Eulerian-Lagrangian Approach Research Articles

Comparison of the CEL and ALE approaches for the simulation of orthogonal cutting of 15-5PH and 42CrMo4 materials

The modeling of cutting processes by the finite element method represents a great challenge for scientific researchers. Indeed, the plastic strain and strain rate in cutting induce a high risk of mesh distortion, especially for models based on a Lagrangian formulation which were the first to be developed. To overcome this problem other formulations, such as the Arbitrary Eulerian-Lagrangian (ALE), which is a combination of the classical formulations (Eulerian and Lagrangian), have been developed. Despite very interesting results in the simulation of orthogonal cutting, the implementation of this type of model remains delicate, and in particular the choice of initial geometrical conditions which can lead to a sudden stop of the calculation induced by a mesh distortion. To overcome these limitations, the Coupled Eulerian-Lagrangian (CEL) approach has been developed to simulate the orthogonal cutting process. In this paper, the CEL and ALE approaches were compared to simulate the orthogonal cutting process. The first objective was to compare the quality of the predicted physical quantities (forces, chips) over a wide range of cutting speeds and cutting thicknesses for two different materials. The second objective was to evaluate the time required for a complete simulation, integrating the time to set up the initial conditions (chip geometry) and finally the computation time of the machining operation. This work has shown that ALE and CEL formulations lead to very similar quantitative results that are pretty close to the experimental results. The ALE formulation has the advantage of having a reduced computation time compared to the CEL formulation. However, the preparation of the simulation is easy and robust for the CEL, whereas the selection of initial geometrical conditions for the ALE calculation requires several trials and errors before finding stable conditions. The CEL formulation is therefore a solution to be favored when launching several simulations in an automated way thanks to its reliability.

Neural Networks Application for the Data of LQG Regulator for the Flexible Joint Robot

This paper describes the investigation of a flexible robotic arm with Degree of Freedom (DOF) through Linear Quadratic Gaussian (LQG) regulator under the influence of noise signals with using diagrams below. The derived model is based on the Euler-Lagrange approach while LQG mode is proposed as a modern control method. A flexible robotic arm that is test in the modern regulator is essential for applications. This is even more interesting while these arms have joints that work independently of each other, but they still ensure a tight connection between the joints. Testing the stability characteristics of the system through this regulator helps readers determine the output signals of a system exactly. From here, the author came up with strategies the match the requirements. Although the initial stage of the operating cycle is not stable with the use of LQG regulator, most of later stages of this process of closed systems of robotic systems gradually become stable. In particular, adjusting LQG for flexible joint robot gives satisfactory simulation results. This promises a positive result of other joint robot. Neural networks applied in this paper have proven its effectiveness in information security issues. It is also very useful for tight control of possible situations such as a large scale attack on network systems, automated control systems. The main contributions of this paper have been clearly demonstrated through two strategies that need to be addressed: LQG, neural networks for the data of LQG regulator.The methods described above have not been previously published for this model. Therefore, this article was born to outline the above objectives and the plans have been satisfactorily implemented. These studies are important because they serve as a necessary database in the selection of control strategies according to the requirements. Simulation results are done by Matlab. The purpose of the study of this paper: the author has searched for a stability of the system through the above methods. The applied method is a thorough study of the structure of the system as well as the construction of algorithms to form the regulator. The result ia a reliable simulation of events after the system is controlled by these regulators.

Numerical analyses of energy balance and installation mechanisms of large-diameter tapered monopiles by impact driving

Large-diameter monopiles are widely used as the foundation to support offshore wind turbines (OWTs) in shallow coastal waters. The benefits of small-to-medium diameter tapered piles have been reported in the past. The potential use of large-diameter tapered monopiles installed by impact driving to support OWTs is thus presented, and then comparatively assessed by numerical analyses in terms of energy balance and installation mechanisms. A three-dimensional large deformation finite element (3D-LDFE) model of monopiles driven in clay was developed using a Coupled Eulerian-Lagrangian (CEL) approach. An advanced user-defined hypoplasticity clay (HC) model was employed to model undrained kaolin clay, featuring nonlinear behavior from small strain to large strain. The force-time curve defined by the operating data of a state-of-the-art hammer in the offshore industry was inputted to explicitly model impact driving. Better agreement between the measured and the simulated results was observed to validate the accuracy of the numerical model. The numerical results obtained give greater confidence to the future use of large diameter tapered monopiles for OWTs.

