Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 5.6.3 - Droplet evaporation and influence on turbulence in a swirling combustor
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 Material Information
Title: 5.6.3 - Droplet evaporation and influence on turbulence in a swirling combustor Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Luo, K.
Pitsch, H.
Desjardins, O.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: DNS
droplet evaporation
spray combustion
swirl combustor
 Notes
Abstract: Direct numerical simulations of n-heptane spray droplet evaporation and combustion as well as their interactions with turbulence in a 3-D model swirl combustor are performed to provide insights into realistic spray evaporation and combustion. The variable-density, low-Mach number Navier-Stokes equations are solved using a fully conservative finite difference scheme in cylindrical coordinates, with second order space and time discretization. Droplet evaporation is described by an equilibrium model with corrections. Vapor combustion is modeled using an adaptive one-step irreversible reaction. Inter-phase two-way coupling of mass, momentum, and energy are applied based on the particle-in-cell approach. It is found that to correctly predict droplet evaporation, the underlying grid size has to be at least ten times the droplet diameter. The presence of droplets and combustion decreases the velocity spectrum in the higher wavenumber region and enhances the central recirculation zones, but increases the turbulent velocity spectrum in the lower wavenumber region and reduces the outer recirculation zones. As expected, the effect of preferential concentration is stronger when the droplet Stokes number is closer to unity.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Droplet Evaporation and Influence on Turbulence in a Swirl Combustor


K. Luo*, H. Pitscht and 0. Desjardinst

State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, Zhejiang 310027, P. R. China
t Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Department of Mechanical Engineering, University of Colorado at Boulder, CO 80309, USA
zjulk@zju.edu.cn, h.pitsch@stanford.edu and Olivier.Desjardins@colorado.edu
Keywords: Direct numerical simulation, droplet evaporation, spray combustion, swirl combustor




Abstract

Direct numerical simulations of n-heptane spray droplet evaporation and combustion as well as their interactions with
turbulence in a 3-D model swirl combustor are performed to provide insights into realistic spray evaporation and
combustion. The variable-density, low-Mach number Navier-Stokes equations are solved using a fully conservative
finite difference scheme in cylindrical coordinates, with second order space and time discretization. Droplet
evaporation is described by an equilibrium model with corrections. Vapor combustion is modeled using an adaptive
one-step irreversible reaction. Inter-phase two-way coupling of mass, momentum, and energy are applied based on the
particle-in-cell approach. It is found that to correctly predict droplet evaporation, the underlying grid size has to be at
least ten times the droplet diameter. The presence of droplets and combustion decreases the velocity spectrum in the
higher wavenumber region and enhances the central recirculation zones, but increases the turbulent velocity spectrum
in the lower wavenumber region and reduces the outer recirculation zones. As expected, the effect of preferential
concentration is stronger when the droplet Stokes number is closer to unity.


Introduction

Turbulent multi-phase combustion is encountered in a
number of engineering applications such as internal
combustion engines and gas-turbine aircraft engines.
The ability to perform accurate numerical predictions of
these systems is of paramount importance to improve
their design and efficiency. However, the underlying
physics of spray combustion are extremely complex.
The liquid phase undergoes primary and secondary at-
omization. The resulting droplets are subject to evapo-
ration, condensation, further break-up, or collision and
coalescence with other droplets. The resulting vapor
in the gas-phase undergoes turbulent mixing supplying
the flame with unburned evaporated fuel. These con-
current processes of liquid phase dynamics and evapo-
ration, turbulence, as well as combustion interact and
strongly affect each other, which makes experimental
measurements, high-fidelity simulations, and modeling
very challenging.
To understand these multi-physics phenomena and
their strong coupling interactions, direct numerical sim-
ulations (DNS) are very helpful. In recent years, DNS
of spray combustion in simple configurations have been


performed by several groups (Domingo et al. 2005;
Reveillon and Vervisch 2005; Nakamura et al. 2005).
However, most studies are limited to 2-D or simple con-
figurations. In the present work, n-heptane spray droplet
evaporation and combustion as well as their interactions
with turbulence in a 3-D model swirl combustor are in-
vestigated by means of direct numerical simulation to
provide insight into realistic spray evaporation and com-
bustion. It should be noted that while the turbulent
physics are treated directly by solving the Navier Stokes
equations, the flow inside the liquid droplets and the flow
in the boundary layers around the droplets is unresolved.
These assumptions will be discussed in more detail be-
low. Also a one-step chemical mechanism is assumed
for the combustion of n-heptane. This is an acceptable
assumption, since for the questions addressed here, only
the heat release and its interaction with mixing and the
turbulence is important, and the details of the chemical
structure of the flame is of minor importance.











