3D Fluid Model Research Articles

3D modeling of positive streamers in air with inhomogeneous density

We study the effect of an inhomogeneous gas density on positive streamer discharges in air using a 3D fluid model with stochastic photoionization, generalizing earlier work with a 2D axisymmetric model by Starikovskiy and Aleksandrov (2019 Plasma Sources Sci. Technol. 28 095022). We consider various types of planar and (hemi)spherical gas density gradients. Streamers propagate from a region of density towards a region of higher or lower gas density , where corresponds to and . We observe that streamers can always propagate into a region with a lower gas density. When streamers enter a region with a higher gas density, branching can occur at the density gradient, with branches growing in a flower-like pattern over the gradient surface. Depending on the gas density ratio, the gradient width and other factors, narrow branches are able to propagate into the higher-density gas. In a planar geometry, we find that such propagation is possible up to a gas density slope of , although this value depends on a number of conditions, such as the gradient angle. Surprisingly, a higher applied voltage makes it more difficult for streamers to penetrate into the high-density region, due to an increase of the primary streamer’s radius.

Quantitative modeling of streamer discharge branching in air

Streamer discharges are the primary mode of electric breakdown of air in lightning and high voltage technology. Streamer channels branch many times, which determines the developing tree-like discharge structure. Understanding these branched structures is for example important to describe streamer coronas in lightning research. We simulate branching of positive streamers in air using a 3D fluid model where photoionization is included as a discrete and stochastic process. The probability and morphology of branching are in good agreement with dedicated experiments. This demonstrates that photoionization indeed provides the noise that triggers branching, and we show that branching is remarkably sensitive to the amount of photoionization. Our comparison is therefore one of the first sensitive tests for Zheleznyak’s photoionization model, confirming its validity.

3D fluid model analysis on the generation of negative hydrogen ions for negative ion source of NBI

A radio-frequency (RF) inductively coupled negative hydrogen ion source (NHIS) has been adopted in the China Fusion Engineering Test Reactor (CFETR) to generate negative hydrogen ions. By incorporating the level-lumping method into a three-dimensional fluid model, the volume production and transportation of H− in the NHIS, which consists of a cylindrical driver region and a rectangular expansion chamber, are investigated self-consistently at a large input power (40 kW) and different pressures (0.3–2.0 Pa). The results indicate that with the increase of pressure, the H− density at the bottom of the expansion region first increases and then decreases. In addition, the effect of the magnetic filter is examined. It is noteworthy that a significant increase in the H− density is observed when the magnetic filter is introduced. As the permanent magnets move towards the driver region, the H− density decreases monotonically and the asymmetry is enhanced. This study contributes to the understanding of H− distribution under various conditions and facilitates the optimization of volume production of negative hydrogen ions in the NHIS.

Preliminary study of supersonic molecular beam injection in Thailand Tokamak-1 using 3D fluid model

Successful operation of a tokamak relies on effective and appropriate methods of plasma fueling. The development plan of Thailand Tokamak-1 (TT-1) will employ the supersonic molecular beam injection (SMBI) which delivers the fueling gas more effectively and deeper than the gas puffing method. In this work, we study the effect of SMBI on the plasma transport of TT-1 plasma by using 3D fluid simulation. The model includes the continuity equation, energy balance equation, momentum equation, continuity of fuel equation, and momentum of fuel. BOUT++ is then used to solve these equations by a finite difference method with the field-aligned coordinates in the edge region. The simulation shows that when hydrogen fuel gas is by the SMBI method from the low-field side into the plasma with a speed of 1000 m/s, the electron density in the edge locally rises as a result of the dissociation and ionization. The ion and electron temperatures then drop. After that, the density spread over the whole plasma volume within about 10 ms. When the injection speed increases, it results in a deeper penetration length of the fuel deposition.

