Two-phase Field Research Articles

Application and comparison of dynamic mode decomposition methods in the tip leakage cavitation of a hydrofoil case

The cavitation of the tip leakage vortex (TLV) induced by tip leakage has always been a difficult problem faced by turbomachinery, and its flow structure is complex and diverse. How to accurately extract the main structures that affect the cavitating flow of the TLV from the two-phase flow field is a key problem. In this study, the main mode extraction and low order mode reconstruction accuracy of the cavitation flow field of TLV downstream of National Advisory Committee for Aeronautics (NACA)0009 hydrofoil by two dynamic mode decomposition (DMD) methods are compared. The research shows that the main modes extracted by the standard DMD method contain a large number of noise modes, while the sparsity-promoting DMD eliminates the noise modes, showing obvious advantages in the reconstruction accuracy of the velocity field. The characteristics of cavitation signals are analyzed, and the cavitation signals are divided into four categories, which explains the reason why DMD methods have low reconstruction accuracy in cavitation. This study provides a theoretical basis and strong guarantee for the extraction of mode decomposition characteristics of the two-phase flow field. This is of great significance for accelerating the prediction of multiphase flow fields based on intelligent flow pattern learning in the future. Meanwhile, it also provides a new method and road for the introduction of artificial intelligence technology in future scientific research.

Load Characteristics and Extreme Response of Straight-Bladed Floating VAWT Using a Fully Coupled Model

Operating Offshore Floating Vertical Axis Wind Turbines (OF-VAWT) have the potential to perform well in the deep-sea area. Some researchers gave performance prediction by developing simplified computing models. However, these models have imperfections in considering load and motion nonlinearity, especially in extreme environments. In this work, a numerical model is developed composed of Computational Fluid Dynamics (CFD) and Dynamic Fluid Body Interaction (DFBI) to acquire the aero-hydrodynamic load and performance of OF-VAWT in general and extreme environments. Unsteady Reynolds-Averaged Navier-Stokes (URANS), SST k-ω and Eulerian Multi-Phase (EMP) models are combined to generate a gas-liquid two-phase flow field; the Volume of Fluid (VOF) model is employed to capture free-surface and make numerical wind-wave. DFBI superposition motion technology is proposed for local motion definition and motion solution, and overset with sliding meshes is introduced to achieve the grid motion. The numerical approach is verified by the tunnel and tank experimental data from the available literature. Simulation results of general cases, such as variable wind speed, wave height and wave length, are compared to discuss the effect of environmental parameters on load and performance. Comparison shows that this straight-bladed OF-VAWT is more susceptible to wind speed. Furthermore, the aerodynamic load generated by the shut-down rotor is still significant in extreme environment, which has implications for the development of OF-VAWT controller.

Effects of droplet deformation, evaporation, and mutual interaction with air on droplet motion and droplet-film impingement in aeroengine bearing chambers

The physically complex oil/air two-phase flow field in aeroengine bearing chambers, incorporating droplet motion and droplet interaction with chamber wall oil film, significantly affects the lubrication and cooling function of bearing chambers. In the present investigation, a theoretical model is established upon the effects of droplet deformation, evaporation, and mutual interaction with air. Based on the model, the droplet motion characteristics and droplet quantities transferred into wall oil film can be obtained. Furthermore, the proposed model is validated by the high-quality experimental data from relevant literatures qualitatively and quantitatively. The mean percentage errors (MPE) of the calculation results, with experimental outcomes of two classical studies, are 9.62 % and 3.99 %. In addition, several interesting phenomena are observed: Droplet undergoes the shape oscillation, the mass and velocity reductions, as well as an increment of temperature during the motion. With the rising droplet diameter, an increase of droplet velocity and decrease of droplet temperature can be found, together with an enhancement of droplet quantities transferred into wall oil film. The proposed theoretical method not only facilitates the quantitative description of complex flow field in bearing chamber, but provides accurate input parameters for the following research of wall oil film flow. That contributes to the precise design of aeroengine bearing chamber lubrication system.