Three-dimensional DEM-CFD simulation of a lab-scale fluidized bed to support the development of two-fluid model approach

The present work is dedicated to the numerical study of the hydrodynamics of a pressurized fluidized-bed using an Euler–Lagrange approach, with the goal to gain insight into the Two-Fluid Model (TFM) approach. The gas phase is modeled by filtered Navier–Stokes equations, and the solid particles are tracked using a Discrete Element Method (DEM). Collisions are handled using a soft-sphere model. Numerical predictions of the mean (time-averaged) vertical particle velocity are compared with experimental measurements available from the literature, obtained from a Positron Emission Particle Tracking (PEPT) technique. In addition, DEM-Computational Fluid Dynamics (CFD) results are extensively compared with predictions from TFM numerical simulations. Results accounting for inelastic frictionless particle–particle collisions show a very good agreement with the experimental data and TFM results in the central zone of the reactor. In the near wall region the numerical simulation overestimates the downward particle velocity with respect to the experimental measurements, especially when the particle–wall friction is neglected. The influence of the friction at the wall is therefore further investigated and a local analysis of the particle–wall interactions is carried out. It is demonstrated that the long sustained contacts of particle assemblies with the wall in such a dense regime play a crucial role on the overall bed behavior. Therefore, it is recommended that this effect is taken into account in the boundary conditions of a TFM approach when it is used to predict bubbling fluidized beds. • DEM-CFD 3D simulation of a lab-scale fluidized bed • Comparison with experiments and Two-Fluid Model predictions • Local statistical analysis to characterize particle–wall interactions • Dominant friction effect at wall due to sustained particle–wall contacts

CFD analysis of the downdraft gasifier using species-transport and discrete phase model

In the present study, a 2-D axisymmetric steady-state computational fluid dynamics (CFD) model has been developed for biomass gasification in a fixed bed Imbert downdraft gasifier. A discrete phase model (DPM) based on the Euler-Lagrangian approach with species transport is applied to the gasifier having the capacity of ≈ 5 kW. The use of DPM for the particle-continuous phase interaction leads to capture more realistic gasification phenomena. The proposed model is an effort to carry forward the CFD technique by implementing an alternative chemical kinetic scheme to study the various gasification parameters. The model is validated at different values of equivalence ratios (0.19–0.33) for producer gas composition and found to be in better agreement with the experimental values reported in the literature. The standard estimated error for the present model is 6.64, 7.55, 2.92, and 5.28 % for carbon monoxide, hydrogen, methane, and carbon dioxide, respectively. Moreover, the calculated standard deviation is 0.44 only. The biomass feed and airflow rates vary from 3.43 to 5.82 kg/h and 2.41–8.02 Nm3/h, respectively. It has been found that an equivalence ratio in the range of 0.25 to 0.30 is the most appropriate condition in the present operating range of the gasifier. The proposed scheme allows accurate prediction under various operating conditions, which may enable the designer to optimise the operating conditions. The model predictions would help to design the process integration of gasification with any existing commercial energy-producing unit based on conventional fuels. Hence, it deliberates significant contribution and value addition in the current literature for the CFD modelling of biomass gasification. The present study not only helps to improve the overall performance of the gasifier but also provides the profiles of essential design variables across the length of the gasifier.

Numerical modeling of gas-solid two-phase flow in a plasma melting furnace

Due to the low leaching rate of heavy metals and high energy utilization, the plasma melting furnace is widely used in the harmless treatment of waste incineration. In this paper, the gas-solid two-phase flow in the plasma melting furnace was numerically modelled by means of Euler-Lagrange approach. Conclusions can be drawn that the raw fly ash should be pelletized in order to successfully participate in the melting reaction and effectively avoid the collisional erosion with the graphite cathode. The velocity and temperature fields in the furnace showed asymmetry due to the interaction between the flue gas and slag particles. The heat-up degree of fly ash was much greater than that of SiO 2 particle while the speed discrepancy was small. The average temperature of slag particles in the effective melting region was relatively higher, which is more beneficial to the melting reaction. In addition, three evaluation indicators were established to analyze the distribution of slag particles on the bath surface. The mass proportions of different slag particles in the effective melting region were >40%, the maximum value of their radial distribution can be obtained in the radius range of 0.9–1.0 m, and the mass ratios of fly ash and SiO 2 particles in the same radius domain were overall closer to that of entering the furnace. Finally, the collisional erosion effect of slag particles on the graphite cathode was discussed in detail. • Particle flow in the plasma melting furnace is studied by Euler-Lagrange approach. • Fly ash pelletizing facilitates melting reaction and avoids collisional erosion. • Distribution of particles on bath surface can be evaluated by three key indicators. • High portion of particles in the effective melting region benefits melting reaction.

