Shock Waves (2013) 23:439–452
DOI 10.1007/s00193-013-0447-6
ORIGINAL ARTICLE
Laser ignition of hypersonic air–hydrogen flow
S. Brieschenk · H. Kleine · S. O’Byrne
Received: 9 October 2012 / Revised: 18 February 2013 / Accepted: 15 April 2013 / Published online: 16 May 2013
© Springer-Verlag Berlin Heidelberg 2013
Abstract An experimental investigation of the behaviour
of laser-induced ignition in a hypersonic air–hydrogen flow is
presented. A compression-ramp model with port-hole injection, fuelled with hydrogen gas, is used in the study. The
experiments were conducted in the T-ADFA shock tunnel
using a flow condition with a specific total enthalpy of
2.5 MJ/kg and a freestream velocity of 2 km/s. This study
is the first comprehensive laser spark study in a hypersonic
flow and demonstrates that laser-induced ignition at the fuelinjection site can be effective in terms of hydroxyl production. A semi-empirical method to estimate the conditions in
the laser-heated gas kernel is presented in the paper. This
method uses blast-wave theory together with an expansionwave model to estimate the laser-heated gas conditions.
The spatially averaged conditions found with this approach
are matched to enthalpy curves generated using a standard
chemical equilibrium code (NASA CEA). This allows us to
account for differences that are introduced due to the idealised description of the blast wave, the isentropic expansion
wave as well as thermochemical effects.
Keywords Hypersonic flow · Supersonic
combustion · Radical farming · Autoignition scramjet
Communicated by K. Hannemann.
S. Brieschenk (B)
Centre for Hypersonics, The University of Queensland,
Brisbane 4072, Australia
e-mail: s.brieschenk@uq.edu.au
H. Kleine · S. O’Byrne
The Australian Defence Force Academy,
The University of New South Wales, Canberra 2600, Australia
e-mail: h.kleine@adfa.edu.au
S. O’Byrne
e-mail: s.obyrne@adfa.edu.au
Planar laser-induced fluorescence imaging · Plasma-assisted
combustion · Laser-induced ignition · Laser-induced plasma
(LIP) · Laser spark ignition · Enthalpy-matching
1 Introduction
Scramjet engines typically operate in autoignition mode,
where the flow temperature at the combustor entrance
exceeds the hydrogen autoignition temperature and spontaneous ignition occurs upon mixing with the fuel after
an ignition delay time τign . Figure 1a illustrates such a
configuration. An isolator is typically necessary for dualmode ram/scramjet configurations and scramjets operating at
speeds below Mach 8 [38]. Locating the fuel injection site further upstream increases the fuel-mixing length, enhances the
air–fuel mixing due to baroclinic torque effects and allows for
radical farming [2,29] to enhance ignition and combustion.
Such a configuration is illustrated in Fig. 1b. Spontaneous
ignition of hydrogen fuel, which occurs at Tign = 750–850 K
[22], requires cycle temperature ratios χ ≥3.4 and therefore
relatively high isentropic compression ratios ΠS=0 >80.
The total pressure recovery for hypersonic inlets at Mach 10
flight does generally not exceed pr ≈0.5–0.6 [21,43], with
pressure ratios of the order of Πreal ≈25–50. Reducing inlet
compression in a scramjet reduces non-isentropic compression losses, the risk of boundary-layer separation [17,18]
and inlet unstart. An external energy source, such as a laser
or an electric arc, can be used to ignite the flow in a configuration with low inlet compression, where autoignition
does not occur. A scramjet operating in radical farming mode
where a flow-external ignitor at the fuel injection site generates radicals and reduces the ignition delay is illustrated
in Fig. 1c. The ignitor may also be located further downstream where the unmixedness is lower, as depicted in Fig. 1d.
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440
(a)
(b)
(c)
(d)
Fig. 1 Scramjet vehicle details of a dual-mode ram/scramjet, designed
to operate in autoignition mode (a), a dual-mode ram/scramjet with inlet
injection, designed to operate in autoignition and radical farming modes
(b), a dual-mode ram/scramjet with inlet injection and a flow-external
ignition source located at the injection site (c) and a scramjet designed
to operate in radical farming and shock-on-lip modes with external
ignition in the combustor (d)
A similar configuration was proposed by Carrier et al. [5],
where a premixed gas is ignited by LIP generated at high
frequency.
The aim of the research conducted in this study is to investigate the effect of laser-induced plasma (LIP) [30] for ignition in a hypersonic flow using a configuration similar to
Fig. 1c. This paper presents new results regarding the effect
of laser-energy deposition on ignition and combustion in a
hypersonic flow. Laser ignition has the potential to fill a gap
in the methods of initiating a combustion process in a hypersonic flow that other methods cannot adequately address.
The key objective in ignition and combustion enhancement lies in either reducing the activation threshold using
catalysts or providing a minimum amount of specific energy
to overcome the activation threshold of a particular combustion reaction and hence, force combustion to occur sooner
or at increased rate. In terms of electromagnetic bandwidth, resonant excitation using lasers represents the narrowest and hence most effective means for specific energy
deposition whereas thermal, broadband heat addition represents the least effective method. Combustion is a process
of electron exchange and therefore, augmentation effects
of electronic nature are observed when applying electric
fields and providing additional electrons, either directly using
a discharge or, through photon interactions, using lasers.
Methods for ignition enhancement, using external energy
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S. Brieschenk et al.
sources [41], include direct electric discharges in the combustible medium [8], electric discharges in a plasma buffer
gas (plasma torches) [42], microwaves [20] and lasers [40].
Optical ignition using lasers can be grouped into four categories, laser thermal ignition, laser photochemical ignition,
non-resonant LIP/spark ignition and resonant LIP/spark ignition [46].