Mathematical models

In the present study, the Navier-Stokes equations for
the gas phase are solved in an Eulerian framework,
whereas the governing equations for the dispersed phase
are formulated in the Lagrangian sense. The droplets are
treated as point sources of mass, momentum, and energy
to the gas phase. This coupling approach is valid for a
mixture with droplet diameter smaller than the smallest
scales of the gas phase.
Governing Equations for the Gas Phase. The gas
phase is described using the variable-density, low-Mach
number Navier-Stokes equations. The influence of spray
droplets appears in terms of a mass source term Sm in
the continuity equation and a momentum source term S,
in the momentum equations. These equations read


9p Opui
at dxi


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Governing Equations for the Liquid Phase. Dis-
persed droplets are known to follow the Basset-
Boussinesq-Oseen equations. However, due to high den-
sity ratio (PL/P > 1) between liquid n-heptane droplets
and air, the Basset history term, the added mass effect,
and other unsteady drag effects can be neglected, since
all these terms are much smaller than the Stokes drag
force (Crowe et al. 1998). Thus, it is assumed here that
the droplet momentum equations can be described by the
dominant drag force and gravity only. Collisions and co-
alescence are also neglected, as the volumetric loading
of droplets is small. Then, the equations for the droplet
displacement (Xd) and velocity (Ud) can be written as
(Maxey and Riley 1983)

dxd,i _-


(1) and


dud,i fi
S- (i Ud,i) + gi


Opui .' .. ..
at Oxj


Op i dj


where


aij = /( Oaz + O ]


2 au e
32i OJk
3' ) k


(3)


Three additional scalar transport equations correspond-
ing to the mass fractions of fuel (F), oxidizer (0) and
products (P) are solved based on a one-step combustion
model that will be described later. They include a chem-
ical source term ci, i E {F, O, P} as well as the same
mass source term as that in the continuity equation from
spray evaporation, 8.


In Eq. (9), gi is the gravitational force, and Td is the par-
ticle time constant, defined as

pLd2
Td (10)
18P

where d is the droplet diameter, and PL is the liquid den-
sity. fl is an empirical correction to the Stokes drag law
for larger droplet Reynolds numbers, which is here taken
to be (Kurose et al. 2003)

1 + 0.0545Red,slip + 0 1 I;,' ,lip (1 0.03Red,slip)
f1 b
1 + aReb,b


where


a = 0.09 + 0.077exp (-0.4Red,slip)


a (pDF )+F+Sm (4)
Oxj Oxj

-j pDo aO)z +o (5)



a (pD YPj + (6)
9xj O xj


In addition, a transport equation for the gas temperature
is solved


OpT CpTuj
P tCp --
8 8yj


O + WT + ST (7)
axyj axjJ


where ST is the energy exchange rate with the droplets,
and DT is the rate of heat release by combustion.


b = 0.4 + 0.77exp (-0.04Red,slip) (13)
The local droplet Reynolds number based on the slip ve-
locity between the droplet and the gas, Red,slip, is de-
fined by
p |u(xd) Ud d
Red,slip = (14)

and Red,b = is the local droplet Reynolds number
based on the blowing velocity ub due to evaporation.
Droplet Evaporation Model. For liquid droplet evapo-
ration, there exist a variety of models (Miller et al. 1998;
Sirignano 1999; Sazhin 2006). In terms of complexity,
these models can be divided into six groups, i.e. constant
droplet temperature model, infinite thermal conductiv-
ity model, finite thermal conductivity model, effective
conductivity model, vortex model and model based on


dpY, dpYYUj
at Oxj
-+
apYo0 +pYoUj
at Oxj
nd

OpYp dpYpUj
9t Oxj











full solution of the N-S equation. Recently, Sazhin
et al. (2007) have suggested an approach to numerical
modeling of droplet heating and evaporation with radi-
ation based on analytical solutions of the heat conduc-
tion equation of a single droplet. In the present study,
considering both the complexity and the accuracy, we
use the infinite thermal conductivity model with some
corrections, and assume that there is no temperature
gradient inside droplets. Heating and evaporation of a
single-component droplet can be expressed in terms of
the mass-transfer number defined by
Tysurf YF
BM = u -Y (15)
1 _ypurf

where YF is the ambient mass fraction of fuel at the
droplet position, and ypurf is the mass fraction of fuel
at the surface of the droplet, obtained by assuming lo-
cal equilibrium between the droplet and the ambient gas.
From the Clausius-Clapeyron saturation law, the mole
fraction of fuel at the droplet surface can be expressed
as

