thermal mode nonequilibrium in gas dynamic and plasma ... · plasmadynamics and lasers award...

Plasmadynamics and Lasers Award Lecture

Nonequilibrium Thermodynamics Laboratories The Ohio State University

Thermal Mode Nonequilibriumin Gas Dynamic and Plasma Flowsin Gas Dynamic and Plasma Flows

byIgor Adamovich, Walter Lempert,

Vish Subramaniam and William Rich

The Michael A. ChaszeykaNonequilibrium Thermodynamics Laboratories

Dept of Mechanical EngineeringDept. of Mechanical EngineeringThe Ohio State University

AIAA 39th Plasmadynamics and Lasers ConferenceSeattle, Washington, June 25, 2008

Outline


• What is thermal mode nonequilibrium?Emphasis on high density, collision-dominated flows,cold molecular plasmas

• Environmentsi) Cool Electric Discharge Plasmas

Self-Sustained vs. Preionized ii) Optically Pumped Plasmas

Excitation of Vibrational StatesKinetics and Energy Transfer Studies

iii) Gas Dynamic Flowsiii) Gas Dynamic FlowsSupersonic Expansions of High Enthalpy GasesStrong Shock Waves

A li ti• Applications i) Plasma Wind Tunnelsii) Gas Lasersiii) Chemistry: Isotope Separation

• Summary: Where do we go with this?

What is thermal mode equilibrium?


ni/gi ~ exp ( - Ei/kT ), ln (n /g )i/gi e p ( i/ ),

N = ∑ ni , and E = ∑ niEi

ln (ni/gi)Increasing T

If we know the energy levels, Ei, and the gas temperature, T, we cancalculate the whole ideal gascalculate the whole ideal gas thermodynamic table: Ei

What is thermal mode nonequilibrium?


Thermal nonequilibrium exists whenever:

• The populations, ni/N, of one or more modes are distributed according to the Boltzmann law but thedistributed according to the Boltzmann law, but thetemperature, T, of at least one mode differs from thatof the others.OR• The populations, ni/N, of one or more modes are notdistributed according to the Boltzmann law.

Environments: Energy Input Among NonequilibriumPlasma Modes in a Self-Sustained Electrical Glow Discharge


g

Fraction of Power intoeach Mode, as a function

f E/N E/N i i t lof E/N. E/N is approximatelyproportional to the meanenergy of the free electrons.

1. Rotational mode2. Vibrational mode3. Electronic mode

Ratio of Electric Field, E, to total

3. Electronic mode 4. Ionization

Plasma Tube Ratio of Electric Field, E, to total number density of molecules, N

L

Plasma Tube

Electric Field = Voltage/Electrode Separation_ +

L Electric Field = Voltage/Electrode SeparationE = V/L

Environments: Preionized Electrical Glow DischargeShort Pulse HV Ionizer, D.C. Sustainer - Geometry


Pulser electrodes in top and bottom walls

DC electrodes in side walls

Flow direction left to right

Dimensions: 1 cm x 5 cm, 10 cm long

Mach number: M~0.2

Discharge pressure: up to 160 torr

(O2-He, O2-Ar)

M fl t t 12 /Mass flow rate: up to 12 g/sec

Environments: Preionized Electrical Glow DischargeShort Pulse HV Ionizer, D.C. Sustainer -Performance


Ionizing pulse (~10 nsec duration)~10 μsecVoltage

1E+13

1E+14Species concentrations

DC (MHD) voltage

~1O kV

1E+11

1E+12

electrons

O atoms

Time1E+10

1E+11

1E-9 1E-8 1E-7 1E-6 1E-5 1E-4

1E+9

Time, sec

O th l ft i t ti ft th i i i lOn the left, species concentrations after the ionizing pulse,on the right, schematic of the pulsed and d.c. dischargeoperation. P=0.1 atm, T=300 K, E/Nmax=350 Td, Emax=8.5a akV/cm, τpulse=10 nsec

Environments: Preionized Electrical Glow DischargeShort Pulse HV Ionizer, D.C. Sustainer -Photos


P=300 torr, 10 kHz P=500 torr, 10 kHz

Environments: Optical Pumping – Excitation of Vibrational Mode by CO Laser Radiation. Vibration-Vibration (V-V) Exchange


EEk ⎞⎛ ΔΔ1

TEE

expkk w,1w1v,v

r

k >⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−Δ= +−

krkfw+1

w

v

.

