7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
3D Simulation of the Production of Gasphase synthesized Nonaggregated
Spherical Nanoparticles in Continuous Gasdynamic Flow
Giglmaier Marcus, AIHasan Nisar S. and Adams Nikolaus A.
Lehrstuhl fur Aerodynamik, Technische Universitat Mtinchen,
D85747 Garching, Germany
marcus.giglmaier@aer.mw.tum.de
Keywords: gas dynamics, nanoparticles, aerosol modeling, CFD
Abstract
The scope of this work is the predictive simulation of particles properties produced by a novel process of "Gasdynamically
induced nanoparticle synthesis" (Grzona et al. 2007). We provide and analyze fully coupled 3D simulations of the entire
gasdynamic flow and of particle growth including injection and mixing of a precursor, ignition delay, heat release, formation of
monomers and coagulation. The governing equations for the flow are the 3D timedependent Favreaveraged NavierStokes
equations for compressible mixtures of gases. For the simulation of particle growth, we investigate an efficient bimodal
monodisperse model based on the work of Kruis et al. but extended by an additional mode for the monomer concentration
(AlHasan 2010). The particlesizes predicted by the 3D CFD simulation are validated against experimentally obtained results
for the generator facility. In particular, we analyze the sensitivity of the processes with respect to operation condition variations,
such as stagnation conditions, precursor mass flow and wall cooling. We provide a detailed insight into the complexity of this
novel process of gasphase synthesized, nonaggregated nanoparticle generation, and display the potential of coupled 3D
NavierStokes/particlegrowth simulations as tool for the design and analysis of innovative particleproduction processes and
particle reactors.
Introduction
Within the ongoing research project "Gasdynamically
induced particle synthesis" a novel method for the
production of gasphase synthesized, nonaggregated
spherical nanoparticles is being developed (Grzona et al.
2007). A low degree of particle aggregation is required in
particular for manufacturing electronic devices, ceramics
and composites (Pratsinis 1998). Especially for dental nano
composites nonaggregated silica nanoparticles are of great
interest (Mueller et al. 2004). The production of
nonaggregated spherical particles is typically achieved by
wet chemistry but tends to be costly and to have limited
scaleup capability (Pratsinis and Mastrangelo 1989).
Furthermore, the crystalline particle phase may not be
obtained in low temperature processes, and the thermal
stability is reduced (Wegner and Pratsinis 2003). The
disadvantage of gasphase synthesized particles in large
scale production, e.g. flame synthesis, is the broad size
distribution due to the inhomogeneous flow conditions and
due to a large degree of endproduct aggregation
(Pratsinis 1998) as consequence of too low temperatures for
full coalescence and/or low cooling rates.
The key idea of the novel process is to provide homogeneous
thermodynamic conditions for particle growth with nearly
instantaneous ignition of the precursor, a constant time of
particle growth and high cooling rates with dT/dt=O(107)
K/s in order to suppress agglomeration. For this purpose a
doubly chocked Lavalnozzle system as shown in Fig. 1 is
used. The carrier gas is accelerated to supersonic speed
within the first Laval nozzle. A gasdynamic shock leads to
an instantaneous rise of the static temperature and thus to the
ignition and the decomposition of the precursor. Within the
reactor part with constant cross section, downstream of the
first Laval nozzle, particle growth occurs at constant
thermodynamic conditions (T=1300 K, p=6bar). After a
growth time of about t 02102 s the particleladen carrier gas
is reaccelerated to supersonic speed within the second Laval
nozzle. Due to high acceleration the static temperature
decreases below the sintering temperature within
At=O(104) s, and particle dynamics, i.e. coagulation and
coalescence, are instantaneously suppressed. Downstream of
the second Laval
supersonic flow is
Schaber 2010).
