport equation. For particles with inertia, drag and other force terms such as gravity appears in the computation [4]. The evolution of large-scale supercomputers in combination with efficient algorithms has enabled numerical simulations of turbulent flow and transport of millions of particles.…”

“…Bappy et al conducted several numerical studies on the Lagrangian transport of tracers and finite sized bubbles in homogeneous isotropic turbulence [33]- [35]. Comparing Reλ of 150 to 418, they have found that for tracer particles higher concentrations are observed at higher Taylor microscale Reynolds numbers [4]. Their subsequent studies were concerned with preferential concentrations of finite-sized bubbles in lowpressure regions of flow concerned with cavitation inception.…”

“…Stokes number is often used to determine the extent of such clustering, particles with 𝑆𝑡 ≪ 1 tend to follow fluid streamlines where particles with 𝑆𝑡 ≫ 1 do not significantly respond to the fluid within the times the fluid motions are coherent [2]. The dynamics of preferential concentration can significantly influence different fluid dynamics systems, for example, cloud droplet formation [2], respiratory droplet transport [2], aerosol and suspension production and transport [2], cavitation [3], [4], and even formation of planet and nebulae [2].…”