Particle Source Term Research Articles

A solution method of slowing-down distribution of energetic particles in tokamaks

The eigen equation of pitch-angle distribution derived from the slowing-down distribution equation with an energetic particle source term is solved by using the Legendre series expansion method. An iteration matrix is established when pitch-angle scattering terms become important. The whole pitch-angle region is separated into three parts, two passing regions, and one trapped area. The slowing-down distribution for each region is finally obtained. The method is applied to solve the slowing-down equations with source terms that the pitch-angle distribution is Maxwellian-like, neutral beam injection, and radial drifts. The distribution functions are convergent for each source with different pitch-angle distribution. The method is suitable for solving a kinetic equation that pitch-angle scattering collision is important.

Acoustic multipole source–simplified lattice Boltzmann method for simulating acoustic propagation problems

AbstractCombining the advantages of the acoustic multipole source (AMS) method and the simplified lattice Boltzmann method (SLBM), a method called AMS–SLBM is proposed for simulating the propagation of acoustic multipole sources in fluids. A particle source term is introduced to the right‐hand side of the lattice Boltzmann equation using the AMS method, and the macroscopic equations with source terms are derived via the Chapman–Enskog expansion analysis. Employing the fractional step technique, the solving process of the macroscopic equations can be divided into three steps: the predictor, corrector, and supplement steps. In the predictor and corrector steps, macroscopic equations without source terms are solved by SLBM, and in the supplement step, the time advancement of the source terms is solved using the finite difference method. AMS–SLBM uses SLBM to simulate the propagation of sound waves by directly evolving the macroscopic variables, which evades the evolution and storage of the distribution function, and the computational process is simpler and memory can be reduced compared to the standard LBM. Moreover, since the acoustic source term is introduced to the right‐hand side of the lattice Boltzmann equation by the AMS method, AMS–SLBM avoids the disadvantage that the traditional forced equilibrium distribution function method will interfere and cover the original flow field during the calculations. Several cases including the propagation of a plane wave, a Gaussian pulse and acoustic monopole, dipole, and quadrupole sources are simulated to validate the robustness and accuracy of the present method. The results show that AMS–SLBM can well simulate acoustic multipole sources propagation, and it affords second‐order accuracy.

Study on the Equivalence of Metallic-Cerium-Simulated Uranium-Aerosol Generation under Fire

Uranium aerosols are released from uranium-containing materials in high-temperature environments caused by nuclear accidents or other processes. Research on the generation characteristics of uranium aerosols under such conditions is an important part of nuclear-safety analysis. In this experiment, the similarity between metal cerium aerosols and uranium material aerosols was evaluated from the aspects of particle size distribution and source term. Combined with the experiment data, the effect of air flow rate and sampling time is discussed. The calculation result of the air release fraction (ARF) is 6.07 × 10−3–4.8 × 10−2, and the respirable fraction (RF) is 0.810–0.978, respectively, showing that the size distribution of particles and ARF of the cerium aerosol are different from the results of the uranium aerosols in the literature, while the RF is similar to the results obtained by using the uranium–niobium alloy in the literature.

Accumulation times for diffusion-mediated surface reactions

In this paper we consider a multiparticle version of a recent probabilistic framework for studying diffusion-mediated surface reactions. The basic idea of the probabilistic approach is to consider the joint probability density or generalized propagator for particle position and the so-called boundary local time. The latter characterizes the amount of time that a Brownian particle spends in the neighborhood of a totally reflecting boundary; the effects of surface reactions are then incorporated via an appropriate stopping condition for the local time. The propagator is determined by solving a Robin boundary value problem, in which the constant rate of reactivity is identified as the Laplace variable z conjugate to the local time, and then inverting the solution with respect to z. Here we reinterpret the propagator as a particle concentration in which surface absorption is counterbalanced by particle source terms. We investigate conditions under which there exists a non-trivial steady state solution, and analyze the relaxation to steady state by calculating the corresponding accumulation time. In particular, we show that the first two moments of the stopping local time density have to be finite.

