Subgrid Model Research Articles

Cold Gas Subgrid Model (CGSM): a two-fluid framework for modelling unresolved cold gas in galaxy simulations

ABSTRACT The cold ($\sim 10^{4}\, {\rm K}$) component of the circumgalactic medium (CGM) accounts for a significant fraction of all galactic baryons. However, using current galaxy-scale simulations to determine the origin and evolution of cold CGM gas poses a significant challenge, since it is computationally infeasible to directly simulate a galactic halo alongside the sub-pc scales that are crucial for understanding the interactions between cold CGM gas and the surrounding ‘hot’ medium. In this work, we introduce a new approach: the Cold Gas Subgrid Model (CGSM), which models unresolved cold gas as a second fluid in addition to the standard ‘normal’ gas fluid. The CGSM tracks the total mass density and bulk momentum of unresolved cold gas, deriving the properties of its unresolved cloudlets from the resolved gas phase. The interactions between the subgrid cold fluid and the resolved fluid are modelled by prescriptions from high-resolution simulations of ‘cloud crushing’ and thermal instability. Through a series of idealized tests, we demonstrate the CGSM’s ability to overcome the resolution limitations of traditional hydrodynamics simulations, successfully capturing the correct cold gas mass, its spatial distribution, and the time-scales for cloud destruction and growth. We discuss the implications of using this model in cosmological simulations to more accurately represent the microphysics that govern the galactic baryon cycle.

Bursty Star Formation in Dwarfs is Sensitive to Numerical Choices in Supernova Feedback Models

Simulations of galaxy formation are mostly unable to resolve the energy-conserving phase of individual supernova events, having to resort to subgrid models to distribute the energy and momentum resulting from stellar feedback. However, the properties of these simulated galaxies, including the morphology, stellar mass formed, and the burstiness of the star formation history, are highly sensitive to the numerical choices adopted in these subgrid models. Using the SMUGGLE stellar feedback model, we carry out idealized simulations of an M vir ∼ 1010 M ⊙ dwarf galaxy, a regime where most simulation codes predict significant burstiness in star formation, resulting in strong gas flows that lead to the formation of dark matter cores. We find that by varying only the directional distribution of momentum imparted from supernovae to the surrounding gas, while holding the total momentum per supernova constant, bursty star formation may be amplified or completely suppressed, and the total stellar mass formed can vary by as much as a factor of ∼3. In particular, when momentum is primarily directed perpendicular to the gas disk, less bursty and lower overall star formation rates result, yielding less gas turbulence, more disky morphologies, and a retention of cuspy dark matter density profiles. An improved understanding of the nonlinear coupling of stellar feedback into inhomogeneous gaseous media is thus needed to make robust predictions for stellar morphologies and dark matter core formation in dwarfs independent of uncertain numerical choices in the baryonic treatment.

Energy-consistent discretization of viscous dissipation with application to natural convection flow

A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and by requiring that continuous identities like the product rule are mimicked discretely. The proposed viscous dissipation function has a quadratic, strictly dissipative form, for both simplified (constant viscosity) stress tensors and general stress tensors. The proposed expression is not only useful in evaluating energy budgets in turbulent flows, but also in natural convection flows, where it appears in the internal energy equation and is responsible for viscous heating. The viscous dissipation function is such that a consistent total energy balance is obtained: the ‘implied’ presence as sink in the kinetic energy equation is exactly balanced by explicitly adding it as source term in the internal energy equation.Numerical experiments of Rayleigh–Bénard convection (RBC) and Rayleigh–Taylor instabilities confirm that with the proposed dissipation function, the energy exchange between kinetic and internal energy is exactly preserved. The experiments show furthermore that viscous dissipation does not affect the critical Rayleigh number at which instabilities form, but it does significantly impact the development of instabilities once they occur. Consequently, the value of the Nusselt number on the cold plate becomes larger than on the hot plate, with the difference increasing with increasing Gebhart number. Finally, 3D simulations of turbulent RBC show that energy balances are exactly satisfied even for very coarse grids. Therefore, the proposed discretization also forms an excellent starting point for testing sub-grid scale models and is a useful tool to assess energy budgets in any turbulence simulation, with or without the presence of natural convection.