Modified Zerilli-Armstrong and Khan-Huang-Liang constitutive models to predict hot deformation behavior in a powder metallurgy Ti-22Al-25Nb alloy

In order to establish constitutive models for a fine-grained Ti-22Al-25Nb alloy fabricated by spark plasma sintering under high vacuum, isothermal uniaxial compression tests are conducted at the different deformation conditions of 950–1070 °C and 0.001–1 s−1. Using the friction-corrected experimental data, the modified Zerilli-Armstrong model and the Khan-Huang-Liang model are developed in the α2 + β/B2 + O triple-phase and α2 + B2 two-phase fields, respectively. The determination coefficient (R2) and average absolute relative error (AARE) of the developed models are 0.9773 and 8.73%, 0.9831 and 12.36%, respectively. Based on the analyzing the reason of large deviation, the modified Zerilli-Armstrong and Khan-Huang-Liang models are improved. The prediction accuracy of the improved constitutive models is improved to 0.9896 and 6.14%, 0.9891 and 6.82%, respectively. This indicates that the improved versions of the modified ZA and KHL models are very appropriate for predicting the hot deformation behavior of a fine-grained Ti-22Al-25Nb alloy fabricated by spark plasma sintering.

Multiphysics Coupled Simulation of Electrolytic Machining of Toothed Grooves of Contrate Gear

In the field of aviation, the contrate gear is an important component, the material of the contrate gear is the basis for ensuring the reliability and high performance of the aircraft engine, the commonly used material for contrate gear is 20Cr2Ni4A. In order to fully understand the electrolytic machining of the toothed groove of the contrate gear, a multiphysics coupling model of the electric field, the gas-liquid two-phase flow field and the temperature field was established to study the distribution of bubble rate, temperature, conductivity and current density in the processing gap. Simulation results show that the temperature and bubble rate gradually increase along the process direction in the processing gap, the conductivity and current density of the electrolyte gradually decrease.

Numerical simulation of particle erosion in the internal flow field of solid rocket motor nozzle using Rocstar

Solid composite propellants often contain metal particles, such as aluminum particles, and the internal flow field in a solid rocket motor is a typical gas–solid two-phase flow field. In this study, to address the problem of the erosion of particles on the wall during the working process of an engine, a particle erosion model was established based on the interaction mechanism between the particles and the wall. From the perspective of particle dynamics, the interaction mechanism between the moving particles and the wall was analyzed. The force of the particles on the wall surface was obtained, and a formula for solving the particle erosion rate was deduced by using the strength theory and the energy conservation principle. It was combined with Hertz’s contact theory to analyze the factors influencing the erosion rate. In this paper, the particle erosion experiments revealed not only the relationship between erosion rate and erosion angle but also the correlativity between erosion rate and particle concentration. In addition, the experimental results are consistent with the deduced results, which proves the reliability of the model established in this paper. The multiphysics simulation program Rocstar, developed by the Center for Simulation of Advanced Rockets at the University of Illinois, was used to perform a numerical simulation of the two-phase flow in the Jet Propulsion Laboratory nozzle. The results agreed well with the literature and the experimental data. The feasibility and accuracy of the calculation of the gas-phase and two-phase flow fields of the solid rocket motor nozzle were confirmed, laying the foundation for the numerical simulation of the entire process of the full flow field of the engine.

CMAS corrosion resistance characteristics of RE50TaxZr50-xO175+0.5x thermal barrier oxides in RE2Zr2O7-RETaO4 systems

The corrosion resistance characteristics of RE-rich RE50TaxZr50-xO175+0.5x oxides in RE2Zr2O7-RETaO4 systems to calcium-magnesium-alumino-silicate (CMAS) at 1300 °C, and the influence of RE3+ and Ta5+ on chemical reactions and reactive crystallization of CMAS melts were investigated. The results show that following the thermochemical reactions, apatite, pyrochlore, reprecipitated fluorite and residual Yb(Y)TaO4 phases were the predominant reaction products. Formation abilities of apatite and pyrochlore were found to be proportional to the ionic radius of RE3+. The increase of Ta5+ amount can decrease the number of available RE3+ to form apatite. Moreover, the resistance characteristic to CMAS corrosion in RE50TaxZr50-xO175+0.5x systems was decided by the combined action of apatite and pyrochlore phases. The cohesive mixture of apatite and pyrochlore phases can generate a dense layer near the reaction front, which had a positive effect on suppressing CMAS infiltration. The ability of the fluorite + RETaO4 two-phase field was determined to be sufficient to mitigate CMAS corrosion.

