Session J41: Multiphase Flows: Modeling and Theory I

Risk assessment using a fluid-mechanics informed statistical framework for short and long-term exposure for indoor airborne viral transmission

The risk of airborne viral contagion in indoor spaces can be greatly mitigated or aggravated by the quality of the ventilation system. Theoretical models [1] have been used extensively to predict the spread of infectious diseases in such settings. This work is aimed at providing a statistical framework to act as an improvement on the well-mixed theory by leveraging LES and RANS simulations of fluid flow and droplet nuclei dispersal in multiple room and ventilation configurations. The developed framework provides a simple multiplicative correction factor, that accounts for the roles of separation distance and filtration efficiency, to quantify the deviation of the simulations from the theory [2,3].

The framework is then used to provide guidelines for short and long-term occupancy in indoor spaces. The effect of factors such as separation distance, time of exposure and size of the indoor space on increasing or decreasing the probability of infection is relatively well understood. The contradictory effects of increasing flow rate on turbulent dispersion and rate of removal of droplet nuclei lead to a worst-case ACH for relatively short exposure times (under 30 minutes). The statistical framework is used to quantify this worst-case ACH for differing separation distances, filter efficiencies, and exposure times. For long-term exposure (more than an hour), the general guideline of operating at as high an ACH as possible is still applicable. For such scenarios, the role of the parameters mentioned above is used to provide guidelines for occupancy as a function of the cumulative exposure time.

 

References:

[1] M. Z. Bazant and J. W. Bush, A guideline to limit indoor airborne transmission of COVID-19, Proceedings of the National Academy of Sciences 118 (2021).

[2] J.S. Salinas, K.A. Krishnaprasad, N. Zgheib, and S. Balachandar, Improved guidelines of indoor airborne transmission taking into account departure from the well-mixed assumption, Physical Review Fluids 7, 064309 (2022).

[3] K.A. Krishnaprasad, J.S. Salinas, N. Zgheib, and S. Balachandar, Fluid mechanics of air recycling and filtration for indoor airborne transmission, Physics of Fluids 35, 013344 (2023).   

Evaluation of a Subgrid Surface Dynamics Model for Dual-Scale Modeling of Surface Tension Effects

Direct Numerical Simulation remains a prohibitively expensive task in Computational Fluid Dynamics, even more so for cases involving atomization. Instead of DNS, a dual-scale modeling approach (Gorokhovski and Herrmann, 2008) that describes turbulent phase interface dynamics in a Large Eddy Simulation spatial filtering context is proposed. Spatial filtering of the equations of fluid motion introduce several sub-filter terms that require modeling. Instead of developing individual closure models for the interface associated terms, the dual-scale approach uses an exact closure by explicitly filtering a fully resolved realization of the phase interface. This resolved realization is maintained using a Refined Local Surface Grid approach (Herrmann, 2008) employing an unsplit geometric Volume-of Fluid method (Owkes and Desjardins, 2014). Advection of the phase interface on this DNS scale requires a reconstruction of the fully resolved interface velocity. In this work, adaptations for a Sub-Grid Surface Dynamics (SGSD) model (Herrmann 2013) are applied to the VOF context. The SGSD model creates velocities that are not divergence-free and therefore must be corrected with a projection/correction step as in the Fractional Step Method. Since divergence-free velocities are needed only in the direct proximity of the phase interface, one can restrict the projection/correction to a narrow band surrounding the interface. Several implementations involving the size and boundary conditions of the Poisson equation are explored. Various test cases such as the oscillation period and damping of a weakly deformed mode 2 drop, the behavior of a stable and unstable Rayleigh-Plateau column, and viscous capillary break up of a ligament are used to evaluate the SGSD model.   

Volume of Fluid based study of the three phase dynamic contact line in the wetting of a thin channel.

To investigate the three-phase dynamic contact line in the wetting of thin channels, we numerically design a setup consisting of a pressure gradient driven two-phase flow inside a thin pore (width ~ 30-50 nm). The two phases are separated by an interfacial layer with surface tension, that meets the moving pore wall, hence, a three-phase dynamic contact line is formed, whose modelling is a significant scientific challenge [1], [2]. This setup is then studied numerically by solving the 2D two-phase Navier-Stokes equation subject to three contact line boundary conditions: The Navier slip boundary condition, the super-slip boundary condition and the generalised Navier boundary condition (GNBC). We use the Basilisk flow solver to do Volume-of-Fluid method based simulations with the surface tension force computed using the Continuous surface force method and curvature calculation using the height function. Steady state solutions are found and a critical capillary number, based on the contact line velocity, is predicted beyond which no steady-state solution exists. We see that the Navier slip model with a constant microscopic contact angle is weakly singular, however, sufficient to predict the critical capillary number for wetting. A parametric study with nanometric slip length is done and scaling laws for the interface bending are discovered in the vicinity of the contact line. Then we study the problem using the super-slip boundary condition and a novel VoF based implementation of the generalised Navier boundary condition GNBC. The results from these methods give direct evidence of more regularised solution in the vicinity of the contact line.