Laser thermal and photochemical ignition appear to be
promising methods at first sight, as ignition is achieved
without ionisation of the gases. The absorption of photons with a wavelength of λ<7–10 μm can cause thermal ignition in a hydrogen–air mixture, however, coupling
infrared/microwave photons into gaseous fuel/air mixtures
is difficult as symmetric molecules such as H2 , O2 or N2 do
not have dipole moments and are transparent to these wavelengths. Photochemical ignition does not cause ionisation and
produces little direct heating of the gas [33], representing an
energy-efficient method for laser ignition. Dissociating H2 or
O2 using single-photon excitation, however, requires ultraviolet wavelengths below λ<250 nm. These circumstances
leave, using currently available technology, no effective pathway for laser thermal and/or photochemical ignition using a
practical laser system that could be flown on-board a flight
system.
For successful ignition, where a self-propagating flame
front is generated, the form of energy deposition appears to
be of secondary importance, and the ignition criterion can
be defined by simply the amount of energy deposited in the
gas [33]. By focusing a powerful laser, thermal-equilibrium
plasma can be formed with core electron temperatures up to
100,000 K [16] using non-resonant excitation. This allows
the use of energy-efficient, high-power laser systems as the
wavelength is no longer dictated by spectral absorption considerations. The laser beam must be focussed to a point and
therefore, laser energy can be deposited precisely where it is
most effective for promoting ignition. For these reasons, ignition is provided by a non-resonantly generated LIP/spark for
the experimental study presented in the following sections.
This study focusses on using LIP to provide ignition to
a hypersonic air–hydrogen stream. Laser energy deposition
can be useful for a number of different applications that are
closely related to the content of this paper. LIP can be used for
drag reduction when generated upstream of a vehicle [34],
for flameholding in supersonic combustors and for triggering deflagration-to-detonation transitions, with the potential
of rendering the combustion process more efficient due to
the increased thermal efficiencies of detonation-wave cycles
[45,47].
The purpose of this paper is the estimation of temperatures and pressures in the laser-heated gas kernel, the ignition results of this study have been published before [4]. The
conditions in the laser-heated gas kernel are estimated using
blast-wave theory together with an enthalpy-matching pro-
Laser ignition of hypersonic air–hydrogen flow
cedure. This requires knowledge of the gas composition at
the focal point of the laser-focussing optics, the laser energy
absorbed in the plasma and the geometry of the laser spark.
The determination of these parameters is the focus of the
subsequent sections of this paper.
2 Experimental arrangement
441
Table 1 Flow condition parameters, averaged over a 1 ms test time.
Uncertainties refer to the run-to-run variations in the shock tunnel experiments
Total flow properties
h 0 (MJ/kg)
2.5
±0.1
T0 (K)
2,140
±100
p0 (MPa)
13
±0.7
Freestream properties
2,075
±55
Ma∞ (−)
equi
5.7
±0.5
t/r
Ma∞ (−)
equi
T∞ (K)
t/r
T∞ (K)
vib (K)
T∞,N
2
vib (K)
T∞,O
2
vib
T∞,NO
(K)
9.0
±0.6
u ∞ (m/s)
2.1 The T-ADFA free-piston shock tunnel
The experiments described in this paper were conducted
in the free piston shock tunnel at the University of New
South Wales, Australian Defence Force Academy (T-ADFA).
The facility is operated in reflected-shock mode with the
freestream generated by a 7.5◦ half-angle conical nozzle with
a 203-mm diameter exit and a 12.7-mm diameter throat. Gas
conditions in the stagnation region are calculated by solving the inviscid, ideal-gas, normal shock equations [28] for
the initial and reflected shock waves. This is done numerically using the ‘Equilibrium Shock Tube Code’ (ESTC)
[26]. The flow condition used for this study is under-tailored
[3], and the shock speed is chosen such that the calculated
peak stagnation pressure matches the measured peak stagnation pressure. ESTC accounts for high-temperature effects
using the appropriate chemical equilibrium compositions
and thermodynamic properties of air [23]. Using the total
conditions in the stagnation region, the freestream properties are calculated using the one-dimensional, inviscid nozzle code ‘Shock Tube’ (STUBE) [44]. STUBE accounts for
thermal and chemical non-equilibrium in the nozzle flow.
Table 1 outlines the flow condition used for the laser ignition experiments where h 0 , T0 and p0 are the total specific flow enthalpy, the total temperature and the total pressure, u ∞ , Ma∞ , T∞ , p∞ and ρ∞ are the freestream velocity, Mach number, static temperature, pressure and density
of the flow. The superscripts equi and t/r represent equilibrium and transrotational-vibrational nonequilibrium condivib , T vib
vib
tions, respectively. T∞,N
∞,O2 and T∞,NO refer to the
2
frozen vibrational temperatures of nitrogen, oxygen and
nitric oxide. The subscript ramp refers to estimated flow properties behind the oblique leading-edge shock wave. Due to
the flow divergence, the flow properties change with downstream distance. The properties given in Table 1 are obtained
133 mm downstream of the nozzle exit, which corresponds to
the position half-way along the compression ramp during the
experiment.
2.2 Compression ramp model and instrumentation
The compression ramp model for the laser ignition experiments is illustrated in Fig. 2. The ramp is angled 9◦ to the
freestream and the fuel injectors are inclined 45◦ to the com-
325
±25
130
±10
1,740
±70
930
±20
295
±10
p∞ (Pa)
720
±50
ρ∞ (g/m3 )
18.8
±1.4
Approximate compression ramp
flow properties
u ramp (m/s)
2,000
equi
Maramp (−)
t/r
Maramp (−)
equi
Tramp (K)
t/r
Tramp (K)
equi
pramp (Pa)
t/r
pramp (Pa)
4.6
6.5
470
240
2,260
3,820
pression ramp surface. A Ludwieg tube supplies the hydrogen
fuel injected through port holes in the compression ramp. In
the experiment, LIP is formed in the shear layers immediately downstream of four transversely orientated port hole
injectors. The port holes are separated by 10 mm and located
120 mm from the leading edge on the compression ramp.