Study of the Two-Phase Flow Characteristics of a Damping Orifice in an Oleo-Pneumatic Shock Absorber

The oleo-pneumatic shock absorber involves a complex two-phase flow in the working process. In this paper, a simple oleo-pneumatic shock absorber model was established, and the volume-of-fluid (VOF) two-phase flow model was adopted to accurately simulate the distribution of the two-phase flow field in the shock absorber through the commercial software FLUENT 2020 R2. The accuracy of the simulation model was verified by the method of engineering damping force estimation, and the error of the numerical simulation results compared with the engineering estimation results was 7–8%. By numerical simulation, the influence of different orifice lengths and diameters on the maximum pressure, temperature, velocity and oil damping force inside the shock absorber was studied. The results showed that with the increase of the orifice length, the maximum pressure, flow rate and oil damping force in the shock absorber decreased. The temperature decreased first and then increased, but the overall effect was small. However, according to the oil volume fraction contour, the gas–liquid distribution in the shock absorber with an orifice larger than 15 mm was more chaotic. Increasing the diameter of the orifice had a great impact on the shock absorber. The maximum pressure, flow rate and damping force of the oil inside the shock absorber were sharply reduced, and the temperature continued to rise. These research results can provide reference for the optimization design of oleo-pneumatic shock absorbers.

Analysis of two-phase flow in cavitation condition of pump-turbine based on dynamic mode decomposition method in turbine mode

Cavitation is an inevitable and important problem in the design, manufacture and operation of pump-turbine. The research on cavitation of pump-turbine is mainly focused in the pump mode, but the cavitation characteristics of turbine mode are also very important. Traditional research methods are unable to dig a large amount of research data in cavitation flow. Therefore, the dynamic mode decomposition (DMD) method is used in this study to investigate the incipient cavitation and critical cavitation of a model pump-turbine. The results show that the DMD method can accurately extract the characteristics of the runner in pump mode under cavitation conditions. The development of cavitation makes the mode decomposition of the two-phase flow field and the reconstruction of the low order modes significantly different. DMD method is more suitable for signals with clear frequency and simple mean value and pulsation. The development of cavitation makes the reconstruction of low order modes change obviously, from the inception cavitation condition of first waveform reconstruction and then mean-value reconstruction to the critical cavitation condition of first mean-value reconstruction and then waveform reconstruction. It provides a new research idea for cavitation research of pump-turbine.

Numerical investigation on flow and mixing characteristics of powder fuel under strong shear and shock wave interaction

In this investigation, the mixing process of powder fuel transverse jet and supersonic airflow are discussed. The effects of particle size and induced shock wave on flow and mixing characteristics are also analyzed. The Eulerian-Lagrange method is utilized to simulate the gas-solid two-phase supersonic flow field. This numerical method has been verified using experimental data and simulation data from the open literature. The results reveal that the powder fuel transverse jet interacts violently with the supersonic airflow and forms complex shock wave structures in the flow field. The motion and distribution of particles are affected by their size and the interaction of shock wave/particle. The powder fuel composed of small size particles enhances mixing performance and has less impact on stagnation pressure loss. The existence of induced shock waves leads to part of the particles into the cavity and the stagnation pressure loss is large. With the increase of induced shock wave intensity, the mixing performance of the local region is continuously improved. The case with the inclination angle of 30° owns the best effect with improving the mixing efficiency by 28.33%, but the total pressure loss is increased by 33.88％.