Simulation of particle size distribution and source term for uranium aerosols based on zinc generated under fire conditions

Fire is a typical scenario for nuclear accidents, in which uranium-containing materials will release uranium aerosols. Limited by many aspects, uranium aerosols cannot be used directly to carry out nuclear emergency training and equipment development research under real conditions. Therefore, it is necessary to filter and evaluate available surrogate materials through experiments. In this paper, metallic zinc is used to study the source term and particle size distribution of zinc aerosols under fire conditions, and the feasibility of zinc as a surrogate material for uranium aerosol research is evaluated based on the data of uranium aerosols in the literature. The experimental results show that the mass median aerodynamic diameter obtained by fitting with lognormal distribution is between 0.36 and 0.59 µm. The cumulative mass fraction distribution data are consistent with those given in the literature, indicating that the zinc aerosols generated under fire have a nice simulation effect on uranium aerosols in terms of particle size distribution. As for air release fraction (ARF) and respirable fraction (RF), the experiment of zinc aerosols is greater than that of uranium aerosols, which means the simulation in ARF and RF is not so good.

Study of numerical error of a Eulerian–Lagrangian scheme in the presence of particle source

Eulerian–Lagrangian (EL–LG) scheme is a numerical scheme that tracks pseudo particles in Eulerian cells. It is widely used in the computational fluid dynamics, however, numerical errors associated with a particle source term has not yet been investigated much. Hence this study focuses on numerical errors of EL–LG caused by particle sources. The purposes are: (i) to clarify causes and situations that bring larger numerical errors by source terms and (ii) to suggest an idea to reduce them. For those purposes, we focus on the particle continuity equation and carry out systematic analysis of the numerical error by setting the following three simple cases: Case (A) No source, Case (B) Constant source, and Case (C) source with arbitrary spatial profile. For each case, we have obtained a theoretical expression of the numerical error. It has been clarified that the errors become relatively large when (i) the spatial profile of the particle source has a large gradient and (ii) the source is localized in the region with high flow-velocity. These were caused by the treatment of the particle source: If pseudo particles due to the source are added in a simple way at the start or the end of the time step, this can lead to larger numerical errors. To reduce those errors, a time-averaging scheme has been suggested. Although the analyzed cases are simple, the results obtained in this study would give important knowledge and insight into numerical errors associated with particle sources in EL–LG schemes.

Detached helium plasma simulation by a one-dimensional fluid code with detailed collisional-radiative model

To increase the accuracy of a particle, momentum, and energy source terms in the detached helium plasma simulation, rate coefficients with the collisional-radiative model were introduced into the fluid code LINear Divertor Analysis (LINDA). Obtained effective rate coefficients and related source terms were compared with those from the conventional empirical databases. It is shown that a high-density condition in future fusion devices causes larger deviation between the effective and the empirical source terms. One-dimensional detached plasma simulation indicated that the peak amplitude of the plasma density during the rollover is sensitive to the source term difference related to the recombination. This study additionally revealed that the heating effect in the three-body recombination process strongly affects the detached plasma formation and downstream plasma parameters.

Regularization of the Lagrangian point force approximation for deterministic discrete particle simulations

The current article presents a regularization procedure of the Lagrangian point-force approach commonly used to account for the perturbation of a fluid phase by a dispersed particle phase. The regularization procedure is based on a nonlinear diffusion equation to naturally ensure parallel efficiency when the regularization length scale extends over several grid cells. The diffusion coefficient thus becomes a function of the particle source term gradient and expressions allowing to approximately adjust the regularization length scale according to the local particle to mesh size ratio are proposed, so that mesh refinement or polydisperse sprays may be handled. Elementary numerical test cases confirm the convergence of the present procedure under mesh refinement and its ability to locally adapt the regularization length scale. Furthermore, the chosen regularization length scale allows to match the leading order term of the perturbation flow field set by the particle beyond approximately two particle diameters in the Stokes regime.When applying the presented source term regularization procedure, the terminal velocity of a particle settling under gravity in the Stokes regime becomes relatively insensitive to mesh refinement. However, errors with respect to the theoretical settling velocity remain substantial and removal of the particle’s self induced velocity appears necessary to recover the undisturbed fluid velocity at the particle location and correctly evaluate the drag force. As the current regularization procedure yields source terms that are close to Gaussian, an analytic expression from the literature is used to estimate the particle’s self induced velocity. When combining source term regularization and removal of the particle’s self induced velocity, good results are obtained for the terminal settling speed in the Stokes regime. Results obtained for horizontally separated particle pairs settling under gravity in the Stokes regime show equally good agreement with theoretical results. Because analytic expressions for the particle’s self-induced velocity are no longer available at finite particle Reynolds numbers, correlations recently proposed in the literature are used to obtain correct settling velocities beyond the Stokes regime.