Rationale Behind EU-DEMO Limiter’s Plasma-Facing Component Design Under Material Phase Change

The protection strategy adopted for the European DEMOnstration (EU-DEMO) fusion power reactor foresees the use of sacrificial components–referred to as limiters–dealing with plasma-wall contacts. Their aim is to protect the first wall (FW) against the huge amount of plasma energy (up to GigaJoules) released in a few milliseconds during disruptive events, which might lead to melting and/or vaporization of the foreseen plasma-facing tungsten armor. The current limiter design concepts rely on actively water-cooled plasma-facing components (PFCs) made of tungsten. As water is not allowed inside the main chamber, limiter’s PFCs must be designed to preserve the cooling system integrity under any scenario, therefore the estimate of the thickness of material undergoing any phase change is crucial. Given the initial assessment of plasma magnetic configurations during off-normal events, this article describes the procedure followed for designing the limiter’s PFC, which includes a novel approach for estimating the molten thickness of material under high heat flux. A simplified 1-D model has been implemented in MATLAB, which deals with multiphase moving boundary problems, hence its name Thermal Analysis foR Tracking InterFaces under meLting&vaporizaTion-induced plasma Transient Events (TARTIFL&TTE). This model takes its inspiration from the way phase change interface tracking problems are tackled in food industry (i.e., freeze-drying processes) and solute concentration diffusion-controlled problems. It overcomes the complexity of solving a strongly coupled non-linear system of partial and ordinary differential equations in moving spatial domains by adopting a change of coordinate system based on the Landau transformation. As a result, an equivalent and fixed spatial coordinate system is defined where the spatial domain boundaries of the different phases are constrained, and the systems of governing equations are easy to solve. Both the solid and liquid phases are modeled, while the vapor is assumed to be removed once formed. Its benchmark against computational results found in the literature has shown a very good agreement, which paves the way to further development of it. For phase change interface tracking problems in 2-D/3-D and more complex geometries, a commercial Multiphysics software adopting the Lagrangian–Eulerian approach in moving mesh frames will be used for tackling problems where material is removed following a phase change. Although the vapor domain is not simulated, a set of gas kinetics boundary conditions couples the interface between vapor and liquid phases, driving its position over time. This will be detailed described in a future companion article.

Optimization of a gas turbine model combustor due to variations in geometrical characteristics of stabilizing air jets

• Interaction of input parameters (diameter, angle, and position) is considered. • ANN is used to extract fitness (trained) function for GA. • NOx, CO, and PF are improved by up to 11.31%, 2.88%, and 21.07%, respectively. • Soot is decreased by up to 24.46%. The main purpose of this paper is to optimize the objective parameters in a gas turbine model combustor. These parameters include N O x and C O pollutants as well as pattern factor. C O is based on a maximum produced value in the model combustor. To optimize the objective parameters, the input characteristics (such as diameter, angle, and position of the stabilizing air jets) are varied. Simulation of the combustion process comprises turbulent flow, combustion, radiative heat transfer, and fuel injection modeling. The models employed for this simulation, based on RANS approach, are realizable k - ε for flow turbulence, steady flamelet model for combustion, discrete ordinates model for radiative heat transfer, and Eulerian-Lagrangian approach for fuel injection. A diesel fuel (C 10 H 22 ) is used in the model combustor and N O x modeling is conducted via post-processing. Artificial neural network is applied to gain an approximated trained function based on results and input geometrical characteristics. Data for training the artificial neural network is generated by means of design of experiments. For finding the optimum point, genetic algorithm is utilized. The obtained neural network function is applied to genetic algorithm so as to extract the optimum points. Since there is more than one objective parameter a set of optimum points is obtained which is called the Pareto front. Using multiple-criteria decision making method (LINMAP model), the final optimum point is achieved. The optimum point shows that the amounts of N O x , C O , and pattern factor are improved by up to 11.31 %, 2.88 %, and 21.07 %, respectively. The value of soot which is not a part of optimization is also improved by up to 24.46 %.

