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  • 1.
    Liu, Lipeng
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Physics of Electrical Discharge Transitions in Air2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Electrical discharges with a variety of different forms (streamers, glow corona, leaders, etc.) broadly exist in nature and in industrial applications. Under certain conditions, one electrical discharge can be transformed into another form. This thesis is aimed to develop and use numerical simulation models in order to provide a better physical understanding of two of such transitions, namely the glow-to-streamer and the streamer-to-leader transitions in air.

    In the first part, the thesis includes the two-dimensional simulation of the glow-to-streamer transition under a fast changing background electric field. The simulation is performed with a fluid model taking into account electrons. An efficient semi-Lagrangian algorithm is proposed to solve the convection-dominated continuity equations present in the model. The condition required for the glow-to-streamer transition is evaluated and discussed. In order to enable such simulations for configurations with large interelectrode gaps and long simulation times, an efficient simplified model for glow corona discharges and their transition into streamers is also proposed.

    The second part of the thesis is dedicated to investigate the dynamics of the streamer-to-leader transition in long air gaps at atmospheric pressure. The transition is studied with a one-dimensional thermo-hydrodynamic model and a detailed kinetic scheme for N2/O2/H2O mixtures. In order to evaluate the effect of humidity, the kinetic scheme includes the most important reactions with the H2O molecule and its derivatives. The analysis includes the simulation of the corresponding streamer bursts, dark periods and aborted leaders that may occur prior to the inception of a stable leader. The comparison between the proposed model and the widely-used model of Gallimberti is also presented.

  • 2.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    A Parallel Projection Method for the solution of Incompressible Navier-Stokes Equations based on Position-State Separation Method2015Conference paper (Other academic)
    Abstract [en]

    A simple parallel numerical algorithm with P1/P1 velocity-pressure elements for solving the incompressible Navier-Stokes equations is proposed. In order to circumvent the Babuška-Brezzi condition (i.e. inf-sup condition), a velocity-pressure separation strategy following the idea of projection method is presented. Thus, the velocity and pressure terms are separated using operator-splitting, dividing the problem into two individual governing equations. The velocity equation is solved using an extension form of the position-state separation method (POSS), which has very good performance to solve convection-diffusion-reaction equations. The parallel computation of the method is easy to implement. Classical numerical experiments are conducted which show the efficiency, robustness and accuracy of the method.

  • 3.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    An efficient model to simulate stable glow corona discharges and their transition into streamers2017In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 50, no 10, p. 105204-Article in journal (Refereed)
    Abstract [en]

    A computationally efficient model to evaluate stable glow corona discharges and their transition into streamers is proposed. The simplified physical model referred to as the SPM is based on the classic hydrodynamic model of charge particles and a quasi-steady state approximation for electrons. The solution follows a two-step segregated procedure, which solves sequentially the stationary continuity equation for electrons and then time-dependent continuity equations for ions. The validity of using the SPM to simulate glow corona discharges and their transition into streamers is demonstrated by performing comparisons with a fully coupled physical model (FPM) and with experimental data available in the literature for air under atmospheric conditions. It is shown that the SPM can obtain estimates similar to those calculated with the FPM and those measured in experiments but using significantly less computation time. Since the proposed model simulates efficiently the ionization layer without prior knowledge of the surface electric field or the discharge current, it is a computationally efficient alternative to calculations of glow corona discharges based on Kaptzov's approximation (KAM). The model can also be employed to efficiently calculate the conditions for the transition of glow corona into streamers, overcoming the limitations of KAM to provide such estimates.

  • 4.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    An Efficient Semi-Lagrangian Algorithm for Simulation of Corona Discharges: The Position-State Separation Method2016In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375, Vol. 44, no 11, p. 1-10Article in journal (Refereed)
    Abstract [en]

    An efficient algorithm without flux correction for simulation of corona discharges is proposed. The algorithm referred to as the position-state separation method (POSS) is used to solve convection-dominated continuity equations commonly present in corona discharges modelling. The proposed solution method combines an Eulerian scheme for the solution of the convective acceleration, the diffusion and the reaction subproblems, and a Lagrangian scheme for the solution of the linear convection subproblem. Several classical numerical experiments in different dimensions and coordinate systems are conducted to demonstrate the excellent performance of POSS regarding low computational cost, robustness, and high-resolution. It is shown that the time complexity of the method when dealing with the convection of charged particles increases linearly with the number of unknowns. For the simulation of corona discharges where local electric fields do not change strongly in time, the time step of POSS could be much larger than the Courant–Friedrichs–Lewy (CFL) time step. These special features enable POSS to have great potential in modeling of corona discharges in long interelectrode gaps and for long simulation times.

