Characterising Single and Two-Phase Homogeneous Isotropic Turbulence with Stagnation Points
Abstract
:1. Introduction
2. Numerical Simulations
- DNS-512-1: , tracers, .
- DNS-512-2: , inertial particles with .
- DNS-512-3: , tracers, .
- DNS-512-4: , inertial particles with .
3. Results
3.1. Validation of the Generalized Rice Theorem in Single-Phase Turbulent Flows
3.2. Validation of the Rice Theorem in Two-Phase Turbulent Flows
4. Conclusions
- We verified the validity of the generalized Rice theorem for our dataset, which covers the range . Furthermore, we showed that the prefactor B in Equation (1), that quantifies the non-Gaussianity of velocity derivatives, has a weak dependence with , and that it tends to decrease when this parameter is increased.
- Furthermore, we showed that the generalized Rice theorem applies for time-averaged three-dimensional velocity fields, but also for instantaneous realizations.
- We proposed an interpolation scheme to reconstruct the stagnation points using the particles’ velocity field. Our results indicate that the Rice theorem cannot be applied in practice to two-phase three-dimensional turbulent flows, as the clustering of stagnation points forms very dense structures that require a very large number of particles to accurately sample the flow stagnation points. Even with tracers or inertial particles, we did not manage to apply the Rice theorem satisfactorily.
- We find that this lack of resolution of stagnation points is consistent with the strong clustering of STPS, as it implies the presence of very dense regions of these points, which require the injection of a very high number density of particles to be resolved. Another possible explanation for the lower number of STPS detected with the particles’ velocity field is the local stability of 3D STPS with unstable manifolds.
- While the number of the carrier phase STPS is always larger than the one obtained when using the interpolation scheme proposed here, we do find that they evolve over time following similar trends. This feature requires further study to be validated.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Dataset | N | # Snapshots | STPS | |||
---|---|---|---|---|---|---|
DNS-64 | 64 | 0.304 | 50 × 10 | 40 | 80 | 68 |
DNS-128 | 128 | 0.291 | 24 × 10 | 70 | 50 | 267 |
DNS-256 | 256 | 0.291 | 12 × 10 | 120 | 50 | 700 |
DNS-512 | 512 | 0.238 | 6 × 10 | 240 | 15 | 5707 |
DNS-1024 | 1024 | 0.309 | 3 × 10 | 520 | 9 | 7078 |
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Ferran, A.; Angriman, S.; Mininni, P.D.; Obligado, M. Characterising Single and Two-Phase Homogeneous Isotropic Turbulence with Stagnation Points. Dynamics 2022, 2, 63-72. https://doi.org/10.3390/dynamics2020004
Ferran A, Angriman S, Mininni PD, Obligado M. Characterising Single and Two-Phase Homogeneous Isotropic Turbulence with Stagnation Points. Dynamics. 2022; 2(2):63-72. https://doi.org/10.3390/dynamics2020004
Chicago/Turabian StyleFerran, Amélie, Sofía Angriman, Pablo D. Mininni, and Martín Obligado. 2022. "Characterising Single and Two-Phase Homogeneous Isotropic Turbulence with Stagnation Points" Dynamics 2, no. 2: 63-72. https://doi.org/10.3390/dynamics2020004