Experimental study of Fe-rich region in the Fe–Nb–Zr system at 1000 °C

The Fe-rich corner of the Fe–Nb–Zr phase diagram was studied at 1000 °C by using synchrotron x-ray powder diffraction (SXPD) technique and quantitative electron probe microanalysis (EPMA). The MgCu2 (C15) and MgZn2 (C14) structures corresponding to Fe2Zr and Fe2Nb Laves phases were observed in the Fe2Zr–Fe2Nb pseudo-binary system. The MgNi2 (C36) structure corresponding to Fe2(Zr1-xNbx) Laves phase was not found in any of the compositions explored at this temperature. The existence of two three-phase fields (C15 + Fe23Zr6 + C14) and (C14 + Fe(α) + Fe23Zr6) and five two-phase fields (Fe(α) + C14), (Fe(α) + Fe23Zr6), (C15 + Fe23Zr6), (C15 + C14) and (Fe23Zr6 + C14) is proposed in the present work.

A data-driven stochastic model for velocity field and phase distribution in stirred particle-liquid suspensions

A computationally efficient Lagrangian stochastic model driven by short 3D experimental trajectories determined by a technique of positron emission particle tracking, has been developed to study two-phase particle-liquid flow in a mechanically agitated vessel and unravel the complex behaviour of both phases. Using a small set of trajectory driver data, the stochastic model is used in conjunction with a particle-wall collision model to simulate the full velocity field and spatial distribution of particles. The performance of a first and a second order model is evaluated in particle suspensions of various concentrations. Both models are able to predict local phase velocities to a high degree of accuracy. Predictions of spatial particle distribution are reasonable by the first order model but very accurate by the second order model. Furthermore, the latter is able to accurately predict the two-phase velocity field and spatial phase distribution under flow conditions outside the experimental range. • Deterministic multiphase flow models are challenging and computationally costly • A stochastic model accurately predicts 3D two-phase flow field in a stirred vessel • The stochastic model is driven by a small set of Lagrangian input data • The stochastic model is capable of extrapolating flow predictions • The stochastic model is highly computationally efficient

Research on Multi-physics Field Coupling Dynamic Process in Forward Flow Electrochemical Trepanning Blades

In this work, a multi-physics field coupling model based on electric field, gas-liquid two-phase flow field and temperature field of the forward flow electrochemical trepanning (FFECT) blades was established, and the distribution law of hydrogen bubble volume fraction, electrolyte temperature and electrolyte conductivity in machining gap was obtained. Based on the simulation results, the time-varying process of electrolyte flow velocity distribution was divided into three stages according to the change in machining gap corresponding to different blade machining heights H, and the effects of the machining voltage U and the cathode feed rate v on the side gap Δ s and the end gap Δ e were investigated. The simulation analysis and experimental results show that both side gap and end gap increase as machining voltage increases while decrease with the increase in cathode feed rate. The model predictions are in good agreement with the experimental results, and the maximum errors of side gap and end gap are 10.6% and 17.7% respectively. In addition, the effects of machining voltage and cathode feed rate on the surface quality were studied experimentally. Results reveal that surface roughness can be reduced by appropriately decreasing the machining voltage and increasing the cathode feed rate.

Improvement of mode selection criterion of dynamic mode decomposition in a hydrofoil cavitation multiphase flow case

With the improvement of cavitation prediction, how to extract key information from massive data of cavitation flow field accurately and quickly has become an urgent requirement. Reduced-order modeling method has been used to extract the key information and simplify the data of restored flow field. However, its applicability to two-phase flow field and how to select main modes have not been well-studied. Therefore, this study uses dynamic mode decomposition (DMD) method to analyze cavitation flow field of a two-dimensional hydrofoil with three cavitation numbers by mode decomposition and reconstruction, and to analyze the applicability of DMD method and two tradition main mode selection criteria for cavitation. The results show that DMD method is effective for the inversion of two-phase flow field, but due to the complexity of unstable cavitating flow, the applicable range of different criteria has been significantly reduced. Therefore, this study combines the advantages of clustering method, presents a new main mode selection criterion based on clustering analysis, which plays an important role in cavitation flow analysis. This method provides a strong guarantee for the use of reduced-order modeling method, and also provides a good basis for the introduction of artificial intelligence in the future.