  • 5.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Application of the Position-State Separation Method to Simulate Streamer Discharges in Arbitrary Geometries2017In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375Article in journal (Refereed)
    Abstract [en]

    In this paper, we extended the recent work of Liu and Becerra to employ the position-state separation (POSS) method to simulate filamentary streamer discharges. POSS is a semi-Lagrangian method, which solves convection-dominated continuity equations without numerical flux correction. An improved interpolation strategy for POSS is here introduced to overcome the excessive numerical diffusion of the method when very small time step is used. Several benchmark tests in the literature are used to validate the improved method. Numerical experiments show that POSS is an accurate, efficient, and robust numerical method to simulate streamer discharges in arbitrary geometries when combined with finite-element method.

  • 6.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Gas heating dynamics during leader inception in long air gaps at atmospheric pressure2017In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 50, no 34, article id 345202Article in journal (Refereed)
    Abstract [en]

    The inception of leader discharges in long air gaps at atmospheric pressure is simulated with a thermo-hydrodynamic model and a detailed kinetic scheme for N2/O2/H2O mixtures. In order to investigate the effect of humidity, the kinetic scheme includes the most important reactions with the H2O molecule and its derivatives, resulting in a scheme with 45 species and 192 chemical reactions. The heating of a thin plasma channel in front of an anode electrode during the streamer to leader transition is evaluated with a detailed 1D radial model. The analysis includes the simulation of the corresponding streamer bursts, dark periods and aborted leaders that may occur prior to the inception of a propagating leader discharge. The simulations are performed using the time-varying discharge current in two laboratory discharge events of positive polarity reported in the literature as input. Excellent agreement between the simulated and the experimental time variation of the thermal radius for a 1m rod-plate air gap discharge event reported in the literature has been found. The role of different energy transfer and loss mechanisms prior to the inception of a stable leader is also discussed. It is found that although a small percentage of water molecules can accelerate the vibrational-translational relaxation to some extent, this effect leads to a negligible temperature increase during the streamer-to-leader transition. It is also found that the gas temperature should significantly exceed 2000 K for the transition to lead to the inception of a propagating leader. Otherwise, the strong convection loss produced by the gas expansion during the transition causes a drop in the translational temperature below 2000 K, aborting the incepted leader. Furthermore, it is shown that the assumptions used by the widely-used model of Gallimberti do not hold when evaluating the streamer-to-leader transition.

  • 7.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering and Computer Science (EECS), Electromagnetic Engineering.
    On the critical charge required for positive leader inception in long air gaps2018In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 51, no 3, article id 035202Article in journal (Refereed)
    Abstract [en]

    The amount of the electric charge injected by the streamer corona bursts during the stage of leader inception determines the energy deposited to thermalize the corona stem into a leader segment. This paper is aimed at investigating the critical charge required for positive leader inception in air by using a thermo-hydrodynamic model with a detailed kinetic scheme. In order to simplify the analysis and to speed up the simulation, a reduced kinetic scheme for air is proposed. Numerical comparisons show that the reduced scheme can obtain almost the same results as the previous comprehensive kinetic scheme but with only half of the number of species and reactions. The thermo-hydrodynamic model with the reduced kinetics is then used to solve the radial dynamics of a single stem heated by current pulses typical of streamer corona bursts. The critical charge necessary for the direct transition of a first streamer corona into a leader under electrodes with large curvature radius is estimated between 0.08 and 0.5 uC per stem. Furthermore, the simulation shows that the gas heating of corona stem formed from electrodes with small curvature radius is mainly determined by the total accumulated charge injected by previous streamer corona bursts and the length of the dark periods in between the current pulses. The shape and the number of the corona current pulses in the discharge also play a role and their effects are discussed. It is suggested that the transition into a leader is triggered when a secondary streamer burst is initiated after the gas temperature is increased by the heating of previous streamers to about 1200 K. In addition, it is found that the heating produced by the charge injected by previous streamer corona bursts can be neglected if the dark period to the next burst is larger than few hundreds of  for a corona stem with moderate initial stem radius. This indicates that the critical charge criterion obtained from laboratory experiments does not hold to evaluate the inception of positive leaders under conditions when long dark periods are present.