Toward Implementation of the Pressure-regulated, Feedback-modulated Model of Star Formation in Cosmological Simulations: Methods and Application to TNG

Traditional star formation subgrid models implemented in cosmological galaxy formation simulations, such as that of V. Springel & L. Hernquist (hereafter SH03), employ adjustable parameters to satisfy constraints measured in the local Universe. In recent years, however, theory and spatially resolved simulations of the turbulent, multiphase, star-forming interstellar medium (ISM) have begun to produce new first-principles models, which when fully developed can replace traditional subgrid prescriptions. This approach has advantages of being physically motivated and predictive rather than empirically tuned, and allowing for varying environmental conditions rather than being tied to local-Universe conditions. As a prototype of this new approach, by combining calibrations from the TIGRESS numerical framework with the pressure-regulated feedback-modulated (PRFM) theory, simple formulae can be obtained for both the gas depletion time and an effective equation of state. Considering galaxies in TNG50, we compare the “native” simulation outputs with postprocessed predictions from PRFM. At TNG50 resolution, the total midplane pressure is nearly equal to the total ISM weight, indicating that galaxies in TNG50 are close to satisfying vertical equilibrium. The measured gas scale height is also close to theoretical equilibrium predictions. The slopes of the effective equations of states are similar, but with effective velocity dispersion normalization from SH03 slightly larger than that from current TIGRESS simulations. Because of this and the decrease in PRFM feedback yield at high pressure, the PRFM model predicts shorter gas depletion times than the SH03 model at high densities and redshift. Our results represent a first step toward implementing new, numerically calibrated subgrid algorithms in cosmological galaxy formation simulations.

TriPoD: Tri-Population size distributions for Dust evolution

Context. Dust coagulation and fragmentation impact the structure and evolution of protoplanetary disks and set the initial conditions for planet formation. Dust grains dominate the opacities, they determine the cooling times of the gas via thermal accommodation in collisions, they influence the ionization state of the gas, and the available grain surface area is an important parameter for the chemistry in protoplanetary disks. Therefore, dust evolution is an effect that should not be ignored in numerical studies of protoplanetary disks. Available dust coagulation models are, however, too computationally expensive to be implemented in large-scale hydrodynamic simulations. This limits detailed numerical studies of protoplanetary disks, including these effects, mostly to one-dimensional models. Aims. We aim to develop a simple – yet accurate – dust coagulation model that can be easily implemented in hydrodynamic simulations of protoplanetary disks. Our model shall not significantly increase the computational cost of simulations and provide information about the local grain size distribution. Methods. The local dust size distributions are assumed to be truncated power laws. Such distributions can be fully characterized by only two dust fluids (large and small grains) and a maximum particle size, truncating the power law. We compare our model to state- of-the-art dust coagulation simulations and calibrate it to achieve a good fit with these sophisticated numerical methods. Results. Running various parameter studies, we achieved a good fit between our simplified three-parameter model and DustPy, a state-of-the-art dust coagulation software. Conclusions. We present TriPoD, a sub-grid dust coagulation model for the PLUTO code. With TriPoD, we can perform twodimensional, vertically integrated dust coagulation simulations on top of a hydrodynamic simulation. Studying the dust distributions in two-dimensional vortices and planet-disk systems is thus made possible.

