Lecture 11: Shock Tube Techniques/Applications
Motivation: Shock tubes with lasers is a chemical kinetics research frontier!
1. Introduction to Shock Tubes 2. Vibrational Relaxation 3. Ignition Studies 4. Advances in Shock Tube Modeling 1. Introduction to Shock Tubes
Pressure Detector Diaphragm transducers
4 1 2 1 5 High PLow P Driver section Driven section (high‐pressure) (low‐pressure) Laser
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
2 1. Introduction to Shock Tubes
Incident Shock Pressure Detector Diaphragm transducers
1 2 5 High PLow P Driver section Driven section (high‐pressure) (low‐pressure) Reflected shock Laser
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
3 1. Introduction to Shock Tubes
Pressure Detector Diaphragm transducers
1 2 5 High PLow P Driver section Driven section (high‐pressure) (low‐pressure) Reflected shock Laser
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)
4 1. Introduction to Shock Tubes
1900 1920 1940 1960 1980 2000
1970’s: First use Primary uses 1899: Vieille 1940’s: of lasers for • Astrophysics/ (France) first US/Canada/GB species detection comets shock tube mine safety, (Stanford/Ames) constructed shock-induced • Blast waves (e.g. explosions, nuclear aerodynamics 1960’s: re-entry explosions) studies • Chemical kinetics • Gasdynamics/ 1950’s: first aerodynamics applications to high-temperature • Heat transfer chemical kinetics (radiation + (CalTech) convection) • Spectroscopy
5 1. Introduction to Shock Tubes
1-D Shock Wave Theory Laboratory-fixed coordinates
p p p p 2 V 1 2 V 5 T2 s T1 T2 r T5 ρ2 ρ1 ρ2 ρ5 v2 v1 = 0 v2 v5 = 0
Incident shock Reflected shock
Incident shock speed governed by Boundary condition u5 = 0 diaphragm burst pressure determines the speed of the reflected shock
All Region 5 conditions governed by incident shock speed
See Gaydon and Hurle
6 1. Introduction to Shock Tubes
Shock Jump Values
P2/P1 P5/P2 WR/WS 2.95 10 4.95 2.62 1.76 3.82 2.82 0.423 7/5 6.56 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 0.589 5/3 6.34 50 5.54 13.4 2.37 3.72 2.31 0.517 6.00 2.40 4.00 2.50 0.500
100
100 ) ) 1 1 /P /T 5 5 10
(or T (or (or P (or 1 1 /T /P
10 2 2 T P P /P ( 5 1 T5/T1 ( P /P ( T /T ( 5 1 5 1 P /P ( T /T ( 2 1 2 1 P /P ( T /T ( 2 1 2 1 1 1 246810 246810 M S M S 7 1. Introduction to Shock Tubes
Test Time in Reflected-Shock Experiments
Particles are stationary behind the reflected shock:
Expansion lab time = particle time Wave Test time is limited by the reflected Test Contact Time shock interaction with the contact Surface surface
Typical test time ~ 1-3 ms
t Reflected
Time, Shock
Incident Shock a2 a3 Position, x
Diaphragm Test Location 8 1. Introduction to Shock Tubes
Test Time in Reflected-Shock Experiments
Tailored driver gases optimize the reflected-shock-contact surface, Expansion increasing the test time Wave Tailored test times 10 ms Test Contact Time Surface t
Reflected
Time, Shock
Incident Shock Position, x
Diaphragm Test Location 9 2. Vibrational Relaxation
Molecular energy depends on inter-nuclei Recall our previous lectures on spacing and fundamental frequency the vibrational energy in diatomic 1 ukxxrr 2, difference in nuclei spacing from equilibrium molecules 2 e 1 k Use a simple harmonic oscillator ,k spring constant; = fundamental frequency of vibration u(r)model (HO) 2 m
i=5 But energy levels are quantized! i=4 Simple i ih energy in level i i=3 Harmonic i=2 Oscillator Can use Boltzmann statistics (PGD) to determine distribution i=1 i/ T N * e v x *i fractional population in level i i=0 i N 1 Q v /T 1e r hhc 1 with v characteristic vibrational temperature kk R r e v average vibrational energy per molecule v /T e1v
10 2. Vibrational Relaxation
Vibrational energy distribution function (from Boltzmann statistics)
i/ T N * e v 1 x *i fractional population in level i i N 1 Q /T 1e v *
i 0.1 More molecules in lower vibrational levels than high T in high vibrational levels
0.01 Higher energy levels get populated at higher population, x T=300 K temperatures Temperature refers to the vibrational 1E-3 temperature (T = Tv), the same as translational 01234temperature in vibrational equilibrium vibrational level, i If Tv = Ttrans then vibrational energy transfer will occur until the system reaches equilibrium → vibra onal relaxa on!
11 2. Vibrational Relaxation
V-T Energy Transfer
How fast does relaxation occur?
Rate of relaxation follows the Bethe-Teller relationship .E ET* E / v vvtr v t Ev vibrational energy (e.g. per mole, unit mass, etc.)
