Eulerian Fluid Research Articles

Mixed material point method formulation, stabilization, and validation for a unified analysis of free-surface and seepage flow

This paper presents a novel stabilized mixed material point method (MPM) designed for the unified modeling of free-surface and seepage flow. The unified formulation integrates the Navier-Stokes equation with the Darcy-Brinkman-Forchheimer equation, effectively capturing flows in both non-porous and porous domains. In contrast to the conventional Eulerian computational fluid dynamics (CFD) solver, which solves the velocity and pressure fields as unknown variables, the proposed method employs a monolithic displacement-pressure formulation adopted from the mixed-form updated-Lagrangian finite element method (FEM). To satisfy the discrete inf-sup stability condition, a stabilization strategy based on the variational multiscale method (VMS) is derived and integrated into the proposed formulation. Another distinctive feature is the implementation of blurred interfaces, which facilitate a seamless and stable transition of flows between free and porous domains, as well as across two distinct porous media. The efficacy of the proposed formulation is verified and validated through several benchmark cases in 1D, 2D, and 3D scenarios. Conducted numerical examples demonstrate enhanced accuracy and stability compared to analytical, experimental, and other numerical solutions.

Improved Heat Transfer Capabilities of Nanofluids—An Assessment Through CFD Analysis

AbstractConventional fluids used in fission‐based water‐cooled nuclear reactors have lower heat transfer coefficients (HTCs) and thermal conductivity, which has led researchers to explore high‐performance fluids that can enhance heat transfer in routine operation and prevent core meltdown in the case of accidents. It is important to investigate a wide range of fluids that can help designers improve thermal hydraulic characteristics, such as HTC, critical heat flux, and minimum departure from nucleate boiling ratio (MDNBR). In this study, the effectiveness of nanofluids in enhancing heat transfer parameters, including thermal conductivity and heat capacity, was investigated. Four different nanofluids (Al2O3–H2O, ZrO2–H2O, Ag–H2O, and Si–H2O) with pure water as the primary coolant in an HPR‐1000 nuclear reactor were compared using computational methods. Due to computational limitations, only the flow channel among four fuel rods with the highest power density in the core was simulated using Eulerian computational fluid dynamics. The results of this study show that silver water (Ag–H2O) nanofluid outperformed other nanofluids and pure water. It had a higher average HTC and MDNBR, with a 67.15 % and 45.23 % improvement, respectively, compared to pure water. The fuel rod wall temperature was also reduced by 28.5 K with Ag–H2O compared to water. Comparison of current simulated results with literature data shows a good agreement.

Monolithic finite element modeling of compressible fluid‐structure‐electrostatics interactions in MEMS devices

AbstractThis work presents a monolithic finite element strategy for the accurate solution of strongly‐coupled fluid‐structure‐electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull‐in phenomena and squeeze film damping in high aspect‐ratio micro‐electro‐mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high‐frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation.

A formulation for fluid–structure interaction problems with immersed flexible solids: Application to splitters subjected to flow past cylinders with different cross-sections

In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

Lagrangian formulation for perfect fluid equations with the ℓ -conformal Galilei symmetry

Lagrangian formulation for perfect fluid equations which hold invariant under the ℓ-conformal Galilei group with half-integer ℓ is proposed. It is based on a Clebsch-type parametrization and reproduces Lagrangian description of the Euler fluid equations for ℓ=12. The transition from the Lagrangian formulation to the Hamiltonian one is analyzed in detail. Published by the American Physical Society 2024

A new microscopic traffic-flow model based on the spatiotemporal continuous system concept considering nonlinear human response

A brand-new traffic model is introduced to precisely simulate the individual movement of vehicles, departing from the traditional macroscopic perspective (Eulerian scope or fluid dynamics concept) to adopt a microscopic approach (Lagrangian scope). This model is built on the first principle of Newton’s kinetic equation, explicitly incorporating nonlinear relations to represent human responses to a physical stimulus (observed information), such as the velocity gap between one’s own vehicle and a certain targeted one or the gap to a preceding vehicle, unlike the conventional car-following concept. The model posits that a driver’s recognition occurs intermittently rather than continuously, following specific probabilistic distributions of which the formulation is physically justified. Overall, the model can be described as a spatiotemporally continuous formulation unlike cellular automaton (CA) traffic models, crucial for capturing traffic dynamics at the micro and macro levels. The model is validated using a real traffic-flow dataset from a highway, and the results of the conventional CA traffic model are compared with those of the present one” along with a note for authorial verification. Animated simulations confirm that the present model can reproduce realistic flow dynamics characterized by smoother acceleration and deceleration compared to the conventional CA traffic model. The complete simulation source code for replicating the model is made publicly available.