Effects of wind-rain coupling on the aerodynamic characteristics of a high-speed train

Simultaneous effect of crosswind and rainfall on railway vehicles has raised concern lately as it threatens the operational safety. In this study, the wind-rain coupling effects on the train aerodynamics have been systematically investigated by means of Euler-Lagrangian approach. The aerodynamic computational model is established based on non-spherical raindrops, and model verification is conducted with the aid of existing measurement results. The flow features as well as the train aerodynamic coefficients under wind-rain environments are systematically studied. The results show that, the mass concentration of raindrops around a train increases with rainfall intensity. The aerodynamic coefficients show linear relationship with the increase of rainfall intensity. Unlike that of a crosswind condition, train aerodynamic coefficients exposed to combined wind and rain are dependent not only on train shape and yaw angles, but also on resultant wind velocity and rainfall intensity. The formulae for predicting the aerodynamic coefficients of the train operating in wind-rain environments are finally obtained in this paper.

Insights on metallic particle bonding to thermoplastic polymeric substrates during cold spray

Metallization of polymers using cold spray technology has reached wide consideration in recent years. However, an effective modeling approach to address the deposition phenomena able to assess bonding formation in polymer metallization is still lacking. This study aims to develop a finite element model to simulate the solid-state deposition of metallic particles on thermoplastic polymeric substrates. Single copper particle impact on the Polyether Ether Ketone substrate was modeled using the coupled Lagrangian–Eulerian approach. Emphasis was given to the polymer material properties and substrate thermal history to account for the sensitivity of the physical and mechanical properties of polymers to temperature. Experimental coating depositions were performed to select an optimized set of spray parameters while single-particle impact tests were conducted for model validation. The substrate temperature was measured using an infrared thermal camera and was used to model the sub-surface temperature gradient during gas spray exposure. The proposed numerical model is shown to be capable of predicting various impact features includi mechanical interlocking and the effect of particle velocity fluctuations and temperature gradients on the extent of bonding. Substrate heating was found to have a distinct effect on the correct prediction of particle bonding. The proposed model enables tuning the appropriate processing conditions for successful copper particle adhesion on PEEK polymeric substrates.

Numerical simulation of nucleating flow and shock capturing in steam turbines by a simple low-dissipation upwind scheme using an Eulerian-Lagrangian model

The rapid expansion of steam leads to non-equilibrium condensation of steam in the supersonic region which the performance of the turbines is reduced. The achievement of an accurate numerical method in a wide range of regimes to capture the aerodynamic and condensation shocks with minimum computation and numerical errors has always been of interest to researchers. Therefore, in this research, an in-house code is developed with a version of Advection Upstream Splitting Methods (AUSM), named Simple Low-dissipation AUSM (SLAU). The results of the SLAU scheme for condensing flow in three convergent-diverging nozzles are presented and compared with experimental data to validate the scheme. Then the SLAU scheme's performance in condensation and aerodynamic shock capturing for two-dimensional turbine blades is evaluated using an Eulerian-Lagrangian approach under different outlet conditions. The governing equations of flow are solved by the Eulerian approach using the SLAU scheme, and to accurately calculate wet parameters of the solution field, the corresponding equations are solved in Lagrangian form. Comparing the results of the SLAU scheme with experimental data, it was found that, despite the simplicity of the SLAU scheme, in the absence of tuning variables, it provided suitable predictions, even within shock zones. The results of the SLAU scheme for modeling steam nucleating flows and the prediction of the droplet radius are in better agreement with the experimental data and the results are improved considerably for the supersonic outlet cascade.