Simba-EoR: early galaxy formation in the simba simulation including a new sub-grid interstellar medium model

ABSTRACT We update the dust model present within the simba galaxy simulations with a self-consistent framework for the co-evolution of dust and molecular hydrogen populations in the interstellar medium, and use this to explore $z \ge 6$ galaxy evolution. In addition to tracking the evolution of dust and molecular hydrogen abundances, our model fully integrates these species into the simba simulation, explicitly modelling their impact on physical processes such as star formation and cooling through the inclusion of a novel two-phase sub-grid model for interstellar gas. Running two cosmological simulations down to $z \sim 6$ we find that our simba-EoR model displays a generally tighter concordance with observational data than fiducial simba. Additionally we observe that our simba-EoR models increase star formation activity at early epochs, producing larger dust-to-gas ratios consequently. Finally, we discover a significant population of hot dust at $\sim 100$ K, aligning with contemporaneous observations of high-redshift dusty galaxies, alongside the large $\sim 20$ K population typically identified.

Apostle–auriga: effects of stellar feedback subgrid models on the evolution of angular momentum in disc galaxies

ABSTRACT Utilizing the apostle–auriga simulations, which start from the same zoom-in initial conditions of Local Group-like systems, but run with different galaxy formation subgrid models and hydrodynamic solvers, we study the impact of stellar feedback models on the evolution of angular momentum in disc galaxies. At $z = 0$, auriga disc galaxies tend to exhibit higher specific angular momenta compared to their cross-matched apostle counterparts. By tracing the evolution history of the Lagrangian mass tracers of the in-situ star particles in the $z = 0$ galaxies, we find that the specific angular momentum distributions of the gas tracers from the two simulations at the halo accretion time are relatively similar. The present-day angular momentum difference is mainly driven by the physical processes occurring inside dark matter haloes, especially galactic fountains. Due to the different subgrid implementations of stellar feedback processes, auriga galaxies contain a high fraction of gas that has gone through recycled fountain (${\sim } 65$ per cent) which could acquire angular momentum through mixing with the high angular momentum circumgalactic medium (CGM). In apostle, however, the fraction of gas that has undergone the recycled fountain process is significantly lower (down to ${\sim } 20$ per cent for Milky Way-sized galaxies) and the angular momentum acquisition from the CGM is marginal. As a result, the present-day auriga galaxies overall have higher specific angular momenta.

Radial properties of dust in galaxies: Comparison between observations and isolated galaxy simulations

We study the importance of several processes that influence the evolution of dust and its grain size distribution on spatially resolved scales in nearby galaxies. Here, we compiled several multi-wavelength observations for the nearby galaxies NGC\,628 (M74), NGC\,5457 (M101), NGC\,598 (M33), and NGC 300. We applied spatially resolved spectral energy distribution (SED) fitting to the latest iteration of infrared data to get constraints on the galaxy dust masses and the small-to-large grain abundance ratio (SLR). We separated each galaxy into radial rings and obtained the radial profiles of the properties mentioned above. For comparison, we took the radial profiles of the stellar mass and gas mass surface density for NGC\,628 combined with its metallicity gradient in the literature to calibrate a single-galaxy simulation using the GADGET4-OSAKA code. The simulations include a parametrization to separate the dense and diffuse phases of the ISM where different dust-evolution mechanisms are in action. We find that our simulation can reproduce the radial profile of dust mass surface density but overestimates the SLR in NGC\,628. Changing the dust-accretion timescale has little impact on the dust mass or SLR, as most of the available metals are accreted onto dust grains at early times ($<3$\,Gyr), except in the outer regions of the galaxy where the metallicity is below $2 $. This suggests we can only constrain the accretion timescale of galaxies at extremely low metallicities where accretion still competes with other mechanisms controlling the dust budget. The overestimation of the SLR likely results from (i) overly efficient shattering processes in the diffuse interstellar medium (ISM), which were calibrated to reproduce Milky Way-type galaxies and/or (ii) our use of a diffuse and dense gas density subgrid model that does not entirely capture the intricacies of the small-scale structure present in NGC\,628. We conclude that future modeling efforts will need to focus on improving the subgrid recipes to mimic the multi-phase gas distribution in galaxies before the efficiency of dust evolution processes can be calibrated for galaxies other than the Milky Way.

