THERMAL PLASMAS:Properties, Generation,

Diagnostics and Applications

Milan HrabovskyInstitute of Plasma Physics AS CR

Praha, Czech Republic

OUTLINEThermal plasma and non-thermal plasmaComposition, thermodynamic and transport properties of thermal plasmasModeling of thermal plasma flows, arc modelingGeneration of thermal plasmasBasic principles of arc plasma torchesFactors influencing properties of plasma jet in arc plasma torches ( design of the torch, properties of plasma gas)Plasma jet fluctuationsDiagnostics of thermal plasma jetsThermal plasma processing

Electron temperatures and densities in plasmas

102

104

106

108

1012 1016 1020 1024 1028108

Fusion plasma

Thermal plasmaGlow discharges

MHDgeneratorsFlame

Solarcorona

Ionosphere

Electron density [m -3]

Ele

ctro

n te

mpe

ratu

re [K

]

Nonequilibrium plasmas

Thermal (equilibrium) plasmas

plasma is not in thermodynamic equilibriumhigh values of E/p low pressureslow densities of electric current

)TT(TT ieie >≠

ie TT ≅

plasma is in thermodynamic equilibrium - LTElow values of E/p higher pressureshigh densities of electric current

Thermal plasmas

Basic plasma propertiesLocal thermodynamic equilibriumTemperatures Te = Th ~ 8 – 50.103 KPressures 10 kPa - 1 MpaE/p ~ 1 – 100 V/m.kPa

Common sources of thermal plasmasInductively coupled discharges in gasesElectric arcs – stabilized by gas flow

– stabilized by vortex of liquid (Gerdien arcs)

1.0E-004 1.0E-001 1.0E+002pressure [kPa

100

1000

10000

100000

tem

pera

ture

[K] Te

Th

Plasma in LTE

Properties of plasma in thermodynamic equilibrium are determined by pressure and temperature

Thermodynamic and transport properties of plasma depend on plasma composition

Composition of plasmaMonoatomic gas – electrons, ions, atoms

Eggert-Saha Equation:

Dalton´s Law:

Quasineutrality:

⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛ π

=kTEexp

hkTm2

QQ2

nnn i

2/3

2eiie

( )kTnnnp ie ++=

ie nn =

Thermal plasmas - compositionMonoatomic gases: atoms, ions, electrons

Argon: Ar, Ar+ , Ar++, … , e

Molecular gases: molecules, atoms, molekular ions, atomic ions, electrons

Nitrogen: N2 , N, N2+ , N+ , N++, … , e

Air: N2 , O2 , Ar, NO, N2O, NO2 , N, O, N2+, N+, O2

+, O+, Ar+, N++, O++, Ar++, … , e

Calculation of composition:Equilibrium between dissociation, ionization and recombinationMinimization of Gibbs free energyDepends on chemical potentials of different species present in plasma – can be determined from thermodynamic considerations

Plasma composition – monoatomic gas

Ar+

Ar

Ar++

e

e

Temperature [K]

Plasma composition-molecular gas

N+

e

e

N2+

N2

N

N++

nitrogen

Temperature [kK]

Composition of air plasma

Temperature [kK]

Thermodynamic properties

Mass densityEnthalpyInternal energySpecific heat Entropy

Evaluated for given plasma composition by methods of thermodynamics

The evaluation of thermodynamic properties is based on calculated partition functions for all species:

( )∑ −=s

ss kT/EexpgQ

Plasma density

∑=ρ iimn Density of nitrogen plasma

Decrease of particle concentration

Disociation, ionisation

Increase of number of particles with low mass

Temperature increase

Specific heat capacity

Increase oftemperature

Increase of kinetic energyof thermal motion - CfDissociation Ionization - CrCp = Cf + Cr

Specific heat capacityof various gases

HydrogenHeliumNitrogenArgon

Transport propertiesDiffusion coefficient D

Thermal conductivity k

Electrical conductivity σ

Viscosity µ

Computations of transport coefficients is based on solution of Boltzmann equation.