Figure 3 illustrates the injector and laser-delivery system.
The LIP is formed in the shear layers 1.7 mm downstream
of four port hole injectors, which are distributed across the
compression ramp. The laser accesses the flow through a
3-mm diameter open port located mid-way between the two
inner port hole injectors. We will show later in the paper
that the LIP is located outside of the barrel shock structures.
There are several reasons why the laser ignitor is located in
this region of the flow, namely:
– The LIP is located in the expansion region of the underexpanded fuel injectors. This opens the possibility of igniting the entire fuel jet, i.e. from its upper to its lower boundaries, even though the initial plasma kernel only measures
few millimetres in height.
– Mixing at the injector site is poor, however, locating the
ignitor at the injector site maximises the time available for
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442
S. Brieschenk et al.
Fig. 3 Fuel injector details for shear-layer laser ignition experiment
Table 2 Choked conditions in the fuel injector
Injector flow condition
Number of injectors
Fig. 2 Experimental arrangement (to scale), top drawing represents
side view, bottom drawing represents top view
the radicals, which are generated by the ignitor, to interact
with the oxygen in the flow.
– The flow turbulence at the chosen focal point is lower than
the turbulence in the mixing layer further downstream,
making it easier to form a LIP spark.
– This configuration allows the ignitor to be integrated into
the fuel injector.
When applied to a flight vehicle, the cavity between the
port hole and the lens would be pressurised with hydrogen
to prevent hot air from the boundary layer to deteriorate the
laser-focusing lens. There is no need for an optical access
window, and the port hole can be used for film cooling [13]
and skin friction reduction [39]. This, however, is not necessary for testing in short-duration impulse facilities. The laser
is focussed using a 100-mm focal length lens. The vertical
position of the LIP can be adjusted by translating the lens
carrier, and is adjusted such that the focal spot of the laser is
located 8 mm above the ramp surface. This results in a distance between the plasma kernel and the combustor floor of
2 mm (this can be seen later in Fig. 5). The choked flow conditions in the sonic fuel injectors are given in Table 2. The
Ludwieg tube was filled to a pressure of p L T =2,600 kPa at
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4
∅injector (mm)
2
Injection angle (to inlet surface)
45◦
p LT (kPa)
2,600
±3
±3
pplenum (kPa)
2,000
T ∗ (K)
229
p ∗ (kPa)
1,052
ρ∗
(kg/m3 )
a ∗ (m/s)
1.11
1,155
γ (−)
1.4
Cd (−)
0.88
ṁ (g/s)
4 × 3.6
φ (−)
>3
±0.02
an ambient temperature of 298 K. T ∗ , p ∗ , ρ ∗ and a ∗ refer to
the temperature, pressure, density and speed of sound in the
sonic throat of the injector. Cd is the discharge coefficient
and φ represents the global equivalence ratio in the scramjet
experiment.
A Q-switched ruby laser (λ=694.3 nm) with a pulse duration of 30–40 ns is used to initiate the plasma. Several weak
O2 absorption lines are present within the lasing wavelength.
Their influence on absorption, however, is only small and
hence, the LIP is formed using primarily non-resonant radiation. Pulse energies of 750 mJ are used in this experiment.
The laser operates in multiple transverse and longitudinal
modes and is guided into the fuel injector through a series
of dichroic mirrors and an optical feed-through port in the
Laser ignition of hypersonic air–hydrogen flow
shock tunnel test section. The laser is focused using a spherical lens in the fuel injector, causing optical breakdown at the
focal spot.
2.3 Optical diagnostics
Planar laser-induced fluorescence (PLIF) [12] on the hydroxyl
(OH) radical was used for combustion visualization. Only a
brief introduction to the technique and its implementation
will be given here, a more complete description can be found
elsewhere [10]. The experimental arrangement of the PLIF
system is depicted in Fig. 4. A Lambda Physik Scanmate II
dye laser operated with Rhodamine 6G dye is used with a
frequency-doubler to generate tunable UV laser radiation.
The dye laser is pumped using the second harmonic of a
Spectraphysics GCR4 Nd:YAG laser. A H2 /air calibration
flame is used for frequency calibration. The laser sheet is
formed using a convex cylindrical lens (30 mm focal length)
followed by a convex spherical lens (1,000 mm focal length).
443
A fused silica plate is used as a beam splitter to record
the intensity distribution of the UV laser sheet by guiding
the sheet onto a dye cell with a methanol/Rhodamine 6G
mixture. A MicroPix 1024 CCD camera captures the sheet
profile and allows the PLIF images to be corrected for spatial sheet-nonuniformity and shot-to-shot variations in laser
energy. The UV fluorescence is captured using a Princeton Instruments intensified charge-coupled device (ICCD576-S/1) camera with a UV-Nikkor 105 mm f/4.5 lens. A
WG 305 filter is used together with the UG 5 filter to protect the ICCD camera from scattered laser radiation. OH is
excited from the ground electronic state X 2 Π , ground vibrational state v = 0 and J =7.5 rotational state via the Q Q 11
transition into their first electronic state A2 + , first vibrational state v =1 and J =7.5 rotational state. Laser radiation
at 283.22 nm is required for this transition to occur. This transition is chosen because its line strength is relatively insensitive to temperature. The line strength of the Q Q 11(J =7.5)
transition increases by only ≈20 % from 1,500 to 3,500 K.
The OH fluorescence signal, therefore, is mostly a function
of OH concentration.