ETv *tr vibrational energy at translational temperature (i.e. equilibrium)
Vibrational energy (Ev) changes at a rate proportional to deviation from the equilibrium value * (Ev ) Dependencies 1 Relaxation time constant: v /T ZMP1,0 1e
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 ? 12 2. Vibrational Relaxation
Vibrational Relaxation in Shock Tubes Reflected Shock T Ttrans
T5 Incident Shock Tv
. Faster relaxation time behind reflected shock
T2 because temperatures are higher. . Note the equilibrium temperature is lower than the vibrationally frozen temperature
t . Translational temperature is instantaneously increased by the arrival of the incident shock . Test mixture of HO’s . Vibrational temperature needs time to relax starts out in vibrational . V-T energy exchange occurs (and energy must be equilibrium (Region 1) conserved 13 2. Vibrational Relaxation
Shock Tube Studies of Vibrational Relaxation
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
White and Millikan, AIAA Journal 1964.
14 2. Vibrational Relaxation
• 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
15 2. Vibrational Relaxation
Experimental Setup absorbance • Reflected shock absorption experiments -(t) • Beer’s law: (I/I0) = exp(-nv” (Trot, Tvib) = e Reflected • Measure (t) Shock Wave
• Infer nv”(t) and ev(t) Shock-Heated Test Gas Mixture
844 nm IR 211 nm UV
Pump 4th MIRA Laser Harmonic Generator
MIRA operating range: 206-1000 nm Pulse rate: 80 MHz, equivalent to CW Average power: 2-20 mW at 206 nm to 245 nm
How does this relate to O2 vibrational populations? 16 2. Vibrational Relaxation
3 - 3 + • Schumann-Runge O2 system (B u ← X g ) 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
Envelope of rovibronic lines for a specific v”
206 nm: v” = 3 245 nm: v” = 7 211 nm: v” = 4 223 nm: v” = 5 235 nm: v” = 6 17 2. Example O2 Data and Model
• 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 18 2. Landau-Teller Plot
1950K 1166K O2 vibrational relaxation measurements
• Current work in close 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)
Mixture Rule for (1/P)mix = Xj/Pj j
19 3. Ignition Studies
1. Kinetics of branched chain reactions 2. Definition of ignition 3. Examples
20 3.1. Kinetics of Branched Chain Reactions: Basic Mechanism for Hydrogen Oxidation
1HO22 HOH 2 + initiation Net effect of branching is to create radicals 2OH H22 H H O propagation Step 1: HO2 OHO 3 HO2 OHO Step 2: OH H22 H H O branching Step 3: OH OHH 4 OH2 OHH 2 Step 4: OH H22 H H O 5 HO M HOM 22 termination net: H OH223 3 HHOH 2 2 2 ! 68HOOH ,, wall removal by adsorbtion, wall-catalyzed reactions stable species
. Build up of a radical pool during oxidation . This characterizes ignition! . Also exothermic reactions generate heat release/pressure increase 21 3.2. Definition of Ignition Time
5 . Ignition delay time in 4% H / 2% O / Ar 2 2 reflected shock 1124 K, 3.1 atm 4 Pressure experiments: time = 170 s ign between passing of the 3 reflected shock and onset of ignition 2 . Onset of ignition: linearly
Pressure [atm] 1 extrapolating the point of Relative Emission Relative ign = 170s steepest rise back in time to 0 OH* emission the pre-ignition baseline -100 0 100 200 300 Time [s]
. Measure through P5(t) and OH*(t) emission at 306 nm (A-X) . Close agreement of pressure and emission measurement
22 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
23 4. Advances in Shock Tube Methods
1. Extended drivers & tailored gas mixtures for longer test times
2. Driver inserts for improved spatial and temporal uniformity
3. New approaches to reactive gas modeling 4.1. Extended drivers & tailored gas mixtures for longer test times
• Conventional shock tube operation: ~ 1-3 ms test time • No overlap with RCM operation~ 10-150 ms test time
1000 2500K 1000K 625K 10atm10atm 100 RCM
10
1 Unmodified Stanford ST 0.1 n-Dodecane/Air 0.01 =1
Test Time,Test Time, Ignition Ignition Time Time [ms] [ms] 1E-3 0.4 0.8 1.2 1.6 1000/T [1/K]
25 4.1. Extended drivers & tailored gas mixtures for longer test times
• Longer driver length and tailored gas mixtures can provide longer test times (50+ ms)
1000 2500K 1000K 625K 10atm 100 RCM
10 Modified ST
1 Unmodified Stanford ST 0.1 n-Dodecane/Air 0.01 =1
Test Time, Ignition [ms] Time 1E-3 2x Driver Extension 0.4 0.8 1.2 1.6 1000/T [1/K] • Shock tubes now can overlap with RCMs 26 4.2. Driver inserts for improved spatial and temporal uniformity