Performance of vertical diffusers carrying Gas-solid flow: experimental and numerical studies

In the present work, numerical and experimental studies are carried out to investigate the performance of vertical straight-walled conical diffusers carrying air-solid two-phase flow. Eulerian-Lagrangian approach is used to numerically simulate the two phases using the Chen-Kim k-ε turbulence model. The continuous phase (gas) is simulated using Eulerian frame by solving Reynolds-Averaged Navier-Stokes equations (RANS), while the dispersed phase (solids) is simulated using particle tracking method. Coupling between the two phases is established by adding particle source terms and void fraction in the continuous phase equations. A 4-way coupling is adapted to include the effect of particle-particle collisions. Lift forces, particle dispersion and particle-wall collisions are also considered in the simulation of solid-phase. The experimental study is carried out on a pilot scale vertical pneumatic transport system. Four different diffuser geometries are tested at various inlet-Reynolds numbers and mass loading ratios. Sand particles of different sizes and mass flow rates are used to represent the solid phase. Comparisons between numerical predictions and experimental results indicated good agreement. The effects of solid parameters are significant for small angled-diffusers and decrease as the diffuser angle increases. It is also found that, there is a significant decrease in the separation zone within diffuser due to the presence of solid particles. Energy is transferred from the gas phase to the solid phase in the upstream pipe. This energy is transferred again to the gas phase through the diffuser and its downstream tangent pipe. The rate of energy transfer is enhanced by increasing the solid mass flow rate and decreasing the particle size. The results show that the mass loading and size of solid particles have significant effects on the diffuser loss coefficient.

Acoustic multipole sources for the lattice Boltzmann method

By including an oscillating particle source term, acoustic multipole sources can be implemented in the lattice Boltzmann method. The effect of this source term on the macroscopic conservation equations is found using a Chapman-Enskog expansion. In a lattice with q particle velocities, the source term can be decomposed into q orthogonal multipoles. More complex sources may be formed by superposing these basic multipoles. Analytical solutions found from the macroscopic equations and an analytical lattice Boltzmann wavenumber are compared with inviscid multipole simulations, finding very good agreement except close to singularities in the analytical solutions. Unlike the BGK operator, the regularized collision operator is proven capable of accurately simulating two-dimensional acoustic generation and propagation at zero viscosity.

Penetration of ambient submicron particles into single-family residences and associations with building characteristics

This work improves knowledge of particle penetration into buildings by (i) refining a particle penetration test method that minimizes the duration and invasiveness required by individual tests without sacrificing accuracy, (ii) applying the method in an unoccupied manufactured test house and 18 single-family homes in Austin, Texas, USA, and (iii) exploring correlations between particle penetration and building characteristics, including results from blower door air leakage tests. The mean (± s.d.) measured penetration factor of submicron particles (20-1000 nm, not size-resolved) was 0.47 ± 0.15 in 19 residences that relied on infiltration for ventilation air, ranging from 0.17 ± 0.03 to 0.72 ± 0.08. Particle penetration factors (P) and outdoor particle source terms (P × air exchange rates) were both significantly and positively correlated with results from blower door air leakage tests. Outdoor particle source terms were also significantly and negatively correlated with the year of construction. These results suggest that occupants of leakier and older homes are exposed to higher indoor concentrations of outdoor submicron particles than those in tighter and newer homes, and that simple air leakage tests may be able to provide an approximate prediction of outdoor particle infiltration into single-family residences. Results from this work suggest that knowledge of simple building characteristics (i.e., the year of construction and blower door test results) may be used to predict the ability of outdoor particles to infiltrate into single-family residences, which could facilitate easier estimates of indoor exposures to outdoor particulate matter across the building stock. The methods within can also be extended to other buildings and can be used to assess possible changes in penetration factors because of envelope retrofits. Because outdoor particle size distributions were not measured during this study, these tests should also be repeated with size-resolved particle instrumentation.