Stability for a 3D Ladyzhenskaya fluid model with unbounded variable delay

<abstract><p>This paper is concerned with the stability of solutions to a Ladyzhenskaya fluid model with unbounded variable delay. We first prove the existence, uniqueness and regularity of global weak solutions to the Ladyzhenskaya model by using Galerkin approximations and the energy method based on some suitable assumptions about external forces. Then we obtain that the stationary solution is locally stable. Finally, we establish that the stationary solution has polynomial stability in a particular case of unbounded variable delay.</p></abstract>

Spatial distribution and transport mechanism of electrons in large and powerful inductively coupled plasma sources with Faraday shield

A large and powerful radio frequency (RF) inductively coupled plasma (ICP) source with a Faraday shield (FS) has been investigated by a 3D fluid model, consisting of a plasma module and an electromagnetic field module. Effects of the structure of the FS, the RF current, and the gas pressure on the spatial distributions of plasma parameters including the electron density, electron temperature, and electron potential barrier are investigated systematically. The results show that the FS has a great influence on the spatial distribution and transport mechanism of electrons. The electron density has a maximum value at the center of the ICP source and declines sharply near the FS. Furthermore, it decreases obviously with the decreasing slit width, due to the electron transport mechanism, which is directly related to the electron potential barrier and electron temperature. In addition, the electron density increases with the RF current and gas pressure; it is noteworthy that the stronger induced electric field heating exists at the slit gap under high RF current that makes the electron temperature increase. The data obtained in this paper could lead to a deeper insight into the characteristics of ICP sources, which is extremely essential for optimizing the FS structure and designing large and powerful radio frequency ICPs in the future.

Research on the Flow-Induced Stress Characteristics of Head-Cover Bolts of a Pump-Turbine during Turbine Start-Up

Nowadays, pump-turbine units have to experience multiple start-stops every day to balance the power production and consumption on the grid. During the transient process of turbine start-up, the hydraulic forces applied to the head-cover would change dramatically and induce high-level stresses on the head-cover bolts. As key components of large hydraulic turbine units, the head-cover bolts are subjected to tens of thousands of tonnes of hydraulic excitation force during operation. Special attention should be paid to the design of the head-cover bolts of large hydraulic pump-turbine units because these units have high water heads and high hydraulic excitation forces. Therefore, the safe design of the head-cover bolts is extremely important to maintain the operational safety of the whole unit. This paper investigates the flow-induced stress characteristics of the head-cover bolts during turbine start-up in a large prototype pump-turbine unit. A complete 3D fluid model and a corresponding 3D structural model, including the head-cover bolts of the pump-turbine unit, were created. The fluid–structure coupling method was used to calculate the structural stresses caused by fluid flow during turbine start-up. The pressure files during turbine start-up calculated by the CFD tool were transferred and mapped to the finite element model of the structural components of the pump-turbine unit. Subsequently, the flow-induced stress characteristics of the head-cover bolts were numerically simulated. The simulation results showed that the hydraulic excitation force on the head-cover bolts increased significantly during turbine start-up, and the displacement and the stress distributions of different head-cover bolts were not uniform. The calculation methods and conclusions in this paper can also be applied to evaluate the flow-induced stress characteristics of head-cover bolts for similar hydraulic pump-turbine units.

Development of a multi-scale topology optimization method for thermal-fluid problems

In this presentation, we discuss how to optimize both microstructure and macrostructure in the topology optimization of 3D thermal fluid. First, the 3D thermal fluid model is approximated by a 2D thermal fluid field. Next, a proxy model of microstructural properties is constructed by learning the relationship between microstructure geometry, permeability, thermal conductivity, and heat transfer coefficient through off-line numerical analysis. The macrostructure optimization is then formulated as a microstructure selection problem from the surrogate model. Finally, a simple numerical example confirms the validity of the method. In this study, as a specific example, topology optimization is performed with two design variables on a two-dimensional model of a 3D forced air-cooled heat sink with prismatic fins. The properties of the 3D prismatic fins are analyzed individually in advance and learned offline using an RBF network so that they can be used in the two-dimensional topology optimization, which requires differentiation.