nozzle, the total temperature of the
reduced by water injection (Rakel and
Figure 1: Sketch of the reactor for "Gasdynamically induced
particle synthesis"
A
cp
d
f
h
M
n
p
S
St
T
t
V
x
Greek
letters
6
'U
Subscripts
area (m2)
heat capacity at const. pressure (Jkg' K 1)
diameter (m)
frequency (s')
height (m)
Mach number
number concentration (kg')
pressure (Nm 2)
saturation
Strouhal number
temperature (K)
time (s)
volume [m3]
axial position (mm)
collision frequency (kg s')
boundary layer thickness
efficiency
heat transfer coefficient (W m 1)
viscosity (Pa s)
density (kg m3)
dimensionless time, stress tensor
0 stagnation condition
1 monomer
50 mean diameter
c coagulation
P particle
s sintering
SiO2 silicon dioxide
TEOS Tetraethoxysilan
tot total mass
Design of the pilot facility and process description
The pilot facility was designed by 3D reactive CFD
simulations that provided a detailed insight into the full
process. Figure 2 shows a numerical simulation of the
doubly choked Laval nozzle system. The shock position is
determined by the critical cross sections AI* and A2* and the
overall losses due to heat release, wall cooling and friction.
As the ignition of the precursor is initiated by the
temperature rise across a gasdynamic shock, 3D simulations
of all thermodynamic conditions of the transonic flow are
required to predict the particle growth correctly. The overall
length of the setup is 1600 mm, and the inlet conditions are
at a stagnation temperature of T..,= 14i K and at a
stagnation pressure of po= 10 bar. At the first minimum cross
section A1*=88.8 mm2 at x=0, the flow reaches sonic speed,
i.e. Mach number M=1, and accelerates further downstream
to supersonic flow speed. The static temperature (red curve)
drops to a minimum of 880 K at x=196 mm. At that position
a pseudo shock system with a preshock Mach number
M=1.8 forms and decelerates the flow to subsonic conditions.
The precursor TEOS (Tetraethoxysilan) is injected into the
flow shortly upstream of the first throat (fig. 1). The
Nomenclature
U
U
A, = 88.8 mm' I I[N I I A
700 1200 1400
i particle growth
ignition delay heat release
igtn'dlar decomposition temperature along axis
1162 K 
1200 mixing 1415 K
9 0 0 n L t e u l a
300 particle diameter along axis
0 200 400 600 800 1000 1200 14(
6 0:2 0:8 2:8 6:6 12.4 18.4 24
Figure 2: Dominating phenomena during "Gasdynamically
induced particle synthesis"
The particle size is controlled by a adjustable length of the
reactor and thus of the dwell time of the particles. To
suppress instantly the growth process, the flow is
reaccelerated from subsonic to supersonic speed through the
second Laval nozzle. This acceleration leads to a drop of the
static temperature below the sintering temperature with a
cooling rate of dT/dt=7106 K/s. Downstream of the second
throat, the total temperature is reduced by water injection
into the supersonic flow.
A basic layout was developed by analytical calculations and
substantially improved by 3D numerical simulations
(AlHasan 2010). The resulting geometry was constructed
and built as a pilot facility (fig. 3).
Figure 3: Pilot facility (Dannehl et al. 2008), overall length
l=2m, pore burner with Pmax=150 kW, pmax=15 bar,
Tmx=1500 K
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
mixinglength from the injector to the pseudoshock system
is 200 mm in order to ensure mixing of the precursor and the
carrier gas. The rise of the static temperature across the
gasdynamic shock leads to the ignition of the precursor.
After the ignitiondelay time, the decomposition of the
precursor starts and Si02monomers are formed. Due to the
high supersaturation of S>>O(103), each monomer is a
critical nucleus and nucleation does not take place. The
particles grow by coagulation and coalescence. The
uniformly high temperature of the carrier gas allows a
uniform particle growth along the reactor.
M 1r.
o 1.0 2.0 2.7
= 138.5 mm'
d ,[10" m]
50
T 40
30
inching 20
10
0o 1606
.4 27.0O
W
Ef~
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
In order to predict accurately the particle size assuming
spherical particles it is necessary to consider the interaction
of gas dynamics with precursor reaction and particle growth
(AlHasan 2010). The governing equations for the flow field
are given by the common 3D time dependent compressible
NavierStokesequations.
a, p+V.pu =0
pu+V.(u pu)= V p+V. + pf,
8, pe + V (peu)= V q, V pu + V zm + pfu + pqb
We assume that particle dynamics do not affect mass and
momentum transfer. The heat release of the reacting
precursor is taken into account as a source term for the
energy. For a proper representation of turbulent secondary
flow and flow anisotropy, an Explicit Algebraic Reynolds
Stress Model (EARSM) is used (Wallin 2000). The mixing
of the gaseous precursor with the carrier gas is modelled by a
passive scalar.
pnEOS + V (nTEOS)= nTEOS k
We assume that mixing processes are dominated by
turbulence and that we can neglect diffusion and
thermophoresis. The decomposition of the precursor TEOS
starts after the ignition delay (Abdali et al. 2007). The
decomposition rate is prescribed by the Arrheniusequation
(Herzler et al. 1997). The decomposition of TEOS
corresponds to the production of monomers.
