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Elbow erosion, defined as wall thinning due to the continuous interactions between solid particles and surface, is a common phenomenon in catalyst addition/withdrawal pipeline systems used in residual oil hydrogenation units. This form of erosion can seriously affect the reliable pipeline operation. The present paper describes the construction of realistic cylindrical catalyst particles using the multi-sphere clump method and computational fluid dynamics/discrete element model simulations to study the erosion of pipe walls under different inlet velocities and particle aspect ratios. An optical shooting experiment is carried out to ensure the accuracy of the calculation method, and the model performance is compared using several existing drag models. The results show that the drag model of Haider & Levenspiel is more accurate than the others in revealing the actual cylindrical particle flow. A higher inlet velocity is observed to increase the kinetic energy of the particles and affect their spatial distribution. Specifically, when the Stokes number is greater than 113.7, the position of the maximum erosion rate shifts from the elbow’s outer wall to the inner wall. Cumulative contact energy is introduced to quantify two different types of particle-wall contacts. With a growing particle aspect ratio, the proportion of tangential energy gradually increases, which indicates that sliding is the main contact mode. The results presented in this paper provide a reference for engineering erosion calculations.

Recovering low‐grade waste heat from coal‐fired flue gas is crucial for improving power plant efficiency and reducing emissions. However, substantial aerosol deposition on heat exchanger tubes undermines long‐term system performance. Although thermophoresis dominates submicron particle transport under thermal gradients, many existing studies overlook the coupled effects of turbulence and particle‐surface interactions in the medium‐to‐low temperature range typical of heat recovery applications. To address these gaps, we developed and validated a comprehensive computational fluid dynamics (CFD) model that integrates large eddy simulation (LES) for resolving turbulent flow around tubes, a discrete phase model (DPM) for tracking particle motion under thermophoretic and Brownian forces, and a user‐defined sticking/rebound criterion for particle‐wall interactions. Model validation against experimental and numerical benchmarks confirmed its accuracy in capturing vortex shedding, thermophoretic deposition, and particle impact behavior. Key results demonstrate that total deposition efficiency reaches a lower particle deposition efficiency at Stokes numbers ( St ) between 0.01 and 0.1, delineating the transition from thermophoresis‐ to inertia‐dominated regimes. For St < 0.01, thermophoresis dominates particle deposition, with deposition efficiency decreasing at higher flow velocities and with larger particles. For St > 0.1, inertial impaction dominates, particularly on tube windward surfaces. Furthermore, while larger gas‐to‐wall temperature gradients enhance deposition—especially for small particles—this effect weakens as particle inertia increases. This work establishes a reliable predictive framework for aerosol deposition under practical flue gas conditions, providing valuable guidance for designing fouling‐resistant heat recovery systems.

The effect of Stokes number on the kinetic energy (KE) budget in particle-laden turbulent channel flows is examined by conducting two-way coupled direct numerical simulations using the Eulerian-Lagrangian approach. The friction Reynolds number of the single phase channel flow is Reτ = 180, the particle mass loading and volume fraction are φm = 0.2, φv ≈ 10−4, and the Stokes numbers range from St+ = 14–92. The statistics show that due to the presence of solid particles, the mean velocity is reduced in the vicinity of the wall but enhanced in the outer region, and the off-streamwise intensity of fluctuated velocity and the Reynolds stress are reduced in the whole channel. The analysis on the budgets of turbulent kinetic energy (TKE) finds that the presence of particles induces a significant reduction on both the production and dissipation rates. With increasing Stokes number St+, both the production and dissipation rates exhibit non-monotonical trends, i.e., both initially decrease for St+ < 40 and then transit to growth after St+ > 40. This suggests that the particle-induced suppression on TKE production and dissipation is the strongest nearly at St+ = 40. It is also found that particles act as an additional sink/source term in the budgets of both mean-flow kinetic energy (MKE) and TKE. In addition, we investigate the influence of St+ on the “zero point” which indicates the balance of exchanging energy between the particle and fluid phases. It is shown that with increasing St+, the “zero point” moves toward the wall, suggesting that the position of perfect following between particle and fluid is closer to the wall with larger St+. The present results reveal the Stokes number effects on the spatial transport mechanisms of MKE, TKE in turbulent channel flows laden with inertial particles.