Knowledge of collision cross sections for all collisionalinteractions between particles is crucial. Transport

coefficients for more complex mixtures are frequently unknown.

ngradD=Γr

Tgradkq =r

Vgradj σ=r

xx vgradf µ=r

Thermal conductivity

Heat transfer

Molecules – kmAtoms - kaIons - kiElectrons - ke

Thermal conductivity of nitrogen

k = km + ka + ki + ke + kD + kI

Dissociation – kDIonization - kI

Copper k = 390 W/mKIron k = 75 W/mKWater k = 0,6 W/mK

Copper σ = 5,8 .107 S/mIron σ = 9,5 .106 S/mGraphite σ = 1,0 .105 S/m

Electric conductivity

Temperature [ 103 K]

Ele

ctri

c co

nduc

tivity

[ S/m

]

Plasma radiationComplex modeling of radiation transfer in plasma with high spatial gradients of temperature is extremely difficult due to

strong dependence of absorption and emission coefficients on temperature. Integration over all wavelengths along the optical path in plasma is necessary. Re-absorption of emitted light is

main problem.

Concept of net emissioncoefficient is frequently used. Net emission coefficientrepresents radiation fromisothermal cylinder of plasma with radius R.

Components of total radiationemission coefficient fo SF6 at 1 atm.

Absorption coefficient of SF6 for temperatures of 300 K and 20 000 K

Components of plasma radiation

Non-equilibrium effectsDeviations from LTE are caused by various mechanisms in

thermal plasma flows.

Flows with high spatial gradients of temperature in the direction of flow

“frozen” plasma composition corresponding to the upstream position

High spatial gradients of temperature – diffusion of species

Higher concentrations of electron in fringes of thermal plasma jets

De-mixing of plasma gases-ambipolar diffusion of ions with different coefficients of diffusion

Rapid changes of plasma temperatureeffect of kinetics of reactions (dissociation, ionization,

recombination) in plasma

Modeling of thermal plasma flowsPlasma can be described as a fluid with thermodynamic and transport properties depending on pressure and temperature

Models of thermal plasma flows are based on solution of equations of balances of mass, momentum and energy.

Equations of fluid dynamics are used with terms representing dissipation of energy by Joule heating,

radiation energy transfer and effect of electromagnetic forces.

Plasma properties are represented by transport and thermodynamic coefficients often calculated separately and given in tables giving dependence on temperature and pressure.

Model of arc column in axial gas flow

continuity equation: ( ) ( )1 vr u 0t r r x

∂ ∂ ∂ρ + ρ + ρ =

∂ ∂ ∂ ,

momentum equations:

( )ru u u p 2 1 uv u j B rvt r x x 3 x r r xθ

⎡ ⎤⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂ρ + ρ + ρ = − + − η + +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠⎣ ⎦

u 1 u v2 rx x r r r x

⎡ ⎤⎛ ⎞ ⎛ ⎞∂ ∂ ∂ ∂ ∂η + η +⎢ ⎥⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎣ ⎦

( )2

xv v v p 2 1 u wv u j B rvt r x r 3 r r r x rθ

⎡ ⎤⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂ ρρ + ρ + ρ = − − − η + + +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠⎣ ⎦ 2

1 v 2 v u v2 rr r r x r xr

⎡ ⎤⎛ ⎞ ⎛ ⎞∂ ∂ η ∂ ∂ ∂η − + η +⎢ ⎥⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎣ ⎦

w w w 1 w wv u rt r x r r r x x

∂ ∂ ∂ ∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ρ + ρ + ρ = η + η −⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ 2vw w wr r rr

ρ η ∂η− −

∂ ,

energy equation: p p p r r x xT T T p p pc vc uc u v j E j Et r x t x r

∂ ∂ ∂ ∂ ∂ ∂ρ + ρ + ρ − = + + + +

∂ ∂ ∂ ∂ ∂ ∂

x r1 T T 5 k T Tr j j Rr r r x x 2 e x r

∂ ∂ ∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞λ + λ + + −⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠&

charge continuity equation:

1 r 0 ,r r r x x

⎛ ⎞ ⎛ ⎞∂ ∂Φ ∂ ∂Φσ + σ =⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠

Inductively coupled plasma torchesInductively coupled discharge is maintained in an open tube in the presence of streaming gas. Low velocity plasma jet is formed at the exit.