A volumetric-smoothed particle hydrodynamics based Eulerian-Lagrangian framework for simulating proppant transport

Different numerical methods have been applied to simulate the proppant transport in petroleum engineering, which can be roughly categorized as the Eulerian-Eulerian and Eulerian-Lagrangian models. Recently, a hybrid Eulerian-Lagrangian (E-L) approach, the multiphase particle-in-cell (MP-PIC) method, has been successfully applied to model large-scale proppant transport problems by introducing the concept of parcels (clusters of particle). In the MP-PIC method, particle-particle interaction force is expressed as the gradient of particle stress. The calculation of this gradient strongly depends on the interpolation between particle properties and Eulerian grids, which could lead to problems such as non-physical particle suspension, particle agglomeration and non-conserved interparticle interactions. In this study, a new method, the volumetric-smoothed particle hydrodynamics (V-SPH) method, is proposed to improve the calculation accuracy of the particle-particle interaction forces in the original MP-PIC method. In the V-SPH method, the calculation of the particle stress gradient no longer depends on the background Eulerian grids and the conservation of the interparticle stress is also guaranteed. In this paper, detailed introduction of the V-SPH based Eulerian-Lagrangian framework is provided. The reliability of the proposed V-SPH method is validated against both the numerical and experimental results in literature. By comparing with the original MP-PIC method, we observe that the non-physical particle agglomeration, as well as non-physical particle suspension problems can be well solved with the proposed new model. In addition, the impact of some key parameters in the V-SPH method on simulation results are also investigated. The choice of the PPP (number of particles per parcel) and the treatment of boundary particle deficiency are found to play important roles in model accuracy and efficiency. The V-SPH method proposed in this work can provide more accurate results than the original MP-PIC method, especially in the regions of dense proppant concentration, with comparable computing efficiency. With proper treatment of boundary deficiencies, it is promising to be used in more complex field-scale proppant transport problems.

An efficient explicit immersed boundary-reconstructed lattice Boltzmann flux solver for isothermal fluid-structure interaction problems with large deformations and complex geometries

In this paper, a novel approach for isothermal fluid-structure interaction (FSI) problems is proposed that not only inherits the advantages of a reconstructed lattice Boltzmann flux solver (RLBFS) in solving the fluid field, but also retains the efficiency found in the explicit boundary condition-enforced immersed boundary method (EIB) for implementation of boundary conditions on the solid wall. Hence, the new approach (EIB-RLBFS) is highly suitable for complex FSI problems such as large deformations and complex geometries. Furthermore, the arbitrary Lagrangian-Eulerian (ALE) approach is integrated with EIB-RLBFS to solve moving boundary problems efficiently. The structural dynamics are solved by a finite difference method for moving objects and flexible structures. The overall framework of EIB-RLBFS is simple yet robust, where a fractional method is applied to split the FSI process into a predictor step and a corrector step. The RLBFS is applied in the predictor step to predict the intermediate flow field, while the EIB is invoked in the corrector step to impose the no-slip boundary conditions within the flow field, thereby, correcting the predicted flow field to satisfy the no-slip boundary conditions. The proposed approach (EIB-RLBFS) has been tested and evaluated extensively in terms of accuracy and efficiency on several benchmark cases such as, a 2D self-propelled unconstrained flapping/undulatory foil, a 2D filament, a 3D streamwise rotating sphere, and a 3D flapping flag. Results obtained using the proposed approach are in good agreement with previous studies, substantiating the capability and flexibility of EIB-RLBFS for solving FSI problems.

Pulverized coal combustion computational modeling approach: A review

CFD (Computational fluid dynamics) is a tool, through which, the entire combustion process for pulverized coal combustion (PCC) can be predicted. The solid fuel combustion modeling is not as simple as gaseous or liquid fuel combustion modeling. In the solid fuel combustion process, various physical transformations and chemical reactions occur simultaneously. Therefore in the computational modeling approach for PCC, basic physical and chemical processes such as; turbulence, radiation, devolatilization, gas-phase combustion, char reaction and soot formation/reduction are integrated to obtain the desired results. However, in order to reach the desired accuracy, different computational models should be chosen carefully. In this review, various common models that are widely used in PCC simulation are discussed scientifically along with their modeling aspects. The basic advantages and disadvantages of these models are also discussed in this study. Moreover, different models preferred by various authors for pulverized coal combustion simulation process are also summarized. From the review, it has been observed that the eddy viscosity based two-equation turbulent models and Eulerian-Lagrangian multiphase approach are mostly preferred due to better computational economy. Two competing rate devolatilization model from various finite rate models and FG-DVC devolatilization model from various phenomenological models are mostly used for PCC. Diffusion kinetic control and Intrinsic char combustion models are mostly chosen to predict the char reaction. Finite reaction rate models are preferred when the computational economy is a concern, whereas phenomenological models provide results with better accuracy because in phenomenological models realistic inputs are given as input for simulation whereas, in finite rate models, finite rate constants are mostly empirical. Most of the gas phase models are given almost equal importance. Discrete ordinate (DO) is mostly used for PCC due to its ability of volumetric radiation calculation and the ability to evaluate radiation effect on the particle phase.