Euler fluid in 2+1 dimensions as a gauge theory and an action for the Euler fluid in any dimension

In this paper we parallel the construction of Tong of a gauge theory for shallow water, by writing a gauge theory for the Euler fluid in 2+1 dimensions. We then extend it to a Euler fluid coupled to an electromagnetic background. We argue that the gauge theory formulation provides a topological argument for the quantization of 2+1 dimensional Euler Hopfion solution. In the process, we find a (nongauge) action for the Euler fluid that can be extended to any dimension, including the physical 3+1 dimensions. We also discuss several aspects of the Arnold-Beltrami-Childress flow. Published by the American Physical Society 2024

Development of boundary layers in Euler fluids that on “activation” respond like Navier–Stokes fluids

We consider the flow of a fluid whose response characteristics change due the value of the norm of the symmetric part of the velocity gradient, behaving as an Euler fluid below a critical value and as a Navier–Stokes fluid at and above the critical value, the norm being determined by the external stimuli. We show that such a fluid, while flowing past a bluff body, develops boundary layers which are practically identical to those that one encounters within the context of the classical boundary layer theory propounded by Prandtl. Unlike the classical boundary layer theory that arises as an approximation within the context of the Navier–Stokes theory, here the development of boundary layers is due to a change in the response characteristics of the constitutive relation. We study the flow of such a fluid past an airfoil and compare the same against the solution of the Navier–Stokes equations. We find that the results are in excellent agreement with regard to the velocity and vorticity fields for the two cases.

Learning Reduced Fluid Dynamics

Predicting the state evolution of ultra high-dimensional, time-reversible fluid dynamic systems is a crucial but computationally expensive task. Existing physics-informed neural networks either incur high inference cost or cannot preserve the time-reversible nature of the underlying dynamics system. We propose a model-based approach to identify low-dimensional, time reversible, nonlinear fluid dynamic systems. Our method utilizes the symplectic structure of reduced Eulerian fluid and use stochastic Riemann optimization to obtain a low-dimensional bases that minimize the expected trajectory-wise dimension-reduction error over a given distribution of initial conditions. We show that such minimization is well-defined since the reduced trajectories are differentiable with respect to the subspace bases over the entire Grassmannian manifold, under proper choices of timestep sizes and numerical integrators. Finally, we propose a loss function measuring the trajectory-wise discrepancy between the original and reduced models. By tensor precomputation, we show that gradient information of such loss function can be evaluated efficiently over a long trajectory without time-integrating the high-dimensional dynamic system. Through evaluations on a row of simulation benchmarks, we show that our method reduces the discrepancy by 50-90 percent over conventional reduced models and we outperform PINNs by exactly preserving the time reversibility.

Experiment and simulation of non-catalytic thermal decomposition of CH4 for CO2-free hydrogen production in a vertical tube

To address climate change issues, there has been growing interest in low-carbon H2 production technologies with the potential for zero-CO2 emissions. Non-oxidative CH4 pyrolysis is a promising method for producing H2 and solid carbon without generating CO2 emissions. This study presents experimental and numerical studies on non-catalytic CH4 pyrolysis using a vertical tube reactor (28 mm in diameter and 1800 mm in height). A three-dimensional (3D) Eulerian computational fluid dynamics (CFD) model coupled with chemical reaction and heat transfer was developed and validated against the experimentally determined axial temperature profiles and methane conversion (XCH4). The hydrodynamics, reaction kinetics, and heat transfer characteristics were investigated using the validated CFD model. The highest XCH4 of 99% was achieved at 1200 °C with a gas flow rate of 0.5 LPM. Heat transfer combined with natural and forced convection was confirmed by the CFD simulation of the tubular reactor. The heat transfer coefficient in the reaction zone ranged from 43 to 46 W/m2/°C. The CFD simulation served as a viable tool for examining the influence of the hydrodynamics, heat transfer, and reaction kinetics on the performance of the reactor with a given geometry and under specified operating conditions in non-catalytic CH4 pyrolysis.