Research on Nozzle Design and Application of Single‐Flow Postcombustion Oxygen Lance in a 120 t Top‐Blown Converter

The flow characteristics and postcombustion behavior of a single‐flow postcombustion (PC) oxygen lance are of paramount significance to optimal design and operation of the lance but not well understood, and there is also no well‐known design criterion for the optimization of the single‐flow PC lance. Herein, the design criteria of a single‐flow PC lance are first proposed. Then, a 3D fluid model is established combined with a 120 t top‐blown converter. The influences of the key parameters of secondary nozzles (i.e., inclination angle, diameter, and number) on the jet characteristics and PC behavior at the steelmaking temperature are studied. Finally, based on the design criteria, an optimal PC lance is designed and its smelting effect is compared with that of the conventional lance by industrial tests. The results indicate that the reasonably designed PC lance can effectively improve the PC zone of CO gas and simultaneously increase both the penetration depth and impact area of the main jet. Compared with conventional lance, the PC oxygen lance can raise the temperature of molten steel by ≈30 °C and reduce the total fe (T.Fe) content in the final slag by 0.86%. Moreover, it has almost no effect on the gas recovery.

A three-dimensional model of streamer discharges in unsteady airflow

A 3D fluid model has been developed to simulate streamer discharges in unsteady airflow. The model couples the drift–diffusion equation for charged particles, the Navier–Stokes equations for air, the Poisson’s equation for the electric field, and the Helmholtz equation for photoionization. It allows us to study electrical discharges at different timescales defined by light and heavy particles and to investigate the effects of unsteady airflow. The model treats the time integration in an implicit manner to allow longer time steps, which makes the simulation of long-duration discharges feasible. Moreover, the model uses an unstructured mesh allowing the calculation around solid bodies with complex geometries, and uses adaptive mesh refinement to lower the computation time. The validity and accuracy of the model has been verified by comparing its results with published results, which compares simulations in steady air from six different streamer codes. Our results are consistent and among the most accurate in terms of charge conservation. In order to investigate the influence of wind on streamer discharges, we present results from simulation of a long-duration discharge, in which two successive positive streamers are initiated from a positive polarity electrode in presence of a transverse airflow. This simulation shows that the impact of airflow on positive streamers is driven by the ions, and therefore the airflow effects are seen in ions timescale. Interestingly, we observe that the positive streamer channel, while tilting in the direction of the wind, remains attached to the surface of the electrode. The subsequent positive streamer emerges from the charges remaining from the initial streamer, which have been moved over the electrode surface toward the trailing edge. This mechanism shows and explains the clear tilting of the successive positive streamers in the direction of the wind.

3D fluid modeling of positive streamer discharges in air with stochastic photoionization

Streamer discharges are thin plasma channels that precede lightning and sparks. They usually evolve in bundles as stochastic tree-like structures and are inherently difficult to model due to their multiscale nature. In this paper, we perform a computer investigation of positive streamer discharges in air using contemporary photoionization models. We report on three-dimensional computer simulations under conditions that are available in laboratory spark-gap experiments. The solutions demonstrate a multiscale morphology consisting of streamer fluctuations, branching, and the formation of a discharge tree. Some branches are comparatively thick and noisy, while others are thin, smooth, and carry electric fields exceeding 250 kV cm−1 at their tips. Our results are consistent with past experiments and clarify the puzzling branching dynamics and stochastic morphology of positive streamer discharges.

Computational Simulation of Synovial Fluid Kinematics of the Scapholunate Joint.

Background: The interaction between wrist kinematics and synovial fluid pressure has yet to be studied. To our knowledge, this is the first study to determine the effect of scapholunate joint kinematics on synovial fluid pressure change using finite volume method. Methods: The carpal bones of a cadaveric hand were obtained from Computed Tomography (CT) scans. CT images of the carpal bones were segmented and reconstructed into 3D model. The 3D synovial fluid model between the scaphoid and lunate was constructed and then used for computational simulations. The kinematics data of scapholunate joint obtained from radioulnar deviation of the wrist was investigated. Results: It was found that the pressure in synovial fluid varied from -1.68 to 2.64 Pa with maximum pressure located at the scaphoid-fluid interface during the radial deviation. For ulnar deviation, the pressure increased gradually from the scaphoid-fluid interface towards the lunate-fluid interface (-1.37 to 0.37 Pa). Conclusions: This new computational model provides a basis for the study of pathomechanics of ligament injury with the inclusion of synovial fluid.

