Modeling and Simulation of Electronic Excitation in Oxygen-Helium Discharges and Plasma-assisted Combustion A thesis accepted by the Faculty of Aerospace Engineering and Geodesy of the University of Stuttgart in partial fulfillment of the requirements for the degree of Doctor of Science (Dr. rer. nat.) by Nikolaj Kuntner born in Vienna main referee: Prof. Dr. rer. nat. Uwe Riedel co-referee: Prof. Dr.-Ing. Stefanos Fasoulas date of defense: 31.5.2017 Institute of Combustion Technology for Aerospace Engineering University of Stuttgart 2018 . Herzlich m¨ochte ich an dieser Stelle meinen Vorgesetzten und Lehrern Uwe Riedel und Nadja Slavinskaya f¨ur eine pr¨agende Zeit am DLR Stuttgart danken sowie meinen Kollegen und Kolleginnen f¨ur wohl etwa 900 Ka↵ees um drei. Ich widme diese Arbeit meiner Mutter Ursula. Contents TableofSymbols .................................... 9 ListofFigures...................................... 11 List of Tables . 14 Kurzfassung . 16 Abstract......................................... 18 I Introduction 20 1 Principles of plasma assisted combustion 20 1.1 Thesis overview . 22 1.2 Typesofplasma.................................. 23 1.3 Redistribution of energy . 24 1.4 Typesofprocessesforplasmachemicalkinetics . 25 1.5 The basic strategy of plasma assisted combustion . 29 1.5.1 Plasma generation . 29 1.5.2 Heuristics ................................. 30 2 Discharge kinetics theory 31 2.1 The interaction cross section . 31 2.2 The reaction rate coefficient . 32 2.3 The Boltzmann equation . 32 2.4 Theelectronenergydistributionfunction . 34 2.5 Macroscopic observables from microscopic physics . 35 2.6 Discharge behavior of the constant current model . 36 3 Chemical species generated in oxygen-helium discharges 37 3.1 Energy hierarchy of electron-oxygen collision processes . 37 3.2 Rotationally and vibrationally excited states . 38 1 1 + 3.3 Singlet oxygen states O2(a ∆g)andO2(b ⌃g )................. 39 3.4 Atomic oxygen and ozone . 40 5 3.5 Charged species and attachment/detachment . 40 3.6 Helium....................................... 41 4 Before this work 42 4.1 On oxygen plasma generation . 42 4.1.1 Excited oxygen yield . 43 4.1.2 On diluents . 45 4.1.3 Validation experiment . 45 4.1.4 Other notable oxygen discharge studies . 48 4.2 Onplasmaassistedcombustion . 49 4.2.1 Hydrogengasstudies . 49 4.2.2 Methane gas studies . 50 4.2.3 Syngas studies . 50 5 Experiment and results at Magdeburg University 51 5.1 Descriptionofthedischargeandburnersetup . 51 5.2 Descriptionofthevoltagegenerator . 53 5.3 Experimental results . 54 5.3.1 Plasma generation . 54 5.3.2 Flame ................................... 54 5.3.3 Temperature development . 54 II Oxygen-helium discharges and combustion mechanisms 56 6 Rates for discharge zone mechanisms 56 6.1 Oxygen plasma . 58 6.1.1 Bimolecularreactionsofneutralmolecules . 58 6.1.2 Third body reactions of neutral species . 61 6.1.3 Elastic electron-atom and electron-molecule collisions . 62 6.1.4 Electron impact excitation of molecules and atoms . 62 6.1.5 Ionization processes . 63 6.1.6 Electron impact dissociation of a molecule . 64 6.1.7 Electron attachment . 65 6 6.1.8 Electron detachment . 65 6.1.9 Ion-moleculereactions . 67 6.1.10 Recombinationofchargedparticles . 68 6.1.11 Di↵usion to the wall and photoprocesses . 68 6.2 Heliumandoxygen-heliumplasmaprocesses . 69 7 Mechanisms for plasma assisted combustion 72 7.1 Principal e↵ect of plasma species on combustion kinetics . 72 7.2 Temperature rise in discharge- and combustion zone . 73 7.3 Hydrogencombustion............................... 74 7.3.1 On basic combustion mechanisms . 74 7.3.2 Excited oxidizer e↵ect on hydrogen combustion pathways . 75 7.4 Methane combustion . 76 7.4.1 On basic combustion mechanisms . 76 7.4.2 Excited oxidizer e↵ect on methane combustion pathways . 77 III Model development and simulation 79 8 Modeling approach 79 8.1 Availabledataandprincipalapproach . 79 8.2 Powerinputandconsumption . 81 8.3 Residence times . 82 8.4 Oxygen species relaxation time estimates . 83 8.5 Physics in the post-discharge zone . 84 8.6 Reduced electrical field and simulation tools . 84 9 Mechanism validation 86 9.1 Simulationapproach ............................... 86 9.2 Simulationresults................................. 86 9.3 Simulationofthepureheliumsystem . 88 10 Simulation of the discharge volume 94 10.1 Summary of approach and settings . 94 10.2 Simulation results . 95 7 10.2.1 Parameter study with respect to current density, I . 95 10.2.2 Species evolution in the discharge zone . 96 10.2.3 Parameter study with respect to current density, II . 103 10.2.4 Yieldfornitrogencontainingmixtures . 106 10.3 Discussion of the discharge zone . 107 11 Simulation of the burner zone 110 11.1 Simulation approach . 110 11.2 Simulation results . 110 11.2.1 Methane combustion . 110 11.2.2 Hydrogencombustion. 112 11.3 Discussion of the burner zone . 