Damage prediction of concrete gravity dams subjected to penetration explosion

The dynamic responses and damage mechanisms of high dams that are subjected to blast loads have become important in recent years. A series of analytical, experimental, and numerical approaches are used to investigate the mechanisms and characteristics of composite damage to concrete gravity dams subjected to penetration explosion. The potential failure modes of the dam resulting from penetration explosion are first analyzed and categorized. Field blast tests are performed to gain the possible damage mechanisms and modes of a small-scale dam model to internal explosion. A fully coupled Eulerian–Lagrangian approach is then adopted and verified through comparisons between the experimental and the numerical results. Following this, detailed numerical simulations and analyses of a typical concrete gravity dam to penetration explosion are presented by using the validated numerical method to examine its dynamic responses and the development of damage in it. Furthermore, the results of damage to the dam in case of different attack locations, explosive equivalents, penetration depths, and critical interfaces are compared. Similarity theory and blasting theory are used to provide a theoretical analysis, and its results are used along with those of numerical simulations to obtain a formula to predict the damage range of the dam. The work here focuses on the dynamic responses and damage mechanisms of dams subjected to penetration explosion, and the authors propose a quantitative and effective method to predict this damage.

Heat generation, plastic deformation and residual stresses in friction stir welding of aluminium alloy

The interactions among thermal history, plastic deformation and residual stresses in the friction stir welding (FSW) process under different welding parameters have been widely considered a crucial issue and still not fully understood. In the present study, a novel three-dimensional fully coupled thermo-mechanical finite element (FE) model based on Coupled Eulerian-Lagrangian approach (CEL) has been developed to simulate the FSW process of aluminium alloy AA 6082-T6 and to analyse the thermo-mechanical interaction mechanisms under different welding conditions. The numerical model successfully simulates the plunge, dwell, and welding steps in FSW and captures the evolution of temperature, plastic deformation, and residual stresses in the welded joint. The obtained results were validated by experimental testing with observed cross-weld thermal history, optical macrography and residual stress measurement using the neutron diffraction technique. The results reveal that the tool rotation speed governs the temperature evolution; the peak temperature increased from 740 to 850 °K when the tool rotation speed rose from 800 to 1100 rpm. The rotational speed also affected the plastic deformation, material flow, and the volume of material being stirred during the welding process. Higher plastic deformation is formed in the stirring zone by increasing the tool angular velocity. This behaviour led to an increase in the stirring effect of the welding tool, reduction of the tunnel defect size and enhancing the quality of weldments. The distribution of residual stresses in different zones of the FSW joints has been found to have an M-shaped profile. A significant tensile residual stress is characterised in the edge of the nugget zone in both longitudinal and transverse directions, balanced by compressive stresses in the thermo-mechanically affected zone, heat-affected zone and base metal. The presented FE modelling provides a reliable insight into the effects of the welding parameters on the weld quality of FSW joints and process optimisation with minimised experimental trials.

Study on the Effect of the Guide Vane Opening on the Band Clearance Sediment Erosion in a Francis Turbine

Sediment erosion is a negative phenomenon for the water turbine. The purpose of this paper is to study the effect of the guide vane opening on the particle motion and sediment erosion in the band chamber using the Euler–Lagrangian approach. The software Ansys CFX and Tabakoff erosion model are used to simulate the sediment laden flow in the full flow passage of the hydraulic turbine. The results are in good agreement with the actual erosion character on site. Results show that the guide vane opening has a positive correlation with the flow in the non-clearance channel. The increase of the guide vane opening will increase the erosion of the runner blade head, but the friction wear on the outlet side of the blade surface will decrease. The rotating action of the runner makes the sediment particles in the band chamber rotate rapidly around the center of the runner and constantly collide with the band chamber wall. Under the small opening, the smaller the opening, the easier the leakage of the band clearance occurs. The unsteady flow in the band chamber will disturb the motion trajectory of particles, change the impact angle of particles, and affect the wear in the band chamber. Under different openings, the change law of the erosion in the band clearance is closely related to the change law of clearance leakage.