Flow visualisations were also obtained using PLIF on the
nitric oxide molecule (NO). NO is generated upon stagnation of the flow in the facility nozzle reservoir, and is chemically frozen in the expanding nozzle flow, allowing NO PLIF
experiments to be performed. For NO PLIF, the dye laser was
operated with Coumarin 2 dye and pumped with the third
harmonic of the Nd:YAG laser. Frequency calibration was
performed using a calibration cell filled with pure NO. The
WG 305 filters are then removed from the experiment.
A standard Z-type arrangement was used for the schlieren
visualizations with 3-m focal length spherical mirrors. During the early stages of the laser ignition process, luminosity
images were obtained using either a Vision Research Phantom v701 camera or a Shimadzu Hypervision HPV-1 camera.
A Minolta 50 mm f/1.2 lens was used on both cameras, with
an object distance set to 450 mm. All images presented in this
paper are adjusted in contrast, brightness and color range for
clear appearance.
3 Results and discussions
3.1 Compression ramp flowfield
Fig. 4 PLIF system for imaging flowfield at the injector site with ruby
laser excitation system
A schlieren visualisation of the flowfield on the compression
ramp is depicted in Fig. 5. Flow features at their approximate
locations are superimposed as a line drawing. The underexpanded hydrogen fuel jet expands into the crossflow forming
a barrel shock (7) which separates the upstream boundary
layer (2, 3) creating recirculation zones in the front of the
jet (4). A recirculation zone (8) forms in the wake of the jet,
with a weak recompression shock (9) forming further downstream.
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S. Brieschenk et al.
Fig. 5 Flow field on
compression ramp, taken from
[4]. The LIP is located in the
shear-layers between the central
two fuel injectors
Fig. 6 NO PLIF image of jet fluorescence caused by mixing with
cold H2 . The superimposed (white) curve indicates locations where the
fluorescence signal is zero. Fluorescence observed downstream of the
superimposed curve, i.e. the right-hand side, is caused by mixing with
cold H2
The LIP is formed in the shear layers mid-way between
the two central fuel injectors (Fig. 3a). Upon laser initiation,
plasma formation is initiated at the focal point, located 8 mm
above the ramp surface. During the laser pulse, the plasma
quickly grows towards the laser source within the laser beam.
This results in a plasma bubble which is typically ellipsoidal
in shape, measuring about 6.5 mm in height and 2 mm in
diameter. The plasma kernel is superimposed on the schlieren
image depicted in Fig. 5.
The LIP is generated in the air–flow mid-way between the
two central fuel injectors. Some hydrogen is shed into this
region, which was qualitatively visualised using NO PLIF.
The R R11 R Q 21 (J = 1.5) doublet transition is selected as it
yields a signal only where cold NO molecules are present.
This allows for a qualitative visualisation of the fuel mixedness at the location where the laser spark is generated. The
NO PLIF image is depicted in Fig. 6. The stream is heated
as it passes through the leading-edge shock wave and the
123
jet interaction shock waves causing the NO signal to extinguish. Fluorescence downstream of these locations can only
occur if the NO is cooled, which can only happen through
mixing with cold hydrogen gas. The locations where the signal is zero are indicated by a curve in Fig. 6. Strong mixing
is observed downstream of the fuel injectors and only little
mixing is observed at the location where the laser spark will
be generated in the laser ignition experiment. The NO PLIF
visualisation suggests that the laser spark is generated outside
the barrel shock structures, primarily in air, with relatively
small amounts of mixed H2 . It will be shown later in the
paper, that H2 concentrations as high as 50 % in the focal
region of the laser beam do not alter the estimated temperatures and pressures of the laser-heated region. For this reason,
absolute species concentration measurements in the region
of the waist of the laser beam were not deemed necessary.
3.2 Laser ignition experiments
Plasma is luminous due to plasma recombination resulting
in continuum radiation [11], recombined plasma is luminous due to radiative de-excitation and recombinations of
atoms into molecules for multiatomic species. Plasma continuum radiation cannot be filtered out spectrally and hence,
PLIF visualisations were not obtained at early time delays.
Two sequences of the luminosity images, superimposed on
schlieren images, are depicted in Fig. 7. The presented images
are obtained at 106 frames per second with an exposure time
of 500 ns. Several sequences were acquired during the experimental campaign. With all sequences being near-identical,
it is concluded that despite the turbulence of the flow at the
injector site and the random elements involved in the LIP formation process, the early evolution of the luminosity cloud is
repeatable (Fig. 7). The size of the luminosity cloud measures
Laser ignition of hypersonic air–hydrogen flow
445
Fig. 7 Plasma/gas luminosity
in the laser ignition experiment,
superimposed on schlieren
visualisations. Images extracted
from two experimental runs.
Sequences recorded using the
Shimadzu Hypervision HPV-1
camera
≈ 10 mm in the horizontal direction at 1 μs delay. At 1 μs
delay, the luminosity from the spark and shock wave spans up
to 3 mm upstream and 8 mm downstream from the focal waist,
corresponding to a bulk motion of around 2,000 ms−1 which
is equal to the flow speed on the compression ramp upstream
of the injection ports. At delay times of 2 μs and later, two
protrusions develop in the luminosity cloud on the upper and
lower extremes. These are the regions in which the longest
luminosity lifetimes are found. The luminosity signal extinguishes in the centre of the luminosity cloud, which effectively splits the cloud into two separate clouds at later delay
times (>3 μs). The shape of the early plasma core is resolved
by taking time-integrated images with reduced camera sensitivity as depicted in Fig. 8a. The dimensions of the plasma
core are measured from these recordings to 6.5±1 mm in
height and 2.0±0.5 mm in width. Figure 8b depicts an image
where the exposure time started 3 μs after LIP generation,
with an integration time of 21 μs. The higher UV sensitivity
of the camera used for these images (Phantom v701) reveals a
strong luminosity signal in the rear recirculation zone (‘8’ in
Fig. 5), extending up to 30 mm downstream of the injectors,
which is not captured in the time-resolved images of Fig. 7.
