Numerical solution of steam flow in a nozzle using different non-equilibrium condensation models

This paper concerns the 3D simulation of corona discharge using high performance computing (HPC) managed with the message passing interface (MPI) library. In the field of finite volume methods applied on non-adaptive mesh grids and in the case of a specific 3D dynamic benchmark test devoted to streamer studies, the great efficiency of the iterative R&B SOR and BiCGSTAB methods versus the direct MUMPS method was clearly demonstrated in solving the Poisson equation using HPC resources. The optimization of the parallelization and the resulting scalability was undertaken as a function of the HPC architecture for a number of mesh cells ranging from 8 to 512 million and a number of cores ranging from 20 to 1600. The R&B SOR method remains at least about four times faster than the BiCGSTAB method and requires significantly less memory for all tested situations. The R&B SOR method was then implemented in a 3D MPI parallelized code that solves the classical first order model of an atmospheric pressure corona discharge in air. The 3D code capabilities were tested by following the development of one, two and four coplanar streamers generated by initial plasma spots for 6 ns. The preliminary results obtained allowed us to follow in detail the formation of the tree structure of a corona discharge and the effects of the mutual interactions between the streamers in terms of streamer velocity, trajectory and diameter. The computing time for 64 million of mesh cells distributed over 1000 cores using the MPI procedures is about 30 min ns−1, regardless of the number of streamers.

https://iopscience.iop.org/article/10.1088/1361-6463/aaa91b/pdf

3D streamers simulation in a pin to plane configuration using massively parallel computing

Noninvasive assessment of carotid artery stenoses by the principle of multiscale modelling of non-Newtonian blood flow in patient-specific models

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

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A three-dimensional model of streamer discharges in unsteady airflow: Paper

Current research on gas discharge theory has made significant development in terms of numerical simulation, but its analytical description of streamer mechanism remains overly simplified, as it is still based on the electron avalanche model characterized with the exponential growth and infinite breakdown current. This paper presents a simple analytical method of gas discharge based on the classic logistic model and covers four aspects. First, it gives the exact definition of generation and mortality rate of electron number, establishes a logistic differential equation and a logistic iteration model for streamer mechanism, and derives deterministic analytical and iterative solution. Second, we also extend the mortality rate to include negative value, thus allowing the logistic model to describe both exponential growth and S shape growth scenarios, and provide criteria for categorizing spark breakdown, Townsend discharge, and stable discharge (glow, arc, aka saturated streamer). Third, the logistic differential model can be transformed into an iterative model. From that we derive the criteria for evaluating discharge instability. Last, although our model is 1-D, but it is still practical and easy to use given its clear analytical expression of underlying physical mechanism.

A Simple Analytical Method of Gas Discharge Based on Logistic Model

Electron-spot-induced multiple branching and trajectory deviation of streamer microdischarges in air was simulated using a 3-D unstructured adaptive mesh finite-volume approach along with the air plasma streamer model proposed by Morrow et al. Images illustrating the effect of electron spots on the propagation trajectory, i.e., deviation, simple branching, multiple branching, are presented and commented.

A Full 3-D Dynamically Adaptive Unstructured Grid Finite-Volume Approach to Simulate Multiple Branching in Streamer Propagation

This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012128/pdf

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

This work presents the numerical solution of laminar incompressible viscous flow in a three dimensional branching channel with circle cross section for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. Numerical solution is based on cetral finite volume method using explicit Runge- Kutta time integration. In the case of unsteady computation artificial compressibility method is considered.

https://iopscience.iop.org/article/10.1088/1742-6596/738/1/012112/pdf

Numerical simulation of steady and unsteady flow for generalized Newtonian fluids

Numerical simulation of circumferentially averaged flow in a turbine

This paper is interested in the numerical simulation of steady flows of laminar incompressible viscous and viscoelastic fluids through the channel with T-junction. The flow is described by the system of generalized incompressible Navier-Stokes equations. For the different choice of fluids model the different model of the stress tensor is used, Newtonian and Oldroyd-B models. Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two outlet parts. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge-Kutta time integration.

David Trdlička

Papers

A Full 3-D Dynamically Adaptive Unstructured Grid Finite-Volume Approach to Simulate Multiple Branching in Streamer Propagation

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

Numerical simulation of steady and unsteady flow for generalized Newtonian fluids

Numerical simulation of circumferentially averaged flow in a turbine

Numerical Simulation of 3D Flow of Viscous and Viscoelastic Fluids in T-Junction Channel