The effect of the stochasticity of photoionization on 3D streamer simulations

Positive streamer discharges require a source of free electrons ahead of them for their growth. In air, these electrons are typically provided by photoionization. Here we investigate how stochastic fluctuations due to the discreteness of ionizing photons affect positive streamers in air. We simulate positive streamers between two planar electrodes with a 3D plasma fluid model, using both a stochastic and a continuum method for photoionization. With stochastic photoionization, fluctuations are visible in the streamer’s direction, maximal electric field, velocity, and electron density. The streamers do not branch, and we find good agreement between the averaged stochastic results and the results with continuum photoionization. The streamers stay roughly axisymmetric, and we show that results obtained with an axisymmetric model indeed agree well with the 3D results. However, we find that positive streamers are sensitive to the amount of photoionization. When the amount of photoionization is doubled, there is even better agreement between the stochastic and continuum results, but with half the amount of photoionization, stochastic fluctuations become more important and streamer branching starts to occur.

GDB: A global 3D two-fluid model of plasma turbulence and transport in the tokamak edge

The global drift-ballooning (GDB) code is developed to study tokamak edge low frequency turbulence and transport, and their relationship to global profile evolution. The code employs a 3D electromagnetic fluid model that does not discriminate between equilibrium and perturbative contributions, capturing arbitrary amplitude fluctuations. Primitive plasma variables, including the E×B flow profiles, are evolved self-consistently in both closed-flux surfaces and the scrape-off-layer (SOL). A suite of numerical techniques described here handle the linear and non-linear components of the model efficiently so as to support realistic discharge parameters (such as realistic deuterium mass ratio mi∕me≈60) and yield good scaling on high performance computing (HPC) systems. GDB resolves turbulence slower than the ion gyrofrequency in simulations that capture the millisecond-scale evolution of global plasma profiles.

Simulated volume loss in the base of tongue in a virtual swallowing model

Dysphagia often occurs in patients with oropharyngeal cancer, particularly in those with base of tongue lesions after surgery both with and without chemoradiation therapy. Tongue volume loss is related to functional impairment in swallowing; however, the physiological mechanisms related to the impairment are still unclear. This study aimed to clarify possible causal links between volume loss and swallowing outcomes by simulating volume loss in a 3D computer fluid model of swallowing. An artificial volume loss was introduced to a reference swallowing model of a healthy subject. Swallowing assessments that are commonly used in clinical practice were used to evaluate the simulations. The simulation of impairment showed an increase in oral and pharyngeal residue. Tongue volume loss appeared to be the mechanism which caused increased pharyngeal residue in the virtual simulations. Major limitations of the simulations were oversimplified models and volume loss as a single parameter with no consideration of biophysical compensations. Discussion of limitations suggested that with improved simulation techniques, mechanisms of dysphagia could be better understood. In conclusion, this study indicated that volume loss of the base of tongue may contribute to increased oropharyngeal residue.

Numerical calculation of CHTC on end metal parts and flow in end region of a turbogenerator

The convection heat transfer coefficient (CHTC) distribution of surfaces of end metal parts directly affects the temperature distribution of end metal parts. In this study, a large turbogenerator is analysed. To study the CHTC distribution of surfaces of end metal parts in detail, a three-dimensional (3D) fluid and thermal analysis model of whole turbogenerator end region is established. The losses of end metal parts from 3D transient electromagnetic field calculation are provided to end metal parts as heat sources. Pressure values of end-region outlets and fluid velocity of fan outlet from flow network calculation are provided to end region as boundary conditions in the 3D fluid and thermal analysis model. CHTC distribution laws of the surfaces of the clamping plate, finger plate, and copper screen are studied in detail by the finite volume method. The fluid flow and temperature distribution of end metal parts are determined in the end region of the turbogenerator. The calculated results are compared with measured data.