Numerical simulation of two-phase flow: Air-mist film cooling over a flat plate

The performance of air-mist film cooling is evaluated for varying mist concentrations (2–7%) and droplet diameters (5–30 μm) using the Euler-Lagrange approach with the k−ε realizable model with enhanced wall treatment. The jet-crossflow interactions induce complex droplet dynamics, illustrating a highly skewed jet at the hole exit with the concentration of droplets and momentum on the windward side, while the counter-rotating vortex pair (CRVP) appears on the leeward side. The downstream evolutions of droplets, their evaporation, and the thermal field are considerably influenced by the mist concentration and droplet diameter. The introduction of droplets in the secondary flow brings in significant improvements in film cooling effectiveness both in streamwise and spanwise directions. Although the spanwise non-uniformity of the thermal field is high, droplets of 10 μm at a mist concentration of 5% provide the optimal protection of the surface, where the trajectory of the secondary jet and that of droplets are in concurrence for the freestream conditions. The droplet dynamics exhibit the two-layer system for a relatively larger diameter, where droplets penetrate more into the crossflow and stay away from the surface.

Modelling of bubble breakage and coalescence in stirred and sparged bioreactor using the Euler-Lagrange approach

Gas-liquid systems are commonly used in industry to carry out biochemical reactions. Such process must be carried out to ensure sufficient mass transfer while there is no damage to the living cells/microorganisms. This is given mainly by the bubble size distribution (BSD) and process parameters such as the impeller speed and gas sparging rate. The correct prediction of BSD is crucial to choosing the optimal process parameters and meeting the requirements of a given culture. This work aimed to use computational fluid dynamics (CFD) to predict the breakage and coalescence of individual bubbles and therefore to predict the whole BSD under broad range of process parameters. The gas-liquid system of the stirred and sparged bioreactor was modelled utilizing the Euler-Lagrange (EL) approach. The continuous phase was modelled as a 3D time-dependent problem using the Reynolds-averaged Navier-Stokes (RANS) method with a realizable k-ε model for the description of turbulence. The motion of discrete Lagrangian bubbles was tracked by Newton's equation of motion. Both the breakage and coalescence of individual bubbles were implemented. For bubble coalescence, the model developed by Prince and Blanch and further modified by Sommerfeld and Sungkorn for use in the Lagrangian approach to bubbles was used. For breakup, a model developed by Martínez-Bazán was used. There, the effect of daughter distribution function (DDF) on the resulting gas dispersion was studied. Experiments and simulations were performed in the Minifors stirred and sparged bioreactor with a working volume of 3.5 L. The impeller speeds ranged from 200 to 500 rpm (corresponding to Reynolds number in the range from 10,889 to 27,222), while the gas feed rate was constant and reached a value of 1.2 L min–1. To validate the whole CFD model, we compared the BSDs obtained from the simulations against experimentally determined BSDs. There, for all cases, the simulations matched the experimental data relatively well. Subsequently, a general characterization of the system studied was performed in terms of the volumetric mass transfer coefficient (kLa) and the maximum hydrodynamic stress (τVS) to which the cell could be exposed. Also in this case, under all tested conditions, we achieved satisfactory agreement with experiments.

Particle deposition and characteristics of turbulent flow in converging and diverging nozzles using Eulerian-Lagrangian approach

The current study conducts a thorough assessment of the deposition of aerosol particles in turbulent flows in both converging and diverging nozzles using the Lagrangian particle tracking model and the RNG k-ε turbulence model. The air-particle interaction depends on flow velocity, particle diameter, and types of flow sections when the particles are injected into the airflow. For the parametric simulation, Stokes number is varied from 0.0354 to 0.8265 with the corresponding particle diameter ranging from 2.00 to 10.00 μm, whereas Reynolds number is varied from 5000 to 10,000. Computational results show how the particle deposition efficiency in converging and diverging nozzles is influenced by Stokes number, diameter ratio of pipe, particle diameter, and Reynolds number. The deposition efficiency of a diverging nozzle is found to be lower than that of a converging nozzle, and the flow Reynolds number increases the deposition efficiency slightly in the diverging nozzle but gradually in the converging nozzle.