• Problem: boundary layers and attenuation induce dP/dt and dT/dt that change ignition dP/dt= 3%/ms times dT/dt= 1.2%/ms
P5 T VRS 5
• Solution: Driver inserts that modify flow to achieve uniform T and P at long test times 27 4.2. Driver inserts for improved spatial and temporal uniformity
Result: dP/dt=0 prior to ignition
Improved ign for comparison with simulations
P5 T VRS 5
• Solution: Driver inserts that modify flow to achieve uniformExample: T and Propane P at long Ignitiontest times 28 4.2. Driver inserts for improved spatial and temporal uniformity
• Modifications yield improved ignition delay times for propane
1250K 1111K 1000K 0.8% C H / O / Ar 3 8 2 = 0.5, 6 atm Const. U,V 10 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) CHEMSHOCK (dP/dt=12%/ms) Mechanism: JetSurF v1.0 (2009) Ignition Time [ms] 1
0.8 0.9 1.0 1000/T [1/K]
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 29 4.3. New approaches to reactive gas modeling
Reactive Gasdynamics Modeling: The Problem
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 4.3. New approaches to reactive gas modeling
• Effect of Energy Release on P Profiles: n-Heptane Oxidation
5
0.4% Heptane/4.4% O2/Ar, =1 4 1380K, 2.3 atm 4 Measured 3 Sidewall P 2 Constant P 2 Model Pressure [atm] 1 ign
0 0 -100 0 100 200 300 400 500 600 Time [us] • This is not a Constant P process! 31 4.3. New approaches to reactive gas modeling
• Effect of Energy Release on P Profiles: n-Heptane Oxidation
5
0.4% Heptane/4.4% O2/Ar, =1 Constant V 4 1380K, 2.3 atm 4 Model Measured 3 Sidewall P
2 Constant P 2 Model
Pressure [atm] 1 ign
0 0 -100 0 100 200 300 400 500 600 Time [us] • This is not a Constant P process! • Also not a Constant V process! • So how can entire process be modeled? 32 4.3. New approaches to reactive gas modeling
• Proposed Solutions to Enable Modeling through Entire Combustion Event
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 4.3. New approaches to reactive gas modeling
• Constrained Reaction Volume (CRV) Approach
Conventional Shock Tube Constrained Reaction Volume
Pre-Shock Pre-Shock
Helium Test Mixture Helium Non-Reactive Mix TM
Post-ReflectedPost-Incident Shock Shock Post-ReflectedPost-Incident Shock Shock
Reflected Shock Wave Large Region of Small Region of Energy Release Energy Release
• Large reaction volume gives large energy release P & T • CRV gives reduced energy release near-constant P • Also eliminates any question of remote ignition! 34 4.3. New approaches to reactive gas modeling
• Use of Constrained Reaction Volume (CRV) Approach 1st Example: Hydrogen Ignition at 950 K
Conventional Shock Tube Constrained Reaction Volume
8 8 4%H -2%O -Ar 4% H -2%O -Ar 2 2 2 2 Normal Filling CRV = 4 cm 6 956K, 3.397 atm 6 979K, 3.44 atm Ignition
Pressure 4 4 Pressure Pressure [atm] Pressure [atm] Pressure 2 2
Emission Emission 0 0 012345 012345 Time [ms] Time [ms]
• Conventional ST exhibits large pressure change! • CRV pressure nearly constant throughout experiment! • Allows 1st kinetics modeling through ignition and combustion in non-dilute systems! 35 4.3. New approaches to reactive gas modeling • Confirmation of CRV Approach nd 2 Example: C2H4 Ignition, Temperature and OH
Temperature Pressure 1600 1.5 0.4% C H /1.6% CO , =0.3 1500 2 4 2 Weak pressure fluctuation 1.2 due to ignition 1400 0.9 1300
Nonreactive 0.6 CRV 1200 JetSurF 2.0 Temperature [K] Pressure [atm] Pressure 0.3 1100 GRI-Mech 2.0 0.4% C2H4/1.6% CO2,=0.3 1130K, 1.0 atm 1000 0.0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Time [ms] Time [ms]
Measured T validates CRV approach and illustrates power of T as a kinetics diagnostic
36 4.3. New approaches to reactive gas modeling
• 3rd Example: Low Temperature 1-Butanol Ignition Data Comparison of Conventional Filling and CRV Experiments
1250K 1000K 833K 714K CRV Strategy 10 Conventional Filling
(ms) 1 ign t
1-butanol/air 20 atm, = 1.0 All data scaled by P-1 0.1 0.81.01.21.4 1000/T (1/K)
• 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 37 4.3. New approaches to reactive gas modeling
• 3rd Example: Low Temperature 1-Butanol Ignition Data Comparison of Conventional Filling and CRV Experiments
1250K 1000K 833K 714K CRV Strategy 10 Conventional Filling Solid Line: Sarathy et al. (2012)
Current models are in
(ms) 1 ign agreement with CRV t constant P data! 1-butanol/air 20 atm, = 1.0 0.1 0.81.01.21.4 1000/T (1/K)
• 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 Next: Shock Tube Applications with Lasers
Elementary Reactions Multi-Species Time-Histories