Lecture 11: Shock Tube Techniques/Applications Lecture Notes/Hanson... · Lecture 11: Shock Tube...

Lecture 11: Shock Tube Techniques/Applications

Motivation: Shock tubes with lasers is a chemical kinetics research frontier!

1. Introduction to Shock Tubes2. Vibrational Relaxation3. Ignition Studies4. Advances in Shock Tube Modeling

2

1. Introduction to Shock Tubes

Basic concept: High-pressure driver gas expands upon diaphragm opening, creating shock wave Test gas is instantaneously compressed and heated to combustion temperatures

by incident and reflected shocks High-temperature experiments monitored near endwall

High P Low P1

Diaphragm

Pressure transducers

52

Driver section(high‐pressure)

Driven section(low‐pressure)

4 1

Detector

Laser

3


Basic concept: High-pressure driver gas expands upon diaphragm opening creating shock wave Test gas is instantaneously compressed and heated to combustion temperatures

from incident and reflected shocks High-temperature experiments monitored at endwall

High P Low P1

Diaphragm


Incident Shock

Reflected shock

52



Detector

Laser

4


Shock Tube Characteristics: Instantaneous heating/compression from shock waves Accurately known incident- and reflected-shock conditions (from incident shock

MS) Wide range of post-reflected shock T and P (600-4000 K, 0.1-1000 atm)

High P Low P1

Diaphragm


Reflected shock

52



Detector

Laser

5


Primary uses• Astrophysics/

comets• Blast waves (e.g.

nuclear explosions)

• Chemical kinetics• Gasdynamics/

aerodynamics• Heat transfer

(radiation + convection)

• Spectroscopy

1900 1920 1940 1960 1980 2000

1899: Vieille (France) first shock tube constructed

1940’s: US/Canada/GB

mine safety, shock-induced

explosions, aerodynamics

1950’s: first applications to high-temperature chemical kinetics (CalTech)

1960’s: re-entry studies

1970’s: First use of lasers for species detection (Stanford/Ames)

6

p1T1ρ1v1 = 0

Vs


Incident shock speed governed by diaphragm burst pressure

Boundary condition u5 = 0 determines the speed of the reflected shock

All Region 5 conditions governed by incident shock speed

See Gaydon and Hurle

p2T2ρ2v2

Incident shock Reflected shock

Vr

Laboratory-fixed coordinates

p2T2ρ2v2

p5T5ρ5v5 = 0

1-D Shock Wave Theory

7


P2/P1 P5/P2 WR/WS2.95 10 4.95 2.62 1.76 3.82 2.82 0.4236.56 50 7.12 9.31 2.28 5.37 3.11 0.351 8.00 2.29 6.00 3.50 0.333

2.87 10 4.22 3.42 1.94 2.92 2.17 0.5896.34 50 5.54 13.4 2.37 3.72 2.31 0.517 6.00 2.40 4.00 2.50 0.500

7/5

5/3

2 4 6 8 101

10

100

T5/T1 ( T5/T1 ( T2/T1 ( T2/T1 (

T 2/T1 (

or T

5/T1)

MS

2 4 6 8 101

10

100

P5/P1 ( P5/P1 ( P2/P1 ( P2/P1 (

P 2/P1 (o

r P5/P

1)

MS

Shock Jump Values

8


Particles are stationary behind the reflected shock: lab time = particle time

Test time is limited by the reflected shock interaction with the contact surface Typical test time ~ 1-3 ms

Diaphragm

Position, x

Time, t

Expansion Wave

IncidentShock

ReflectedShock

Test Location

ContactSurface

TestTime

Test Time in Reflected-Shock Experiments

a2 a3

9

Tailored driver gases optimize the reflected-shock-contact surface, increasing the test time Tailored test times 10 ms


Diaphragm

Position, x

Time, t

Expansion Wave

IncidentShock

ReflectedShock

Test Location

ContactSurface

TestTime

Test Time in Reflected-Shock Experiments

10

2. Vibrational Relaxation

Recall our previous lectures on the vibrational energy in diatomic molecules Use a simple harmonic oscillator

model (HO)

Molecular energy depends on inter-nuclei spacing and fundamental frequency

But energy levels are quantized!