A platinum-coated staggered reactor to intensify lean hydrogen/air combustion: A large eddy simulation study

Catalytic-aided combustion has been proven effective for premixed hydrogen/air mixtures, particularly under lean to ultra-lean conditions. However, minimising the required catalyst sets a significant challenge because noble metals with high catalytic activity are rare and expensive. Therefore, this study aims to intensify the catalytic combustion process by investigating a non-planar reactor comprising an array of platinum-coated half- and full-cylinders through large eddy simulation. A premixed mixture with a fuel-lean equivalence ratio of 0.15 and an incoming Reynolds number of 3500 based on hydraulic diameter is used. For comparison, a planar reactor without cylinders is also studied under the same operating conditions and with the same amount of platinum-coated surface area. The simulation employs the turbulent kinetic energy sub-grid model and the eddy dissipation concept to model the turbulent catalytic reacting flow. The discrete ordinate model is used to account for radiation heat transfer in the catalytic process. Numerical simulations are validated against experimental results prior to analysis. The findings indicate that the placement of cylinders along the reactor length enhances convective mass transfer and intensifies catalytic combustion, resulting in effective combustion over a smaller catalytic surface. Compared to planar models, non-planar reactors demonstrate a much better H2 conversion efficiency throughout the reactor length, saving nearly 62.5 % of the catalyst.

Modeling aeroacoustic interaction of rotating propeller with porous treatments using LBM (Lattice Boltzmann method) simulations

Porous treatments are more and more employed in presence of flow as passive noise control means to mitigate the generated noise. They are generally designed according to their acoustic dissipation properties under no-flow conditions. Nevertheless, in-flow porous treatments can alter the aerodynamic properties, modify the main acoustic source itself or even generate secondary acoustic sources. While most of the modelling methods (analytical, FEM, ...) are able to model the acoustic dissipation, they do not allow to model the interaction with the main source or the possible generation of spurious acoustic sources. The Lattice Boltzmann Method (LBM) is a computational fluid dynamics method able to run Direct Numerical Simulations (DNS) as well as Large Eddy Simulations (LES). The LES method resolves the macroscopic scale of turbulence and uses a sub-grid model for the small scales of turbulence. The low numerical dissipation of the LBM enables to compute both fluid flow and acoustics quantities in a single run. In this work, the LBM implemented in ProLB software is used to model the airborne noise generated by an electric propeller installed on an aircraft wing and the effects of sound absorbing treatments. Various treatments are investigated numerically and compared to experimental data when available.

Large Eddy Simulation of an impinging Jet for Cooling of Blades

Abstract The impinging jet shows extremely high performance in local blade cooling and has been widely applied. In this study, high precision Large Eddy Simulation (LES) was employed to simulate compressible fully turbulent impinging jet under specific conditions, using three subgrid-scale (SGS) models - the Smagorinsky model (SM), the Coherent-structure Smagorinsky Model (CSM), and the Selective Mixed Scale Model (SMSM). The predictive accuracy and computational efficiency of the three SGS models were evaluated. Compared with existing DNS and experimental results, the results indicate that there is no significant difference among the three models in computational efficiency. However, subgrid models have a crucial impact on heat transfer. The SMSM model, which utilizes small-scale turbulence information, can better simulate the heat transfer in the impingement region compared with the SM model and the CSM model.

A Stable Implementation of a Data‐Driven Scale‐Aware Mesoscale Parameterization

AbstractOcean mesoscale eddies are often poorly represented in climate models, and therefore, their effects on the large scale circulation must be parameterized. Traditional parameterizations, which represent the bulk effect of the unresolved eddies, can be improved with new subgrid models learned directly from data. Zanna and Bolton (2020), https://doi.org/10.1029/2020gl088376 (ZB20) applied an equation‐discovery algorithm to reveal an interpretable expression parameterizing the subgrid momentum fluxes by mesoscale eddies through the components of the velocity‐gradient tensor. In this work, we implement the ZB20 parameterization into the primitive‐equation GFDL MOM6 ocean model and test it in two idealized configurations with significantly different dynamical regimes and topography. The original parameterization was found to generate excessive numerical noise near the grid scale. We propose two filtering approaches to avoid the numerical issues and additionally enhance the strength of large‐scale energy backscatter. The filtered ZB20 parameterizations led to improved climatological mean state and energy distributions, compared to the current state‐of‐the‐art energy backscatter parameterizations. The filtered ZB20 parameterizations are scale‐aware and, consequently, can be used with a single value of the non‐dimensional scaling coefficient for a range of resolutions. The successful application of the filtered ZB20 parameterizations to parameterize mesoscale eddies in two idealized configurations offers a promising opportunity to reduce long‐standing biases in global ocean simulations in future studies.