Xsur Psat Patm [LvWp ( 1 1
tF P P R eb T )]
(16)
In this expression, P is the local pressure at the droplet
position, Patm is the atmospheric pressure, Tb is the liq-
uid boiling temperature, R is the universal gas constant,
WF is the molecular weight of the fuel, and Lv is the la-
tent heat of vaporization. The mass fraction of fuel at the
droplet surface yurf can be obtained from Xurt using
Xsurf
ysurf ___ F (17)
f Xysurtf +(1 surt)W/W (17)
Fp +(1 FA )W1WF
where W is the molecular weight of the mixture. Based
on the above assumptions, the following equations for
droplet temperature Td and mass md are obtained


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


This correction was shown to be very important (Miller
et al. 1998). To account for the effect on evaporation
by convection, the Nusselt and Sherwood numbers are
usually corrected. The popular correction A

Nu 2 + 0.552Red,slip Pr (22)

Sh 2 + 0.552Red,slip2 Sc (23)
and correction B

0.552Red,slip 2 Pr3
Nu = 2 + (24)
(1+ 1.232 2'
Red,slipPr3

0.552Red,s ip Sc
Sh = 2 + (25)
(1+ 1.232 4)2
Red,slipSSc
are tested in the present simulations.
Another important issue in droplet evaporation mod-
eling is the choice of the physical properties used in the
above equations. It has been shown that evaporation rate
predictions are sensitive to the choice of property values
of gas and vapor (Law and Law 1976). The general ap-
proach is to define a reference temperature and a vapor
mass fraction that are used to evaluate both the gas and
vapor properties

TR Td + a (T9 Td),YR Yur + (Y- Yr)
(26)
where a is a constant coefficient. Given the vapor and
gas properties evaluated at the reference temperature, the
physical properties for mixture can be calculated using
the reference mass fraction weighted averaging proce-
dure. For example, the heat capacity of mixture sur-
rounding the droplet can be expressed as


Cp,m = YCpy,v + (1 YR)cp, .


F2 rndLv
(T Td) + dLv
Td mdCL


Sh md
Sh In( 1 + B),
3Sc rd


where Pr and Sc are turbulent Prandtl number and
Schmidt number, CL is the heat capacity of liquid, Cp,m
is the heat capacity of ambient mixture, T, is the gas
temperature at the droplet position, and f2 is a correc-
tion for effect of droplet evaporation on droplet heating,
defined as


c 1'


3Prr1 dTd
2md


However, the above property calculation is generally
needed at every time step and can bring Nigiliik.ii com-
putational expense in spray combustion cases, where a
large number of droplets is usually involved. To avoid
this, we follow Miller et al. (1998) and evaluate physi-
cal properties based on the estimated wet bulb tempera-
ture, which has been demonstrated to be efficiently and
sufficiently accurate. In this approach, we only need to
evaluate physical properties at the beginning of the sim-
ulations. The liquid droplet density PL, heat capacity
CL and latent heat of vaporization Lv are assumed to be
constant and computed based on the estimated wet bulb
temperature, too.
Inter-Phase Coupling. Full mass, momentum and en-
ergy coupling between gas and liquid droplets are in-
cluded. The source terms Sm, Si, and ST due to spray
evaporation are written by assuming that each droplet n


dTd Nu c,,m
dt 3Pr CL


dmd
dt







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


in a cell of volume V acts as a point source to the gas
phase, leading to


V dt
Sm (,"Zd (28)
n
1 d
_, (,,) (29)
n
and
1 d en$dn) d
T ( T(-" LT)- htF ( ) (30)
n

where h is the enthalpy of formation of the fuel vapor,
related to Lv by

Lv (T)= h (L cp)T (31)

if we define the reference enthalpies for the liquid and
all species except the fuel to be null at T=0.
Vapor Combustion Model. For gaseous vapor com-
bustion, detailed chemistry is generally preferable. Nev-
ertheless, it is very computationally expensive. In the
present study, we focus on the global characteristics
of spray combustion. Thus the combustion process is
chosen to be represented by a one-step global reaction
model of n-heptane. The choice is motivated by the
low spatial resolution requirements of such a model in
comparison to multiple-step models. However, in order
to retain as much as possible of the physical processes
found in realistic spray combustion, the approach pro-
posed by Fernandez-Tarrazo et al. (2006) will be fol-
lowed, in which the coefficients of the Arrhenius law are
fitted in order to accurately reproduce the burning veloc-
ity for the problem of interest in both the lean and rich
environments. This methodology has been shown also
to be able to reproduce the rate of strain at extinction.
The chemical source terms Cp, wo, wp, and CT in
Eqs. 4, 5, 6, and 7 are obtained from the following one-
step irreversible reaction of n-heptane:


vFF + voO vpP + Qt


Here Qt is not a constant any more, but is specified as
function of the equivalence ratio (Ferandez-Tarrazo et
al. 2006). The pre-exponential factor A is set to be 9.7 x
108 m3/(mols), while the activation temperature TA is
another parameter specified as function of equivalence
ratio to accurately reproduce the burning velocity and
the strain rate at extinction.