8, pn, + V (pnn,)= +p nTs k
P 0", n, p p n n,
Sink terms describe the loss of monomers due to Brownian
coagulation. The collision frequency P is calculated by the
transition scheme of Dahneke (Dahneke 1983). The small
particle size of dp<100 nm renders turbulent coagulation
negligible.
For the production and growth of particles, the number
concentration and the total volume are balanced.
1 1
8, pnp+V(pinp)=2 p, n2 p p p
2 2
a, pV, + V (pVp)=o p01 n2 V + p *, p n, *n V,
The balance of the surface area for describing sintering
(Koch and Friedlander 1990, Kruis 1993) is neglected as
purely spherical particles are found in the experimental
facility. The known sintering times are not applicable to our
process, due to the strong dependence of silica particles on
surface hydroxyl groups (Ehrmann et al. 1998). They need to
be fitted by parameters (Tsantilis et al. 1999) to allow for a
particlesize dependence.
The flow field is simulated with the commercial tool Ansys
CFX and extended by the particle model via Fortran user
routines.
The particle model is validated by application to a generic
test case. The computed particle diameter is compared to
experimentally obtained data from a microwave driven
plasma particle reactor (Abdali et al. 2009) (fig. 4).
sampling
MWAntenna pipe oven (1073 K) quartz tube position
A 
TEOS
particle filter
Figure 4: Sketch of the plasma reactor (Abdali et al. 2009)
In the experiment, a gaseous mixture of Argon and Oxygen
(mAr=6.310 kg/s, mo2=2.410' kg/s) is used as carrier gas,
and TEOS is used as precursor (mTEos=l%'mtot). The
mixture is injected into a quartz tube and a microwave
antenna produces plasma that leads to the ignition of the
precursor. The pipe oven downstream of the antenna ensures
a constant wall temperature of Tw=1073 K. The pressure is
incrementally increased from 4102 bar to 7102 bar.
Consequently, the flow velocity decreases, and the residence
time for the particles increases.
In a first step a 1D flow with constant thermodynamic
conditions and fixed residence time (Abdali et al. 2009) is
assumed. In a second step, the 3D flow with heat supply and
the wall temperature of the pipe oven and heat conduction of
the quartz tube are taken into account. Due to the short
residence time of the flow within the microwave antenna, the
phase change to plasma is negligible. The energy increase is
efficiently realized by adding a source term to the energy
equation that is equal to the power supply of the microwave
antenna, i.e. the efficiency is assumed to be T=100%. The
simulation as well as the experiment demonstrates that the
variation of the power supply has negligible effect on the
particle diameter. A comparison of the experimentally
obtained particle diameter with the calculated diameter is
showed in fig. 5, the calculated temperature distribution in
shown in fig. 6.
dp [104m]
1.5 F
1.20
1.07
 0.98
2.00
1.95
1.90
1.75
V1.63
I1.ss55
1.48
1.35
1 1.30
* 1D Simulation
* 3D Simulation
A Abdali et al. (2009)
o%0
70 p [10bar]
Figure 5: Comparison of simulation and experiment
Numerical scheme / Particle model
Validation
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
To1=1300 K
mTEOS=1 %'mtot
d, [108 m]
Ar+ 02+TS Tw=1073K
Temperature [K]
Figure 6: Photograph of the plasma reactor of Abdali et al.
and the simulated temperature distribution inside.
The temperature plot in fig. 6 shows that the temperature
within the quartz tube is quasi homogeneous. The
temperature of the gas is slightly higher then the wall
temperature due to the heat release of the precursor.
Sensitivity of particle growth
A sensitivity analysis of all relevant factors based on well
known correlations for the particle growth, has been
performed by 1D simulations. The analysis agrees well with
3D simulations and especially with the experimentally
obtained results (fig. 7 ac, AlHasan 2010). Ignition delay is
not considered for comparing particle growth.