The OH PLIF technique is employed to yield conclusive
combustion-diagnostic data for delay times >12 μs. Secondary experiments, where no laser sheet was introduced
into the test section, were conducted to ensure that the signal recorded with the PLIF system is indeed OH fluorescence and not luminosity arising due to plasma recombination or radiative de-excitation.1 The evolution of the OH
signal has been shown elsewhere [4]. The strong turbulence
1
LIP generated in laboratory air, that has some humidity, also shows
OH emission signals [31]. In the shock tunnel experiments presented
here, dry air is taken from compressed gas cylinders to ensure that OH
arises exclusively due to air–hydrogen combustion.
Fig. 8 Self-luminosity in the shear-layer laser ignition experiment,
superimposed on schlieren visualisations. The camera sensitivity for
image (a), which depicts the plasma core, was reduced by a factor of
5,000 using neutral density filters
of the flow, and to a lesser degree the stochastic nature of
spark-ignition [24], result in an inhomogeneous spatial OH
distribution that shows significant variation from one tunnel
run to the next as shown in Fig. 9. The flame stretches from
the upper to the lower boundaries of the fuel jet, which in this
setup is the entire combustor height. The laser-ignited region
measures between 5 and 15 mm in width and increases in
width as it convects downstream. An integrated OH signal is
introduced here as a qualitative parameter, representing the
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S. Brieschenk et al.
Fig. 10 Integrated OH fluorescence signals from 11 different
experiments
Fig. 9 Fluorescence of the OH radical, 17 μs after generation of LIP,
for three experimental runs
spatially integrated, total OH signal at a particular delay time
and experiment. Because of the limited number of shock tunnel runs available for the experiment, the spatially integrated
OH fluorescence signals are shown for repeat runs of the
facility to provide an indication of the run-to-run variability
in the integrated OH signal. The evolution of the integrated
OH signal is depicted in Fig. 10. The integrated OH signal
appears to decrease with time, suggesting that OH is consumed by the combustion process.
3.3 Laser energy requirement for LIP generation
A ruby laser with a nominal pulse energy of 750 mJ (typical
run-to-run variations are ±110 mJ) was used to generate a
LIP in the shear layers. Losses from optical elements in the
beam delivery system are accounted for, hence this energy
represents the energy past the focusing lens. This energy was
123
found to be a threshold value and a further reduction would
not result in a laser spark. Due to the operation of the laser
near threshold energy, laser-breakdown and ignition is not
observed for all experiments conducted [6]. Four out of 25
conducted shock tunnel runs (16 %) did not result in a laser
spark after the laser was fired. Operating close to threshold
energy implies that a significant portion of the laser energy
is simply transmitted through the focal region unable to contribute to plasma formation [7,32]. This is due to the low gas
densities at the focal spot, which require high photon fluxes
for multiphoton ionization to initiate the plasma formation
process [1]. For a laser with a symmetric temporal profile,
the portion of energy transmitted through the focal region is
equal to the portion contributing to the LIP when operating at
threshold. Once lasing is initiated, the photon flux increases
until the maximum irradiance is reached, where half of the
photons have been lost through the focal waist. At maximum
laser irradiance, the intensity threshold is reached and multiphoton ionization renders the focal waist opaque to the laser
beam due to the generation of free electrons and hence, the
second half of the photons are contributing to the LIP formation [7]. More intense laser radiation allows the plasma to
form earlier in the pulse history and a greater proportion of the
laser energy can thus be absorbed. Test cell experiments were
conducted in order to determine the energy portion contributing to the LIP formation process for the current laser system.
With a laser energy of 500 mJ, the threshold pressure in air
was found to be 14 kPa, with the laser pulse energy being
1.85 ± 0.10 times greater compared to the energy absorbed
in the LIP. The fact that this number is less than two can
be attributed to pulse-to-pulse laser energy fluctuations as
well as to an asymmetric temporal laser profile. The test cell
calibration data is shown in Fig. 11. Using the test cell cal-
Laser ignition of hypersonic air–hydrogen flow
447
thermal conductivity are neglected and the change of state
of the fluid is assumed adiabatic. Due to these assumptions,
blast wave theory only gives approximate results, and we will
present an enthalpy-matching procedure later in the paper
that allows us to yield more accurate estimations of the postspark conditions. The obtained self-similar solutions are only
weakly dependent on parameters such as the charge of the
explosive or background pressures. The general solution for
the propagation of a blast wave, where R(t) represents the
distance from the origin with time, can be written as a power
series equation [35–37]
2
4
2 R0 ν
C
C
1
C
= J0 1+λ1
+ λ2
+· · ·
U
R(t)
U
2
U
(1)
Fig. 11 Ratio between laser energy and energy absorbed in LIP. Data
obtained from test cell experiments with laser energies of 500 mJ in air
ibration data, the energy absorbed in the LIP calculates to
405 ± 65 mJ for the 750 ± 110 mJ used in the tests. The focal
spot size in the ignition experiment is limited by the divergence of the laser. With a divergence of 0.5 mrad, the focal
spot size2 becomes 50 μm, and the breakdown threshold for
the ignition experiment can be estimated to ≈ 40 kJ/cm2 or
≈1×1012 W/cm2 for a 40 ns pulse. Using the observed flame
width at a delay time of 17 μs (Fig. 9) and the post-shock
velocity on the compression ramp, the period between individual laser pulses required to form a continuous stream of
OH is ≈10 μs, translating to laser pulse frequencies of the
order of 100 kHz. Having determined, from the test cell data,
the amount of laser energy absorbed to form the LIP, the conditions of the plasma/gas kernel can be estimated as outlined
in the following sections.