Analysis of ansys fluent for Wall-Modeled Large-Eddy Simulation of Turbulent Channel Flow

Abstract This study assesses the accuracy of ansysfluent 19.2, a commonly employed general-purpose finite volume solver, in the context of wall-modeled large-eddy simulation for turbulent channel flow at a moderate Reynolds number, Reτ=2000. The sensitivity of the solution to variations in grid resolution, aspect ratio, grid arrangement (collocated versus staggered), and subgrid-scale (SGS) model is analyzed and contrasted to results from a corresponding direct numerical simulation (DNS) and a mixed pseudospectral and finite differences solver. Results indicate good convergence of first- and second-order statistics from the staggered grid setups as the grid is refined, whereas no clear trend is observed in cases with collocated grid setups. Velocity spectra show a lack of an apparent inertial range trend and rapid decay of energy density at high wavenumbers, with a spurious energy pile-up near the cutoff wavenumber indicating the presence of unphysical oscillations in the velocity fields. Grid refinement strengthens such oscillations in collocated grid setups and reduces them in staggered grid setups. Two-point streamwise velocity autocorrelation maps reveal an underprediction of turbulent structure size. In contrast, cross-stream autocorrelations agree with corresponding curves from direct numerical simulation, showing signatures of alternating high- and low-momentum streaks in the logarithmic layer.

Galaxy clustering in modified gravity from full-physics simulations – I. Two-point correlation functions

ABSTRACT We present an in-depth investigation of galaxy clustering based on a new suite of realistic large-box galaxy formation simulations in $f(R)$ gravity, with a subgrid physics model that has been recalibrated to reproduce various observed stellar and gas properties. We focus on the two-point correlation functions of the luminous red galaxies (LRGs) and emission line galaxies (ELGs), which are primary targets of ongoing and future galaxy surveys such as Dark Energy Spectroscopic Instrument (DESI). One surprising result is that, due to several non-trivial effects of modified gravity on matter clustering and the galaxy–halo connection, the clustering signal does not depend monotonically on the fifth-force strength. For LRGs, this complicated behaviour poses a challenge to meaningfully constraining this model. For ELGs, in contrast, this can be straightforwardly explained by the time evolution of the fifth force, which means that weaker $f(R)$ models can display nearly the same – up to 25 per cent – deviations from Lambda cold dark matter model as the strongest ones, albeit at lower redshifts. This implies that even very weak $f(R)$ models can be strongly constrained, unlike with most other observations. Our results show that galaxy formation acquires a significant environment dependence in $f(R)$ gravity, which, if not properly accounted for, may lead to biased constraints on the model. This highlights the essential role of hydrodynamical simulations in future tests of gravity exploring precision galaxy-clustering data from the likes of DESI and Euclid.

