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Experiments and numerical simulations of inertial particles in underexpanded jets are performed. The structure of the jet is controlled by varying the nozzle pressure ratio, while the influence of particles on emerging shocks and rarefaction patterns is controlled by varying the particle size and mass loading. Ultra-high-speed schlieren and Lagrangian particle tracking are used to experimentally determine the two-phase flow quantities. Three-dimensional simulations are performed using a high-order, low dissipative discretization of the gas phase while particles are tracked individually in a Lagrangian manner. A simple two-way coupling strategy is proposed to handle interphase exchange in the vicinity of shocks. Velocity statistics of each phase are reported for a wide range of pressure ratios, particle sizes, and volume fractions. The extent to which particles affect the location of the Mach disk are quantified and compared to previous work from the literature. Furthermore, a semi-analytic model is presented based on a one-dimensional Fanno flow that takes into account volume displacement by particles and interphase exchange due to drag and heat transfer. The percent shift in Mach disk is found to scale with the mass loading, nozzle pressure ratio, interphase slip velocity, and inversely with the particle diameter.

High-speed disperse multiphase flows are present in numerous environmental and engineering applications with complex interactions between turbulence, shock waves, and particles. Compared to its incompressible counterpart, compressible two-phase flows introduce new scales of motion that challenge simulations and experiments. This review focuses on gas-particle interactions spanning subsonic to supersonic flow conditions. An overview of existing Mach number-dependent drag laws is presented, with origins from 18th-century cannon firings, and new insights from particle-resolved numerical simulations. The equations of motion and phenomenology for a single particle are first reviewed. Multi-particle systems spanning dusty gases to dense suspensions are then discussed from numerical and experimental perspectives.

We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The Reynolds number is held at $Re{\approx}300$ to ensure the flow remains in the continuum regime. At low volume fractions, the drag force increases sharply near a critical Mach number due to the formation of shock waves and reaches a maximum value when the bulk flow is supersonic. Neighbour-induced hydrodynamic interactions reduce the critical Mach number at higher volume fractions. An effective Mach number is introduced to capture the increase in compressibility effects on drag. A new drag correlation is proposed valid for subsonic and weakly supersonic flow from dilute to moderately dense suspensions., Comment: 10 pages, 6 figures

Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity in multiphase flow systems via a multi-fidelity Monte Carlo approach that optimally manages model evaluations for a given computational budget. The approach combines a high-fidelity model based on direct numerical simulation and a lower-order model based on a one-dimensional Eulerian description of the two-phase flow. Significant speedup is obtained compared to classical Monte Carlo estimation. Deposition is found to be most sensitive to electrostatic interactions and exhibits largest uncertainty for mid-sized (i.e., moderate Stokes number) particles.

The interactions between rocket exhaust plumes and the surface of extraterrestrial bodies during spacecraft landings involve complex multiphase flow dynamics that pose significant risk to space exploration missions. The two-phase flow is characterized by high Reynolds and Mach number conditions with particle concentrations ranging from dilute to close-packing. Low atmospheric pressure and gravity typically encountered in landing environments combined with reduced optical access by the granular material pose significant challenges for experimental investigations. Consequently, numerical modeling is expected to play an increasingly important role for future missions. This article presents a review and perspectives on modeling high-speed disperse two-phase flows relevant to plume-surface interactions (PSI). We present an overview of existing drag laws, with origins from 18th-century cannon fire experiments and new insights from particle-resolved numerical simulations. While the focus here is on multiphase flows relevant to PSI, much of the same physics are shared by other compressible gas-particle flows, such as coal-dust explosions, volcanic eruptions, and detonation of solid material.

We derive analytical solutions for hydrodynamic sources and sinks to granular temperature in moderately dense suspensions of elastic particles at finite Reynolds numbers. Modeling the neighbor-induced drag disturbances with a Langevin equation allows an exact solution for the joint fluctuating acceleration-velocity distribution function $P\left(v^{\prime},a^{\prime};t\right)$. Quadrant-conditioned covariance integrals of $P\left(v^{\prime},a^{\prime};t\right)$ yield the hydrodynamic source and sink that dictate the evolution of granular temperature. Analytical predictions are in agreement with benchmark data obtained from particle-resolved direct numerical simulations and show promise as a general theory from gas--solid to bubbly flows.