Can use Boltzmann statistics (PGD) to determine distribution

i energy in level ii h Simple Harmonic Oscillator

i=5i=4i=3i=2i=1i=0

r

u(r)

r

21 , difference in nuclei spacing from equilibrium21 , spring constant; = fundamental frequency of vibration

2

eu kx x r r

k km

v

v

v

i /

/

v

vv /

* e* fractional population in level i1

1 e1 with characteristic vibrational temperature

average vibrational energy per moleculee 1

Ti

i

T

T

NxN Q

h hck k

Re

11

Vibrational energy distribution function (from Boltzmann statistics)

More molecules in lower vibrational levels than in high vibrational levels

Higher energy levels get populated at higher temperatures

Temperature refers to the vibrational temperature (T = Tv), the same as translational temperature in vibrational equilibrium

If Tv = Ttrans then vibrational energy transfer will occur until the system reaches equilibrium→ vibra onal relaxa on!


v

v

i /

/

* e* fractional population in level i1

1 e

Ti

i

T

NxN Q

0 1 2 3 41E-3

0.01

0.1

1

vibrational level, i

T=300 K

high T

popu

latio

n, x

i*

12


How fast does relaxation occur? Rate of relaxation follows the Bethe-Teller relationship

.

Vibrational energy (Ev) changes at a rate proportional to deviation from the equilibrium value (Ev

*)

Dependencies Relaxation time constant:

As T increases, the relaxation time constant decreases The relaxation time constant is independent from the deviation from equilibrium The relaxation time constant is also independent of the initial vibrational distribution

How can we measure ?

v vv

v

v

*

vibrational energy (e.g. per mole, unit mass, etc.)* vibrational energy at translational temperature (i.e. equilibrium)

tr

tr

E T EEt

EE T

v /1,0

1

1 e TZMP

V-T Energy Transfer

v/

13


T

t

Test mixture of HO’s starts out in vibrational equilibrium (Region 1)

Translational temperature is instantaneously increased by the arrival of the incident shock

Vibrational temperature needs time to relax V-T energy exchange occurs (and energy must be

conserved

Faster relaxation time behind reflected shock because temperatures are higher.

Note the equilibrium temperature is lower than the vibrationally frozen temperature

Ttrans

TvIncident Shock

Reflected Shock

T2

T5

Vibrational Relaxation in Shock Tubes

14


White and Millikan, AIAA Journal 1964.

Millikan and White were able to measure the vibrational relaxation speed of CO, O2, N2, and air at various temperatures using shock tubes Seed small amounts of CO into the test gas IR emission of CO near 4.7 microns Optical interferometry to monitor pressure/density

change due to N2/O2 relaxation

Shock Tube Studies of Vibrational Relaxation


15

• Modern Experiments with Laser Diagnostics

Goal:• High-temperature O2 vibration relaxation rates

Experimental Strategy:• Shock heat highly diluted mixtures of O2 in Ar• New diagnostic (MIRA laser) to measure O2 in deep UV

(Schumann-Runge) at 206 to 245 nm


16

ReflectedShock Wave

MIRA LaserPump 4th

Harmonic Generator

844 nm IR 211 nm UV

Shock-HeatedTest Gas Mixture

MIRA operating range: 206-1000 nmPulse rate: 80 MHz, equivalent to CWAverage power: 2-20 mW at 206 nm to 245 nmHow does this relate to O2 vibrational populations?

• Reflected shock absorption experiments• Beer’s law: (I/I0) = exp(-nv” (Trot, Tvib) = e-(t)

• Measure (t)• Infer nv”(t) and ev(t)

Experimental Setup absorbance

17


• Schumann-Runge O2 system (B3u- ← X3g

+) has overlapping features • Select wavelengths sensitive to specific v”• Laser experiments measure total absorption at fixed involves many lines• Goal: Infer nv”(t) for v’ = 3-7 from absorbances at peak ’s

211 nm: v” = 4

223 nm: v” = 5

206 nm: v” = 3

Envelope of rovibronic lines for a specific v”

245 nm: v” = 7

235 nm: v” = 6

2. Example O2 Data and Model

18

• excellent signal-to-noise ratio (noise ~0.3% absorbance)• High-accuracy determination of XO2, T5, P5

• high-accuracy measurement of tvib!• Initial data support an evolving Boltzmann distribution for evib

• tvib can be plotted on a Landau-Teller plot

19

O2 vibrational relaxation measurements

• Current work inclose agreement with classic studies (Millikan and White (1963), but with much lower scatter

• Experiments with varying O2 fraction VT(O2-O2) and VT(O2-Ar)

1950K 1166K

Mixture Rule for (1/P)mix = Xj/Pj j

2. Landau-Teller Plot

3. Ignition Studies

1. Kinetics of branched chain reactions2. Definition of ignition3. Examples

20

21

3.1. Kinetics of Branched Chain Reactions:Basic Mechanism for Hydrogen Oxidation

by adsorb

2 2 2

2 2

2

2

2 2

1 + initiation

2 propagation

3 branching

4

5

6 8 , , wall removal

H O HO H

OH H H H O

H O OH O

O H OH H

H O M HO M

H O OH

tion, wall-catalyzed reactions stable species

termination

Build up of a radical pool during oxidation This characterizes ignition! Also exothermic reactions generate heat

release/pressure increase

2

2 2

2

2 2

2 2 2

Step 1:

Step 2:

Step 3:

Step 4:

net: 3 3 2 2 !