Feasibility analysis of obtaining tri-modal microstructure by multi-pass conventional forging combined with dual heat treatment for near-α titanium alloy with different initial microstructures

Conventional forging followed by dual heat treatment (near-β and two-phase field heat treatments) is a feasible technique aimed at obtaining tri-modal microstructure in near-α titanium alloys. In view of the enlargement and integration of aerospace structural parts as well as the microstructure diversification of original billet, the Ti–6242S alloy specimens with three different initial microstructures were subjected to multi-pass conventional forging and dual heat treatment. The flow behavior and microstructure evolution of material were analyzed. The results indicated that lamellar α has a stronger ability to coordinate deformation than equiaxed α. The more lamellar α in the microstructure, the slower the microstructure reconstruction during deformation interruption. It is feasible to obtain tri-modal microstructure by any pass conventional forging and dual heat treatment for the initial equiaxed or duplex microstructure, and two passes are more appropriate. The difference between initial equiaxed and duplex microstructures is gradually eliminated through a series of microstructure evolutions during the subsequent heat treatment. For initial lamellar microstructure, a kind of microstructure with multi-scale equiaxed α can be formed after multi-pass conventional forging. The spheroidization fraction of lamellar α is significantly increased with the increase of deformation pass. Tri-modal microstructure can be obtained through three-pass forging and dual heat treatment.

Numerical investigation on the performance of internal flow and atomization in the recessed gas-centered swirl coaxial injectors

Recessed gas-centered swirl coaxial (GCSC) injector has been widely applied in the liquid rocket engine (LRE), and its internal flow and atomization have a significant impact on the combustion downstream. The oxygen (gas)-kerosene (liquid) two-phase flow in the recessed chamber of GCSC injectors under the conditions of back pressure of 17 MPa is numerically simulated by the volume-of-fluid (VOF) method. The liquid film, atomization and gas-liquid two-phase flow fields are obtained for liquid flow with or without swirling. The atomization of liquid kerosene does not have typical atomization characteristic of a swirling injector but accomplishes in the recessed chamber by action of pneumatic force. The swirling flow in the outer injector is helpful to achieve higher gas-to-liquid axial momentum ratio for good atomization performance and smaller injector size as well as lower gas-to-liquid momentum ratio for longer liquid-film length and more steady mass flowrate. The droplet sizes of the spray, the length of liquid film and the sizes of GCSC injectors decrease with increase of the gas-to-liquid (axial) momentum ratio, while the liquid mass flowrate in the outer injector becomes much unstable due to a recirculation flow adjacent to the exit of outer injector. Therefore, it is found that increasing the gas-to-liquid (axial) momentum ratio has two contradictory effects on improving atomization performance and promoting combustion instability. To balance these contradiction influences, the corresponding limits of the gas-to-liquid (axial) momentum ratio for well-working GCSC injectors are defined in this paper. The lower and upper limits of the gas-to-liquid momentum ratio are 7.6 and 14, and the gas-to-liquid axial momentum ratio corresponds to 17.6 and 31. In actual engineering project, the gas-to-liquid (axial) momentum ratios of the GCSC injector investigated in this paper is 9 (20). It indicates that the limits proposed in this paper are reasonable.

