Session R39: Turbulence: Multiphase

Clustering of heavy particles in the inertial subrange of isotropic turbulence

The dynamics of inertial heavy particles in high Reynolds number turbulence, notably particle clustering, are important fundamental processes, e.g., for raindrop formation in atmospheric flows. Three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed at resolution 4096^3 for Re_\lambda = 648 and with 3.2 x 10^9 particles for several Stokes numbers. The results show clustering of inertial particles in the inertial subrange at high Reynolds number, in addition to the clustering typically observed in the near dissipation range. The particle number density spectra manifest a bump in the inertial subrange which is shown to be due to modulation of preferential concentration. It is also found that the number density spectra in the inertial subrange are a function of the scale-dependent Stokes number. For details we refer to Matsuda et al., Phys. Rev. Lett., 132, 234001, 2024.   

How sensitive is the near-wall accumulation of inertial particles to settling in a vertical turbulent boundary layer?

For horizontal turbulent boundary layers, it was shown in Bragg, Richter and Wang [Physical Review Fluids, 2021], that even when the settling number Sv is small, settling can strongly modify the near-wall accumulation of inertial particles. In applications, particles can feel a gravitational force either normal to the wall (horizontal flows) or parallel to the wall (vertical flows). For vertical flows, settling does not explicitly impact the transport of the particles in the direction of the walls. However, it does affect it implicitly since settling impacts how the particles interact with the turbulent flow, and the timescales of the flow measured along the particle trajectories. To explore whether the sensitivity to small Sv that was observed for horizontal boundary layers also occurs for vertical boundary layers, we conduct direct numerical simulations (DNS) of particles settling in a vertical turbulent channel flow for a range of Stokes numbers (St) and Sv. Our results also provide insights into how the preferential sweeping of the flow by the particles depends on distance from the wall, which is different from the case of a horizontal flow where other mechanisms also impact the particle settling velocity.   

Analytical Model for Indoor Decay of Airborne Particles

The dispersion of pathogen-laden particles in indoor environments depends on several factors, including room size, airflow strength, temperature, humidity, and the physical properties of expelled droplets and aerosols. Accurately predicting such a phenomenon remains an open challenge. In this presentation, we propose and validate an analytical formulation describing the temporal decay dependence of room-average particle concentration under a range of ambient conditions, including room size, the strength of air circulation, turbulence integral length scales, and particle size distributions. Large-eddy simulations of polydisperse droplets and aerosols are conducted in a horizontally-periodic environment, where air circulation is forced to generate homogeneous isotropic turbulence in the bulk of the flow. An analytical solution is derived for an average room concentration as a function of time, accounting for nuanced variability of flow and ambient room conditions. Model predictions compare well against the numerical data, showcasing the potential of the proposed formulation. The model is tailored for use within agent-based epidemiological modeling frameworks. This study contributes to our understanding of airborne disease transmission in indoor environments and proposes a foundation for improved risk assessment and mitigation strategies.   

Energy equations for gas-liquid compressible turbulent flows with phase change

We have derived the equations of turbulence kinetic energy (TKE), mean-flow kinetic energy (MFKE), and mean internal energy (MIE) for gas-liquid compressible flows with phase change. These equations allow us to explain the pathways of energy exchange within the gas or liquid phase, and between the gas and liquid phases. We explain the role of interfacial surface energy through the power of surface tension, and the role of phase change on the energy exchange through the phase change free energy. We relate the rate of the latter to the powers of mass flux, momentum flux, and heat flux due to phase change. This link explains the effect of evaporation or condensation on the modulation of TKE, MFKE and MIE in gas-liquid compressible turbulent flows. Furthermore, we rewrite these equations for the specific incompressible cases of droplet-laden homogeneous shear turbulence with phase change (DLHST-PC) and droplet-laden decaying homogeneous isotropic turbulence with phase change (DLHIT-PC).   

Anisotropy of particle-pair dispersion in bubble-induced turbulence

Bubble-induced turbulence (BIT) plays an important role in mixing, transport and collision of small particles in many natural and industrial applications. In recent years, Lagrangian measurements following the motion of individual fluid tracers have become possible in bubbly flows. A crucial component of the Lagrangian description of BIT is the relative pair dispersion, based on the relative separation of two particles at the respective positions. The present work aims to address the anisotropic property of particle-pair dispersion in BIT. For this purpose, 3D Lagrangian particle tracking measurements are carried out in an octagonal bubble column in which the flow is generated by a homogeneously distributed bubble swarm rising in water. Our results show that the relative dispersion follows the classical ballistic regime at short times. After this, the dispersion transitions to another regime whose behavior depends on the initial separation. We further developed a new method that allows us to quantify and visualize the anisotropy of particle-pair dispersion for varying initial separation vectors. We are currently obtaining improved data to explore and understand in more detail the anisotropic relative dispersion behavior.   