Thrust Augmentation of Solid Rocket Motors Using Beamed Microwave Energy

Abstract : Feasibility of using beamed microwave energy to increase thrust of solid rocket motors during launch is analyzed. Coupling of microwave radiation with internal energies of micron-sized alumina particles and the successive transfer of internal energy of particles to thermal and then kinetic energy of gas is expected to be the main mechanism of thrust increase. A two-phase two-way coupled capability has been developed. For the gas phase, the capability applies an Eulerian approach based on the solution of the Navier-Stokes equations, and uses VAC code modified to include particle source terms. For the particle phase, a Lagrangian approach is used based on a particle tracker that incorporates the impact of the gas and microwave radiation. The developed numerical capability is applied to compute the nozzle flow for a Castor 120 type motor with and without the microwave radiation. High gas density and thus fast collisional relaxation result in highly efficient transfer of microwave energy the kinetic energy of the flow. The total thrust was found to increase by 1.5% for a 100 MW/m2 beam, and 15% for a 1GW/m2 beam.

In-flight thermal treatment of soda-lime-silica glass powders for glass production by argon–oxygen induction thermal plasmas

In order to investigate the plasma–particle energy exchange dynamics and optimize the plasma discharge and particle parameters during in-flight thermal treatment of soda-lime-silica glass powders, a plasma–particle interaction model was developed. This model solved the conservation equations to predict the plasma temperature and flow fields, and then calculated the injected individual particle trajectories and temperature histories, and the particle source terms to take into account the plasma–particle interaction. It was noticed that particle injection significantly reduced the plasma temperature around the centerline of the torch and hence decreased the heat transfer to particles at higher carrier gas flow-rate and powder feed-rate. As a result the size and composition of quenched particles were affected significantly by the above factors. The simulated results were consistent with those of experiment, which provided valuable guidelines in optimizing the plasma discharge and particle parameters for the efficient thermal treatment of soda-lime-silica glass particles.

Turbulence modulation in dilute particle-laden flow

A new particle source term to account for the effect of particles on the turbulence equations based on the Euler/Lagrange approach is introduced and compared with existing models and experimental data. Three different sizes of particles are considered to cover the range of large particles, where augmentation of the carrier phase turbulence is expected, and small particles, for which attenuation is expected. The new model is derived directly from the balance equations of fluid flow and represents a combination of the so-called standard and consistent approaches. The performance of the new model surpasses that of the standard and consistent models and it is able to predict both the suppression and enhancement of fluid turbulence for small and large particles.

Numerical simulation of gas turbulence enhancement by particle-wake effect

A new turbulence enhancement model was incorporated into the second-order moment two-phase turbulence model and was used to simulate gas-particle flows in swirling chambers and channels with different wall roughness. The results show that compared with the turbulence modification model not accounting for the wake effect, this model, together with the conventional particle source term, gives simulation results in better agreement with the experimental data.

Characterization of the electron distribution function in an electron-cyclotron driven toroidal plasma

The local properties of the electron energy distribution function are investigated in the electron-cyclotron wave driven toroidal device TORPEX (Fasoli et al 2006 Phys. Plasmas 13 055902). The electron energy distribution function is measured by means of a time-resolved electrostatic energy analyser. The measurements indicate that electrons are accelerated to different energies at the electron-cyclotron and upper-hybrid resonances. Electrons from the upper-hybrid resonance have higher energies and can be described by a secondary maxwellian energy distribution function. The electron energy distribution function is found to be invariant with respect to experimental parameters such as the neutral gas pressure, the magnetic field configuration and the injected microwave power. The implications for a correct modelling of the particle source term for TORPEX plasmas are discussed.