Figure 7a shows the resulting particle diameter as a function
of pressure p and growth time t at a fixed temperature of
To1=1300 K and a fixed precursor mass fraction of
mTEos=litot. The dominating effect of pressure increase is
an increased collision frequency P due to the increased
density that leads to faster coagulation i.e. larger particles.
The second plot shows the behaviour for a fixed temperature
To1=1300 K and a fixed pressure of pol=10 bar. Coagulation
decays in time proportional to the square of the particle
number concentration, i.e. dn/dtn2. Therefore, particle
growth is slow at low precursor concentrations. With
increasing precursor concentration both, particle diameter
and growth rate, increase.
In fig. 7c the temperature dependence is presented. From
1200 to 1500 K the change of the particle diameter is small,
whereas the particle diameter decreases at t=30103s
between T=1200K and T=1050K from dp=50nm to
dp=5 nm. Sintering is neglected in this calculation to isolate
the particle growth process by coagulation. The reduced
temperature is associated with a reduced characteristic
sintering time, and strongly agglomerated particles are
expected. Within this temperature regime the diameter is
similar to the primaryparticle diameter of the agglomerates.
Nevertheless, the strong temperature dependency of the
precursor within temperature region explains the high
sensitivity of the produced particles to operating conditions,
such as wall temperature. A temperature above T=1300 K
leads to complete combustion of the precursor and is thus
recommendable.
Figure 7: Dominant parameters for particle growth
7 a Particle growth over time and pressure
for T=1300 K and mTEOS= l%i'tot
7 b Particle growth over time and precursor
concentration for T=1300 K and po= 10 bar
7 c Particle growth over time and pressure
for poi=10 bar and mTEOS =l'tot
Kp
Concept and simulation of
"Gasdynamically induced particle synthesis"
The main requirements for the production of spherical
particles with a narrow size distribution are a homogeneous
mixing of the precursor, a constant time interval of particle
growth at constant thermodynamic conditions and an
instantaneous quenching of growth to suppress
agglomeration.
1. Injection and mixing of the precursor
The precursor TEOS is evaporated and injected with
nitrogen into the subsonic part of the first Laval nozzle. The
velocity of the injected gaseous mixture is 100 m/s and the
velocity of the carrier gas from the burner is 500 m/s at that
position. Therefore, the carrier gas dominates the flow field
near the injector and generates an unsteady wake at the
trailing edge. To consider the effect on the mixing of the
precursor and to determine the required mixing length,
several simulations where performed. In fig. 8, a Large Eddy
Simulation (LES Winnem6ller T, AIA Aachen) with a
detailed description of the gaseous components is compared
with an unsteady Reynolds averaged simulation (URANS)
where the injection of TEOS is described by a passive scalar.
In both simulations, the injected TEOS mass flow is one
percent of the total mass flow. The frequency of the induced
vortex shedding is f=0(105 Hz) and obeys to a Strouhal
number of St=0.2 referred to the height of the trailing edge.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
recirculation zones. The occurrence of such a pseudoshock
system affects the concept of shockinduced particle growth,
as for example the length of the shock system reduces the
heating rate. The high degree of turbulence within a shock
system improves the mixing of the precursor. On the other
hand, a strong heat exchange with the side walls cools the
flow. Besides these thermodynamic effects, shock systems
within slightly divergent nozzles exhibit highly unsteady
behaviour and tend to oscillate in both axial and vertical
direction (Gawehn et al. 2009). First simulations showed that
the entire reaction downstream i.e. the particle size is
affected by the axial oscillation. To reduce the standard
deviation of the particle diameter, studies are carried out to
stabilize the shock by active and passive means (AlHasan
and Schnerr 2007).
Figure 9: Machnumber distribution in a so called
pseudoshock system, preshock Mach number M=2.1
3. Fast gasdynamic quenching
A key factor of the novel process is the quenching method.
By reducing the static temperature the characteristic
sintering time zT increase until coalescence is totally
suppressed. Since coagulation is not affected to the same
degree particles can stick together and partial coalescence
leads to agglomeration (fig. 10). The longer this quenching
process takes the more aggregated particles are to be
expected.