[1] Lācis, U., Pellegrino, M., Sundin, J., Amberg, G., Zaleski, S., Hess, B., & Bagheri, S. (2022). Nanoscale sheared droplet: Volume-of-fluid, phase-field and no-slip molecular dynamics. Journal of Fluid Mechanics, 940, A10.

[2] Liu, C., Vandre, E., Carvalho, M., & Kumar, S. (2016). Dynamic wetting failure and hydrodynamic assist in curtain coating. Journal of Fluid Mechanics, 808, 290-315.   

A Field-Monte-Carlo framework for simulating nucleate-boiling flows

The accuracy of simulations using Reynolds-averaged Navier-Stokes equations for boiling flows strongly depends on the correct modeling of the phase interaction, in particular the interfacial mass transfer. Different modeling approaches exist to address stochastic, non-linear effects in bubbly or droplet flows. Such approaches feature various tuning parameters that require a priori knowledge of the flow. In this study, we utilize a Field-Monte-Carlo method, in a fully Eulerian framework, in our implementation of a nucleate-boiling flow simulation. The Field-Monte-Carlo approach has been successfully applied to reacting flows as well as disperse two-phase flows for cavitation and spray; however, it has not been applied to nucleate-boiling flows. In this study, we implement the presented framework in a finite-volume environment, also combined with a second-order stochastic Runge-Kutta scheme. Additionally, we discuss the relevant closure terms and the solver algorithm. The test case considered is a flow through a duct with a single heated wall. The obtained results are compared to (1) the results of a commercial state-of-the-art model for boiling flows and (2) experimental results. Finally, we highlight the advantages of the presented approach.   

Hystereses in one-dimensional compression of a poroelastic hydrogel

We investigate theoretically the one-dimensional compression of a hydrogel layer by a uniform fluid flow normal to the gel surface. The flow is driven by a pressure drop across the gel layer, which is modeled as a poroelastic medium. Since the pressure simultaneously drives the Darcy flow through the pores and compresses the gel, the flux-pressure relationship can become non-monotonic. Most interestingly, we discover two types of hysteresis when either the pressure drop or the flux is controlled, which are also confirmed by transient numerical simulations. The hystereses stem from the interplay between the gel compression at the upstream interface and that in the bulk of the gel, and would not be predicted by models that ignore the interfacial compression. Finally, we suggest experimental setups and conditions to seek such hystereses in real gels.   

Volume oscillations slow down a rising Taylor bubble

Taylor bubbles -- volumes of gas rising in vertical tubes with an equivalent spherical diameter greater than the diameter of the tube -- are often encountered in the energy, chemical and oil industries. In a recent  paper (Zhou & Prosperetti, J. Fluid Mech.  920, R2, 2021) we have shown that, artificially constraining the bubble diameter by means of a porous surface coaxial with the tube, the rising velocity of the bubble can be considerably increased. This result establishes a connection between the bubble rising velocity and the drainage  liquid flow in the film separating the bubble from the tube wall. In the present work we find by numerical means that, if the bubble is forced to execute small-amplitude volume oscillations, subtle non-linear processes involving liquid inertia and the displacement of stagnation points on the bubble surface cause  the liquid film to become considerably thinner than  for an ordinary constant-volume Taylor bubble. Correspondingly, the bubble rise considerably slows down and very nearly stops.   

Effect of convergent-shaped vessel on the velocity of impact-induced focused liquid jets

The impact-induced focused liquid jet technology can eject high-viscosity liquids (up to about 8,000 mPa・s) with a simple mechanism. The generation of faster jets is expected to make it possible to use this technology in various fields, including industrial and medical fields. In this study, impact-induced liquid jet ejection experiments were conducted with two vessels to investigate the effect of vessel geometry on the jet velocity. We used a Kjeldahl flask, in which the two-dimensional pressure distribution is not negligible, and a test tube used in previous studies, which has a simple cylindrical shape and is considered to have a one-dimensional, linear pressure distribution. Remarkably, as a result, by using a Kjeldahl flask, we successfully generate jets with velocity about twice that of a test tube. To understand the results, the Laplace equation on the pressure impulse inside the vessel is solved numerically and analytically. The distribution of the pressure impulse showed consistent results with the jet velocity measured in experiments. Importantly, unlike the test tube with no cross-sectional area change, a convergent-shaped vessel has a stronger nonlinearity in the pressure impulse distribution, resulting in an increase in the liquid velocity at the gas-liquid interface.