Dissipation of AGN Jets in a Clumpy Interstellar Medium

Accreting supermassive black holes frequently power jets that interact with the interstellar medium (ISM)/circumgalactic medium, regulating star formation in the galaxy. Highly supersonic jets launched by active galactic nuclei (AGN) power a cocoon that confines them and shocks the ambient medium. We build on the models of narrow conical jets interacting with a smooth ambient medium, including the effect of dense clouds, which are an essential ingredient of a multiphase ISM. The key physical ingredient of this model is that the clouds along the supersonic jet beam strongly decelerate the jet head but the subsonic cocoon easily moves around the clouds without much resistance. We propose scalings for important physical quantities—cocoon pressure, head and cocoon speed, and jet radius. For the first time, we obtain the analytic condition on the ambient medium’s clumpiness for the jet to dissipate within the cocoon and verify it with numerical simulations of conical jets interacting with a uniform ISM with embedded spherical clouds. A jet is defined to be dissipated when the cocoon speed exceeds the speed of the jet head. We compare our models with more sophisticated numerical simulations and direct observations of jet–ISM interaction (e.g., quasar J1316+1753), and we discuss implications for the Fermi/eROSITA bubbles. Our work also motivates effective subgrid models for AGN jet feedback in a clumpy ISM unresolved by the present generation of cosmological galaxy formation simulations.

Magnetized Accretion onto and Feedback from Supermassive Black Holes in Elliptical Galaxies

We present 3D magnetohydrodynamic simulations of the fueling of supermassive black holes in elliptical galaxies from a turbulent cooling medium on galactic scales, taking M87* as a typical case. We find that the mass accretion rate is increased by a factor of ∼10 compared with analogous hydrodynamic simulations. The scaling of Ṁ∼r1/2 roughly holds from ∼10 pc to ∼10−3 pc (∼10 r g) with the accretion rate through the event horizon being ∼10−2 M ⊙ yr−1. The accretion flow on scales ∼0.03–3 kpc takes the form of magnetized filaments. Within ∼30 pc, the cold gas circularizes, forming a highly magnetized (β ∼ 10−3) thick disk supported by a primarily toroidal magnetic field. The cold disk is truncated and transitions to a turbulent hot accretion flow at ∼0.3 pc (103 r g). There are strong outflows toward the poles driven by the magnetic field. The outflow energy flux increases with smaller accretor size, reaching ∼3 × 1043 erg s−1 for r in = 8 r g; this corresponds to a nearly constant energy feedback efficiency of η ∼ 0.05–0.1 independent of accretor size. The feedback energy is enough to balance the total cooling of the M87/Virgo hot halo out to ∼50 kpc. The accreted magnetic flux at small radii is similar to that in magnetically arrested disk models, consistent with the formation of a powerful jet on horizon scales in M87. Our results motivate a subgrid model for accretion in lower-resolution simulations in which the hot gas accretion rate is suppressed relative to the Bondi rate by ∼(10rg/rB)1/2 .

A calibrated model for N-body dynamical friction acting on supermassive black holes

Abstract Black holes are believed to be crucial in regulating star formation in massive galaxies, which makes it essential to faithfully represent the physics of these objects in cosmological hydrodynamics simulations. Limited spatial and mass resolution and the associated discreteness noise make following the dynamics of black holes especially challenging. In particular, dynamical friction, which is responsible for driving massive black holes towards the centres of galaxies, cannot be accurately modelled with softened N-body interactions. A number of subgrid models have been proposed to mimic dynamical friction or directly include its full effects in simulations. Each of these methods has its individual benefits and shortcomings, while all suffer from a common issue of being unable to represent black holes with masses below a few times the simulated dark matter particle mass. In this paper, we propose a correction for unresolved dynamical friction, which has been calibrated on simulations run with the code KETJU, in which gravitational interactions of black holes are not softened. We demonstrate that our correction is able to sink black holes with masses greater than the dark matter particle mass at the correct rate. We show that the impact of stochasticity is significant for low-mass black holes (MBH ≤ 5MDM) and propose a correction for stochastic heating. Combined, this approach is applicable to next generation cosmological hydrodynamics simulations that jointly track galaxy and black hole growth with realistic black hole orbits.