Effectiveness of portable air cleaners in mitigating respiratory virus transmission risk

Portable air cleaners (PACs) have shown promising potential in reducing the risk of SARS-CoV-2 infection by effectively removing pollutant particles and optimizing airflow patterns. This study focused on a simulated scenario where an infected source and a susceptible person engage in conversation within a naturally ventilated room. By combining the Eulerian fluid method with the Lagrangian particle tracking model, a comprehensive insight into indoor airflow patterns and the dispersion of virus-laden droplets was gained. As deposited droplets may be resuspended or in contact thereby increasing the potential risk of infection, the deposition of droplets of different sizes in different susceptible areas was also specifically analyzed. The impacts of three variables, namely the configuration of the PAC’s opening, air flow rate, and positioning, on the transmission of virus-laden droplets were investigated. The results highlighted the significant role of PAC utilization in effectively capturing droplets emitted by the infected source and reducing virus concentration in the vicinity of the susceptible person, thereby mitigating the risk of transmission. Notably, the design and orientation of the suction opening emerged as crucial factors. Among the various cases studied, the optimal control and prevention performance against the virus was achieved with a virus concentration reduction rate of 97.4% when the PAC had an opening configuration with a larger single-sided suction opening facing the infected source, an airflow rate of 200 m3 h−1, and was positioned at the center of the tabletop between the infected source and the susceptible person. This research underscored the importance of employing PACs with appropriate settings to enhance indoor air quality and minimize the potential for SARS-CoV-2 transmission in similar scenarios.

Unified gas-kinetic wave–particle method for polydisperse gas–solid particle multiphase flow

The gas-particle flow with multiple dispersed solid phases is associated with a complicated multiphase flow dynamics. In this paper, a unified algorithm is proposed for the gas-particle multiphase flow. The gas-kinetic scheme (GKS) is used to simulate the gas phase and the multiscale unified gas-kinetic wave–particle (UGKWP) method is developed for the multiple dispersed solid particle phase. For each disperse solid particle phase, the decomposition of deterministic wave and statistic particle in UGKWP is based on the local cell's Knudsen number. The method for solid particle phase can become the Eulerian fluid approach at the small cell's Knudsen number and the Lagrangian particle approach at the large cell's Knudsen number. This becomes an optimized algorithm for simulating dispersed particle phases with a large variation of Knudsen numbers due to different physical properties of the individual particle phase, such as the particle diameter, material density, etc. The GKS-UGKWP method for gas-particle flow unifies the Eulerian–Eulerian and Eulerian–Lagrangian methods. The particle and wave decompositions for the solid particle phase and their coupled evolution in UGKWP come from the consideration to balance the physical accuracy and numerical efficiency. Two cases of a gas–solid fluidization system, i.e. one circulating fluidized bed and one turbulent fluidized bed, are simulated. The typical flow structures of the fluidized particles are captured, and the time-averaged variables of the flow field agree well with the experimental measurements. In addition, the shock particle–bed interaction is studied by the proposed method, which validates the algorithm for the polydisperse gas-particle system in the highly compressible case, where the dynamic evolution process of the particle cloud is investigated.

A versatile sharp boundary ghost-node method for moving rigid boundary fluid flow with meshless nodes distribution

A sharp boundary ghost-node method (GNM) is developed to solve the moving boundary fluid flow in a meshless local radial basis function (LRBF) framework. The background Euler fluid node is the mesh-less scattered node based on LRBF rather than the conventional Cartesian grid or unstructured mesh. The present approach (LRBF-GNM) can flexibly treat the steady boundary with the body-fitted nodes and tackle the moving boundary using the ghost-node method. The key idea of GNM is to project the information of fluid nodes into the ghost nodes by considering the boundary conditions of immersed boundary on Lagrangian nodes, and the influence of immersed boundary on the fluid can be explicitly added during the projection. There are some free parameters that should be determined before computing the virtual forcing source term acted only on the ghost nodes. The distribution of the ghost nodes, the projection strategy and the distribution of the image nodes should be treated carefully to balance the penetrability of streamlines over the immersed boundary, the numerical stability and the thickness of the diffusion boundary. A definition of sharp boundary is introduced to estimate the influences of the above free parameters on the immersed boundary. According to the numerical tests for a static boundary, the optimal parameters for GNM to precisely treat the immersed boundary are summarized. The fluid flow over steady and moving rigid boundaries and the vortex-induced vibration (VIV) are conducted and their solutions agree well with published numerical solutions and experimental measurements.