  • 8.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    On the dynamics of streamer-to-leader transition in long air gap discharges2016Conference paper (Refereed)
    Abstract [en]

    In this paper, a self-consistent numerical model is employed to investigate the ionization kinetics of the streamer-to-leader transition in long air gap discharges. The model focuses on the dynamics of the discharge channel in the radial direction using a 1D radial system by taking into account 21 species and 106 chemical reactions. The detailed dynamics of the streamer-to-leader transition after a sequence of streamer bursts, dark periods and aborted leaders are discussed. The calculations are performed for a 1 m long rod-plate configuration using the current measured in experiments reported in the literature. The results show that the average central temperature of a newly formed and a self-propagating stable leader segment is around 2000K and 3000K, respectively. The instant temperature in the gap as a leader segment is incepted can reach 5000K. The predictions of temperature and thermal radius of the leader channel agree well with previous experimental studies.

  • 9.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    On the transition from positive glow corona to streamers in air2014Conference paper (Refereed)
    Abstract [en]

    The transition phase from glow to streamer corona is of significant importance for the evaluation of leader discharges initiated from ultra-high voltage power transmission lines under thunderstorms. In order to study the condition required for streamer inception from a glow-corona generating wire, the continuity equations for electrons, positive ions and negative ions coupled with Poisson’s equation are solved. The calculations are performed for a wire-cylinder coaxial configuration in one dimension. The analysis is performed by considering the generation of glow corona under a DC electric field, followed by the transition to a streamer-like ionization wave under a fastchanging electric field ramp. Thus, the critical rate of rise of the applied voltage on the wire surface required for streamer-like structures to initiate in the presence of a stable glow corona is evaluated for different radii and DC voltages.

  • 10.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    On the transition from stable positive glow corona to streamers2016In: Journal of Physics D: Applied Physics, ISSN 0022-3727, E-ISSN 1361-6463, Vol. 49, no 22, p. 225202-Article in journal (Refereed)
    Abstract [en]

    A 2D numerical simulation of the transition from stable positive glow corona to streamers in coaxial cylindrical configuration is presented. The hydrodynamic model with several convection-dominated continuity equations together with Poisson equation are solved with consideration of the ionization layer. The transition from a stable positive glow corona produced under a DC voltage to streamers is investigated under a sudden change of the applied voltage. The critical rate of rise of voltage required for the transition from positive glow to streamer corona is evaluated with a voltage ramp. By introducing either physical or numerical instabilities into the model, streamers with filamentary structures are observed, which produce a sudden increase of the discharge current by more than two orders of magnitude. It is also found that the surface electric field of the corona-generating conductor deviates from the onset electric field, casting doubts about the validity of Kaptzov's approximation to evaluate the transition from stable glow to streamers.

  • 11.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Two-dimensional simulation on the glow to streamer transition from horizontal conductors2014Conference paper (Refereed)
    Abstract [en]

    It has been recently suggested that glow corona generated during thunderstorms could have an important role in the initiation of streamers and upward connecting leaders from power transmission lines. In order to further investigate this, a two-dimensional evaluation of the glow corona generation is here reported, which takes into account the non-equilibrium ionization layer around the conductors. The critical change rate of the background electric field required for the transition from glow corona to streamer initiation is obtained. A numerical strategy to evaluate the glow corona to streamers transition for large gaps and irregular geometries is proposed and validated. A four-bundled conductor is also studied and results showed that when evaluating the critical rate of rise of the background electric field for a bundle conductor during thunderstorms, it could be viewed as a single conductor with the equivalent geometric mean radius of the wire configuration. Last, a study case is performed to estimate the effect of the glow corona on the streamer inception from UHV transmission lines during thunderstorms.

  • 12.
    Liu, Lipeng
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Becerra, Marley
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Two-dimensional Simulation on the Glow to Streamer Transition from Lightning Rods2015Conference paper (Refereed)
    Abstract [en]

    In the past twenty years, there has been a growing concern regarding the effect of space charge produced by glow corona on lightning attachment. Several studies have been reported in the literature to evaluate the generation and drift of space charge generated by glow corona from the top of high grounded objects under thunderstorm conditions, using one (1D) or two (2D) dimensional simulations. Unfortunately, the actual transition from glow corona to streamers cannot be numerically evaluated in these studies since the ionization layer was ignored. Thus, a fully 2D detailed evaluation of the glow corona to streamer transition in air is reported, which considers the non-equilibrium ionization layer around a scaled lightning rod. The transition criterion is obtained by changing the applied voltage with different rise rates (dV/dt) after a stable glow corona is formed. The discharge currents as well as the distributions of positive ions, electrons and electric field during the transition of glow corona to streamers are presented. Based on the simulation results, a case study regarding a real lighting rod under thunderstorms is performed. The analysis indicates that streamers can be incepted in the presence of glow corona from both the tip and body of lightning rods under the influence of distant downward stepped leaders.

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