3.4 Estimation of plasma spark conditions
The following analysis is presented in order to estimate the
plasma/gas conditions which can be used to simulate the current experiment using computational fluid dynamics without
having to model the early time-regime characterised by the
plasma formation process and the shock wave propagation.
This is done by applying blast wave theory using the data
obtained from the experiment.
Blast wave theory treats the compressible flowfield with
variable entropy, due to the large gradients in observed shock
wave velocities, which is infinite at zero radius and reduces
to the speed of sound for large radii [35–37]. Viscosity and
2 The diffraction-limited focal spot size calculates to 10 μm, and the
spot size due to spherical aberration of the focussing lens calculates to
33 μm.
where C is the speed of sound in the surrounding gas, U
the speed of the shock wave, J0 , λ1 , λ2 , . . . are numerically
determined constants and ν describes the symmetry of the
blast wave. For LIP, where the laser energy is deposited along
a line, the propagation of the laser-driven shock wave can be
accurately described by a cylindrical blast wave [16], for
which ν = 2. The length scale R0 arises due to the finite
background pressure p of the gas. For cylindrical blast waves
the length scale is [16]
1
2
E abs
(2)
R0 =
12π pL
where E abs is the laser energy absorbed by the LIP and L is
the length over which E abs is absorbed. For ν = 2, the second
order solution of (1) can be approximated by [35,36]
1
2
− 21
2 2
R(t) = 2R0 C J0 t − λ1 C t
(3)
or
R(t) =
1
2
K1 t − K2t
1
2
2
(4)
where
4
4R02 C 2
m
γ E abs k B T
=
J0
3π J0 p L m gas s 2
λ1 γ k B T m 2
2
K 2 = λ1 C =
m gas
s2
K1 =
(5)
For diatomic gases with γ = 1.4 and a cylindrical symmetry, the constants are J0 = 0.877 and λ1 = − 1.989 [36].
The particle mass of the ambient gas, given in (kg) is represented by m gas , k B (JK−1 ) is the Boltzmann constant and
T (K) is the temperature of the ambient gas. The early size
of the LIP has been determined in the luminosity experiment
to be 6.5 mm in height and 2.0 mm in width. Assuming that
the shock wave initially travels with the same velocity in all
directions, the line focus is obtained by subtracting the cylin-
123
448
Fig. 12 Cylindrical shock wave radius R(t) for pure H2 , pure air
and a 50 % air/50 % H2 mixture. A calculation where the parameter
E abs /( p L) is taken as half the original value is also shown
drical radius, here 1 mm, from either side. The length L along
which the laser energy of E abs = 405 mJ is deposited is therefore taken as 4.5 mm. Solutions for R(t), assuming different
H2 concentrations are shown in Fig. 12. The gas pressure p
and temperature T are taken as the equilibrium parameters
on the compression ramp, given in Table 1. The exact gas
pressure at the focal spot is not known, but its influence on
R(t) is only small as indicated by 2. The same is true for the
absorbed energy E abs and the absorption length L.
This is demonstrated in Fig. 12 with a calculation where
the parameter E abs /( p L) is taken as half the original value.
At high H2 concentrations, the computed R(t) curves do,
as expected, not coincide with the experimental data point
obtained from the luminosity experiment. The temperature
behind the laser-driven shock wave TS , as a function of the
shock wave radius R, is shown in Fig. 13. These temperatures were calculated using the Rankine–Hugoniot equation
for a normal shock wave assuming equilibrium chemistry
[25]. The calculation is performed for three different initial
gas compositions, pure air, pure H2 and a 50 % air, 50 %
H2 mixture. The computations show that the plasma core,
where the temperature exceeds 10,000 K, extends to about
2 mm in diameter regardless of the H2 concentration at the
focal spot. This is consistent with the luminosity experiment
(Fig. 8), where the strong radiating plasma core was measured to have a cylindrical diameter of 2.0 ± 0.5 mm. At the
dissociation and ionization temperatures of the individual
species, the TS (R) curves exhibit strong curvatures, with the
temperatures decreasing at much slower rates once the shock
wave has decelerated sufficiently to not cause dissociation of
the diatomic species. The flowfield is essentially divided into
123
S. Brieschenk et al.
Fig. 13 Computed temperature TS behind laser-driven shock wave as
a function of shock wave radius. Concentrations refer to initial concentrations before laser-energy deposition
a relatively hot core and a relatively cold gas field due to these
chemical effects. The computations in Fig. 13 also indicate
that the pre-spark H2 concentrations at the focal spot only
play a minor role—the curves are very similar for pure air
and H2 . This is due to the fact that H2 , N2 and O2 have very
similar volumetric heat capacities. The temperature TS represents the peak temperature occurring immediately behind the
shock wave front. Blast waves are shock waves followed by
isentropic expansion waves, and hence, the peak temperature
TS at a given radius R quickly decreases with time. Temperature and pressure far from the origin of an explosion will be
the same before and after the passing of the blast wave [48],
due to the fact that the shock wave at large distances has decelerated to a compression wave travelling at Mach 1 and hence,
has the same strength as its accompanying expansion wave.
At distances close to the origin of the explosion, the postshock temperature decrease follows a power law [48]. For
gases with γ ≤ 1.67, the flow behind the shock front is supersonic for pressure ratios Π ≥ 8, and for γ ≤ 1.40, Π ≥ 4.6,
respectively. In those cases, it is assumed that no gas-dynamic
information is transmitted from the shock wave front back to
the core. The reduction of the temperature behind the shock
wave due to the interaction with the expansion wave is therefore approximated using the isentropic relationship
T (r ) = TS (R)
r 2 (γ −1)
γ
R
(6)
where r is the coordinate between the line focus and the shock
wave front of radius R. For the cylindrical blast wave discussed here, the flow behind the shock wave is supersonic up
to a radius of R = 18 mm. Figure 14 depicts the temperature
distribution behind the shock wave approximated using (6)
Laser ignition of hypersonic air–hydrogen flow
449
Fig. 14 Evaluation of the temperature distribution T (r ) behind shock
wave at various shock wave radii R
for effective values for γ computed using NASA CEA [25].