Numerical Algorithms


The low-Mach number Navier-Stokes equations are dis-
cretized using a second-order finite difference scheme in
space, and a second-order semi-implicit scheme in time
in a staggered space-time grid (Desjardins et al. 2008).
This scheme is an extension of the one from Morinishi
et al. (2004), and has excellent conservation properties.
Mass and momentum can be exactly conserved even on
non-equidistant grids. Kinetic energy is conserved ex-
actly for constant density flows, and to the order of the
scheme for variable density cases. Governing equations
of droplets are advanced first, followed by the scalar and
momentum equations. The velocities are then corrected
by solving a Poisson equation to satisfy continuity. The
equations for species mass fraction and for the temper-
ature are rendered especially stiff because of the chem-
ical source terms. As a result, a fully implicit treatment
of the chemical source terms is required and has been
implemented for an accurate integration of those terms.
The droplets are described using a Lagrangian solver
that uses a second-order, fully coupled Runge-Kutta
time integration of the droplet equations. The informa-
tion from the gas phase is interpolated at the droplet po-
sitions using a tri-linear interpolation. The transfer of
the source terms back to the gas phase from the spray is
based on the commonly used PIC (particle-in-cell) ap-
proach (Crowe et al. 1977). Adaptive time stepping is
required to allow for an accurate integration of the equa-
tions when the droplets become very small without sig-
nificantly increasing the computational cost.


Single Droplet Evaporation


where the stoichiometric coefficients vi are taken
from the global n-heptane oxidation reaction C7H16 +
1102 7CO2 + .TT.0O, and Qt is the heat release.
Then the chemical source terms can be written as:


o F
Ujp
CT


VFWF
voWo
VpWP
Qt


where


S(pYA )CpYo)x (
WF, Wo


TA
T


To study evaporation-combustion interactions, it is nec-
essary to make sure that the droplet evaporation and va-
por combustion models can correctly describe the corre-
sponding physical processes. Although some validations
and comparative analysis of droplet evaporation mod-
els have been presented in previous studies (Miller et
al. 1998; Sazhin et al. 2006), most of them were con-
ducted in zero-dimensional cases and the variation of
gas temperature at the droplet position was neglected.
However, in practical 3-D unsteady simulations, the am-
bient gas temperature and vapor mass fraction are not
constant, but vary both in time and space. In these cases,







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


the gas temperature T, in Eq. (18), which is used to
calculate inter-phase heat and mass transfers, becomes
a key issue for transient heating and evaporation of a
droplet. The local gas temperature obtained by inter-
polation from surrounding grid points appears to be a
good choice. However, since the models for calculat-
ing heat transfer between droplets and gas are typically
formulated in terms of far-field ambient gas tempera-
ture or mainstream gas temperature, the employed lo-
cal gas temperature must approximately satisfy this con-
dition. Evidently, the local gas temperature is strongly
dependent on grid size and influenced by the cooling
effect from droplet evaporation, which imposes another
complication for droplet evaporation predictions. In the
present study, the heating and evaporation model of a
single droplet is validated against available experimen-
tal data in 3-D simulations initially based on constant
ambient gas temperature. Then the local gas tempera-
ture obtained by interpolation is used and the grid-size
dependence is discussed.


4
t/d2, s/mm2


Figure 1: Time variations of normalized squared droplet
diameter of n-heptane using the constant ambient tem-
perature in the evaporation model (---- Tg=741 K,
predicted; 0 Tg=741 K, exp.; --- Tg=648 K, pre-
dicted; Tg=648 K, exp.; ---- Tg=555 K, predicted;
E Tg=555 K, exp.; Tg=471 K, predicted; U
Tg=471 K, exp.).