Effect of graphene nanoplatelets induced ethylene glycol/water mixture (50:50) fluid on lithium-battery cooling

Battery technology is the main driving force behind the shift towards emission-free transportation. However, a major obstacle to the widespread adoption of this technology is the need to maintain the battery's temperature at a standard of 27 °C. Traditionally, a mixture of ethylene glycol and water is circulated through the battery pack for cooling, but this method is not sufficient. By contrast, the use of graphene nanoplatelets (GNPs) can improve heat transfer, reducing temperature rise in the battery cell. In this study, a customized battery pack has been simulated using coolants containing varying concentrations of GNPs (ranging from 0.001 vol% to 0.01 vol%) to assess their effectiveness in lowering the operating temperature. The Lagrangian approach has been employed to track the discrete phase particles which couples with Eulerian continuous phase fluid. Results have shown that the pure EG/Water coolant decreases the peak temperature of the system by 16.67% (60 °C–50 °C) which further decreases to 26.85 °C (reduction of 55.25%) till the addition of optimum 0.03 vol% GNP. With the addition of only 0.001 vol% of GNPs, the difference in the peak temperature in the model increases from 10 °C to 31.15 °C as compared to the pure mixture. Higher thermal conductivity, greater surface area and higher specific heat capacity of the particles are attributed for this enhanced cooling.

Study of the breathing mode development in Hall thrusters using hybrid simulations

We use a 2.5D hybrid simulation to study the breathing mode (BM) dynamics in Hall thrusters (HTs). This involves a 1D Euler fluid simulation for neutral dynamics in the axial direction, coupled with a 2D axial–azimuthal Particle-in-Cell (PIC) simulation for charged species. The simulation also includes an out-of-plane virtual dimension for wall losses. This setup allows us to replicate the BM’s macroscopic features observed in experiments. A comprehensive analysis of plasma parameters in BM’s phases divides it into two growth and two decay sub-phases. Examining 1D axial profiles of electron temperature, gas and plasma densities, and particle creation rate shows that an increase in electron temperature alone cannot sustain ionization. Ionization seems to be influenced by the spatial correlation between electron and gas densities and the ionization rate coefficient. Investigating ion back-flow reveals its impact on modulating neutral flux entering the ionization region. The hybrid simulation’s outcomes let us assess the usual 0D predator–prey model’s validity and identify its limitations. The ionization and ion convection term approximations hold, but the gas convective term approximation does not. Introducing an alternative gas convective term approximation involving constant density ejection from the ionization region constructs an unstable BM model consistent with simulation results. In addition, this paper explores how varying the imposed voltage and mass flow rate impacts the BM. The BM frequency increases with imposed voltage, aligning with theoretical predictions. The mass flow rate variation has a limited effect on BM frequency, following the theoretical model’s trend.

Detection of onset of agglomeration in a bubbling fluidized bed biomass combustor using reactive Eulerian computational fluid dynamics

The choice of a type of combustion technology to be used for heat or power generation depends on economic, technical, operational and fuel availability constraints. The benefits associated with the evolving market driven by the fluidised bed combustion (FBC) technology cannot be overlooked especially when gauged at 65 GWth of worldwide installed capacity alongside added benefits of handling fuel variation, low pollutant emissions and high combustion efficiency. Biomass or biomass waste will continue to have a vital role to play in the future FBC technology-based power generation. Biomass often contains high levels of inorganic species that can form sticky agglomerates posing a significant risk to boiler operation resulting in unscheduled outages. This added complexity of the behaviour of the fuel and bed material mix highlights the requirement for simulation models to identify agglomeration to help improve the overall performance and reliability of FBC technology. To resolve this problem, this research devised a simulation strategy for the detection of agglomeration using the Eulerian–Eulerian approach. The developed modelling strategy is validated with the experimental data available in literature for two-dimensional simplified geometry of a pilot-scale fluidised bed combustor. The model results were found promising and robust to predict bed defluidisation times and other parameters consistent with the experimental data.