Multiphysics Simulation and Experimental Investigation on Jet Electrochemical Milling of Ti-6Al-4V Alloy

Jet electrochemical milling (jet-EC milling) is a promising technique to machine hard-to-cut metallic materials with high machining efficiency and flexibility. The process of the jet-EC milling of Ti-6Al-4V Alloy is difficult to predict due to the interaction of multiple physical fields and the formation of passivation film. In this work, a novel model is established to simulate the jet-EC milling and predict machining profile. In this model, the interactional relationships among electric field, two-phase flow field, and geometry deformation are considered using a multiphysics approach, and the breakdown process of the passivation film is involved for accurately predicting the machining results. In addition, the passivation film breakdown process of Ti-6Al-4V alloy is studied experimentally. Finally, several experiments on the jet-EC milling of Ti-6Al-4V alloy are conducted to verify the simulation results and discuss the influence of the travel rate on the material dissolution. The current density distribution on the anode surface is clarified. The proposed model is more in line with the experiments. By applying an appropriate travel rate, a sharp edge is obtained without stray corrosion as the electrolyte forms an upward reflection and the un-machined surface is free from stray corrosion due to the absence of the electrolyte.

Research on the Characteristics of the Solid–Liquid Two-Phase Flow Field of a Submersible Mixer Based on CFD-DEM

Submersible mixers are widely used in the sewage treatment process in various fields, such as agriculture and industry. They are mainly responsible for pushing flow and mixing activated sludge particles in a pool. Based on the CFD-DEM coupling method under the Euler–Lagrange framework, the solid–liquid two-phase flow of a submersible mixer was simulated in this paper, and the motion characteristics and distribution laws of particles in the pool were studied in axial, horizontal, and lateral directions, respectively. An evaluation method of distribution uniformity was proposed to analyze the velocity distribution of the flow field, the velocity distribution of particles, and the mixing uniformity of particles. The results show that the movement process of activated sludge particles in the pool can be roughly divided into three stages: the horizontal development stage, absorption–injection stage, and reflux-mixing stage, in which the reflux-mixing stage is the main stage for the uniform distribution of particles in the whole flow field. Particle accumulation occurs mainly in the dead zones of the flow field. Distribution of particles in the axial direction has the most homogeneous extent. Vortices can be generated near pool walls, causing accumulation of particles. This method can be a good guide for engineering practice.

Practice the Purpose Preach: The Effect of Purpose on Workers’ Willingness to go the Extra Mile

Commercial organizations increasingly (re)define their corporate purpose beyond profit maximization to create value by contributing to the welfare of society and planet. In that context, this paper employs a two-phase natural field experiment to explore whether, when and how corporate purpose affects workers’ willingness to complete unrequired extra work. The main findings show that receiving information about an organization’s corporate purpose causes workers to complete more extra work. Workers whose personal preferences match with the organization’s purpose are most responsive. However, in case an organization does not authentically practice its purpose preach a backfiring effect can occur. Furthermore, the findings show that the underlying mechanism is driven primarily by a change in workers’ perceived meaning of work. In a broader context, the findings – that workers are willing to go the extra mile when working for an organization with purpose – provide some empirical indications in support of the theoretically proposed business case of purpose.

Study on Dust Suppression of Air Curtain Soft-Sealing System of Grab Ship Unloader

In order to suppress the irregular diffusion of dust in the unloading process of grab ship unloaders, an air curtain soft-sealing system was designed that can effectively block the air flow and restrict the diffusion of pollutants and reduce the average mass fraction of pollutants outside the air curtain plane by 70.02%. The grab unloading model was constructed using the Computational Fluid Dynamics–Discrete Element Method (CFD-DEM) coupling method, and the diffusion law of the gas–solid two-phase flow field of the falling bulk material was studied. Moreover, the motion trajectory and velocity distribution of the particle flow field and air flow field were obtained, as well as the maximum air flow field velocity of five planes above the hopper. The three-dimensional model of the air curtain jet was used and simplified, and the air curtain parameters were set based on the maximum air flow field velocity. The barrier performance of the air curtain under different air curtain jet modes, jet widths, jet velocities and induced wind velocities was simulated by the control variable method. The results show that selecting the appropriate jet widths and jet velocities can significantly reduce dust diffusion; under different jet modes, the order of influence was blow and suction, unilateral blowing and bilateral blowing; under a certain range of induced wind velocities, the air curtain had an obvious blocking effect. These results can provide a reference for the design and improvement of dust suppression of the air curtain soft-sealing system.