Erosion of the leading edge of blades in windy and sandy environments can cause wind turbines to lose up to 25% of their annual power generation. Traditional studies have mostly focused on the impact of single factors on erosion rates, but the effects of multiple parameters on erosion rates within the framework of the Stokes number (Stk) of dust particles have not yet been clarified. This study employs a numerical approach based on the Euler–Lagrange framework, integrating the SST k-ω turbulence model with a discrete phase model (DPM) to simulate the unsteady gas–solid two-phase flow around a NACA 0012 airfoil. The computational model was rigorously validated through grid independence tests and comparison with experimental aerodynamic data from the database, showing strong agreement under steady conditions. Systematic simulations were conducted with particle diameters ranging from 10 to 360 μm, densities from 2650 to 3580 kg/m3, and inflow velocities from 1.5 to 21 m/s, comprehensively covering Stokes number regimes from Stk << 1 to Stk >> 1. Through parametric analysis, we quantify the control effect of Stk on erosion rate and erosion hot spots. Simulation results indicate that Stk has a zone-specific control effect on airfoil erosion: erosion hot spots in low-Stk zones migrate from the mid-to-rear edge to the leading edge. Erosion rate peaks when Stk ≈ 0.8. Inertial impact in the high-Stk zone dominates surface damage propagation. Based on the simulation results, an erosion model with an error of ≤3.6% was established for the E = K∙Stka∙dpb∙vc zone, providing a quantitative physical basis to inform wind turbine blade protection strategies.

A numerical simulation of the particle-gas flow in a vertical turbulent pipe flow was conducted. The main objective of the present article is to investigate the effects of dispersed phase (particles) on continuous phase (gas). In so doing, two general forms of Eulerian-Lagrangian approaches namely, one-way (when the fluid flow is not affected by the presence of the particles) and two-way (when the particles exert a feedback force on the fluid) couplings were used to describe the equations of motion of the two-phase flow. Gas-phase velocities which are within the order of magnitude as that of particles, volume fraction, and particle Stokes number were calculated and the results were subsequently compared with the available experimental data. The simulated results show that when the particles are added, the fluid velocity is attenuated. With an increase in particle volume fraction, particle mass loading and Stokes number, velocity attenuation also increases. Moreover, the results indicate that an increase in particle Stokes number reduces the special limited particle volume fraction, according to which one-way coupling method yields plausible results. The results have also indicated that the significance of particle fluid interaction is not merely a function of volume fraction and particle Stokes number.

We study experimentally the spatial distribution, settling and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from $Re_{\\unicode[STIX]{x1D706}}\\approx 200{-}500$ , while the particle Stokes number based on the Kolmogorov scale varies between $St_{\\unicode[STIX]{x1D702}}=O(1)$ and $O(10)$ . Clustering is confirmed to be most intense for $St_{\\unicode[STIX]{x1D702}}\\approx 1$ , but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and with sizes that can reach the integral scale of the turbulence. Remarkably, the settling velocity of $St_{\\unicode[STIX]{x1D702}}\\approx 1$ particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the turbulence. The particle–fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.