Lagrangian melting in homogeneous isotropic turbulence

In so-called Lagrangian melting problems, the melting of a solid object immersed in a fluid medium is coupled to a fluid-structure interaction problem, where the melting solid is free to translate and rotate according to the hydrodynamic loads exerted by the fluid. This in turn alters the ambient fluid flow surrounding the object, thereby altering the fluid convection which drives melting. Here, we aim to understand Lagrangian melting under turbulent flow conditions in an idealized setup by conducting direct numerical simulations of a melting sphere in homogeneous isotropic turbulence. We will consider variations in the turbulent forcing (the Taylor Reynolds number, Re_λ) as well as the Stokes number of the melting sphere. Both will play a critical role in determining the melting dynamics, as the dominant turbulent eddies which mix and drive fluid convection will ultimately be governed by these two key control parameters.   

Significance of Length Scale Models and Realizability in Free Surface Flows for NWTs Application

Numerical Wave Tanks (NWTs) necessitate a turbulent model that meets specific criteria: in regions of breaking waves and wave structure interactions that have very high shear rates, it must accurately compute the eddy viscosity to capture turbulent dynamics effectively. Conversely, in areas of regular non-breaking waves which has very low levels of turbulence, the model should preserve wave energy without unnecessary dissipation. This delicate balance ensures the numerical wave tank's capability to simulate both breaking and non-breaking wave phenomena with precision and fidelity. High shear rates are handled by the constitutive relationship, whereas the transport length scale equation deals with low Reynolds number effects. In this study, we will combine various constitutive relations and transport models to thoroughly understand and explain the physics underlying realizability and length scale model. A numerical study focuses on regular waves interacting with a fixed cylinder in a deep wave tank, with results validated against implemented DNS simulations and available experimental data. Results underscore the crucial rule of selecting an appropriate length scale model in conserving wave energy in low-turbulence regions and accurately capturing turbulent dynamics during wave-structure interactions, such as the secondary load cycle phenomenon. Moreover, the study indicates that non-breaking waves, characterized by high strain rates, cause turbulence to behave more like an elastic medium than a viscous one, rendering conventional Boussinesq constitutive relations physically inaccurate. Realizability conditions play a pivotal role in ensuring physically consistent Reynolds stresses in NWTs, thereby enhancing the fidelity of turbulence modeling.   

Divergence of critical fluctuations on approaching catastrophic phase inversion in turbulent emulsions

Catastrophic phase inversion, the breakdown of a concentrated emulsion characterized by the most puzzling sudden feature, is crucial in numerous industrial applications. Here we combine well-controlled experiments and fully-resolved numerical simulations to study the critical dynamics of catastrophic phase inversion in oil-water emulsions under turbulent flow as the phase-inversion volume-fraction is approached. We reveal that the phase inversion is characterized by the critical power-law divergence of fluctuations in the global drag force. We determine the enhanced dynamical heterogeneity in the local droplet structures at approaching the phase inversion, and tightly connect it to the diverging drag fluctuations. Moreover, we show that near to the critical point the phase inversion is triggered as a stochastic process by large fluctuations at both large and small scales. Our findings pave the way to modeling the phase inversion process as an out-of-equilibrium critical-like phenomena.   

Validation of Multiphase Interface Turbulence Modeling Technique for Cryogenic Fluid Management Applications

Modeling of turbulence transport at a gas-liquid interface has significant impact on phase change and heat transfer at the interface, which directly modulate pressure inside the cryogenic tank – an important quantity of interest for NASA’s deep space flight mission goals. A large range of length scales and time scales encountered in such problems – the interfacial physics has length scale of an order of tens to hundreds of micrometers and time scale of the order of milliseconds or less, but propellant tank length scale is an order of a meter with time scale for operations of interest spanning as long as days – make the modeling very challenging. An elegant interface turbulence modeling strategy was chosen to validate Loci-Stream-VOF – a Computation Fluid Dynamics (CFD) solver used by propulsion fluid dynamics branch at NASA Marshall Space Flight Center (MSFC) – for flight mission predictions. Following the evidence from experiments and direct numerical simulations (DNS), turbulence was damped near the gas-liquid interface in Reynolds Averaged Navier Stokes (RANS) modeling. The gas at orders of magnitude higher density than the liquid, exhibits reduced turbulence transport at the interface, i.e., “wall-like turbulence”. Depending on the flow regime the liquid side turbulence can either be damped (“wall-like”) or undamped or slightly enhanced turbulence (“freestream-like”). This approach was validated by three sets of flight-sized tests performed at NASA with liquid hydrogen, each with unique operations and flow features. Five axial jet driven pressure control tests and six self-pressurization tests conducted at NASA Glenn Research Center using K-site tank along with an unsubmerged autogenous pressurization test conducted at NASA MSFC with Engineering Design Unit (EDU) tank successfully validated this technique. Satisfactory validation using these parsimonious interface turbulence modeling approaches across operations demonstrates that the interfacial turbulence transport, and associated flow and thermal physics can be modeled with reasonable fidelity to predict at least some of the cryogenic tank operations in flight-sized tanks on large time scales in a practical manner.