GAS PHASE PARTICLE GROWTH A
SPHERICAL
Figure 8: Mixing of the precursor with the carrier gas 
Comparison of LES (top) and URANS (bottom)
To describe the subsequent mixing of the precursor in the
square duct the occurrence of secondary motion, such as the
corner vortices, must be represented correctly. The
disadvantage of the detailed LESsimulation is the high
computational cost to resolve the wall near flow. To simulate
the flow in the entire facility, an Explicit Algebraic Reynolds
Stress Model (EARSM) is used.
2. Shock induced reaction and particle growth
The turbulent shockboundarylayer interaction with a
preshock Reynolds number Rex=9106 and a ratio of
boundarylayer thickness to channel height of 6/h=0.14 at
the shock location causes a series of weak compression and
expansion regions, the so called pseudoshock system
(Matsuo et al. 1999). In fig. 9, a vertical plane with the local
Mach number in the shock system is shown. The streamlines
in the upper half indicate the redirection of the flow due to the
oblique shocks and reflected expansions as well as the
AGGLOMERATE
Sr
NUCLEATION
TIME
Figure 10: Degree of aggregation depending on the
characteristically sintering time zT and the characteristically
coagulation time zT. (Zachariah and Carrier 1999)
A gas dynamic technique is supplied in order to reach
cooling rates up to AT/At=107 K/s. By accelerating the
particle laden flow to supersonic conditions, the static
temperature drops below the sintering temperature within
At=104 s. In contrast to current quenching methods, e.g.
water quenching, the second important advantage of this
method is the homogeneous quenching of the entire flow.
The efficiency of gasdynamic quenching can be seen in
Fig. 11. Here, the Mach number distribution in the second
nozzle and the following coaxial annular gap is shown in a
vertical plane. The temperature distribution is given along
the indicated streamline. The cooling rate is AT/At=7.9106
K/s. At x=70 mm, water is injected through circumferential
nozzles on a slender cone and from the side walls into the
supersonic flow (not simulated here), to reduce the total
temperature of the flow (Rakel and Schaber 2010).
M 27
0 50 100 150 200 250 [mm]
TI[K]
1200  T=1250 K ATAt7.910 KI
100 &T=550 K
8  T=700 K
600 At= 7 10's
0 50 100 150 200 250 x [mm]
Figure 11: Fast quenching of a particle laden flow by
applying gasdynamic technique.
Top: Mach number distribution
Bottom: Temperature on streamline
Results and discussion
A result of the reactive 3D CFD simulation with the coupled
particle model is shown in fig. 12. The boundary conditions
were taken from the experiment. At the inlet, the stagnation
pressure is pol=8.17 bar and the stagnation temperature is
To1=1427 K. The measured wall temperature along the
facility is considered for every part. During the experiment
particles deposit at the cooled wall and reduce the effective
second nozzlethroat cross section. Hence, the pressure at the
end of the reactor p=4.18 bar is used as outlet boundary
condition for the reactor instead of considering the second
Laval nozzle.
The vertical slice (fig. 12a) shows the Mach number
distribution of the flow. Within the primary nozzle, the
carrier gas accelerates to M=1.8. The shock system of the
stationary simulation is shown in the inset. The total
temperature distribution in fig. 12 b reflects the mentioned
effect of a high heat exchange with the cooled side walls.
The rise of the total temperature within the supersonic part of
the first Laval nozzle relates to the mixing of the cold
precursor with the hot carrier gas.
The blue curve shows the static temperature distribution
along the axis. At x=205 mm the static temperature jumps
across the gasdynamic shock from T=905 K to T=1153 K.
The maximum static temperature with Tmax=1242 K is
reached shortly downstream of the shock at x=308 mm.
Once the ignitiondelay time has elapsed, the production of
SiO2monomers (green curve) starts and reaches a maximum
number concentration of n,.mx=7.51019 kg 1.
Consequentially the production of particles starts (red curve)
and reaches np,max=2.71019 kg1. Both concentrations subside
downstream by coagulation.
Figure 12 c shows the calculated pressure distribution and
the measured pressure along the side walls. The simulation
shows a good agreement for both, shock location and
strength.