Figure 14 only depicts the temperature distributions assuming an initial H2 concentration of 50 %, but the curves are
very similar for pure air and pure H2 . Various studies have
found different spatial profiles for temperature and pressure
within the plasma/gas kernel [9,27]. For a computational
fluid dynamics calculation, these profiles may be chosen arbitrarily, as long as the total enthalpy remains unchanged. Due
to this reason, average values for the temperature and pressure within the plasma/gas kernel are found for the following
analysis. At a shock wave radius of R = 5 mm, the cylindrical
blast wave theory, coupled with the chemical equilibrium calculation of the post-shock flow properties, predicts an average temperature T2 of 4,300 K and a pressure p2 of 730 kPa
inside the shock-wave-enclosed volume V . The expansion
wave reduces the temperature and pressure to 3,300 K and
122 kPa, respectively. The cooling effect of the expansion
wave is only weak, due to the low effective values for γ ,
which can be as low as γ = 1.1 for the gas mixture at temperatures in the range of 3,000–15,000 K. Average temperature
Table 3 Gas parameters
obtained from blast wave theory
assuming an initial gas mixture
of 50 % air and 50 % H2
and pressure values for the LIP at various delay times are
given in Table 3.
For temperatures below 3,500 K, air–hydrogen mixtures
release heat due to combustion. This analysis does not
take this heat release into account. Chemical equilibrium is
assumed throughout this analysis, but the combustion reactions between hydrogen and air are assumed frozen. The values given in Table 3 refer to the gas conditions after heating
by the shock/blast wave. Any of the spark conditions given
in Table 3 may be used to simulate the laser spark in a timeaccurate computational fluid dynamics (CFD) simulation.
The spark conditions at shorter delay times can give more
physically accurate results, but the spark pressures for these
conditions will generate shock waves, implying greater computational efforts. The spark condition at t = 8.35 μs, with an
average temperature of 1,000 K and an average pressure of
14 kPa, can be patched into a CFD simulation with relative
ease, but the heat release observed in the CFD simulation
will be somewhat delayed as compared to using any of the
earlier spark conditions.
The conditions given in Table 3 are only approximate,
due to the assumptions and boundary conditions associated
with blast wave theory as well as the extension of the coupled expansion wave (6). An enthalpy-matching procedure
is therefore performed to adjust the values given in Table 3
such that the enthalpy of the gas volume V , considering equilibrium chemistry, matches the energy absorbed in the LIP,
which was measured in the gas cell experiment. Given is the
control volume V , with the initial temperature T1 and pressure p1 before laser initiation. The laser induces a plasma in
the centre of volume V upon which a blast wave forms. The
absorbed laser energy E abs is used to heat the gas through
multiphoton dissociation, multiphoton ionization, electron
impact ionization and shock heating. Once the shock wave
has propagated to the boundaries of the control volume,
the average temperature and pressure inside volume V have
increased to T2 and p2 , respectively. Since the control volume V has not changed in size, the density ρ1 is equal to
the average density ρ2 , as the change of state is essentially
isochoric. The change of energy d E enclosed by volume V
is therefore given by
t (μs)
0.14
0.84
3.20
8.35
R (mm)
2
5
10
17
V (cm3 )
0.06
0.35
1.42
4.10
Past laser-driven shock wave
T2 (K)
8,200
4,300
2,200
1,300
p2 (kPa)
3,200
730
230
100
Past shock and expansion wave
exp
T2
(K)
7,800
3,300
1,700
1,000
exp
p2
(kPa)
710
122
35
14
123
450
S. Brieschenk et al.
Fig. 15 Increase in enthalpy of gas cloud as a function of temperature
d E = dU + V dp;
(7)
d E = V (ρcv dT + dp)
where dU is the inner energy, cv is the heat capacity at constant volume and dp is the change in pressure. For fluid
dynamic computations, the LIP is commonly approximated
with a region of increased temperature and pressure [15],
and therefore, the kinetic energy of the flow inside volume
V is deliberately not treated as an explicit parameter in (7).
Integration of (7) with substitution of cv = c p − R gives
⎛
⎞
T2
T2
⎜
⎟
E = V ⎝ρ c p dT − Z R dT + p2 − p1 ⎠
(8)
T1
T1
The compressibility factor Z [14,19], which scales linearly with the specific gas constant R, is introduced here to
account for non-ideal gas behaviour due to repulsive intermolecular forces at high temperatures. Equation 8 can be
rearranged using the isochoric relationship p2 = (T2 /T1 ) p1
and the ideal gas law to
⎛
⎞
T2
T2
E
1
⎜
⎟ T2 − T1
=
(9)
⎝ c p dT − Z R dT ⎠ +
V p2
Z 1 R1 T2
T2
T1
T1
A portion of the laser energy is lost through radiation, and
hence
E rad
(10)
E = E abs 1 −
E abs
Equation 9 is independent of p1 and only requires the
knowledge of the initial temperature T1 , since Z 1 and R1 are
functions of T1 . Radiative losses E rad /E abs in LIP have been
123
evaluated to 22–34 % at relatively small values of E abs = 15–
50 mJ [32]. For higher absorbed laser energies E abs , radiative
losses may be as large as the energy used to drive the shock
wave, i.e. <50 % of E abs .3 More than half of the absorbed
laser energy is typically used to drive the shock wave, and
less than 10 % of the absorbed energy is available to cause
ignition [32]. The parameter E/(V p2 ) (mJ cm−1 kPa−1 ) of
the gas cloud is plotted against the average temperature T2 in
Fig. 15. The computation is performed for various initial gas
mixtures (air, H2 and a 50 % air, 50 % H2 mixture) using the
equilibrium temperature on the compression ramp (Table 1)
for T1 . The value of T1 , however, has only a small influence
on the curves plotted in Fig. 15 and when using the transrotational temperature on the compression ramp for T1 , the results
are similar. The conditions behind the shock wave (Table 3)
yield, as expected, values of E/(V p2 ) lower than those predicted by (9). These data points are denoted with index I in
Fig. 15. This is due to the overestimated pressure, which, for
these data points, is equal to the pressure immediately behind
the shock front. The conditions calculated by accounting for
the expansion wave through (6) yield more realistic values
for E/(V p2 ). These data points are denoted with index II in
Fig. 15. They overestimate E/(V p2 ) at lower temperatures
and underestimate E/(V p2 ) at higher temperatures. For the
lower temperatures, this can be explained by the fact that for
blast wave theory, an absorbed laser energy of 405 ± 65 mJ
was used, rather than a reduced value according to (10).
