Verification of detailed Simulations for Two-Stage Ignition
of Single Droplets by Ignition Radius
S. Schnaubelt, M. Tanabe(1), C. Eigenbrod, H. J. Rath
ZARM, Center of Applied Space Technology and Microgravity,
University of Bremen, Am Fallturm, 28359 Bremen, Germany
(1)
Department of Aerospace Engineering, Nihon University,
Narashinodai 7-24-1, Funabashi, Chiba 274, Japan
The self-ignition process of single n-heptane droplets in the two-stage ignition regime (600-1100 K,
0.3-1 MPa) was numerically investigated with a detailed 62-step chemical model for n-heptane (437
elementary reactions, 92 species) where special attention has been paid on the low temperature
branch. This detailed numerical simulations presents results for both ignition delay and ignition radius.
Thus beyond the standard validation for the numerical model by ignition delays a further parameter is
the comparison of ignition radii. This comparison of ignition radii was carried out with interferometric
measurements done with a Michelson interferometer under microgravity conditions at Drop Tower
Bremen. As result of this study all experimental and simulated ignition radii are of the same order of
magnitude and within the estimated error. A calculus of potential errors has been done carefully.
Keywords: two-stage ignition; detailed simulation; droplets
Introduction
All known numerical models for the two-stage self ignition process were mostly verified by the
comparison of first (τ1) and total (τt) induction times between experiment and simulation.
τ t = τ 1 ( T ) + τ 2 ( p)
physics (d, V)
>>
chemistry
(1)
chemistry (kinetic)
influence of
>>
physics
Equation 1 depicts the relation between the induction times. The low temperature reactions, which
are determined from the physics (i.e. evaporation, transport properties, geometry) lead to a
temperature increase (cool flame, measured with the first induction time τ1) and activate the hightemperature reactions so that a hot flame occurs. The second induction time τ2 depends almost only
on the chemical kinetics. Figure 1 depicts the two-stage temperature rise and the appropriate cool
flame and hot flame ignition radii. The maximum temperature is cut off in this diagram for a better
representation of the region of interest.
Space Forum, pp. 299-306, 2000 (Proceedings of Drop Tower Days, Sapporo, 1998)
2
Tmax ≈ 2000 K
hot flame ignition
cool flame ignition
FIGURE 1:
Temperature history over time and radius. Simulation, n-heptane, Ta =600K, p a =5bar, d0=0.7mm
Due to interferometric measurement of ignition processes under microgravity conditions at Drop
Tower Bremen [1] by a Michelson Interferometer it is possible to measure ignition delay times and
ignition radii. The determination of the ignition radii from the interferograms is shown in Figure 2. So
there is a further parameter to validate the numerical model.
rc
rh
(a) rc =1.7mm
FIGURE 2:
(b) rh=1.3mm
Interferogram of (a) cool flame and (b) hot ignition. n-heptane, Ta =600K, p a =5bar, d0=0.7mm
The present work compares results from experiments on single n-heptane droplets under microgravity conditions at ambient pressures pa= 5 bar and ambient temperatures Ta= 600 - 800 K with
the appropriate numerical simulations.
Model Description and Experimental Setup
A spherical droplet of liquid n-heptane with an initial temperature T0≈ 300K and diameter d0≈ 0.7
mm is rapidly (t =120 ms) inserted into a hot pressurized combustion chamber with uniform
temperature Ta and pressure pa. Figure 3 depicts the experimental setup.
Up to now the cool flame ignition is experimentally determined by the instant when the temperature
rises above ambient temperature, caused by low temperature reactions. The hot ignition is marked
by a very high temperature gradient. The temperature field is evaluated by a Michelson
interferometer with a He-Ne laser (632.8 nm) of 1.2 mW as light source where the light beam is
expanded to a parallel beam of 15 mm in height. All experiments were recorded with a high speed
camera with a time resolution of 500 frames per second [2].
He - Ne LASER
Beam splitter
Mirror
3
Gas exhaust
gas
exhaust
heater
Heater
controler
controller
Mirror
beam
splitter
T.C.
1
T.C.1
Heatinsulator
insulator
heat
Heater
heater
Glas window
glas window
T.C.11
T.C.
Amp.
amplifier
Mirror
mirror
suspender
Suspender
T.D.
traverse device
Needle
needle
T.C.2
T.C. 2
T.D.
T.D.
controler
controler
T.C.2
T.C.
Amp.2
amplifier
C.C.D.
C.C.D.