7th International Conference on Multiphase Flow
ICMF 2010. Tampa, FL USA, Mav 30June 4, 2010
primary nozzle diffuser reactor
A,2' 79 mm'
2y=5.32 M W aM
0 0.5 1 1.5 2
T [K total temperature T,
measured temperature
1200
static temperature T
1000 monomer number concentration n,
particle number concentration n,
u.i
1000
1500
2000 XI
measured pressure
0UU
U.1
1UUU
1,Z
13DUU
o0
boundary conditions at 13:48 h:
calculated dp= 2.6.10 m
13:48 h:
measured dp,= 2.510 m
13:27 h:
measured d ,,= 2.2.10r m
boundary conditions at 13:27 h
calculated dp =2.110" m
1000
1500
2000 x mml
Figure 12: Comparison of simulation and measurement
12 a Mach number distribution within the facility
12 b total temperature To along axis (pink)
static temperature T along axis (blue)
monomer number concentration (green)
particle number concentration (red)
measured temperature (black square)
12 c static pressure p along the wall (blue)
measured pressure (black square)
12 d simulated particle diameter along the axis
boundary conditions 13:48 h (red)
boundary conditions 13:27 h (green)
In fig. 12 d the red curve shows the calculated particle
diameter along the axis. The boundary conditions are taken
from the experiment and correspond to the simulation above
(fig. 12 ac). A maximum diameter at the end of the facility
of dp,max=2.610'8 m is calculated and agrees well with the
measured particle diameter of dp,50=2.5.108 m.
A measurement performed 20 minutes earlier (green curve)
showed an average particle diameter that was more than ten
percent smaller, albeit with the same inlet conditions. The
stagnation temperature and the stagnation pressure were
To1=1444K and poi=8.19, i.e. even slightly higher,
indicating larger particles as can be seen in fig. 7a and 7c.
But a detailed simulation showed, that the smaller particle
diameter is a result of the slightly lower wall temperature
(AT=30 K) in the primary nozzle and the diffuser. Thus, the
temperature loss in the shock train is higher which leads to a
',' I[lusj
2tU x immi
, t[1osJ
.... ...,,:
Gi
1,
l.2
2.0
lower static temperature in the reactor and smaller particles
at the end of the reactor. The deviation of ten percent in the
diameter can be explained by the strong temperature
dependency in this regime (see fig. 7c). This effect is
qualitatively and quantitatively calculated correctly. The
simulated particle diameter of d,max=2.1. 108 m matches well
the measured diameter of dp,5=2.210'8 m.
Conclusions
The reactive flow within a gasdynamic particle reactor was
successfully simulated by coupling the 3D NavierStokes
simulation with a bimodal monodisperse particle model. A
sensitivity analysis revealed the main factors controlling the
TEOS decomposition and coagulationdriven particle
growth. The basic validation for the model was performed
with the experimental data of a rotational symmetric pipe
reactor. The application of a coupled CFD and
particlegrowth simulation to the complex process of the
gasdynamic particle production resulted in a good
qualitative and quantitative agreement with the
measurements. The effect of all boundary conditions
including wall temperatures has been demonstrated.
We can conclude that the coupled 3D
NavierStokes/particlegrowth simulation is a feasible tool
for the design and analysis of innovative particleproduction
processes and particle reactors.
Acknowledgements
The support of the Deutsche Forschungsgemeinschaft (DFG)
by grant PAK 75/2 "Gasdynamically induced particle
production" is gratefully acknowledged
References
Abdali, A., Fikri, M., Wiggers, H., and Schulz C.
"Shocktube study of the ignition delay time of
tetraethoxysilane (TEOS)" Proc. ISSW26, pp. 781785.
(2007)
Abdali, A., Moritz, B., Gupta, A., Wiggers, H. and
Schulz C., "Hybrid microwaveplasma hotwall reactor
for synthesis of silica nanoparticles under wellcontrolled
conditions" Journal of Optoelectronics and advanced
Materials, Vol.12, No.3, (2010)
AlHasan, N. S. and Schnerr, G H., "Aerodynamic
optimization of Laval nozzle flow with shocks: Numerical
investigation of active/passive shock control via expansion
fans", Proc. 6th ICIAM, GAMM 2007, Zurich, Switzerland
(2007)
AlHasan, N.S. "Numerische Untersuchung der
Nanopartikelbildung in transsonischer Strimung"
Dissertation under preparation, Technische Universitit
Miinchen (2010)
Dahneke, B., "Simple kinetic theory of Brownian
diffusion in vapors and aerosols", In: Meyer, R.E., Editor,
Theory of Dispersed Multiphase Flow, Academic Press,
New York, U.S.A.. (1983)
Dannehl, M., Maisels, A., Leibold, W., Olivier, H.,
Grzona, A., WeiB, A., Giilhan, A., Gawehn, T, Schnerr,
GH., AlHasan, N.S., Abdali, A., Luong, M., Wiggers, H.,
Schulz, C., Weigand, B., Chun, J., Schroder, W., Meinke,
M., Winnemoller, T., Nirschl, H., Goertz, V, Schaber, K.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
and Rakel, T, "Nanoparticle tailoring by gasdynamically
induced heating and quenching" EAC2008, Thessaloniki,
Greece (2008)
Ehrman, S.H., Friedlander, S.K., and Zachariah, M.R.