113 12 Summary 115 References 116 Appendix 125 A)Physicalconstants.................................. 125 B) Implementation of the Boltzmann equation . 125 8 Table of Symbols Latin Character Physical quantity Unit A cross section m2 3 c species concentration m− 2 2 C heat capacity kg m s− /K d discharge gap distance m 3 E electrical field strength kg m s− /A 2 2 Ea threshold energy J = kg m /s 2 2 Ekin kinetic energy J = kg m /s f distribution function various 1 f0 pulse frequency s− 1 frep repetition rate s− 3 3 F distribution function m− s F force N = kg m/s2 g relative velocity m/s I electrical current A Boltzmann cross section m2 jI current density A/m2 Boltzmann current term m2 kJ reaction rate coefficient m3n/s l tube length m m mass kg M mass kg 3 n particle density m− N particle number 1 1 2 p pressure Pa = kg m− s− P electrical power W = kg m2/s microscopic power W = kg m2/s qP gas flow rate m3/s q electrical charge C = A s collision integral m s/kg Q 3 r reaction rate m− /s r radial distance m 2 3 2 R electrical resistance ⌦= kg m s− /A t time s T temperature K 2 3 U electrical voltage V = kg m s− /A v particle velocity m/s V volume m3 x spatial distance m xspeciesmolefraction1 9 Greek Character Physical quantity Unit ✏ energy kg m2/s2 ⌘ efficiency 1 ⌘P power efficiency 1 µ mobility A s2/kg 1 ⌫ frequency s− 3 2 3 ⇢ resistivity m kg A− s− % charge density A s/m3 σ interaction cross section kg m2/s2 2 3 3 1 σe− conductivity A s m− kg− ⌧ characteristic time s Asubscripti, j, k, l always denotes either a numerical index or a species index (as in ni). Symbols such as species names are often used as index as well (as in nO2 ). The prefix ∆is used either to signify di↵erences (as in ∆E := Ekin Ekin0 )ortodenotean interval on a grid (as in ∆V vs. infinitesimal dV ). Several auxiliary− greek letters are used 3 for angles and to denote detailed information about chemical states (as in O2(X ⌃g−)). Symbol Usage A, B, Cauxiliaryspeciesname M collision partner in third body reactions 3 O2 molecular oxygen in the ground state, O2(X ⌃g−) O2⇤ molecular oxygen in an excited state O⇤ atomic oxygen in an excited state h⌫ photon particle 10 List of Figures 1 DischargegeneratorattheUniversityofMagdeburg. 21 2Electron-andionmotioninaTownsendbreakdown(graphicfrom[29])....30 3Energylossfractionforanoxygen-heliummixture(O2 : He = 1 : 30) vs. constant reduced electrical field strengths at one nanosecond - this system is discussed in more detail in subsection 8.6; The dissociation process presented here (dark blue line) must be understood as production of the dissociative 3 intermediate O2(B ⌃u−); The largest electron energy fraction is transferred in elastic collisions with helium in He + e− He + e− and is not shown in the graph; The energy fractions for ionization! by electron impact, e.g. + O +e− O +e− +e−,arealsonotshown. 44 2 ! 2 4 Discharge gap in the experiment performed at Bochum University [34]. 46 5 Working conditions without arcing established for the He-flow of 1.5 slpm [47]. 47 6TheconcentrationsofOfor0.6% oxygen in helium, graphic from [47]. [O] has been obtained by TALIF and MBMS measurements, inside the tube as well as at the e✏uent. .............................. 47 7Left:Computergenerateddesignofthedischargezone,alsodepictedinfig- ure8; Right: Cross section of the burner module on top of the discharge outlet. ........................................... 51 8Fullplasmaassistedcombustionsetup;Right:Di↵erentlycoloredcablespro- vide oxidizer, fuel and cooling gas; Left: The voltage cables on both ends of the discharge are black. 52 9Temperaturedi↵erencesbetweentheinjectionandtheburneroutlet,vs.tem- perature at the burner outlet. For each duty cycle, a gray line connects the values for pure helium (left) and a mixture with 3.2% oxygen addition (right). For those pairs, temperature at the outlet di↵ers by a factor of about 0.86 and this value is largely independent of duty cycle. 55 10 Experiment and associated computational model for the plasma discharge. 80 11 Varying values of E/n for a species ratio of O2 : He = 1 : 30. 85 12 Development for di↵erent mechanisms for I = 2 mA. Low to high O concen- tration: variation of Chernysheva et al. [18], version of [18] augmented with oxygen-helium interaction processes, variation of Waskoenig et al. [107]. 87 13 Comparison of the final concentrations at t =1.6msoftherelevantspecies vs. current. 88 11 14 EEDF (log-scale) for the j =3.5mA/mm2 simulation of the pure helium system for a broad variety of times. The almost horizontal line corresponds 9 to the first time step at t 10− s. ....................... 89 15 Electrical field for the j =3.5mA/mm2 simulation of the pure helium system. 90 16 Selection of rates for the j =3.5mA/mm2 simulation. 91 17 Selection of species concentration for the j =3.5mA/mm2 simulation. 92 18 Electrical field for a simulation run, where 3.2% O2 has been added to helium.