Camera
camera
Fuel supply
fuel
supply
Gas supply
gas
supply
D.G.
droplet
controler
generator
controler
Needle
needle
controler
controler
M
T.D.: Traverse Device
T.C.: Thermocouple
FIGURE 3:
Schematic model of the experimental setup
In the numerical model mass and energy conservation for the liquid and gas phase is considered. In
the gas phase also species conservation and equation of state by Peng-Robinson is included. Vapor
pressure and latent heat are calculated by fugacity equilibrium and all liquid and gas phase properties
are calculated temperature and pressure dependent. A complex 62-step reduced reaction kinetic
(437 elementary reactions, 92 species, [3]) with special attention to the low temperature branch was
used for the present results. The numerical criteria for detecting the cool flame (temperature T)
T(τc) ≥ Ta + 10 K
(2)
and hot ignition (temperature gradient in time ∂T/∂τ)
∂T/∂τ (τt) ≥ 107 K/s
(3)
are chosen for the comparison with the experimental results.
Results and Discussion
Five microgravity experiments (pa= 5bar, d0=0.7mm, Ta= 600K,650K,700K,750K,800K) were
done at Drop Tower Bremen and evaluated concerning their ignition radii. There can be seen a
reasonable agreement between experimental and numerical results for both cool and hot flame
ignition. The comparison of the ignition radii from cool flame ignition and hot flame ignition is shown
in Figure 4 and Figure 5 respectively. All calculated and measured ignition radii are of the same order
and within an estimated error, which is discussed later.
The simulations show at those conditions where the cool flame behavior is most intensive that the
ignition radius for the cool flame has a minimum. After an ambient temperature of about Ta≈ 640 K
the hot flame ignites always at nearly the same radius. Despite these results new measurement
techniques like LIF are necessary for a more detailed understanding and review of the described
phenomena.
4
3,0
ignition radius [mm]
R_c, Experiment [mm]
R_c, Simulation [mm]
2,0
1,0
0,0
550
FIGURE 4:
600
650
700
temperature [K]
750
800
Comparison of cool flame ignition radii between experiment and simulation.
n-heptane, p a =5 bar, d0=0.7mm.
3,0
ignition radius [mm]
R_h, Experiment [mm]
R_h, Simulation [mm]
2,0
1,0
0,0
550
FIGURE 5:
600
650
700
temperature [K]
750
800
Comparison of hot flame ignition radii between experiment and simulation.
n-heptane, p a =5 bar, d0=0.7mm.
Aside from the experimental uncertainties [1] the error bar is determined by two main factors, the
inaccuracy by determining the radii from interferogram (Figure 2) and the assumption of the place of
ignition (Figure 6).
For finding the center of the droplet as well as the center of disturbance caused by the temperature
rise, in the interferograms a uncertainty (U) of 1mm is assumed. To conclude from the projection to
the original experimental order of magnitude (scaling factor fS), an error
e1 = 2⋅U⋅fS = 0.6 mm
(4)
arises.
The Michelson interferometer observes a two-dimensional temperature field with high temperature
and time resolution. Deviations for the place of ignition in the axis of the line of sight are not visible for
this process. In all interferograms the place of ignition was measured within a cone of a maximum half
opening angle of ϑ= 15° (Figure 2, Figure 6) in the upper region of the droplet.
5
ϑ = 15°
e2
r
ϑ
line of sight
droplet
suspender
FIGURE 6:
Error due to deviation in the axis of line of sight.
r: measured radius in interferogram
Therefore a maximum error
e2 ≈ r ⋅ ϑ ⋅ sinϑ ≈ 0.068 ⋅ r ≅ 6.8%
(5)
for radius r occurs. This error is about an order of magnitude less than that induced due to the
inaccuracy by determining the radii from interferogram, so it is neglected here.
Responsible for this observation is a temperature non-uniformity in the combustion chamber
(approximately 1 K/mm in the vertical direction and less in the horizontal one) and the cooling
influence of the suspender. Compared with numerical simulation this disturbance has been clarified to
be very small on droplet evaporation rate and it is small for ignition process as well.
Conclusions
The developed numerical model is additionally verified by comparison with measured ignition radii.
This procedure of comparing not only ignition delays but also ignition radii has to be done for other
one component fuels like n-decane as well as for two component model fuels [4]. Further
investigation of ignition radii will be done in future investigations by modern laser diagnostics like LIF
or LIPF at Drop Tower Bremen.
Acknowledgements
The research was funded within the DROP-COS project by the DLR (DARA), Germany
(FKZ 50 WM 9448)
References
[1]
[2]
[3]
[4]
Tanabe, M.: Ph. D. Thesis, ZARM, 1996
Tanabe, M.; Kono, M.; Rath, H.J.: Comb. Sci. and Tech., 108: 103-119 (1995)
Rath, H.J.: DROP-COS Research Project, 1997
Eigenbrod, C.; Rath, H.J.: 28th Int. Annual Conf. of Fraunhofer Inst. (1997)