Effect of particle Froude number on sub-grid effective drag, filtered and residual stresses in fluidized gas-particle flows

Sub-grid effective drag, filtered and residual stresses in the meso-scale of gas-particle fluidized flows are intrinsically affected by underlying micro-scale conditions as well as non-local effects related to macro-scale conditions. In this work we applied microscopic two-fluid modeling to experiment with particle Froude number in order to evaluate the impact of this micro-scale condition over the concerning meso-scale derived sub-grid parameters. We performed highly resolved simulations in periodic domains for particle Froude numbers from 12.21 to 799.22, for a wide range of macro-scale conditions. Results were filtered and classified by ranges of meso-scale markers for the various particle Froude numbers. The particle Froude number was found to considerably affect the structural refinement of the heterogeneous flow fields thereby directly impacting effective drag, filtered and residual stresses. All of those parameters showed systematic behaviors in relation to particle Froude number, thereby providing sound data for new sub-grid modeling propositions.

A sub-grid gas–solid interaction model for coarse-grained CFD–DEM simulations

Computational fluid dynamics has been coupled with coarse-grained discrete element method (CFD–CGDEM) to study industrial-scale gas–solid fluidized beds. However, solving the fluid flow at a grid size of several coarse-grained particles (CGPs) cannot accurately predict the gas–solid interaction, and thus reasonable correction model is required. This study develops a sub-grid model to correct the gas–solid interaction and thereby improve the accuracy of coarse-grid CFD–CGDEM simulation. First, the fluid grids with the size of several CGPs are divided into the auxiliary three-dimensional sub-grids. Then, the CGPs are mapped onto the sub-grids by the weight function to reconstruct the local solid velocities and solid fractions of the sub-grids. After that, the simplified mass and momentum conservation equations are solved to resolve the local gas velocities of sub-grids. Finally, the drag on each CGP is corrected based on the local gas-phase hydrodynamics of sub-grids. Results show that the sub-grid model resolving the local gas velocity in all the three directions works better than that just in the main stream direction. The coarse-grid CFD–CGDEM simulations with this sub-grid model agree well with the experiment for the bubbling, turbulent and rapid fluidized beds. Besides, by solving the simplified conservation equations with graphics processing units, the coarse-grid CFD–CGDEM coupled with the sub-grid model achieves 674 times speedup compared to the fine-grid simulation, demonstrating a much more efficient method to study industrial-scale gas–solid fluidized beds.

Particle image velocimetry in the impeller of a centrifugal pump: Relationship between turbulent flow and energy loss

Turbulent flows play a dominant role in the operation of centrifugal pumps, which find widespread use in industrial settings and various aspects of human life. The dissipation rate of turbulent kinetic energy emerges as a key parameter within these devices, with its local values exerting a significant influence on centrifugal pump performance. Recent advances in particle image velocimetry (PIV) techniques have expanded the ability to analyze complex turbulent flows across a broad spectrum of scales. In this context, this paper aims to deepen our understanding of the turbulent flow field and its correlation with energy loss in centrifugal pump impellers. To achieve this, experiments were conducted using PIV on a transparent pump operating under different conditions. Statistics of the turbulent flow were then obtained from phase-ensemble averages of velocities, vorticity, turbulence production, and local dissipation of turbulent kinetic energy. To overcome the limited spatial resolution constraint of PIV, the large-eddy PIV (LES-PIV) method was employed to estimate the local dissipation rate. In this method, it is assumed that the motion of larger scales is measured by the PIV technique, while the smaller scales (unresolved scales) are modeled by a sub-grid scale model, calculated from the strain rate tensors obtained from the measured fields. Energy losses in the impeller were studied using two methodologies: (i) a conventional method based on power measurements, and (ii) an alternative approach based on the budget of turbulent kinetic energy. Our results reveal that turbulent loss caused by turbulence production is the main source of energy loss in the pump impeller, and it is particularly pronounced in low-flow operating conditions characterized by large-scale structures. On the other hand, in situations where flow rates exceed the best efficiency point (BEP) condition, the predominant flow structures are marked by small-scale features, mainly attributed to local dissipation of turbulence. Our findings clarify the characteristics of energy losses in centrifugal pump impellers and their relationship with the turbulent flow field, and, in addition, providing a methodology for calculating the local turbulent dissipation rate and its limitations when derived from PIV measurements.