.

.

w

v-1

krkf

CO(v)+CO(w) → CO(v-1)+CO(w+1)

Environments: Optical Pumping – Excitation of Vibrational Modeby CO Laser Radiation. Measurement of Vibrational State

Populations Vibrational Distribution FunctionNonequilibrium Thermodynamics Laboratories The Ohio State University

Populations – Vibrational Distribution Function

1E+0Relative population

1E-2

1E-1 T=1200 K

1E-3Measured nonequilibriumdistribution

1E-5

1E-4Boltzmann distrubitionat T=4100 K

0 10 20 30Vibrational quantum number

Environments: Optical Pumping of Nitrogen Vibration byRaman Absorption – Excitation of High Vibrational

States by V-V Energy Exchange


States by V V Energy Exchange

(b)(a)Each peak is from a (b)

6.E+04

8.E+04

1.E+05

tens

ity

(a)

6.E+04

8.E+04

1.E+05

tens

ity v=0

psuccessive vibrational state, v, ground state signal on the right. The time

0.E+00

2.E+04

4.E+04

Int

0.E+00

2.E+04

4.E+04

Int

delay between the pump and probe pulse is (a) 150 ns, (b) 1 ms, (c) 5 ms, (d) 10

(d)1.E+05

600 602 604 606 608 610nm

(c)1.E+05

600 602 604 606 608 610nm

10 ms.

4.E+04

6.E+04

8.E+04

Inte

nsity

4 E+04

6.E+04

8.E+04

Inte

nsity

0.E+00

2.E+04

4.E 04

600 602 604 606 608 610nm

0.E+00

2.E+04

4.E+04

600 602 604 606 608 610nm

Optically Pumped Plasmas: Kinetics StudiesExperimental Setup for CO Plasma


CO laserCO laser

Optically Pumped Plasmas: Kinetics StudiesEnergy Transfer and Kinetics Processes in a CO Plasma


gy

Relative population

1 0E 1

1.0E+0

CO laserIonization:

CO(v)+CO(w) →(CO)2+ + e-

V-E:

1.0E-2

1.0E-1

V V

V-E: CO(X1Σ,v~40)+M→CO(A1Π)+M

Chem. Reactions:

1.0E-3

V-V CO(v)+CO(w) →CO2+C

1.0E-4 V-T

0 10 20 30 401.0E-5

Vibrational quantum numberT = 600 K

2 torr CO, 100 torr Ar, T=600 K, Tv=3300 K

CO Laser power 10 W c.w.

2 Torr CO, 100 Torr Ar, CO laser power 10 W c.w.

T 600 KTv = 3300 K

Optically Pumped Plasmas: Kinetics StudiesOptically Pumped CO Plasma Photo


Optically Pumped Plasmas: Kinetics StudiesSteady –State Vibrational Excitation of a Flowing Dry Air Mixture


Steady State Vibrational Excitation of a Flowing Dry Air Mixture

Vibrational energy level populations for an optically pumped air plasma. If energy were equilibrated, temperature of

Intensity 1.0E+0Relative population

vibrational modes would be ~ 2000K. Measured as kinetic temperature is only 500 K. Extreme nonequilibrium is created in a steady state, atmospheric pressure, molecular gas plasma. Gas mixture is CO/N2/O2=5/75/20, P=1 atm. Pump laser power is 10 W.