Figure 1 shows the comparisons of the predicted time
variations of normalized squared droplet diameter of n-
heptane with those obtained in the experiments (Nomura
et al. 1996). The predicted results agree well with the
experimental data, especially for the higher temperature
cases. Note that we use the constant ambient tempera-


0.8


0.6 -


0.4


0.2


0 1 2 3
t/d2, s/mm2

Figure 2: Time variation of normalized squared droplet
diameter of n-heptane at P=latm and ambient tem-
perature of 741 K for different mesh resolutions us-
ing the constant ambient temperature in the evapora-
tion model(0, exp.; A/do=l; ---- A/do=5;
--- A/dn=10: --- A/dn=20: ---- A/dn=100).


t/d2, s/mm2


Figure 3: Time variations of normalized squared droplet
diameter of n-heptane at P=latm and ambient tem-
perature of 741K for different mesh resolutions us-
ing the local temperature in the evaporation odel(0,
exp.; A/do=l; ---- A/do=5; --- A/do=10;
--- A/do=20;---- A/do=100).







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


0.5 1 1.5 2
t/d2, s/mm2


2.5 3 3.5


I-


350



300 ,, ,,
0 1 2 3 4 5
t, S

Figure 4: Time variation of the droplet diameter squared
(top) and the droplet temperature (bottom) for decane
(-- predicted; U exp.). The experimental data are
from Wong and Lin (1992), and the conditions are:
Tg=1000K, Td=315K, do=2mm and Redo=17.



ture and neglect the variation of the local gas tempera-
ture. In this case, the effect of the grid size on droplet
evaporation may be negligible, as shown in Fig. 2. How-
ever, in practical simulations, the ambient temperature is
not constant, and a local gas temperature has to be used,
which obviously depends on the ratio of the cell size to
the droplet diameter. Figure 3 shows that when the grid
size is on the order of or larger than ten times the droplet
diameter, using the local gas temperature can yield re-
sults consistent with the experimental data. Otherwise,
the predicted droplet evaporation will significantly devi-
ate from the experiment data. This would indicate that


Figure 5: Effect of different corrections to the Nus-
selt and Sherwood numbers on n-heptane evaporation at
P=latm and ambient temperature of 741 K.


V0.4


0.2


1.5 2
t/d s/mm2


Figure 6: Effect of initial droplet position in a cell on
n-heptane evaporation at P= latm and ambient tempera-
ture of 741 K.



the cooling effect resulting from evaporation can only
influence the gas temperature within a range of about
ten times the droplet diameter, which is in good agree-
ment with the recent analytical solutions of the heat con-
duction equation to a sphere obtained by Sazhin et al.
(2007). It also suggests that the grid size has to be at
least ten times the droplet diameter if the local gas tem-
perature is used for 3-D evaporation prediction in prac-
tical numerical simulations.


- B..


0.8


06


06

V0.4


0.2F


o Exp.
--------- No correction
----- Correction A





r\
rr
CorcinB


n


I







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


The validation of the evaporation model is also ex-
tended to other fuels, such as decane and hexane. Fig-
ure 4 shows the time variations of droplet diameter
squared and the droplet temperature for decane. The ex-
perimental data reported by Wong and Lin (1992) are
also plotted. The predicted results based on the applied
model are generally in good agreement with available
experimental data, which further validates the evapora-
tion model used in the present study.
The Nusselt and Sherwood numbers are crucial pa-
rameters for heat and mass transfer. Figure 5 presents
the effect of corrections A and B on droplet evaporation.
Both corrections can correctly predict n-heptane evapo-
ration, but the results from correction B are more con-
sistent with the experimental data (Nomura et al. 1996).
In actual two-way coupling calculations, the gas-
phase quantities at the droplet position are usually ob-
tained by interpotation from surrounding grid points.
For certain interpolation scheme, different initial droplet
positions may influence the convergence of the solu-
tions. In the present study, a tri-linear interpoation
scheme is used. To check the effect of initial droplet
position in a grid cell on the droplet evaporation predic-
tion based on the tri-linear interpoation scheme, three
cases with different initial droplet positions in a grid cell
are tested and compared with the experimental data (No-
mura et al. 1996). Here (0,0) means that the droplet is
put at the grid node, (0.5,0.5) denotes that the droplet
is put at the center of the cell, and (0.25,0,25) indicates
that the droplet is put at the location between the grid
node and the cell center. As demonstrated in Fig. 6, the
tri-linear interpotation scheme is not sensitive to the ini-
tial droplet position. The numerical solutions converge
to the experimental data for all cases.