For the higher temperatures, E/(V p2 ) is underestimated,
which can be explained by the fact that for early delay times
and small volumes V , the kinetic energy of the gas behind
the blast wave is significant and should not be neglected.
The enthalpy-matched data points, denoted with index III in
Fig. 15, are obtained by adjusting the pressures p2 of the data
points II , given in Table 3. The enthalpy-matched data points
are listed in Table 4. Radiative losses are assumed as 40 %,
resulting in an energy of 243 mJ for increasing the enthalpy
of the gas cloud. The additional enthalpy release due to the
combustion is not included in this analysis, however, this is
not an issue when using gas conditions where T2 ≥ 2,800 K,
since no heat is released in air/H2 mixtures above this temperature.
4 Conclusions
A compression ramp model with port-hole injection was used
to experimentally study the behaviour of laser-spark ignition.
Time-resolved luminosity imaging indicated a rapid growth
of the LIP within the first microsecond after laser initiation
due to the laser-driven shock wave. The luminosity cloud
was found to break up into two separate regions, travelling
3
Detailed energy balances for laser sparks can be found elsewhere [32].
Laser ignition of hypersonic air–hydrogen flow
Table 4 Enthalpy-matched gas
parameters for laser-heated gas
region
451
Past laser-driven shock wave
E (mJ)
405
405
405
T2 (K)
8,200
4,300
2,200
1,300
p2 (kPa)
3,200
730
230
100
E
V p2
2.1
1.6
1.2
1.0
E (mJ)
405
405
405
405
exp
T2 (K)
exp
p2 (kPa)
ΔE
−3 kPa−1 )
V p2 (mJ cm
7,800
3,300
1,700
1,000
710
122
35
14
9.5
9.5
8.2
7.1
(mJ cm−3 kPa−1 )
405
Past shock and expansion wave
Enthalpy-matched, corrected pressures p2
E rad /E abs (−)
0.4
0.4
0.4
0.4
E (mJ)
243
243
243
243
T2 (K)
7,800
3,300
1,700
1,000
LIP generated in air (IIIa)
E
V p2
(mJ cm−3 kPa−1 )
p2 IIIa (kPa)
18.1
6.7
3.1
2.4
224
104
55
25
LIP generated 50 % air, 50 % H2 mixture (IIIb)
Enthalpy matching is performed
by adjusting pressure p2
E
V p2
(mJ cm−3 kPa−1 )
p2 IIIb (kPa)
along the shear layer behind the injector bow shock. The LIP
is generated in the expansion region of the fuel injectors and
the experiments have shown that this configuration allows the
LIP to generate OH from the upper to the lower boundaries of
the fuel jet, although the initial plasma kernel only measures
few millimetres in height. The period between individual
laser pulses required to form a continuous stream of OH is
evaluated as ≈ 10 μs, translating to laser pulse frequencies of
the order of 100 kHz. The turbulence of the flow at the injector
site and the random elements involved in the LIP formation
process do not seem to influence the early evolution of the
plasma/luminosity cloud.
Relatively high laser energies of the order of 750 mJ were
used to ignite the shear layers due to the high LIP threshold energy of the current laser system at low gas densities
and the turbulent flow at the spark location. A significant
portion of the laser energy is transmitted through the focal
region, and is unable to contribute in the plasma formation process. Only 54 % of the laser energy is absorbed
by the LIP in the current experiment, but the laser energy
requirement was only of secondary concern and several techniques exist to decrease the energy requirement in future
experiments.
Blast wave theory has been used together with a simple
expansion wave model, which assumes the flow behind the
laser-driven shock wave to be supersonic. The method presented accounts for equilibrium chemistry and the conditions
calculated using blast wave theory coupled with the expansion wave yield enthalpies of the same order of magnitude
14.5
10.7
3.1
2.4
280
65
55
25
as those predicted by NASA CEA. To account for the differences that are introduced due to the idealised description
of the blast wave, the isentropic expansion wave as well as
thermochemical effects, an enthalpy-matching procedure has
been performed. The theoretical analysis has shown that the
cooling effect of the expansion wave is only weak, due to
low effective values for γ at high temperatures and therefore, enthalpy-matching has been performed by altering the
pressures of the conditions in the laser-heated gas kernel.
The estimated conditions of the laser-heated gas kernel can
be used for future computational fluid dynamic simulations
of this experiment without having to model the early timeregime characterised by the plasma formation process and
the shock wave propagation.
Acknowledgments The authors gratefully acknowledge the mechanical workshop at the Australian Defence Force Academy as well as the
outstanding technical and scramjet design support received from Paul
Walsh and Gianfranco Foppoli.
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