v=0

N2

1.0E-1

1.0E+0

N2 , experiment

CO, experiment

O2 , experiment

N calculation

601 602 603 604 605 606 607 608 609

Wavelength, nm

v=41.0E-2

N2 , calculation

CO, calculation

O2 , calculation

Intensity

v=0O2

1.0E-4

1.0E-3

570 572 574 576 578 580

Wavelength, nm

v=8

0 10 20 30Vibrational quantum number

Experimental Vibrational State Populations

Raman SpectraInferred from Raman Spectra. Calculated State Populations from Master Equation Kinetic Model

Optically Pumped Plasmas: Kinetics StudiesAssociative Ionization in Optically Pumped Plasmas I

CO(v) + CO(w) → (CO) + + e- E + E > E


CO(v) + CO(w) → (CO)2 + e , Ev + Ew > Eion

Thomson discharge Microwave absorption

DC Electrodes

Laser

MicrowaveWaveguideg

Electron density: Electron production rate: k 10 13 3/ ne≅ 1011 cm-3kion~10-13 cm3/s

Optically Pumped Plasmas: Kinetics StudiesAssociative Ionization in Optically Pumped Plasmas II

CO(v) + CO(w) → (CO)2+ + e- , E + E > Ei


CO(v) + CO(w) → (CO)2 + e , Ev + Ew > Eion

Current-voltage characteristicsof the DC Thomson discharge atdifferent helium partial

Vibrational distribution functionsof carbon monoxide at differenthelium partial pressuresdifferent helium partial

pressureshelium partial pressures

Optically Pumped Plasmas: Kinetics StudiesCoupling of Vibrational Populations with Free Electrons


p g p

Optically Pumped Plasmas: Kinetics StudiesMeasurements of Electron Density Decay (by microwave attn)

for E beam Created Plasma Experimental Schematic


for E-beam Created Plasma – Experimental Schematic

Optically Pumped Plasmas: Kinetics StudiesMeasurements of Electron Density Decay (by microwave attn) for E-beam

C t d Pl I hibiti f El t L P i C ld Ai


Created Plasma – Inhibition of Electron Loss Processes in Cold Air

Plasma Power Consumption at 1013 Electrons/cm3 in 1 Atm, 560 K Air:

Electron-Ion Recombinationβ=2.5x10-7 cm3sec-1

Nonequilibrium: 56 W cm-3

Electron Attachment to O2keff=2.3x10-33cm6sec-1

Nonequilibrium: 1 2 W cm-3

as a owe Co su pt o at 0 ect o s/c t , 560 :

Nonequilibrium: 56 W cmEquilibrium: 450 W cm-3

Nonequilibrium: 1.2 W cmEquilibrium: 1.4 kW cm-3

Optically Pumped Plasmas: Kinetics StudiesInhibition of Electron Loss Processes in Cold Air

Influence of Temperature on O Attachment and Detachment Rates


Influence of Temperature on O2 Attachment and Detachment Rates

Attachment is weakly dependent upon heavy species temperatureAttachment is weakly dependent upon heavy species temperature whereas detachment is highly dependent

MOMeO +⇔++ −−22

O2 Electron Affinity ~0.43 eV ( T Vib ti l Q t )(~Two Vibrational Quanta)

Optically Pumped Plasmas: Kinetics StudiesInhibition of Electron Loss Processes in Cold Air

Radially-Resolved Filtered Rotational Raman Temperature Measurement


Radially Resolved Filtered Rotational Raman Temperature Measurement

200/18/35 N /CO/O O ti ll P d200/18/35 N2/CO/O2 – Optically Pumped(Diameter of Vibrationally Excited Region ~ 1 mm)

345350

k)

330335340

pera

ture

(k

315320325

Tem

p

310-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Radial Position (mm)

Gas Dynamic Flows: Vibrational mode nonequilibrium in a supersonic nozzle expansion


in a supersonic nozzle expansion

Average energy permolecule in electronV ltVolts. (0.1 eV = 1,161 ºK)

Expansion of a gasExpansion of a gasmixture of 20% CO,20% N2, 60% Ar, Stagnation Pressure =Stagnation Pressure 100 atm.Stagnation Temperature =2,000 ºK.