DNS of a Model Combustor

Flow Configuration and Grid System. Most previous
DNS studies on spray combustion are limited to 2-D or
very simple 3-D configurations. In the present study, we
simulate a more realistic 3-D swirl combustor. The flow
geometry of the model combustor is shown in Fig. 7.
The central swirl air of temperature 500 K is injected
through a pipe of inner diameter Din = 3.75 mm with a
mean axial velocity Uinj = 4.5 m/s and a mean swirl ve-
locity Winj = 4.5 m/s. The secondary swirl air of temper-
ature 500 K is injected through an annular pipe of inner
diameter Din = 5 mm and outer diameter Dout = 10 mm
with the same mean axial and swirl velocities as those
of the central one. This corresponds to a geometric swirl
number S=1.0. The combustion chamber is 40 mm wide
and 60 mm long, and the outside injection pipe is 10 mm
long. The flow Reynolds number based on the mean ax-
ial velocity and outer diameter of the pipe is about 3000.


Figure 7: Geometry of the 3-D model combustor.


The spray is assumed to have been fully atomized and
the resulting n-heptane droplets are issued from the tip
of the wall regions between the central and the annular
pipes with temperature of 300 K. When the droplets are
issued, they are assumed to be in dynamic equilibrium
with and have the same velocities as the carrier air. This
leads to a spray cone angle of 900 and a low Weber num-
ber limit. Thus, secondary break-up of droplets is not
considered in the present simulations. For droplet size
distribution, a commonly used log-normal distribution
with mean diameter 10 pm, maximum diameter 20 /m,
and minimum diameter 1 pm is used in the simulations.
In DNS of spray combustion, there are strict require-
ments on grid resolution. On one hand, the grid size
has to be small enough to resolve both the Kolmogorov
length scale and the reaction zone thickness of the flame.
On the other hand, the grid size has to be around ten
times larger than the droplet size to get correct droplet
evaporation dynamics if the point-source assumption of
droplets is used, as demonstrated above. To determine
the grid resolution, we have performed grid-dependence
studies. Figure 8 shows the influence of grid resolution
on the 1-D axial velocity spectrum. The spectrum is
calculated based on a position in the shear layer region
with 10 mm distance to the nozzle and 10 mm distance
to the centerline for each case. It is observed that the
velocity spectrum becomes independent of grid resolu-
tion when 384x 192x256 points are used. Considering
the resolution requirements for the flame, the grid res-
olution with 768 points along the axial direction, 384
along the radial direction and 256 along the swirl direc-
tion is chosen in the present study which consists of ap-
proximately 75 million grid points. In order to capture
the important structures as much as possible, the mesh
is non-uniform. In the regions of interest, such as the
recirculation, strong shear, and near wall regions, finer
spacing is used, while in other regions a coarser spac-
ing is used. This clustering is believed to resolve both
the turbulent and chemical scales in the interesting re-












10-2
10-3
10-4
10-5

10-6
W 10-7

10-8 -
10-9
10-10
10-11 _
102


103 104


Figure 8: Dependence of 1D axial velocity
spectrum on grid resolutions. k5/3;
------ 192x96x32 (Two-phase); ---- 384x192x128
(Two-phase); --- 384x192x256 (Two-
phase); ---- 768x384x256 (Single-phase);
---768 x 384 x 256 (Two-phase).


gions. The accuracy of the mesh has been confirmed by
the DNS results.
In addition, it is also interesting to point out from
Fig. 8 that the presence of droplet evaporation and
combustion decreases the velocity spectrum in the
higher wavenumber region, but increases it in the lower
wavenumber region, compared with the single phase
case. This turbulence modulation due to reacting
droplets is consistent with the previous study of Yang
(2004).
Boundary Conditions and Computational Cases.
The flow is periodic in the azimuthal direction, and no-
slip boundary conditions are used for all walls. The
downstream convective outflow condition is obtained by
solving a convection equation, allowing for a smooth
exit of all structures without perturbing the rest of the
flow significantly. To generate turbulent inflow con-
ditions for the swirl air jets, separate pipe flow DNS
computations are conducted in the present study and the
data from these pipe simulations are used as the inflow
boundary conditions for the spray combustion DNS. At
first, hot air at a temperature of 1500 K is injected to ac-
celerate the evaporation and trigger combustion. Then,
the temperature is reduced to 500 K. Data for post-
processing are stored when the flames become approxi-
mately stable.
The spray combustion DNS cases presented here sup-
posedly represent the physics found in aircraft engines.
Different designs for gas turbine propulsion engine com-
bustors have been proposed. Two designs that have been


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Parameter Turbine Model
Spray cone angle 90 90
Density ratio 0(103) 0(103)
Swirl number 1.0 1.0
Damkhler number Da 0(50) 0(50)
Karlovitz number Ka 0(0.1) 0(0.1)
Reynolds number Re 0(106) 0(103)
Stokes number St 2.5 10 0.1 0.4
Weber number We 0(50) 0(0.1)

Table 1: Comparison of major parameters between re-
alistic gas turbine combustor and the model combustor
in the present DNS.