Impact of displacement ventilation and underfloor air distribution systems on concentrations of indoor particle in different seasons

The particle motion in a room is affected by the thermal environment and the air supply conditions caused by seasonal changes. In the study, a Lagrangian discrete trajectory model combined with the Eulerian fluid method was adopted to simulate the characteristics of indoor airflow and the diffusion of two typical indoor particles with considering different air supply conditions in different seasons. Specifically, the thermal comfort perception, draught rating (DR) of the indoor personnel, and the contaminant removal effectiveness (CRE, ε) of indoor particles under the influences of displacement ventilation (DV) and underfloor air distribution (UFAD) systems were investigated. The results revealed that when considering the indoor thermal comfort under summer and winter air supply conditions, UFAD was found be more effective than the DV system in protecting the temperature difference of indoor personnel. Additionally, the removal effect of PM1 in the breathing area was superior compared to that of the DV system. Regarding the removal effectiveness of PM2.5, the removal performance of both ventilation systems decreased, but the removal effect of the DV system on PM2.5 in the breathing area (with the largest εl of 1.55) was significantly better than that of the UFAD system under winter operating conditions. It is essential for the selection of the ventilation system to consider the thermal comfort of indoor occupants, as different ventilation systems have varying capabilities to remove particles of different sizes. Therefore, choosing an appropriate ventilation system is crucial for enhancing indoor air quality, and the findings of this study provide a basis for improving indoor air quality.

Stabilized mixed material point method for incompressible fluid flow analysis

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method’s capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of water sloshing and dam break scenarios.

An adaptive approach to remove tensile instability in SPH for weakly compressible fluids

Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile instability, which is the occurrence of short wavelength zero energy modes resulting in unphysical clustering of particles. The root cause of the instability is the shape of derivative of the compactly supported kernel function which may yield negative stiffness in the particle interaction under certain circumstances. In this work, an adaptive algorithm is developed to remove tensile instability in SPH for weakly compressible fluids. Herein, a B-spline function is used as the SPH kernel and the knots of the B-spline are adapted to change the shape of the kernel, thereby satisfying the condition associated with stability. The knot-shifting criterion is based on the particle movement within the influence domain. This enables the prevention of instability in fluid problems where excessive rearrangement of particle positions occurs. A 1D dispersion analysis of an Oldroyd B fluid material model is performed to show how the algorithm prevents instabilities for short wavelengths but ensures accuracy at large wavelengths. The efficacy of the approach is demonstrated through a few benchmark fluid dynamics simulations where a visco-elastic Oldroyd B material model and a non-viscous Eulerian fluid material model are considered.

Effect of stenotic shapes and arterial wall elasticity on the hemodynamics

The present study employs an arbitrary Lagrangian–Eulerian fluid–structure interaction approach to investigate pulsatile blood flow through a deformable stenosed channel. The flow is modeled by solving the incompressible continuity and momentum equations using finite element-based commercial solver COMSOL Multiphysics®. In this work, we explore the effects of different stenotic shapes—elliptical, round, and sinusoidal, degrees of stenosis (30%, 50%, and 70%), and arterial wall stiffnesses—0.5, 1.5, and 2.5 MPa on the velocity profile, pressure and wall shear stress distribution, and wall deformation. The oscillatory shear index (OSI) is analyzed to predict further plaque formation in the stenosed artery. We find that the flow velocity, wall shear stress, and pressure difference across the stenosed region increase with an increase in the stenotic severity and artery stiffness. The velocity profiles intersect at a radial location in the stenotic region termed critical radius, where relative magnitudes get reversed. With the increase in stenotic severity, the wall displacement decreases at the throat and increases at the upstream side. With the increase in wall stiffness, the wall deformation decreases, and shear stress increases, thereby increasing the pressure drop across the stenosed region. At a lower mass flow rate and a higher degree of stenosis, the vortices are formed upstream and downstream of the stenosed region for all stenotic shapes. The vorticity magnitude is found to be more than 21% higher for sinusoidal stenotic shape than round and elliptical ones. The effect of stenotic profile on the pressure drop characteristics shows that blood experiences maximum wall shear stress for the sinusoidal stenotic geometry, whereas the pressure drop is the maximum for the elliptical stenotic shape. The elliptical stenotic shape is more prone to further plaque formation than round and sinusoidal stenotic shapes. At lower Womersley number (Wo=2.76) corresponding to 60 beats per min heart beat rate, secondary vortices are formed downstream of the channel, causing higher OSI.