Frequencies: 100 kHz – 100 MHzPower: 1 kW – 1 MWPressure: 104 – 106 PaPlasma temperature: 6 000 – 10 000 KPlasma velocity: 10 – 102 m/s

gas flow

plasma

RF

Thermal plasma generation

Electric arcs

High current densities– arc column ~ 100 A/cm2

– electrode spots ~> 106 A/cm2

High radiation intensityLow electrode potential drops Vc ~ 10 VDischarge current often limited only by power

supplyArc currents 1 A – 106 AIntensity of electric field 1 V/cm – 103 V/cmArc column length 1 mm – 101 m

liquidvapor

cathode

anode

gas

cathode

anode

Principles of arc stabilization

Gas-stabilized arc Liquid-stabilized (Gerdien) arc

• Gas flows along the arc in the nozzle• Usually gas flow has vortex component

for better stabilization and for anodespot movement

• Anode created by exit nozzle or transferred arcs

• Power level: 1 kW – 10 MW• Plasma temperatures: 6 000 – 20 000 K

• Liquid vortex is created in cylindrical chamber with tangential injection• Arc is stabilized by its interaction with the vortex• Anode is outside of arc chamber • Power level: 10 – 200 kW• Plasma temperatures: 8 000 – 50 000 K

Gas-stabilized arc plasma torches

Non transferred arcs Transferred arcsHot cathode

Cold cathode

+-

gas plasma

Gas-stabilized plasma torches

Water Stabilized Plasma Torch

arc current: 300 - 600 Aarc power: 80 - 176 kWarc voltage: 267 - 293 V

exit centerline temperature: 19 000 - 28 000 K

exit centerline velocity: 2500 - 7000 m/s

centerline plasma density:0.9 - 2.0 g/m-3

Basic factors determining properties of plasma jetin arc torches

Principal design factors: arc chamber geometry, arc currentplasma gas, gas flow rate

Dominant mechanisms of energy balance of unit length of arc columnin axial flow:

Energy dissipationby Joule heating

Increase of axialenthalpy flux

Power loss byradial conduction

Power lossby radiation

Following simple relations can be derived from energy balance equation for basic torch parameters:

Torch Power:

Torch Efficiency:

= + +

21

2G

F hRG.L.IU.IP ⎟⎟

⎠

⎞⎜⎜⎝

⎛σπηθ

θθ== σ

1

F

Gn2

F

G2

hS

GL2

hGLR41

−

⎟⎟⎠

⎞⎜⎜⎝

⎛++=

θπθε

θθπη

design factors plasma gas properties

Properties of plasma gases

8000 12000 16000 20000temperature [K]

0

10000

20000

30000

40000

50000

h/σ

[J.m

.V/k

g.A

10000 20000 30000temperature [K]

0

2000

4000

6000

8000

h/S

[m.s

/kg]

steam argon/hydrogen 3:1 argon nitrogen/hydrogen 2:1

Torch operation parameters are determined by physical properties of plasma gas.Decisive gas properties:

Power:ratio between enthalpy and electrical conductivity

Efficiency:Ratio between enthalpy and heat conductivityRatio between enthalpy and radiation emissivity

10000 20000 30000temperature [K]

0.001

0.01

0.1

1

h/ε n

Efficiency of utilizing plasma enthalpy for processing

Plasma inPlasma and reaction products out

Reaction space

Temperature T0Enthalpy h0

Temperature T TREnthalpy h hR

Reaction TemperatureTR

≥≥

0

R

0

R0R h

h1h.G

)hh.(G −=−=η

Only enthalpy ∆H = G.h0 – G.hR can be used for the treatment of material

Treated material

Process efficiency:

Enthalpy fllow rate G.h0 Enthalpy flow rate G.hR

Operation regimes of gas-stabilizedand water-stabilized dc arc torches

Mean plasma enthalpy:

Gas torches:10 – 40 MJ/kg

Water torches:100 – 300 MJ/kg

0 2 4 6mass flow rate [g/s]

0

50

100

150

200

pow

er [k

W]

Gas torches

Water torches

Operation regimes are expressed by the relation betweenarc power and mass flow rate

0 2 4 6mass flow rate [g/s]

0

50

100

150

200

pow

er [k

W]

Gas torches

Water torches

Principle of hybrid gas/water plasma torch

Operation regimes of dc arc plasma torches

Hybridtorches

Hybrid gas/water dc arc plasma torch

Ar

Ar

Water

Water

Plasma Jet

RotatingAnode

Arc

Ar

Ar

Water

Water

Plasma Jet

RotatingAnode

Arc

6 200240.105.0200500N2/H2 (235/94)

10 80015.30.151.9344500Ar/H2 (65/3)

17 5003200.0060.33176600water

15 8002520.0040.284300water

12 10013.50.080.9825750Ar/H2(33/10)

2 5002.96.432115300N2

3 0003.68.040180700N2

Tbulk

[K]Hbulk

[MJ/kg]G/L

[kg/s.m]G

[g/s]Power[kW]

Current[A]