specifically designed to lower NOx emissions are the
so-called Lean Direct Injection (LDI) combustor and
the Rich-bum/Quick-quench/Lean-burn (RQL) combus-
tor. To simulate these two cases, the droplet mass flow
rate is adjusted to achieve global equivalence ratios of
0.7 (lean) and 2.1 (rich), respectively. Here, the central
and secondary air jets rotate in the same direction (co-
swirl). Recent experimental measurements (Hadefa and
Lenzeb 2008) show that counter-swirl (flows rotates in
opposite directions) imposes different effects on spray
combustion. To investigate these effects, lean and rich
cases with counter-swirl air jets are also simulated. To
further examine the importance of the incoming turbu-
lence to spray combustion, a lean case with a laminar
top-hat velocity profile inflow boundary condition is in-
cluded. Additionally, a single phase cold flow case is
simulated for reference. To see how the model com-
bustor in the present DNS matches realistic gas turbine
combustor conditions, Table 1 gives a comparison of
the main parameters used in the DNS and those typi-
cally found in realistic engines. The main differences are
the flow Reynolds number, droplet Stokes number, and
droplet Weber number, all of which are chosen within
the capability of current DNS of spray reacting flows.


Results and Discussions

Instantaneous Vortex Structures. Swirl-stabilized
combustion technology has been widely utilized in en-
ergy conversion systems. The underlying mechanisms
and benefits are well documented in the literature and
depend mainly on the formation of large-scale struc-
tures in swirl flows, including a central toroidal recircu-
lation zone which recirculates heat and reactive chem-
ical species to the root of the flame and allows flame
stabilization and an outer recirculation zone (ORZ). Fig-
ure 9 shows the three-dimensional vortex structures for
different cases. In the reacting cases, there are vor-











tex tubes originated from the Kelvin-Helmholtz insta-
bilities due to strong shear in both swirl and axial di-
rections between the CRZ and the ORZ. These vortex
tubes don't show the so-called helical dipoles (Okulov
and Fukumoto 2004), but form anti-parallel vortex pairs
(Goto and Kida 2003). These self-organized structures
identify the inherent tendency of vortex tubes to align
themselves anti-parallelly in turbulent flows, which is
consistent with previous numerical analysis (Goto and
Kida 2003). The self-organized vortex structures are
also observed in counter-swirl flow, but the cone angle is
smaller. When looking at the single-phase case, obvious
differences appear. In the single-phase case, the vortex
structures are finer and more numerous. Since the CRZ
is not well developed, the cone angle of structures is
smaller. This also reflects the influence of droplet evap-
oration and combustion on turbulence.


7'
4-? '


Figure 9: Instantaneous vortex structures characterized
by Q criterion (Dubief and Delcayre 2000) for different
cases (Top left: lean co-swirl case A; Top right: lean
counter-swirl case B; Middle left: rich co-swirl case C;
Middle right: rich counter-swirl case D; Bottom left:
lean counter-swirl with bulk inflow condition case E;
Bottom right: single-phase case F. Droplets are colored
by diameter).


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Instantaneous Flame Structures. Previous DNS
shows that spray combustion is composed of premixed
and diffusion flames. To visualize the flame struc-
tures in the present swirl spray configuration, the nor-
malized flame index (Domingo et al. 2005) is used.
As seen in Fig. 10, for examples, the spray flame is
quite complicated. There are not only isolated diffu-
sion and premixed flames, but also composite struc-
tures, for instance, pocket diffusion flames enclosed by
pocket premixed flames, pocket premixed flames en-
closed by diffusion flame sheets, and premixed flame
bands connecting diffusion flames. In addition, there


Figure 10: Instantaneous spray flame structures in
the lean co-swirl case A (--- : stoichiometric mix-
ture fraction iso-line; : diffusion flame iso-line;
---- : premixed flame iso-line).

are local non-burning pockets in burning flames. All
these complex structures are related to the swirl fluid dy-
namics and turbulent mixing, and bring igniliik.iiii chal-
lenges for spray combustion modeling. In particular, the
coupled structures always consist of one thick layer and
another very thin one. It is impossible to resolve all these
thin layers in practical simulations. Although equiva-
lence ratio, co- or counter-swirl and bulk inflow condi-
tion have an influence on fluid dynamics, droplet dis-
tribution and flame structures, the spray combustion is
typically characterized by lean premixed, rich premixed,
and diffusion flames for each case.
Time-Averaged Gas-Phase Velocity. Time-averaged
statistics are obtained over a period of several charac-
teristic time scales to provide information for the mean
gas-phase characteristics. Averaging is also performed