"Characteristics of SiO2/TiO2 Nanocomposite Particles
Formed in a Premixed Flat Flame", J. Aerosol Sci., 29, pp.
687706. (1998)
Gawehn, T., Giilhan, A., AlHasan, N.S. and Schnerr,
GH., "Experimental and Numerical Analysis of the
Structure of PseudoShock Systems in Laval Nozzles with
Parallel Side Walls" ISSW27 (2009)
Grzona, A., Wei3, A., Olivier, H.., Gawehn, T., Giilhan,
A. AlHasan, N.S., Schnerr, GH., Abdali, A., Luong, M.,
Wiggers, H., Schulz, C., Chun, J., Weigand, B.,
Winnemoller, T., Schroder, W., Rakel, T., Schaber, K.,
Goertz, V, Nirschl, H., Maisels, A., Leibold, W. and
Dannehl, M., "GasPhase Synthesis of NonAgglomerated
Nanoparticles by Fast Gasdynamic Heating and Cooling"
Proc. ISSW26, pp. 857862. (2007)
Herzler J., Manion, J.A. and Tsang W., "SinglePulse
Shock Tube Study of the Decomposition of
Tetraethoxysilane and Related Compounds" J. Phys. Chem.
A.,101 (30), pp 55005508, (1997)
Koch, W. and Friedlander S. K., "The effect of particle
coalescence on the surface area of coagulating aerosol"
Journal of Colloid Interface Science, 140, pp. 419427
(1990)
Kruis, F.E., Kusters, K.A. and Pratsinis, S.E., "A simple
model for the evolution of the characteristics of aggregate
particles undergoing coagulation and sintering" Aerosol
Science and Technology 19, p. 514526 (1993)
Matsuo, K. Miyazato, K.Y and Kim, H.D., "Shock train
and pseudoshock phenomena in internal gas flows",
Progress inAerospace Sciences, Vol. 35, No. 1, pp. 33100,
(1999)
Mueller, R., Kammler, H.K., Pratsinis, S.E., Vital, A.,
Beaucage, G and Burtscher, P., "Nonagglomerated dry
silica nanoparticles" Powder Technology, V 140, Issues
12,, pp. 4048. (l2 4)
Pratsinis, S.E. and Mastrangelo, S.VR., "Material
synthesis in aerosol reactors" Chem. Eng. Prog. 85, pp.
6266. (1989)
Pratsinis, S.E. "Flame aerosol synthesis of ceramic
powders" Prog. Energy Combust. Sci. 24, pp. 197219.
(1998)
Rakel, T and Schaber, K., "Water Quenching of
ParticleLaden hot Supersonic Gas Flows", ICMF7 Tampa,
Fl USA, (2010)
Tsantilis, S., Briesen, H. and Pratsinis, S.E., "Sintering
Time for Silica Particle Growth", Aerosol Science and
Technology, Volume 34, Issue 3, pp. 237 246 (2001)
Wallin, S., "Engineering turbulence modelling for CFD
with a focus on explicit algebraic Reynolds stress models"
PhD thesis, Royal Institute of Technology, Stockholm
(2000)
Wegner, K. and Pratsinis, S.E., Winacker und Kiichler,
Band 2: "Neue Technologien" pp. 836871, ISBN:
9783527310326 (2003)
Zachariah, M. R. and Carrier, M. J. "Molecular dynamics
computation of gasphase nanoparticle sintering: a
comparison with phenomenological models" Journal of
Aerosol Science, Vol. 30, Issue 9, pp. 11391151, (1999)