Distance from nozzle throat, in centimeters

15 º Half Angle Nozzle, Expands to M = 10 at100 cm downstream of throat ,

Gas Dynamic Flows: Thermal mode nonequilibrium behind a hypersonic shock wave


yp

Tt = translational mode temperatureTr = rotational mode temperatureTv = vibrational mode temperature

ModeTemperature

v pDegrees K

Distance behind shock front, in meters

Plasma Wind Tunnels: A supersonic tunnel with energy loadingof selected internal states in the plenum


Nozzle throatNozzle exit Test section exitCrossed discharge section

M i

DC electrode

Main Gas flow To vacuum

Gas Injection Pulsed electrode block

Optical access

Schematic of the wind tunneldischarge section / nozzle / test section assembly

Plasma Wind Tunnels: A supersonic tunnel with energy loadingof selected internal states – photo of plenum in operation


Photograph of a discharge in the nozzle plenum. Dimensions 4x4x10 cm. A uniform cold gas fills the plenum;A uniform, cold gas fills the plenum;

O2/He mixture shown, similar uniformity for air; P0 to 1 atm.

Plasma Wind Tunnels: A supersonic tunnel with energy loadingof selected internal states – objects in a 2-D, M = 3 test section


Plasma Wind Tunnels: Calculated M =4 Flow over a 0.5 cm Diasemicylinder. Vibrationally Excited N2 Expanding from 1 atm.


From E. Josuyla, AFRL

Plasma Wind Tunnels: An M = 4 MHD Tunnel,with transverse pre-ionized discharge and a 2 Tesla Field in test section


Plasma Wind Tunnels: An M = 4 MHD Tunnel. Lorentz force effect on turbulent boundary layer density fluctuation spectra


Signal dB

turbulent boundary layer density fluctuation spectra

-30Signal, dB

j

jxB

40

-35j

B

-45

-40

Both B field directions Laser beam midway

B jxB

-50

500 W RF, B=1.5 T, U=1500 V (accelerating MHD force)

500 W RF, B=1.5 T, U=1500 V (decelerating MHD force) j

10000 100000Frequency, Hz

Nitrogen, M=3, P0=1/3 atmNitrogen, M 3, P0 1/3 atmBoth accelerating and decelerating Lorentz force are created

for two possible combinations of B and E fields, as shown

CO potentialNonequilibrium Thermodynamics Laboratories The Ohio State University

V(R)

R

R is the separation ofthe C and O nuclei.Re is the equilibrium e q(nonvibrating) separation.

V(R) = 1/2 K(R – Re)2 is the potential energy stored in the oscillator

RRe

Gas Lasers: Carbon Monoxide Electric Discharge Laser - Schematic


Gas Lasers: Carbon Monoxide Electric Discharge Laser –Photo during operation


Gas Lasers: Carbon Monoxide Electric Discharge Laser –Kinetic Modeling of CO Fundamental Band Laser,

Comparison with OSU Laser Performance



P W

2 0

2.5Power, W

experiment

1.5

2.0 experiment

calculations

1.0

0.0

0.5

0 2 4 6 8 10 12 14 16 18 20

0.0

Vibrational quantum number

.

Gas Lasers: Carbon Monoxide Electric Discharge Laser –Kinetic Modeling of CO Overtone Band Laser,




Theoretically Predicted Output Line IntensitiesExperimentally Measured

Output Line Intensities

Gas Lasers: An Electric Discharge-Excited Oxygen-Iodine Laser (DOIL) –Boltzmann equation solver results: electron energy balance

Nonequilibrium Thermodynamics Laboratories The Ohio State University45

25

30

35

40

a Pr

oduc

tion

5

10

15

20

% S

ingl

et D

elta

10% Oxygen-Helium 20% Oxygen-Helium

Pure Oxygen

O2-He

0

5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

E/N (10^-16 V cm^2)

50

30

35

40

45

Prod

uctio

n

O2-Ar

10

15

20

25

% S

ingl

et D

elta

P

10% Oxygen-Argon 20% Oxygen-Argon

Pure Oxygen

O2 ArHighest estimated

O2(1Δ) yield achieved

0

5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

E/N (10^-16 V cm^2)

so far ~10 %

Gas Lasers: An Electric Discharge-Excited Oxygen-Iodine Laser (DOIL) Schematic of Electric Discharge SDO Generator


Schematic of Electric Discharge SDO Generator

Advantages of transverse vs. axial discharge: Large volume, stable at high pressures / powers, rapid convective cooling vs. slow wall cooling. Used in most high power electrically excited lasers.