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


0.8,


over the homogeneous azithumal direction to obtain a
two-dimensional averaged field. Figure 11 presents


0.61


> 0.4


0 I I I I
0 100 200 300
Evaporation rate
0.8 i 1.5


> 0.4


x


2
1.5
1

0.5

0.
-1


x


Figure 11: Contours of time-averaged axial velocity for
different cases (Top left: lean co-swirl case A; Top right:
lean counter-swirl case B; Middle left: rich co-swirl case
C; Middle right: rich counter-swirl case D; Bottom left:
lean counter-swirl with bulk inflow condition case E;
Bottom right: single-phase case F. The solid lines rep-
resent locations of zero axial velocity).


the contours of time-averaged axial velocity for differ-
ent cases. In the single-phase case F, the CRZ is not
developed well. It has an irregular shape and smaller


-. 4.


0 I -l I I
0 0.5 1 1.5
d


Figure 12: Radial profiles of averaged evaporation rate
(top,x=0.25) and droplet diameter (bottom left: x=0.25;
bottom right: x=1.00)for different cases (- : case
A; --- : case B; --- : case C; ---- : case D;
---- : case E).



size. On the contrary, the ORZ develops well with larger
size compared with reacting cases. This indicates that
the spray evaporation and combustion are able to en-
hance the central recirculation zones, and reduce the
outer ones. Among the reacting cases, co-swirl leads to
stronger CRZ, but smaller ORZ compared with counter-
swirl. Although counter-swirl helps to enhance turbu-
lent mixing, it depresses the magnitude of the CRZ and
potentially causes instability. In addition, counter-swirl
slightly increases the maximum values of axial veloc-
ity. When comparing turbulent inflow case B with the
laminar top-hat inflow case E, it is interesting to see that
both the CRZ and ORZ are similar inside the combus-
tor, though the axial velocity values have obvious differ-
ences.
Time-Averaged Liquid Phase. Some time-averaged


x 4
X


-1 0


2 3 4 5
x


r
r'
r
r











statistics for the liquid droplets are also obtained. Here
only the most interesting features are briefly presented.
Figure 12 shows the radial profiles of averaged evapo-
ration rate and droplet diameter. Although the droplets
are distributed in a wider space, the evaporation occurs
in a narrower region and high equivalence ratio leads
to higher evaporation rates. It is also observed that the
profiles of droplet diameter at x = 0.25 are close to the
initial log-normal distribution, but they change signifi-
cantly at the downstream location of x = 1.0, especially
for the rich cases. The larger droplet diameter is found
to be located in the spray boundaries. This means that
the droplets with larger diameter move towards the spray
boundary with increasing distance from the nozzle exit.
Previous numerous studies on muliphase flows (Squires
and Eaton 1991; Ling et al 1998) have demonstrated that
when the particle Stokes number is close to unity, pref-
erential concentration will become important and lead to
high levels of particle dispersion. In the present study,
the droplet Stokes number is limited to below 0.4 due to
resolution requirement. This implies that the larger the
droplet diameter is, the stronger the influence of prefer-
ential concentration, and the higher level of the disper-
sion, which is consistent with the above observation.


Conclusions

n-heptane droplet evaporation and combustion as well
as their coupling interactions with turbulence in a 3-D
model swirl combustor are investigated by means of di-
rect numerical simulation. The gas-phase is formulated
in an Eulerian framework, and dispersed droplets are
tracked in a Lagrangian sense. An equilibrium evapo-
ration model is used to describe the droplet evaporation,
and an adaptive one-step irreversible reaction is used for
gas combustion. Full inter-phase two-way coupling is
applied. The results show that the underlying grid size
has to be at least ten times the droplet diameter to get
correct droplet evaporation dynamics. Compared with
single-phase case, droplet evaporation and combustion
are able to decrease the velocity spectrum in the higher
wavenumber region and enhance the central recircula-
tion zones, while increase the velocity spectrum in the
lower wavenumber region and reduce the outer recircu-
lation zones.


Acknowledgements

The authors are grateful to NASA's support of this
project. K. Luo appreciates inspiring discussions
and help from Professor Parviz Moin, Professor Luc
Vervisch, Dr. Madhusudan Gurpura Pai, Dr. Edward
Knudsen, Dr. H. El-Asrag, Dr. Mehdi Raessi, and other


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


colleagues at Stanford University. Computational re-
sources at Texas Advanced Computing Center (TACC)
are acknowledged. Funding from a Foundation for the
Author of National Excellent Doctoral Dissertation of
PR China (2007B4) and NSFC (50976098) are also ap-
preciated.


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