Plasma gas

Typical parameters of dc arcplasma spraying torches

Thermal efficiency of water-stabilizedand gas-stabilized torches

η = (Pjet – G.hT )/ Pjet

= (1 – hT . G/Pjet )

hT=h(T) … T …S(T)

0.001 0.01 0.1 1 10 100heat flux potential S [kW/m]

0

0.2

0.4

0.6

0.8

1

effi

cien

cy η

waterargon/hydrogen (3/1)nitrogen/hydrogen (2:1)

Thermal Plasma Jets

0 10 20 30 40 50z [mm]-3

-2-10123

r [m

m]

T = 13 kK

161820

14In most plasma generators gas (water) is supplied into the discharge chamber and plasma jet is produced at the exit nozzle

Plasma Jet Instabilities

Gas dynamic instabilities:Fluctuations and turbulences in the arc chamberInteraction of plasma jet with ambient gas outside the

arc chamberArc instabilities:

Fluctuations of arc power due to ripple of rectifieredarc current

Arc column instabilities, changes of arc lengthInstabilities caused by electrode processes

Plasma jet interactionwith ambient gas

Production of vortex structures at the jet boundaryEntrainment of cold gas into plasma flowFormation of plasma flow turbulence

0 10000 20000 30000t [20 ns]

-100

0

100

200

300

Ua[ V

]

-3

-2

-1

0

1

2

3

Ud[ V

]

Ua

Ud3

Ud2

Ud1

Arc voltage and light fluctuations at various axial positions.

Positions of diodes: zd1 = 2.4 mmzd2 = 4.3 mmzd3 = 6.2 mm

d1 d2 d3

anode

arc

anode jet

nozzle

Development of gas-dynamic instabilityand effect of anode attachment

anode

arc

jet heating

production of jetinstability

anode jet

plasma jet

top view

side view

exit nozzle

anode anode jet

laminar jet turbulent jet

anode

Jet instability caused by anode attachment

Arc anode attachment:-anode jet-movement in the restrike mode

exposure time 3µs

0.05 0.10 0.15t [ms]280

300

Ua[V

]

0.20 0.24 0.28 0.32t [ms]

260

270

280

U a[V]

1 2 3 4 3 4 1 2

Anode restrike and movement of anode attachment

Fluctuations of arc voltage Fluctuations of arc power

Sequence of four images of anode region of plasma jetexit nozzle

anode

Effect of fluctuations of arc current

time

curr

ent

For classical 6-way rectifiers:∆I/I = 0.1 – 0.15Frequency : 300 Hz

Amplitude of fluctuations of arc power depends on relation between τΙ and τα

1

a

1

I

dtdg

g1

dtdI

I1

−

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=τ

⎟⎠⎞

⎜⎝⎛=τTime constant of current

changes

Arc time constant

1. τI << τa Arc has constant conductance: U = U + Rs . ∆IAmplitude of fluctuations of arc power: ∆P/P = 2 ∆I/I + (∆I/I)2

For ∆I/I = 0.1 – 0.15 ………. ∆P/P = 0.21 – 0.32

2. τI >> τa Arc voltage follows static characteristic: Constant arc voltage : ∆P/P = ∆I/IFalling static arc characteristic: ∆P/P < ∆I/I

~ 10-4 – 10-2 s

Diagnostics of thermal plasma jets

Fluctuations:Spatial distributionFrequency spectraPhase velocity of oscillations

Shape of the jetJet structure

Plasma jet core:High gradients of temperatureand velocityLaminar flow

Turbulent jet:Smooth T and v profilesHeterogeneous mixtureof plasma and cold gas

Time averaged characteristics:Temperature profilersVelocity profilesPlasma compositon

Basic plasma characteristics evaluatedfrom measurements:

Electron number densityTemperatureMolar concentrations of components

Basic methods:Absolute intensities of spectral linesLine intensity ratiosStark Broadening

725 730 735 740 745 750 755 760 765 7700

1

2

3

4

5

6

7

8x 10

5

ArII ArII

ArI

OI

ArI ArI

ArI ArII OII

TS ArII/ArI: 420/745 , 745/745 nm

470 480 490 5000

2

4

6

8

10

x 106

e xpe rime ntcalculation

Problems:Non LTE conditionsHigh gradients of temperatureelectron diffusionde- mixing of plasma gases