Turbulent wall-bounded flows exhibit a wide range of regimes with significant interaction between scales. The fluid dynamics associated with single-phase channel flows is predominantly characterized by the Reynolds number. Meanwhile, vastly different behaviour exists in particle-laden channel flows, even at a fixed Reynolds number. Vertical turbulent channel flows seeded with a low concentration of inertial particles are known to exhibit segregation in the particle distribution without significant modification to the underlying turbulent kinetic energy (TKE). At moderate (but still low) concentrations, enhancement or attenuation of fluid-phase TKE results from increased dissipation and wakes past individual particles. Recent studies have shown that denser suspensions significantly alter the two-phase dynamics, where the majority of TKE is generated by interphase coupling (i.e.  drag) between the carrier gas and clusters of particles that fall near the channel wall. In the present study, a series of simulations of vertical particle-laden channel flows with increasing mass loading is conducted to analyse the transition from the dilute limit where classical mean-shear production is primarily responsible for generating fluid-phase TKE to high-mass-loading suspensions dominated by drag production. Eulerian–Lagrangian simulations are performed for a wide range of particle loadings at two values of the Stokes number, and the corresponding two-phase energy balances are reported to identify the mechanisms responsible for the observed transition.

The formation of inhomogeneities within fluidized beds, both in terms of the particle configurations and flow structures, have a pronounced effect on the interaction force between the fluid and particles. While recent numerical studies have begun to probe the effects of inhomogeneities on the drag force at the particle scale, the applicability of prior microscale constitutive drag relations is still limited to random, homogeneous distributions of particles. Since an accurate model for the drag force is needed to predict the fluidization behaviour, the current study utilizes the lessons of prior inhomogeneity studies in order to derive a robust drag relation that is both able to account for the effect of inhomogeneities and applicable as a constitutive closure to larger-scale fluidization simulations. Using fully resolved lattice Boltzmann simulations of systems composed of fluid and monodisperse spherical particles in the low-Reynolds-number (Re) regime, the fluid–particle drag force, normalized by the ideal Stokes drag force, is found to significantly decrease, over a range of length scales, as the extent of inhomogeneities increases. The extent of inhomogeneities is found to most effectively be quantified through one of two subgrid-scale quantities: the scalar variance of the particle volume fraction or the drift flux, which is the correlation between the particle volume fraction and slip velocity. Scale-similar models are developed to estimate these two subgrid measures over a wide range of system properties. Two new drag constitutive models are proposed that are not only functions of the particle volume fraction and the Stokes number ( $St$ ), but also dependent on one of these subgrid measures for the extent of inhomogeneities. Based on the observed, appreciable effect of inhomogeneities on drag, these new low-Re drag models represent a significant advancement over prior constitutive relations.

The streaming instability is a promising mechanism for planetesimal formation. The instability can rapidly form dense clumps that collapse self-gravitationally, which is efficient for large dust grains with Stokes number of the order of 0.1. However, dust growth models predict that collisional fragmentation prevents dust grains from growing to such sizes. We perform local simulations of the streaming instability and measure characteristic collision velocities and collision rates of dust grains based on their trajectories in moderate clumping. The collision velocities are of the order of 0.1% of the sound speed or lower, implying that dust grains can overcome the fragmentation barrier via clumping. We also find that the collision rates are appreciably high regardless of the low collision velocities. Corresponding timescales are of the order of 10 Keplerian periods or shorter, suggesting that dust grains can overcome the drift barrier as well. This streaming-instability-assisted coagulation greatly relaxes the conditions for planetesimal formation as recently implied.

The initial mass function (IMF) of planetesimals is of key importance for understanding the initial stages of planet formation, yet theoretical predictions so far have been insufficient in explaining the variety of IMFs found in simulations. Here, we connect diffusion-tidal-shear limited planetesimal formation within the framework of a Toomre-like instability in the particle midplane of a protoplanetary disk to an analytic prediction for the planetesimal IMF. The shape of the IMF is set by the stability parameter Q p, which in turn depends on the particle Stokes number, the Toomre Q value of the gas, the local dust concentration, and the local diffusivity. We compare our prediction to high-resolution numerical simulations of the streaming instability and planetesimal formation via gravitational collapse. We find that our IMF prediction agrees with numerical results and is consistent with both the paradigm that planetesimals are born big and the power-law description commonly found in simulations.