H O OH O

OH H H H O

O H OH H

OH H H H O

H O H H H O H

Net effect of branching is to create radicals

22

3.2. Definition of Ignition Time

Ignition delay time in reflected shock experiments: time between passing of the reflected shock and onset of ignition

Onset of ignition: linearly extrapolating the point of steepest rise back in time to the pre-ignition baseline

-100 0 100 200 3000

1

2

3

4

5

OH* emission

Rel

ativ

e E

mis

sion

Pre

ssur

e [a

tm]

Time [s]

ign = 170 s

4% H2 / 2% O2 / Ar1124 K, 3.1 atm Pressure

ign = 170s

Measure through P5(t) and OH*(t) emission at 306 nm (A-X)

Close agreement of pressure and emission measurement

23

3.3. Examples

Able to examine correlations for ignition times in different alkanes Negative temperature dependence of ignition times is seen at low-intermediate

temperatures

P=15 atm

4. Advances in Shock Tube Methods

1. Extended drivers & tailored gas mixturesfor longer test times

2. Driver inserts for improved spatial andtemporal uniformity

3. New approaches to reactive gas modeling

4.1. Extended drivers & tailored gas mixturesfor longer test times

• Conventional shock tube operation: ~ 1-3 ms test time• No overlap with RCM operation~ 10-150 ms test time

0.4 0.8 1.2 1.61E-3

0.01

0.1

1

10

100

1000

Test

Tim

e, I

gniti

on T

ime

[ms]

1000/T [1/K]

2500K 1000K 625K

UnmodifiedStanford ST

n-Dodecane/Air

10atm

0.4 0.8 1.2 1.61E-3

0.01

0.1

1

10

100

1000

Test

Tim

e, I

gniti

on T

ime

[ms]

1000/T [1/K]

2500K 1000K 625K


RCM

n-Dodecane/Air

10atm

=1

25

0.4 0.8 1.2 1.61E-3

0.01

0.1

1

10

100

1000

Test

Tim

e, I

gniti

on T

ime

[ms]

1000/T [1/K]

2500K 1000K 625K


Modified ST

RCM

n-Dodecane/Air

10atm

• Longer driver length and tailored gas mixturescan provide longer test times (50+ ms)

2x Driver Extension

• Shock tubes now can overlap with RCMs

=1

4.1. Extended drivers & tailored gas mixturesfor longer test times

26

4.2. Driver inserts for improved spatial andtemporal uniformity

• Problem: boundary layers and attenuation induce dP/dt and dT/dt that change ignition times

dP/dt = 3%/msdT/dt = 1.2%/ms

• Solution: Driver inserts that modify flow to achieveuniform T and P at long test times

P5T5VRS

27


Result: dP/dt = 0 prior toignition

Improved ign for comparison with simulations

P5T5VRS

Example: Propane Ignition• Solution: Driver inserts that modify flow to achieve

uniform T and P at long test times28


dP/dt = 0 data provide improved targets for constant U,V simulations

Experimentalists must report facility dP/dt to allow modelers to make useful comparisons with detailed mechanisms, e.g. via CHEMSHOCK

0.8 0.9 1.0

1

10

CHEMSHOCK(dP/dt=12%/ms)

CHEMSHOCK(dP/dt=1.5%/ms) Current Study (dP/dt~0%/ms)

Current Study (dP/dt=1-3%/ms) Cadman (2002) (dP/dt=12+%/ms)

1000K1111K1250K

Igni

tion

Tim

e [m

s]

1000/T [1/K]

0.8% C3H8/ O2/ Ar= 0.5, 6 atm

Const. U,V

Mechanism: JetSurF v1.0 (2009)

29

• Modifications yield improved ignition delay times for propane

4.3. New approaches to reactive gas modeling

Most current reflected shock modeling assumes Constant Volume or Constant Pressure

But: Reflected shock reactions are not Constant V or Constant P

processes!