3D Monte Carlo simulation of grain growth in friction stir welding

The 3D fluid model was used to simulate the friction stir welding process. Three-dimensional Monte Carlo model with nucleation in each MC step was then applied to simulate the grain growth. The validity of this model is verified by comparison with the experimental and numerical results. The influences of tool shoulder diameter and rotational speed are further studied. Equiaxed grains in the stirring zone are increased with the increase of the diameter and the rotation speed of the shoulder. The grain sizes tend to be more uniform from retreating side to advancing side when the rotational speed or shoulder diameter is increased.

Reservoir monitoring using borehole radars to improve oil recovery: Suggestions from 3D electromagnetic and fluid modeling

The recently developed smart well technology allows for sectionalized production control by means of downhole inflow control valves and monitoring devices. We consider borehole radars as permanently installed downhole sensors to monitor fluid evolution in reservoirs, and it provides the possibility to support a proactive control for smart well production. To investigate the potential of borehole radar on monitoring reservoirs, we establish a 3D numerical model by coupling electromagnetic propagation and multiphase flow modeling in a bottom-water drive reservoir environment. Simulation results indicate that time-lapse downhole radar measurements can capture the evolution of water and oil distributions in the proximity (order of meters) of a production well, and reservoir imaging with an array of downhole radars successfully reconstructs the profile of a flowing water front. With the information of reservoir dynamics, a proactive control procedure with smart well production is conducted. This method observably delays the water breakthrough and extends the water-free recovery period. To assess the potential benefits that borehole radar brings to hydrocarbon recovery, three production strategies are simulated in a thin oil rim reservoir scenario, i.e., a conventional well production, a reactive production, and a combined production supported by borehole radar monitoring. Relative to the reactive strategy, the combined strategy further reduces cumulative water production by 66.89%, 1.75%, and 0.45% whereas it increases cumulative oil production by 4.76%, 0.57%, and 0.31%, in the production periods of 1 year, 5 years, and 10 years, respectively. The quantitative comparisons reflect that the combined production strategy has the capability of accelerating oil production and suppressing water production, especially in the early stage of production. We suggest that borehole radar is a promising reservoir monitoring technology, and it has the potential to improve oil recovery efficiency.

Modeling of low pressure plasma sources for microelectronics fabrication

Chemically reactive plasmas operating in the 1 mTorr–10 Torr pressure range are widely used for thin film processing in the semiconductor industry. Plasma modeling has come to play an important role in the design of these plasma processing systems. A number of 3-dimensional (3D) fluid and hybrid plasma modeling examples are used to illustrate the role of computational investigations in design of plasma processing hardware for applications such as ion implantation, deposition, and etching. A model for a rectangular inductively coupled plasma (ICP) source is described, which is employed as an ion source for ion implantation. It is shown that gas pressure strongly influences ion flux uniformity, which is determined by the balance between the location of plasma production and diffusion. The effect of chamber dimensions on plasma uniformity in a rectangular capacitively coupled plasma (CCP) is examined using an electromagnetic plasma model. Due to high pressure and small gap in this system, plasma uniformity is found to be primarily determined by the electric field profile in the sheath/pre-sheath region. A 3D model is utilized to investigate the confinement properties of a mesh in a cylindrical CCP. Results highlight the role of hole topology and size on the formation of localized hot-spots. A 3D electromagnetic plasma model for a cylindrical ICP is used to study inductive versus capacitive power coupling and how placement of ground return wires influences it. Finally, a 3D hybrid plasma model for an electron beam generated magnetized plasma is used to understand the role of reactor geometry on plasma uniformity in the presence of E × B drift.

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces.

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D-0D fluid-structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier-Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier-Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.