Magnetic presheath in a weakly turbulent multicomponent plasma

A fluid model of the magnetic presheath in a weakly turbulent multicomponent plasma consisting of electrons and several positive ion components is presented. Turbulent particle source terms in the continuity equations and turbulent momentum source terms in the momentum balance equations for the ion components are derived from basic principles [Plasma Phys. Controlled Fusion 47, 685 (2005)], i.e., by means of the ensemble averaging procedure from the statistical theory of plasma turbulence. Then the unknown correlations between the fluctuating quantities occurring in the turbulent source terms derived are replaced with phenomenological expressions based on analogy with classical transport. The remaining correlation terms in the momentum balance equations, which are responsible for explicit coupling of the equations for different ion components, reduce to the corresponding classical terms when the turbulent transport corrections are negligible (i.e., for “quiescent” plasmas). Under certain conditions regarding the nature of the boundary plasma turbulence, the analysis of the planar magnetic presheath performed in this study yields results for the ion component fluid velocities and particle flux densities at the magnetic presheath entrance that are directly applicable to the boundary conditions of multifluid plasma transport and turbulence codes. A fluid formulation of the Bohm criterion, valid for weakly turbulent multicomponent plasmas as treated in this study, is also derived.

Influence of Particles on Fluid Turbulence in Pipe and Diffuser Gas‐Solids Flow

AbstractThe influence of glass particles with different Reynolds numbers ReP = |u–uP|dPρ/η on axial and radial gas fluctuations as well as on Reynolds stresses was investigated for pipe and diffuser (continuous pipe expansion) gas‐solids flow. Measurements were carried out using phase‐Doppler anemometry distinguishing between velocity signals of the solid and fluid phase due to particle or tracer size. In fully developed pipe flow small particles (ReP = 60) damp turbulence but with increasing ReP vortex shedding behind the particles reduces attenuation and finally leads to turbulence enhancement. Behind the diffuser particles are decelerated and cause a steeper velocity gradient and, thus, an increase in turbulence. The measured data are compared to CFD calculations investigating Reynolds stress model and k‐ϵ model for the description of turbulence. Using small particles good agreement is achieved considering the momentum transfer between the phases. For larger particles the modeling of vortex shedding by turbulent particle source terms is needed for a satisfactory prediction.

Influence of Particles on Fluid Turbulence in Pipe and Diffuser Gas‐Solids Flow

AbstractNo abstracts.

On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles

The present study is concerned with answering the question: What are the physical mechanisms responsible for the modification of the turbulence structure by solid particles dispersed in a homogeneous shear flow? We employ DNS (direct numerical simulations) to examine the effects of the two-way interaction between the two phases on the turbulence structure. Our results indicate that particles affect the rate of production of turbulence energy via modifying the vorticity dynamics. It is known that regions of large production rate of turbulence energy are sandwiched between counter rotating vortices whose vorticity, ωs, is aligned with the axes of the longitudinal vortex tubes. These longitudinal vortex tubes are strongly inclined toward the streamwise direction due to the imposed mean shear. The stronger ωs is, the larger the production rate. The dispersed solid particles modify the alignment of the local vorticity vector, ω, with the axis of the longitudinal vortex tube. Increasing this alignment increases ωs, which in turn augments the turbulence production rate, and vice versa. In addition, due to the enhanced strain rate of the carrier fluid by the particles, the dissipation rate of turbulence energy is always increased. The particles also reduce the alignment of the vorticity vector with the intermediate eigenvector (β) of the strain rate tensor. This reduction in alignment is due to an increase in the rotational term and particle-source term in the governing equation of the cosine of the angle between the vorticity vector and the intermediate strain eigenvector.