Example: Heptane Ignition

30

Reactive Gasdynamics Modeling: The Problem


• This is not a Constant P process!

-100 0 100 200 300 400 500 6000

1

2

3

4

5

0.4% Heptane/4.4% O2/Ar, =11380K, 2.3 atm

Pre

ssur

e [a

tm]

Time [us]

ign

0

2

4

MeasuredSidewall P

Constant PModel

31

• Effect of Energy Release on P Profiles: n-Heptane Oxidation


• This is not a Constant P process!• Also not a Constant V process!• So how can entire process be modeled?

-100 0 100 200 300 400 500 6000

1

2

3

4

5

0.4% Heptane/4.4% O2/Ar, =11380K, 2.3 atm

Pre

ssur

e [a

tm]

Time [us]

ign

0

2

4

MeasuredSidewall P

Constant PModel

Constant V Model

32

• Effect of Energy Release on P Profiles: n-Heptane Oxidation


Minimize fuel loading to reduce exothermically- or endothermically-driven T and P changes- enabled by high-sensitivity laser diagnostics

Use new constrained reaction volume (CRV) concept to minimize pressure perturbations- enables constant P (or specified P) modeling

33

• Proposed Solutions to Enable Modeling through Entire Combustion Event


• Large reaction volume gives large energy release P & T• CRV gives reduced energy release near-constant P• Also eliminates any question of remote ignition!

Conventional Shock Tube Constrained Reaction Volume

Helium Test Mixture

Pre-Shock

Post-Incident Shock

Pre-Shock

Post-Incident Shock

Helium Non-Reactive Mix TM

Large Region ofEnergy Release

Small Region ofEnergy Release

ReflectedShock Wave

Post-Reflected Shock Post-Reflected Shock

34

• Constrained Reaction Volume (CRV) Approach

• Conventional ST exhibits large pressure change!• CRV pressure nearly constant throughout experiment!• Allows 1st kinetics modeling through ignition and combustion in

non-dilute systems!

Conventional Shock Tube Constrained Reaction Volume

0 1 2 3 4 50

2

4

6

8

Pressure

4%H2-2%O2-ArNormal Filling979K, 3.44 atm

Pres

sure

[at

m]

Time [ms]

Emission

0 1 2 3 4 50

2

4

6

8

Pressure

4% H2-2%O2-ArCRV = 4 cm956K, 3.397 atm

Pre

ssur

e [a

tm]

Time [ms]

Emission

Ignition


35

• Use of Constrained Reaction Volume (CRV) Approach1st Example: Hydrogen Ignition at 950 K


Measured T validates CRV approach and illustrates power of T as a kinetics diagnostic

36

Temperature Pressure

0.0 0.5 1.0 1.5 2.0 2.51000

1100

1200

1300

1400

1500

1600

JetSurF 2.0

0.4% C2H4/1.6% CO2, =0.3

Time [ms]

Tem

pera

ture

[K]

GRI-Mech 2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.3

0.6

0.9

1.2

1.5

Nonreactive CRV

Time [ms]

Pre

ssur

e [a

tm]

Weak pressure fluctuation due to ignition

0.4% C2H4/1.6% CO2,=0.31130K, 1.0 atm

• Confirmation of CRV Approach2nd Example: C2H4 Ignition, Temperature and OH

• CRV & conventional filling data agree at at high T

• CRV yields longer delay times at lower T than conventional filling

• CRV provides true constant H, P data, conventional data are difficult to model


0.8 1.0 1.2 1.40.1

1

10 CRV Strategy Conventional Filling

1-butanol/air20 atm, = 1.0

All data scaled by P-1

714K833K1000K1250K

1000/T (1/K)

t ign (

ms)

37

• 3rd Example: Low Temperature 1-Butanol Ignition DataComparison of Conventional Filling and CRV Experiments

• CRV & conventional filling data agree at at high T

• CRV yields longer delay times at lower T than conventional filling

• CRV provides true constant H, P data, conventional data are difficult to model


38

• 3rd Example: Low Temperature 1-Butanol Ignition DataComparison of Conventional Filling and CRV Experiments

0.8 1.0 1.2 1.40.1

1

10 CRV Strategy Conventional Filling

1-butanol/air20 atm, = 1.0

714K833K1000K1250K

1000/T (1/K)

t ign (

ms)

Solid Line:Sarathy et al. (2012)

Current models are in agreement with CRV constant P data!

Next: Shock Tube Applications with Lasers

Elementary Reactions Multi-Species Time-Histories

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