Nozzle throatNozzle exit Cavity exitCrossed discharge section DC electrode

Resonator arm

Main O2 / He flow To vacuum

Iodine injectorPulsed electrode blockGain window or laser mirror

DC electrodeOptical window

Optical access

Flow

Discharge volume 50 cm3, pressures up to 460 torr, flow rate up to 0.1 mole/sec (O2), 1 mole/sec (He)

Pulsed electrode

Gas Lasers: An Electric Discharge-Excited Oxygen-Iodine Laser (DOIL) Gain at Optimized Conditions: 0.12 %/cm at T=100 K (Currently!)


Gain at Optimized Conditions: 0.12 %/cm at T 100 K (Currently!)

0.05

0.06

Absorption/gain, %/cm

0 035

0.045

Gain, %/cm

Experiment Doppler Fit

0.02

0.03

0.04

0.015

0.025

0.035

-0.01

0.00

0.01

0 2 4 6 8 10 12 14 16

-0.005

0.005

2900 3100 3300 3500 3700

Adding NO: major discharge stabilization factor

0 2 4 6 8 10 12 14 16

Time, secFrequency, MHz

Adding NO: major discharge stabilization factor

Discharge power increased from 1.9 kW to 2.4 kW

P0=107 torr, 15% O2 - He flow, NO 0.2 mmole/sec (550 ppm), ν=34 kHz, UPS=3.1 kV I 1 54 A di h 2 4 kW I 70 l / (190 )kV, I=1.54 A, discharge power 2.4 kW, I2 70 μmole/sec (190 ppm).

Gain may be limited by I2 flow rate

Chemistry: Separation of Heavy Carbon Isotopes I


1

12CO: experiment

0.01

0.1

popu

latio

n

12CO: model 13CO: model

1E-4

1E-3

rela

tive

0 5 10 15 20 25 30 35 40

1E-4

vibrational level

Vibrationally excited CO prepared in cell reacts according to:

CO(v)+CO(w) → CO2 +C

Chemistry: Separation of Heavy Carbon Isotopes II


25

30 13CO/12CO 13CO2/

12CO2

15

20

s ra

tio

10

15

isot

opes

2 4 6 8 10 12 14 16 18 20 220

5

CO content in mixture, %

Summary


What have we learned?• Improved methods to sustain extreme mode disequilibrium in gases:

High densities, low gas kinetic temperatures, large volumes• New data on mechanisms and rates of some critical energy transfer

processes in molecular gases of aerospace interest• Methods for selective excitation of internal energy states • New applications: improved high power c.w. gas lasers, novel chemical

syntheses, new aerodynamic control techniques y , y qFuture directions?• Special purpose supersonic aerodynamic testing• Modeling code validation• Modeling code validation• High power c.w lasers and applications: novel refrigeration?• More chemistry: new products

Thanks!


Support:USAF:AFOSR Space Power & Propulsion Programp p gAFOSR Unsteady Aerodynamics and Hypersonics ProgramAFRL Air Vehicles DirectorateAFRL Directed Energy DirectorateNASA Glenn Research CenterNSFThe Michael A. Chaszeyka Gift

Collaborators:Univ. of Bonn Physics Dept; Heat and Mass Transfer Institute, Belarussian

Academy of Physics; Gas Laser Lab Lebedeev Physical InstituteAcademy of Physics; Gas Laser Lab, Lebedeev Physical Institute, Moscow Physical Technical Institute

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