The transport of virus-laden aerosols from a host to a susceptible person is governed by complex turbulent airflow, and physics related to breathing, coughing and sneezing, mechanical and passive ventilation, thermal buoyancy effects, surface deposition, masks, and air filtration. In this paper, we study the infection risk via airborne transmission on an urban bus using unsteady Reynolds-Averaged Navier--Stokes equations and a passive-scalar model of the virus-laden aerosol concentration. Results from these simulations are directly compared to the widely-used well mixed model, and show significant differences in the concentration field and number of inhaled particles. Specifically, in the limit of low mechanical ventilation rate, the well-mixed model will over-predict concentration far from the infected passenger, and substantially underpredict concentration near the infected passenger. The results reported herein also apply to other enclosed spaces., Comment: 21 pages and 8 figures

Standard Eulerian--Lagrangian (EL) methods generally employ drag force models that only represent the mean hydrodynamic force acting upon a particle-laden suspension. Consequently, higher-order drag force statistics, arising from neighbor-induced flow perturbations, are not accounted for; with implications on predictions for particle velocity variance and dispersion. We develop a force Langevin (FL) model that treats neighbor-induced drag fluctuations as a stochastic force within an EL framework. The stochastic drag force follows an Ornstein-Uhlenbeck process and requires closure of the integral time scale for the fluctuating hydrodynamic force and the standard deviation in drag. The former is closed using the mean-free time between successive collisions, derived from the kinetic theory of non-uniform gases. For the latter, particle-resolved direct numerical simulation (PR--DNS) of fixed particle assemblies is utilized to develop a correlation. The stochastic EL framework specifies unresolved drag force statistics, leading to the correct evolution and sustainment of particle velocity variance over a wide range of Reynolds numbers and solids volume fractions when compared to PR--DNS of freely-evolving homogeneous suspensions. By contrast, standard EL infers drag statistics from variations in the resolved flow and thus under-predicts the growth and steady particle velocity variance in homogeneous suspensions. Velocity statistics from standard EL approaches are found to depend on the bandwidth of the projection function used for two-way momentum coupling, while results obtained from the stochastic EL approach are insensitive to the projection bandwidth.

Airborne respiratory diseases such as SARS-CoV-2 (COVID-19) pose significant challenges for public transportation. Several recent outbreaks of SARS-CoV-2 indicate the high risk of transmission among passengers on public buses if special precautions are not taken. This study presents a combined experimental and numerical analysis to identify transmission mechanisms on an urban bus and assess strategies to reduce risk. The effects of the ventilation and air-conditioning systems, opening windows and doors, and wearing masks are analyzed. Specific attention is made to the transport of sub-micron and micron-size particles relevant to typical respiratory droplets. High-resolution instrumentation was used to measure size distribution and aerosol response time on a University of Michigan campus bus under these different conditions. Computational fluid dynamics was employed to measure the airflow within the bus and evaluate risk. A risk metric was adopted based on the number of particles exposed to susceptible passengers. The flow that carries these aerosols is predominantly controlled by the ventilation system, which acts to uniformly distribute the aerosol concentration throughout the bus while simultaneously diluting it with fresh air. The opening of doors and windows was found to reduce the concentration by approximately one half, albeit its benefit does not uniformly impact all passengers on the bus due to recirculation of airflow caused by entrainment through windows. Finally, it was found that well fitted surgical masks, when worn by both infected and susceptible passengers, can nearly eliminate the transmission of the disease., Comment: 22 pages, 15 figures

This study is concerned with the statistics of vertical turbulent channel flow laden with inertial particles for two different volume concentrations ($\Phi_{V} = 3 \times 10^{-6}$ and $\Phi_{V} = 5 \times 10^{-5}$) at a Stokes number of $St^{+} = 58.6$ based on viscous units. Two independent direct numerical simulation models utilizing the point-particle approach are compared to recent experimental measurements, where all relevant nondimensional parameters are directly matched. While both numerical models are built on the same general approach, details of the implementations are different, particularly regarding how two-way coupling is represented. At low volume loading, both numerical models are in general agreement with the experimental measurements, with certain exceptions near the walls for the wall-normal particle velocity fluctuations. At high loading, these discrepancies are increased, and it is found that particle clustering is overpredicted in the simulations as compared to the experimental observations. Potential reasons for the discrepancies are discussed. As this study is among the first to perform one-to-one comparisons of particle-laden flow statistics between numerical models and experiments, it suggests that continued efforts are required to reconcile differences between the observed behavior and numerical predictions.

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