Non symmetrical cross section of the jet

Emission spectroscopy

1. Tare – no plasma flowQ – Heat flow rate P – Pressure

2. Sampling – plasma flows into the probeQ – Heat flow rateG – plasma flow rate

3. Mass spectrum

Measurements:Isokinetic coefficientppiso vR/GK ρπ 2=

Enthalpy probe

Plasma composition

Evaluation of plasma jet characteristicsfrom enthalpy probe measurements

Local plasma velocity

Plasma enthalpy:

Plasma temperatureThermodynamic and transport coefficients

Measurement of flow velocity

Enthalpy probe - Pitot tubeTime of flight of fluctuations - emitted light

- electric probe currentPropagation of waves in plasma

amplifier30 Hz – 50 MHz

measurement oftorch parameters

synchronizationunit

short shuttercamera

plasma torch

array of photodiodes

objectiveDiagnostics of jet fluctuationsand instabilities

0 50 100 150 200 250t [20 ns]

-1.5

-1

-0.5

0

0.5

1

Ud

[V]

240

260

280

300

Ua

[V]

Ud1Ud2

Ud3

Ud4Ud5Ua

Ua - Arc voltage

Signals of photodiodes:d1 = 1 mm (z/D = 0.167)d2 = 4.3 mm (z/D = 0.717) d3 = 7.7 mm (z/D = 1.28)d4 = 11 mm (z/D = 1.83)d5 = 14.3 mm (z/D = 2.38)

Determination of flow velocity from propagation of disturbance caused by an anode restrike

Anode restrikein the position d3

300 350 400 450 500arc current [A]

02468

1012141618202224

velo

city

[km

/s] streamwise

counter-streamwise

Stream-wise and counter-stream-wise velocities of perturbationscaused by a formation of new anode spot

and flow velocity evaluated as their difference

280 320 360 400 440 480 520I [A]

0

2000

4000

6000

8000

10000

12000

v [m

/s]

present measurementsmeasurements [4]

Determination of flow velocity

0 100 200 300 400 500t [0.1µs]

-1.5

-1

-0.5

0

0.5

1

1.5

phot

odio

des v

olta

ge [V

]

d6 d5

d4d3

d2

d1

Determination of flow velocityfrom phase shift of jet fluctuations

Fluctuations of emitted lightat various distances from the torch exit

D - Distance between points∆Φ - Phase shift

Velocity of movementof oscillations

∆Φπ fDv 2=

Determination of flow velocity

smfDv /3002 ==∆Φ

π

Fourier spectrum and dependence of phase shiftof oscillations on frequency – argon, 10 kW

D = 5 mm D = 1 mm

laser

plasma

lens screenlens increasingn(ρ)

Schlieren photography

plasma jet produced in water stabilized arc

screendiameter D

0

t [µs]:

10

20

30

5

15

25

35

High speed photography

Interaction of plasma jet with arc anode attachment

Ii [A]

U [V]Upl

I = U/Ra

I = U/Rb I = U/Ra - UB

y

z

r

U

-110 V

to voltage dividers

R = 10 kΩ

cathode

waterswirl

anode

vprobe

y

z

r

U

-110 V

to voltage dividers

R = 10 kΩ

cathode

waterswirl

anode

vprobe

anode

vprobe

Electric probes in thermal plasma jets

Ion collecting electric probes are used for study of structure of plasma flow

Determination of probe potential

High biasing resistance – probe potential close to floating potentialLow biasing resistance – probe current close to ion saturation currentNegative biasing voltage increases sensitivity of probe measurement

Lines of the same probe current at the plasma flow in the jet boundary

r

t

Structure of the jet boundary

Thermal plasma processing

Plasma technologies and decisive mechanisms

Heat transferPlasma meltingPlasma cutting

Heat and momentum transferPlasma sprayingSurface modifications

Chemical processes – decomposition and/or synthesis

Waste treatment, gasification, vitrificationPlasma CVD – production of filmsPlasma synthesis

Plasma spraying

Treatedmaterial Syngas

H2 + CO

vitrified lava

Gasification+

vitrification

Plasmatorch

Decomposition of Persistent ChemicalCompounds and Waste Treatment

Plasmareactor

CONCLUSIONSBasic thermal plasma jet properties:

Temperature and velocity profiles, plasma enthalpy, plasma compositionFlow structure and (in)stability

Basic plasma torch design parameters:Arc chamber geometry, length and diameterGas composition, gas flow rate

Basic diagnostics for thermal jetsSpectroscopyEnthalpy probesHigh speed photography, schlieren photographyElectric probes

Thermal plasma applications:Metallurgy, welding, cuttingSurface modifications, coatingsMaterials synthesisDecomposition, waste treatment